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Analysis of Code-expanded Random Access
JY Park
Wireless and Mobile Communication Lab 1
Introduction(Random Access Procedure)
When a device want to access Base Station Random Access Procedure is processed
In this paper Message 1 is the main issue
A device should transmit a preamble at a specific
subframe
There are 64 different preambles
bull For M2M H2H
Devices randomly select preambles
If more than 2 devices select same preamble
collision occur and collided devices try
Random Access again at next opportunity
If large number of devices try random access
simultaneously the probability of collision will
be increased
2
Introduction[1]
By utilizing code-expanded random access collision probability can be decreased
M of preamble used for M2M L length of codeword
Codeword combination of preamble by virtual frame
bull Play a role as a preamble
bull Number of codeword (M+1)L ndash 1
bull If preamble pa pb and length= 2
possible codewords (pa idle) (pa pb) (pa pa) (pb idle) (pb pa) (pb pb) (idle pa) (idle pb)
3
Introduction Consider if ( of codeword) gtgtgt ( of devices)
of codeword = (M+1)L ndash 1
M of preamble to use L length of codeword
To increase the number of codeword M or L should be larger
of preamble for M2M is restricted
Length of codeword can be infinitely long however it can cause long access time
bull Access time constraint
Phantom-codeword
It reduces the resource for data transmission
Codewords that are not used are candidate for phantom-codeword
bull Reduce the number of codewords that are not used
bull Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 constraint
4
Introduction[1]
Consider there are 2 preambles available A B
user1 sends codeword (B I)
user2 sends codeword (I A)
user3 sends codeword (A A)
Phantom codeword (B A)
Codeword that is not used but perceived
by Base Station
Base station perceive that there is a device
sending codeword (B A)
Base Station sends message2 to non-exist device
bull Decrease of downlink resource for data transmission
Base Station allocate a certain uplink resource to non-exist device to get message3
bull Decrease of uplink resource for data transmission
Shortcoming of Code-expanded random access
5
Introduction In [1]
Efficiency = 119900119891 119906119899119888119900119897119897119894119889119890119889 119888119900119889119890119908119900119903119889119904
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119900119889119890119908119900119903119889119904 119904119890119897119890119888119905119890119889 119887119910 119886 119889119890119907119894119888119890
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904
=119873
1119862119882
(1 minus1119862119882)119873minus1
119862119882
119908ℎ119890119903119890 119862119882 = (119872 + 1)119871minus1 and N number of device
Compare efficiency of code-expanded with reference for specific M L
bull Does not give algorithm to get optimal of preamble (M) and length of codeword (L)
bull Does not consider access time
6
Proposed Optimization Problem Goal
Minimize the collision probability while guaranteeing idle codeword ratio requirement and
average access time of devices requirement
Solution (M L)
bull M of preamble used for M2M
bull L length of codeword
For given M
bull As length of codeword longer
bull of codeword increase collision probabilitydarr codeword usage ratiodarr
bull Average access timeuarr
7
Proposed Optimization Problem (M L) = argmin Pcollision
s t
C1 Pidle lt Preq
C2 119865119860119903119890119902 lt α
Access time time difference between the first subframe after its arrival and the
subframe at which it successfully transmit codeword
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
C1 codeword idle ratio requirement should be satisfied
C2 Fail to access until Areq ratio requirement should be satisfied
α fail rate requirement
8
Assumption
At each frame N new devices arrive with the rate of λ
Uniformly distributed arrivals over a fixed time interval [0 T]
Uniformly distributed arrival model can be a realistic scenario in which MTC devices
access the network uniformly over a period of time [2]
There may be remaining unsuccessful devices from the prior Random Access
There is single subframe for Random Access per frame
9
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Introduction(Random Access Procedure)
When a device want to access Base Station Random Access Procedure is processed
In this paper Message 1 is the main issue
A device should transmit a preamble at a specific
subframe
There are 64 different preambles
bull For M2M H2H
Devices randomly select preambles
If more than 2 devices select same preamble
collision occur and collided devices try
Random Access again at next opportunity
If large number of devices try random access
simultaneously the probability of collision will
be increased
2
Introduction[1]
By utilizing code-expanded random access collision probability can be decreased
M of preamble used for M2M L length of codeword
Codeword combination of preamble by virtual frame
bull Play a role as a preamble
bull Number of codeword (M+1)L ndash 1
bull If preamble pa pb and length= 2
possible codewords (pa idle) (pa pb) (pa pa) (pb idle) (pb pa) (pb pb) (idle pa) (idle pb)
3
Introduction Consider if ( of codeword) gtgtgt ( of devices)
of codeword = (M+1)L ndash 1
M of preamble to use L length of codeword
To increase the number of codeword M or L should be larger
of preamble for M2M is restricted
Length of codeword can be infinitely long however it can cause long access time
bull Access time constraint
Phantom-codeword
It reduces the resource for data transmission
Codewords that are not used are candidate for phantom-codeword
bull Reduce the number of codewords that are not used
bull Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 constraint
4
Introduction[1]
Consider there are 2 preambles available A B
user1 sends codeword (B I)
user2 sends codeword (I A)
user3 sends codeword (A A)
Phantom codeword (B A)
Codeword that is not used but perceived
by Base Station
Base station perceive that there is a device
sending codeword (B A)
Base Station sends message2 to non-exist device
bull Decrease of downlink resource for data transmission
Base Station allocate a certain uplink resource to non-exist device to get message3
bull Decrease of uplink resource for data transmission
Shortcoming of Code-expanded random access
5
Introduction In [1]
Efficiency = 119900119891 119906119899119888119900119897119897119894119889119890119889 119888119900119889119890119908119900119903119889119904
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119900119889119890119908119900119903119889119904 119904119890119897119890119888119905119890119889 119887119910 119886 119889119890119907119894119888119890
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904
=119873
1119862119882
(1 minus1119862119882)119873minus1
119862119882
119908ℎ119890119903119890 119862119882 = (119872 + 1)119871minus1 and N number of device
Compare efficiency of code-expanded with reference for specific M L
bull Does not give algorithm to get optimal of preamble (M) and length of codeword (L)
bull Does not consider access time
6
Proposed Optimization Problem Goal
Minimize the collision probability while guaranteeing idle codeword ratio requirement and
average access time of devices requirement
Solution (M L)
bull M of preamble used for M2M
bull L length of codeword
For given M
bull As length of codeword longer
bull of codeword increase collision probabilitydarr codeword usage ratiodarr
bull Average access timeuarr
7
Proposed Optimization Problem (M L) = argmin Pcollision
s t
C1 Pidle lt Preq
C2 119865119860119903119890119902 lt α
Access time time difference between the first subframe after its arrival and the
subframe at which it successfully transmit codeword
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
C1 codeword idle ratio requirement should be satisfied
C2 Fail to access until Areq ratio requirement should be satisfied
α fail rate requirement
8
Assumption
At each frame N new devices arrive with the rate of λ
Uniformly distributed arrivals over a fixed time interval [0 T]
Uniformly distributed arrival model can be a realistic scenario in which MTC devices
access the network uniformly over a period of time [2]
There may be remaining unsuccessful devices from the prior Random Access
There is single subframe for Random Access per frame
9
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Introduction[1]
By utilizing code-expanded random access collision probability can be decreased
M of preamble used for M2M L length of codeword
Codeword combination of preamble by virtual frame
bull Play a role as a preamble
bull Number of codeword (M+1)L ndash 1
bull If preamble pa pb and length= 2
possible codewords (pa idle) (pa pb) (pa pa) (pb idle) (pb pa) (pb pb) (idle pa) (idle pb)
3
Introduction Consider if ( of codeword) gtgtgt ( of devices)
of codeword = (M+1)L ndash 1
M of preamble to use L length of codeword
To increase the number of codeword M or L should be larger
of preamble for M2M is restricted
Length of codeword can be infinitely long however it can cause long access time
bull Access time constraint
Phantom-codeword
It reduces the resource for data transmission
Codewords that are not used are candidate for phantom-codeword
bull Reduce the number of codewords that are not used
bull Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 constraint
4
Introduction[1]
Consider there are 2 preambles available A B
user1 sends codeword (B I)
user2 sends codeword (I A)
user3 sends codeword (A A)
Phantom codeword (B A)
Codeword that is not used but perceived
by Base Station
Base station perceive that there is a device
sending codeword (B A)
Base Station sends message2 to non-exist device
bull Decrease of downlink resource for data transmission
Base Station allocate a certain uplink resource to non-exist device to get message3
bull Decrease of uplink resource for data transmission
Shortcoming of Code-expanded random access
5
Introduction In [1]
Efficiency = 119900119891 119906119899119888119900119897119897119894119889119890119889 119888119900119889119890119908119900119903119889119904
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119900119889119890119908119900119903119889119904 119904119890119897119890119888119905119890119889 119887119910 119886 119889119890119907119894119888119890
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904
=119873
1119862119882
(1 minus1119862119882)119873minus1
119862119882
119908ℎ119890119903119890 119862119882 = (119872 + 1)119871minus1 and N number of device
Compare efficiency of code-expanded with reference for specific M L
bull Does not give algorithm to get optimal of preamble (M) and length of codeword (L)
bull Does not consider access time
6
Proposed Optimization Problem Goal
Minimize the collision probability while guaranteeing idle codeword ratio requirement and
average access time of devices requirement
Solution (M L)
bull M of preamble used for M2M
bull L length of codeword
For given M
bull As length of codeword longer
bull of codeword increase collision probabilitydarr codeword usage ratiodarr
bull Average access timeuarr
7
Proposed Optimization Problem (M L) = argmin Pcollision
s t
C1 Pidle lt Preq
C2 119865119860119903119890119902 lt α
Access time time difference between the first subframe after its arrival and the
subframe at which it successfully transmit codeword
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
C1 codeword idle ratio requirement should be satisfied
C2 Fail to access until Areq ratio requirement should be satisfied
α fail rate requirement
8
Assumption
At each frame N new devices arrive with the rate of λ
Uniformly distributed arrivals over a fixed time interval [0 T]
Uniformly distributed arrival model can be a realistic scenario in which MTC devices
access the network uniformly over a period of time [2]
There may be remaining unsuccessful devices from the prior Random Access
There is single subframe for Random Access per frame
9
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Introduction Consider if ( of codeword) gtgtgt ( of devices)
of codeword = (M+1)L ndash 1
M of preamble to use L length of codeword
To increase the number of codeword M or L should be larger
of preamble for M2M is restricted
Length of codeword can be infinitely long however it can cause long access time
bull Access time constraint
Phantom-codeword
It reduces the resource for data transmission
Codewords that are not used are candidate for phantom-codeword
bull Reduce the number of codewords that are not used
bull Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 constraint
4
Introduction[1]
Consider there are 2 preambles available A B
user1 sends codeword (B I)
user2 sends codeword (I A)
user3 sends codeword (A A)
Phantom codeword (B A)
Codeword that is not used but perceived
by Base Station
Base station perceive that there is a device
sending codeword (B A)
Base Station sends message2 to non-exist device
bull Decrease of downlink resource for data transmission
Base Station allocate a certain uplink resource to non-exist device to get message3
bull Decrease of uplink resource for data transmission
Shortcoming of Code-expanded random access
5
Introduction In [1]
Efficiency = 119900119891 119906119899119888119900119897119897119894119889119890119889 119888119900119889119890119908119900119903119889119904
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119900119889119890119908119900119903119889119904 119904119890119897119890119888119905119890119889 119887119910 119886 119889119890119907119894119888119890
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904
=119873
1119862119882
(1 minus1119862119882)119873minus1
119862119882
119908ℎ119890119903119890 119862119882 = (119872 + 1)119871minus1 and N number of device
Compare efficiency of code-expanded with reference for specific M L
bull Does not give algorithm to get optimal of preamble (M) and length of codeword (L)
bull Does not consider access time
6
Proposed Optimization Problem Goal
Minimize the collision probability while guaranteeing idle codeword ratio requirement and
average access time of devices requirement
Solution (M L)
bull M of preamble used for M2M
bull L length of codeword
For given M
bull As length of codeword longer
bull of codeword increase collision probabilitydarr codeword usage ratiodarr
bull Average access timeuarr
7
Proposed Optimization Problem (M L) = argmin Pcollision
s t
C1 Pidle lt Preq
C2 119865119860119903119890119902 lt α
Access time time difference between the first subframe after its arrival and the
subframe at which it successfully transmit codeword
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
C1 codeword idle ratio requirement should be satisfied
C2 Fail to access until Areq ratio requirement should be satisfied
α fail rate requirement
8
Assumption
At each frame N new devices arrive with the rate of λ
Uniformly distributed arrivals over a fixed time interval [0 T]
Uniformly distributed arrival model can be a realistic scenario in which MTC devices
access the network uniformly over a period of time [2]
There may be remaining unsuccessful devices from the prior Random Access
There is single subframe for Random Access per frame
9
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Introduction[1]
Consider there are 2 preambles available A B
user1 sends codeword (B I)
user2 sends codeword (I A)
user3 sends codeword (A A)
Phantom codeword (B A)
Codeword that is not used but perceived
by Base Station
Base station perceive that there is a device
sending codeword (B A)
Base Station sends message2 to non-exist device
bull Decrease of downlink resource for data transmission
Base Station allocate a certain uplink resource to non-exist device to get message3
bull Decrease of uplink resource for data transmission
Shortcoming of Code-expanded random access
5
Introduction In [1]
Efficiency = 119900119891 119906119899119888119900119897119897119894119889119890119889 119888119900119889119890119908119900119903119889119904
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119900119889119890119908119900119903119889119904 119904119890119897119890119888119905119890119889 119887119910 119886 119889119890119907119894119888119890
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904
=119873
1119862119882
(1 minus1119862119882)119873minus1
119862119882
119908ℎ119890119903119890 119862119882 = (119872 + 1)119871minus1 and N number of device
Compare efficiency of code-expanded with reference for specific M L
bull Does not give algorithm to get optimal of preamble (M) and length of codeword (L)
bull Does not consider access time
6
Proposed Optimization Problem Goal
Minimize the collision probability while guaranteeing idle codeword ratio requirement and
average access time of devices requirement
Solution (M L)
bull M of preamble used for M2M
bull L length of codeword
For given M
bull As length of codeword longer
bull of codeword increase collision probabilitydarr codeword usage ratiodarr
bull Average access timeuarr
7
Proposed Optimization Problem (M L) = argmin Pcollision
s t
C1 Pidle lt Preq
C2 119865119860119903119890119902 lt α
Access time time difference between the first subframe after its arrival and the
subframe at which it successfully transmit codeword
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
C1 codeword idle ratio requirement should be satisfied
C2 Fail to access until Areq ratio requirement should be satisfied
α fail rate requirement
8
Assumption
At each frame N new devices arrive with the rate of λ
Uniformly distributed arrivals over a fixed time interval [0 T]
Uniformly distributed arrival model can be a realistic scenario in which MTC devices
access the network uniformly over a period of time [2]
There may be remaining unsuccessful devices from the prior Random Access
There is single subframe for Random Access per frame
9
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Introduction In [1]
Efficiency = 119900119891 119906119899119888119900119897119897119894119889119890119889 119888119900119889119890119908119900119903119889119904
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119900119889119890119908119900119903119889119904 119904119890119897119890119888119905119890119889 119887119910 119886 119889119890119907119894119888119890
119900119891 119905119900119905119886119897 119888119900119889119890119908119900119903119889119904
=119873
1119862119882
(1 minus1119862119882)119873minus1
119862119882
119908ℎ119890119903119890 119862119882 = (119872 + 1)119871minus1 and N number of device
Compare efficiency of code-expanded with reference for specific M L
bull Does not give algorithm to get optimal of preamble (M) and length of codeword (L)
bull Does not consider access time
6
Proposed Optimization Problem Goal
Minimize the collision probability while guaranteeing idle codeword ratio requirement and
average access time of devices requirement
Solution (M L)
bull M of preamble used for M2M
bull L length of codeword
For given M
bull As length of codeword longer
bull of codeword increase collision probabilitydarr codeword usage ratiodarr
bull Average access timeuarr
7
Proposed Optimization Problem (M L) = argmin Pcollision
s t
C1 Pidle lt Preq
C2 119865119860119903119890119902 lt α
Access time time difference between the first subframe after its arrival and the
subframe at which it successfully transmit codeword
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
C1 codeword idle ratio requirement should be satisfied
C2 Fail to access until Areq ratio requirement should be satisfied
α fail rate requirement
8
Assumption
At each frame N new devices arrive with the rate of λ
Uniformly distributed arrivals over a fixed time interval [0 T]
Uniformly distributed arrival model can be a realistic scenario in which MTC devices
access the network uniformly over a period of time [2]
There may be remaining unsuccessful devices from the prior Random Access
There is single subframe for Random Access per frame
9
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Proposed Optimization Problem Goal
Minimize the collision probability while guaranteeing idle codeword ratio requirement and
average access time of devices requirement
Solution (M L)
bull M of preamble used for M2M
bull L length of codeword
For given M
bull As length of codeword longer
bull of codeword increase collision probabilitydarr codeword usage ratiodarr
bull Average access timeuarr
7
Proposed Optimization Problem (M L) = argmin Pcollision
s t
C1 Pidle lt Preq
C2 119865119860119903119890119902 lt α
Access time time difference between the first subframe after its arrival and the
subframe at which it successfully transmit codeword
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
C1 codeword idle ratio requirement should be satisfied
C2 Fail to access until Areq ratio requirement should be satisfied
α fail rate requirement
8
Assumption
At each frame N new devices arrive with the rate of λ
Uniformly distributed arrivals over a fixed time interval [0 T]
Uniformly distributed arrival model can be a realistic scenario in which MTC devices
access the network uniformly over a period of time [2]
There may be remaining unsuccessful devices from the prior Random Access
There is single subframe for Random Access per frame
9
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Proposed Optimization Problem (M L) = argmin Pcollision
s t
C1 Pidle lt Preq
C2 119865119860119903119890119902 lt α
Access time time difference between the first subframe after its arrival and the
subframe at which it successfully transmit codeword
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
C1 codeword idle ratio requirement should be satisfied
C2 Fail to access until Areq ratio requirement should be satisfied
α fail rate requirement
8
Assumption
At each frame N new devices arrive with the rate of λ
Uniformly distributed arrivals over a fixed time interval [0 T]
Uniformly distributed arrival model can be a realistic scenario in which MTC devices
access the network uniformly over a period of time [2]
There may be remaining unsuccessful devices from the prior Random Access
There is single subframe for Random Access per frame
9
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Assumption
At each frame N new devices arrive with the rate of λ
Uniformly distributed arrivals over a fixed time interval [0 T]
Uniformly distributed arrival model can be a realistic scenario in which MTC devices
access the network uniformly over a period of time [2]
There may be remaining unsuccessful devices from the prior Random Access
There is single subframe for Random Access per frame
9
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Proposed Optimization Problem(obj func)
Collision probability (Pcollision)= 119900119891 119888119900119897119897119894119904119894119900119899 devic119890119904
119905119900119905119886119897 119900119891 119886119905119905119890119898119901119894119899119892 devic119890119904 [6]
Total random access arrival rate in the i-th virtual frame slot λ119879[i](new+backlogged) [5]
λ119879[i] = λT + Pcollision λ119879 [i-1]
Pcollision collision probability
T period of subframe for preamble transmission (10ms)
In steady state drop slot index i
λ119879 = λT + Pcollisionλ119879
λ119879 = 120582119879
1minus119875119888119900119897119897119894119904119894119900119899
Collision probability p can be estimated by
Pcollision = 1 ndash Pr[no device select a given codeword] ndash Pr[one device select a given codeword] = 1 - (1 minus1
119862119882)λ119879 -
λ119879119862119882(1 minus
1
119862119882)λ119879minus1
Where of codewords(CW) (M+1)L ndash 1
Pcollision = 1 ndash 119890119882[ln 1minus
1
119862119882]λ119879
where W[] is a lambert W function [5]
10
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Proposed Optimization Problem(C1)
Pidle 119900119891 119899119900119905 119906119904119890119889 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904 = 119900119891 119888119886119899119889119894119889119886119905119890 119891119900119903 119901ℎ119886119899119905119900119898 119888119900119889119890119908119900119903119889119904
119905119900119905119886119897 119900119891 119888119900119889119890119908119900119903119889119904
let X be a random variable that is of MNs selecting per codeword
Probability that a given codeword is selected by k MNs among N devices
bull Pr[X = k] = 119873119896(1
119862119882)119896(1 minus
1
119862119882)119873minus119896 [1]
of codewords(CW) (M+1)L ndash 1
Probability that a given codeword is not selected
bull Pr[X = 0] = (1 minus 1
119862119882)119873
bull of idle codewords in a cycle = Pr[X=0] CW
Total of codewords in a cycle CW = (M+1)L ndash 1
bull M of preamble L length of codeword
Pidle = Pr 119883=0 lowast119862119882
119862119882 = Pr[X=0] = (1 minus
1
119862119882)119873= (1 minus
1
(M+1)L minus 1 )119873
11
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Proposed Optimization Problem(C2) Access time requirement
New devices arrive to the channel at the following uniform rate
λ = 119873
119879 0 lt t lt T = 10ms (1 frame)
0 otherwise
12
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Proposed Optimization Problem(C2)
Ni = total number of devices trying to access base station at i-th virtual frame
bull N1 = N
Pi = collision probability at i-th virtual frame
Ni = Pi-1Ni-1 + N
Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894 where W[] is a lambert W function [5]
of codewords(CW) (M+1)L ndash 1
13
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Proposed Optimization Problem(C2) Acess time requirement Areq
Time (횟수) limit (Tlimit) to satisfy Areq lfloor119860119888119888119890119904119904 119905119894119898119890 119903119890119902119906119894119903119890119898119890119899119905
119905119894119898119890 119897119890119899119892119905ℎ 119900119891 119886 119907119894119903119905119906119886119897 119891119903119886119898119890rfloor = lfloor
119860119903119890119902
119871119879rfloor
L length of codeword T time length of a frame(10ms)
Ratio of devices fail to access base station among N devices after Tlimit virtual frame
119865119860119903119890119902= 119875119894119879119897119894119898119894119905119894=1
Constraint 2
119865119860119903119890119902 lt α
α fail rate requirement
14
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Performance (Environment)
λ = 5000 ndash 60000 arrivals10sec [7]
Max number of preamble for M2M 30
Areq 22ms(delay sensitive) 60ms(delay nonsensitive) [9]
Fail rate requirement (α) 02 005
Time between subframes for preamble transmission T = 10ms
There are one subframe for preamble transmission per frame
Codeword idle ratio Pidle = 05 03
15
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Performance (GA)
(M L) = argmin Pcollision = argmin (1 ndash eW[ln(1-1119862119882)]λT )
st
C1 (1 minus 1
(M+1)L minus 1 )119873 lt Preq
C2 119875119894119879119897119894119898119894119905119894=1 lt α
bullWhere Pi = 1 ndash 119890119882 ln 1minus
1
119862119882119873119894
Mixed Integer Nonlinear Programming
The optimization of such model is typically difficult due to their combinatorial nature and
potential existence of multiple local minima in the search space
GAs are powerful tools for solving MINLP problems [8]
16
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Performance (GA) Chromosome format (X1 X2)
X1 number of preamble X2 length of codeword
Fitness function
f = Pcollision + 10max(0 Pidle ndash Preq) + 10max(0 119865119860119903119890119902- α)
Penalty when constraints are not met
Population size 500
Mutation rate 001
Elitist one per generation was keeped (no mutation)
Natural Selection
Chromosome which has function value bigger than average function value is discarded
Binary tournament selection
Stopping criteria Fbest n ndash Fbest (n+1) lt 0001 17
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Performance
18
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Performance
19
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Performance
20
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Performance
21
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
Performance
22
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
reference
23
[1] Nuno K Paratas Henning Thomsen ldquoCode-Expanded radio access protocol for machine-to-machine
communicationsrdquo TRANSACTIONS ON EMERGING TELECOMMUNICATIONS TECHNOLOGIES
[2] 3GPP Generation Partnership Project 3GPP TR 37868 v1100 (2011-09) Technical Report
[3] Nuno K Paratas Henning Thomsen ldquoCode-Expanded Random Access for Machine-Type
Communicationsrdquo
[4] Mehmet Koseoglu ldquoLower bound on the LTE-A Average Random Access Delay under Massive M2M
Arrivalsrdquo IEEE TRANSACTIONS ON COMMUNICATIONS
[5] Dan Keun Sung ldquoSpatial Group Based Random Access for M2M Communicationsrdquo IEEE
COMMUNICATIONS LETTERS VOL 18 NO 6 JUNE 2014
[6] Challenges of Massive Access in Highly-Dense LTE-Advanced Networks with Machine-to-Machine
Communications
[7]Lower Bound on the LTE-A Average Random Access Delay under Massive M2M Arrivals
[8]A genetic Algorithm for Mixed Integer Nonlinear Programming Problems Using Separate Constraint
Approximations
[9]Joint Access Control and Resource Allocation for Concurrent and Massive Access of M2M Devices
