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Multiple Criteria Optimisation for Base Station Antenna Arrays in Mobile Communication Systems
By Ioannis Chasiotis
PhD Student
Institute for Communications and Signal Processing
Department of Electronic and Electrical Engineering
Supervisor: Prof. T. S. Durrani
Presentation Outline
Aims and Objectives Why Antenna Arrays? Multiple Criteria Optimisation Algorithm Example Results Conclusions & Future Work
Aims & Objectives
Develop an optimisation algorithm to provide system designers with optimal design solutions for a modern base station antenna array Antenna Array Size Capital Cost
Different Mobile System Architectures GSM CDMA
Develop a graphical user interface (GUI) for use as a separate decision making software package
Why Antenna Arrays?
Antenna arrays introduce significant improvement in system performance
Transmit and Receive Gain Interference Capacity/Spectral Efficiency Area of Coverage
Improvement in performance criteria is greatly influenced by array size
However…This improvement is accompanied by escalating costs
Antenna Array
Trade-Off
Capital Investment
Performance
To obtain the optimal array size given the trade – off between the performance criteria and the increase in cost
All objective functions are combined into one scalar function to be maximised
Two simple approaches to achieve this Additive Aggregation
Multiplicative Aggregation
Multiple Criteria Optimisation
k
iii xfwxJ
1
)()(
k
i
wi
ixfxJ1
)]([)( k
w
f
i
iIndividual objective functions
Weighting coefficients
Number of objective functions
Multiple Criteria Optimisation II
Uplink Criteria under consideration
Spectral Efficiency (ηs) Overall Antenna Gain (G) Area of Coverage (A) Capital Costs (Cuplink)
Optimisation Function Additive Aggregation
Multiplicative Aggregation
Downlink Criteria under consideration
Spectral Efficiency (ηs) Overall Antenna Gain (G) Area of Coverage (A) Transmission Efficiency (ηTr)
Capital Costs (Cdownlink)
Optimisation Function Additive Aggregation
Multiplicative Aggregation
5
4321
)]([
)]([*)]([*)]([*)]([))((
wdownlink
wTr
wwws
MC
MMAMGMxfJ
4
321
)]([
)]([*)]([*)]([))((
wuplink
wwws
MC
MAMGMxfJ
)()()()()())(( 54321 downlinkTrs CwwAwGwwxfJ )()()()())(( 4321 uplinks CwAwGwwxfJ
Weighting Factors Computation
Weights Scale influence of criteria in the
overall optimisation function J(f(x))
Reflect the relative importance of the considered criteria
“Swing” weight method Computing efficient – few
computations per cycle Rank weights-criteria based on
their contribution to J(f(x)) Measured in terms of the swing
from the worst to the best value of each criterion
Assign weight values according to their rank
Normalise weights
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Number of Sensors (M)
Wei
ght
valu
es
Spectral EfficiencyAntenna Array GainArea of Coverage IncreaseCapital Costs
Example: Weight computation for the uplink mode of operation. Weights are computed for an increasing array size and adapt to the different effect that each criterion will have at each value of M (number of sensors – array size)
n
iiwwSum
1
)()(wSum
ww i
normalisedi
Optmisation Algorithm (Additive Aggregation)
SWING Weighti ng Method
SWING
Weighting Method
Uplink
Spectral Efficiency Antenna Gain
Area of Coverage Capital Costs
Downlink
Spectral Efficiency Transmission
Efficiency Antenna Gain
Area of Coverage Capital Costs
Define Performance Criteria
Uplink Additive Value Function Formulation
n
i i i uplink x f w x f J 1 ) ( )) ( (
Downlink Additive Value Function Formulation
n
i i i downlink x f w x f J 1 ) ( )) ( (
Weights Computed?
Complete Communications Link ) ( ) ( )) ( (
1 x f w x f w x f J downlink i n
i uplink i
Yes
Yes
Weights Computed?
Weights Computed?
Yes
Optimal Set of Solutions
No
No
SWING Weighting Method
No
Weight Check/Computation
Optimisation Parameters
Multiple Criteria Framework
Formulation
Optimisation Cost
Functions
Start
Example: Simulation Parameters
SIMULATION PARAMETERS
Bandwidth (B)
5MHzMobile Terminal Antenna Height
(Hm)
2m
Reference Noise Temperature
(Tp)
290oK
Carrier Frequency (Fc)
2GHz
Receiver Noise Figure (F)
3
Path Loss Exponent (gama)
4
Base Station Antenna Height
(Hb)
30m
Environment Set-Up
urban
Results I (Uplink)
05
1015
2025
30
05
1015
2025
30-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Number of Sensors (M)SNR Value (in dB)
Add
itive
Fun
ctio
n R
esul
t (J
)
05
1015
2025
30
05
1015
2025
300
0.2
0.4
0.6
0.8
1
Number of Sensors (M)SNR Value (in dB)
Add
itive
Fun
ctio
n R
esul
t (J
)
Additive Aggregation Multiplicative Aggregation
Maximum at 11 sensors in both cases
Results II (Downlink)
05
1015
2025
30 05
1015
2025
30
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
Number of Sensors (M)Transmitted Power
Add
itive
Fun
ctio
n R
esul
t (J
)
05
1015
2025
30 05
1015
2025
30
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of Sensors (M)Transmitted Power
Add
itive
Fun
ctio
n R
esul
t (J
)
Additive Aggregation Multiplicative Aggregation
Maximum at 13 sensors in both cases
Complete Communications Link (Uplink & Downlink)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
05
1015
2025
30
0
10
20
300.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
No. of Sensors (M)Transmitted Power
Add
tive
Val
ue F
unct
ion
(J)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
010
2030
010
20300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
No. of Sensors (M)Transmitted Power
Add
tive
Val
ue F
unct
ion
(J)
Additive Aggregation Multiplicative Aggregation
Maximum at 12 sensors in both cases
Conclusions & Future Work
Increasing antenna array size of base station does not yield the best results
There is an optimum number of sensors that balances the cost-performance trade-off in the best possible way
Results show that the aggregation method used to formulate the optimisation functions does not affect the findings of the algorithm
The algorithm is currently under further development to be able to provide a potential system designer with optimum solution for cases of MIMO (Multiple Input – Multiple Output) systems, where arrays are used at both end of the communications link.
