Soft capacity analysis of TDMA systems with slow …mhahmed/publications/ma02-j01.pdf636 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 4, JULY 2002 Soft Capacity Analysis

636 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 4, JULY 2002

Soft Capacity Analysis of TDMA Systems WithSlow-Frequency Hopping and Multiple-Beam

Smart AntennasMohamed H. Ahmed, Member, IEEE,and Samy A. Mahmoud, Senior Member, IEEE

Abstract—Smart antenna is considered as one of the most effec-tive means for enhancing wireless system capacity. When fractionalloading is accompanied with slow-frequency hopping (SFH), softcapacity can be realized in time-division multiple access (TDMA)wireless networks. Then, the interference reduction due to smartantennas, power control, and discontinuous transmission can bedirectly translated into capacity gain. This paper addresses the ca-pacity gain due to multiple-beam (MB) smart antennas in TDMAwireless systems with soft capacity. The system capacity is deter-mined analytically and by simulation. MB smart antennas withpractical antenna pattern are used in this study. Perfect powercontrol and discontinuous transmission are assumed in the sim-ulation and the theoretical analysis. A novel call admission con-trol algorithm is proposed to enhance the system capacity withoutdegrading the signal quality. The TDMA system is assumed to beglobal system for mobile communications (GSM)-like, however, theanalysis can be extended and applied to other TDMA systems.

Index Terms—Call admission control, performance analysis ofwireless systems, slow-frequency hopping (SFH), smart antennas,soft capacity, wireless network simulation.

I. INTRODUCTION

M ANY cellular networks are currently facing substantialgrowth, which requires efficient utilization of the avail-

able spectrum in order to maximize network capacity. Varioustechniques have been explored to enhance the available systemcapacity. Examples of such techniques include cell splitting, hi-erarchal cell structure, dynamic channel allocation, power con-trol (PC), discontinued transmission (DTX), smart antennas,and slow-frequency hopping (SFH).

When SFH is incorporated, the carrier frequency allocated toeach user is changed periodically at a rate, which is muchslower than the symbol rate. In GSM, the carrier frequency ishopped at every time frame (4.614 ms) so that s .Consequently, the set of cochannel interferers changes at everytime frame; that is, at each time frame, each user encounters adifferent group of interferers having different spatial and propa-gation parameters. Hence, unlike traditional time division mul-tiple access (TDMA), no users will receive high interference,while others receive low interference, i.e., the interference levelis averaged out. In addition to the interference averaging prop-erty, SFH enhances the performance of TDMA wireless net-

Manuscript received May 18, 2000; revised April 26, 2001.The authors are with the Department of Systems and Computer Engineering,

Carleton University, Ottawa, ON K1S 5B6, Canada.Publisher Item Identifier S 0018-9545(02)02480-5.

works through the frequency diversity property, which is usedto combat fading [1]–[8].

Great attention is currently directed to smart antennas. Dif-ferent issues have been addressed such as implementation tech-niques, capacity gain in different wireless systems and the fea-sibility of space division multiple access (SDMA). Smart an-tennas are essentially used in wireless systems to minimize thecochannel interference. Four main implementation techniqueshave been proposed: multiple (switched) beam antennas, adap-tive beam forming, null forming, and optimum combining.

The capacity enhancement in TDMA networks due to the useof SFH has been studied in [1]–[7]. Most of these studies arebased on computer simulation rather than analytical methods.Although analytical methods rely on certain assumptions andapproximations, they are important for two reasons. First,they can reduce the computational time and simulation efforts.Second, analytical solutions are useful for the validation andverification of the simulation approach and results. The perfor-mance of SFH-TDMA systems has been studied analyticallyin [5] and [6]. However, neither of these studies consideredsmart antennas in the analysis. In this paper, we presentboth analytical and simulation studies for GSM-like wirelesssystems to estimate the capacity enhancement due to the useof smart antennas with SFH. At first, the dependence of theoutage probability on the loading factor (LF), definedas the traffic in Erlang per the available number of channels,is determined. Since is defined as the probability that thecarrier-to-interference ratio (CIR) is less than or equal to theminimum acceptable value (e.g., dB inGSM), CIR analysis is used to derive the dependence ofonthe LF. Then the maximum LF that keeps the outage probabilityunder a certain threshold value (e.g., 2%) is evaluated andused to estimate the maximum system capacity. Also, a noveladmission control algorithm is proposed to enhance the systemcapacity without degrading the signal quality. The rest of thepaper is organized as follows. Soft capacity in TDMA systemsis described in Section II. Section III presents the system modelsincluding channel model, frequency planning and hoppingmodel, and smart antenna models. The simulation tool usedin the performance analysis is discussed in Section IV, whilethe stochastic analysis used to estimate the outage probabilityis presented in Section V. Section VI presents the proposedcall admission control algorithm. Finally, the summary andconclusions are given in Section VII.

0018-9545/02$17.00 © 2002 IEEE

AHMED AND MAHMOUD: ANALYSIS OF TDMA SYSTEMS WITH SFH AND MB SMART ANTENNAS 637

II. SOFT CAPACITY IN TDMA WIRELESSNETWORKS

There are two main approaches for frequency planning inTDMA wireless networks [2], [7], [8]. Both approaches aimto achieve high capacity associated with an acceptable signalquality in terms of CIR.

In the first approach, a large frequency reuse factor (e.g., 12)is used to keep the cochannel users distant enough from eachother. The large reuse factor guarantees the signal quality butlimits the number of channels allocated to each cell. Conse-quently, calls are blocked when the number of users exceeds thenumber of available channels. Thus, hard blocking limits thesystem capacity at a specific value, which is a function of therequired blocking rate. Hence, this scheme provides the systemwith a hard capacity.

In the second approach, a small frequency reuse factor (e.g.,3) is used. Accordingly, a large number of channels can be allo-cated to each cell. Since a large number of channels are availablein each cell, channels are always available but calls are blockedto preserve the signal quality and keep the interference levelbelow the threshold value. Thus, only a certain fraction of theavailable channels can be used simultaneously. In this case, SFHis usually employed to distribute the interference evenly over allthe allocated channels using the interference averaging propertydiscussed in the previous section. Call blocking, which is due tothe interference level restriction rather than channels unavail-ability, is called soft blocking. This soft blocking introduces thesoft capacity concept in TDMA systems [2], [8].

With the first approach, the hard blocking limit (unavailabilityof channels) is reached first, while in the second approach, thesoft blocking limit (high interference level) is encountered be-fore experiencing hard blocking [2].

It is shown in [2] that the soft capacity can enhance the systemcapacity of GSM systems by more than 74%. In TDMA systemswith soft capacity, the inclusion of interference reduction tech-niquessuchasDTX,PC,andsmartantennascanbedirectly trans-lated into capacity enhancement without changing the frequencyreuse plan. This is because the system capacity can be improvedby increasing the maximum LF. On the contrary, in TDMA sys-temswithhardcapacity, interference reduction techniquescanbetranslated into capacity enhancement by using smaller frequencyreuse factor, which requires changing the frequency plan.

With soft capacity, an admission control algorithm must beemployed to preserve the signal quality by limiting the LF atmaximum value [7]. Admission control algorithmscan be performed at different levels (central or distributed),based on different criteria (LF, interference level, or calldropping rate) and individually or combined with other controlalgorithms such as power control and channel allocation.

Soft capacity can be evaluated by determining the max-imum LF . Then, the maximum network capacity inErlang/cell is given by

(1)

where is the total number of available channels per cell.The value of the maximum LF depends on the admission con-trol strategy. In admission control algorithms based on interfer-ence measurements, users are admitted as long as the interfer-

ence level does not exceed the threshold value. In this case, themaximum LF is a variable, which depends on the propagationconditions and spatial distribution of users. In admission con-trol techniques based on the number of users (either per cell orper set of cells as in [7]), the dependence of the outage prob-ability (or other measures of the signal quality) on the LF isdetermined analytically by simulation or from field measure-ments. The maximum LF is determined as the LF atwhich the outage probability is equal to the maximum accept-able value . Then, the admission control algorithm uses thisvalue to admit or reject any access request dependingon the instantaneous LF.

III. SYSTEM MODEL

In this section, a description of the system model used in thesimulation and the analytical study is presented. The model in-cludes channel characterization, frequency planning and hop-ping algorithm, smart antennas, and teletraffic models.

A. Propagation Model

Wireless channels are usually characterized by the path loss,shadowing,andfading.Thepath loss isanexponential functionofthedistancebetween thebasestastion (BS)and themobilestation(MS). The path-loss exponent depends on the environmentof the wireless network and it ranges from three to five in shad-owedurbanareas [9]. Shadowing is distributed lognormally witha standard deviation that ranges from 5 to 10 dB dependingon the environment [2]. Fast multipath fading is usually modeledby Raleigh distribution. If SFH is employed, the frequency diver-sitypropertymitigates theeffectof fading.Other techniquessuchas equalization and interleaving will also reduce the impact offading considerably and make it possible to ignore its effect [14].Hence,exponentialpath lossand log-normalshadowingaresuffi-cient tomodel thewirelesschannel.Thepath-lossexponentisassumed to be 3.5, while the standard deviation of the log-normalshadowing is equal to six.

B. Frequency Planning and Hopping Algorithm

The frequency reuse factor of the SFH carriers is. Thismeans that theallocated frequenciesareentirelyallocated toeachcell. Since each cell has three sectors, each sector is given onethird of these frequencies. This tight frequency plan can be usedwithout degrading the signal quality because fractional loadingis employed as explained in the previous section. Broadcast con-trol channels (BCCH) are allocated using a frequency reusefactor since neither fractional loading nor frequency hopping isemployed. Thus, BCCH carriers are entirely allocated to eachcluster of four cells. Then, these carriers are equally assigned tothe twelvesectorsof the fourcells.Non-BCCHcarrierarehoppedusing the GSM hopping algorithm [2].

C. Smart Antennas

As mentioned above, there are four basic implementationstructures for smart antennas [10]–[12]: Multiple-beam (MB)antennas, adaptive beam forming, null forming, and optimumcombining. In MB (or switched-beam) antennas, M-beams areused to cover each cell. MSs are connected to BSs using the


beams providing with the best signal quality in terms of the re-ceived power or CIR. Switching from one beam to anotheris needed when a MS crosses the boundary between two beams.Unlike other implementation schemes, this technique does notrequire complex hardware or sophisticated weight computationalgorithms, yet its performance is comparable to those of theother techniques [12]. In this paper, we adopt this technique(MB antennas) because of its simplicity and effectiveness.

D. Teletraffic Model

New calls arrive according to Poisson distribution with an av-erage arrival rate per cell, while the call duration is expo-nentially distributed with a mean value . Average new calltraffic intensity per cell is equal to . In the analyticalstudy, handover calls are also modeled as Poisson traffic witha rate per cell. is linearly proportional to , as shownin Section VI. Exponential call dwelling time is assumed witha mean value , which depends on the user mobility modeland cell size.

IV. SIMULATION DESCRIPTION

A dynamic wireless simulation tool has been developed toanalyze the performance. This simulator is built as a set of inde-pendent modules so that any module can be modified, enhanced,or even replaced without changing other modules. The simulatorgraphical output shows the BSs distributed throughout the cov-erage area, while the moving MSs are linked to the best servers.The blocking and dropping probabilities are estimated and up-dated on each multiframe. The different modules of the simu-lator are briefly explained as follows.

— Traffic Generation: Traffic generation module gener-ates the arrival time and call duration of each user usingthe teletraffic model given above. It then schedules andsaves the arrival time and call duration of all users ina data file. Uniform spatial traffic distribution is as-sumed. However, nonuniform and hot-spot traffic canalso be included. This module generates these valuesoff line to reduce the simulation time. When the dy-namic simulation starts, these values are retrieved bycall startup module as explained below.

— Initialization and Parameters Setting: This module ini-tializes the variables used in the simulation such as thestatistics collection variables. It also generates and setsthe user profile for each user including its position,speed, and movement direction.

— Call Startup: Call startup module can be consideredas the first step of the dynamic simulation. Once thesimulation starts, this module retrieves the call arrivaltime, the call duration, and the users profile from theschedule stored in the data file. Subsequently, it initi-ates the calls according to the simulation clock.

— Admission Control and Channel Assignment: Admis-sion control module admits (or rejects) the new gener-atedcallsaswellasthehandovercallsusingaloading-in-formation-basedadmissionpolicy.Thereafter, itassignschannels for the admitted users according to the avail-able resources and the allocation algorithm.of the

best serving base station is measured before granting anetwork access to that user. The connection is not estab-lished unless exceeds the receiver sensitivity with acertain margin . The received power is determinedaccording to the propagation model explained above.

— Power Control: When perfect power control is em-ployed, the transmit power is adjusted to achievea constant received power. Downlink and uplinktransmit powers are controlled separately using twoindependent feedback loops [2].

— Beam Selection: This module selects the best servingbeam (based on or CIR) for each user in the net-work. 12 beams are assumed to cover each cell site(four beams per sector). Practical antenna beam pat-tern (with a shape) is used in the system model.

— User Movement and Handover process: This modulemoves all active users in linear directions using the pa-rameters generated in the initialization and parametersetting module including their initial location, direc-tion, and speed. A wrap-around grid is used to avoidthe boundary effect of the simulated rectangular area. Italso determines and CIR of each active user from itsserving cell and its neighbor cells in addition toandCIR at the BS from each MS. Based on these measure-ments ( and CIR), the mobile user might be switchedto another serving cell if it can provide the user with abetter quality.

— Frequency Hopping: The carrier frequency of eachuser is changed at every time frame using the GSMrandom hopping algorithm [2].

— Call Termination: It terminates the active call whenits arrival time plus the call duration is equal to thesimulation clock. It releases the channel assigned tothat user and removes the user from the active user list.

— Statistics Collection: This module collects and up-dates the statistics required to estimate the systemperformance such as the blocking rate, dropping rate,handover rate, and the CIR cumulative density func-tion (CDF). This updating process is done every timeframe. A final report describing the final statistics isgenerated at the end of the simulation.

V. OUTAGE PROBABILITY ANALYSIS

Fig. 1 illustrates the geometry of the problem of the downlinkinterference from the BS in theth cell to an MS in sector 1 incell 0.

A. Downlink Analysis [13]

1) MB Antennas Without Power Control:The interferencepower at an MS in cell 0 from theth cell is expressed as

(2)

whereBernoulli random variable representing the activityof the th interferer MS. is equal to 1 with proba-bility , which is equal to the product of the averageLF with the DTX factor (DTXF);


Fig. 1. Downlink interference from the BS in thejth cell to the MS in cell 0.The solid arrows represent the desired signals, while the dashed arrow representsthe interference signal.

cochannel interferer index ;transmit power;constant that depends on the carrier frequency,and antenna heights, and and antennagains;distance between the BS in theth cell and the MSin cell 0;path loss exponent;shadowing parameter of theth interferer;antenna gain as a function of the interferer angle

and beam angle; it is defined as.

Due to the interference averaging property of SFH, we are inter-ested in the mean value of the interference power rather than theinstantaneous value. The mean value of the interference powerfrom the th cell is given by

(3)

where is the mean value, is the pmf of the beamangle, and it is equal to if users are uniformly distributed,

are the possible values of . It can bereadily shown that where

[14]. Then (3) can be rewritten as

(4)

As shown in Fig. 1, and are functions of and whereand are the coordinates of the MS in cell 0 in polar form.

Therefore, the total interference can be expressed as

(5)

while the received carrier power at the MS in cell 0 is

(6)

where is the shadowing parameter of the MS in cell 0 andis the beam angle serving this MS. The outage probability

is defined as

(7)

where is equal to in absolute value. By substitutingfor from (6), the outage probability is given by

(8)

Using the total probability law the outage probability is givenby

(9)

where is the pdf of the MS to be at the locationdefined with . When users are uniformly distributed

is equal to . Since is normally distributed,the first term in the integrand in (10) is determined as follows:

(10)

where .Therefore, the outage probability can be expressed as

(11)

2) Sectorization Without Power Control:This case can beconsidered as a special case of the MBs antenna with .The antenna mainlobe gain is assumed to be 0 dB with adB sidelobe gain. Thus, is defined as follows:

otherwise.(12)

The outage probability is still given by (11). However, the di-rective gain function is to be modified as in (12).

3) MB Antennas With Perfect Power Control:With perfectpower control, each mobile receives a constant powerfromits BS regardless of its location. Consequently, the transmitpower from the BS is a function of the MS coordinatesas follows:

(13)

while the interference from theth BS is given by

(14)


where is the shadowing parameter inside theth cell, whileand are the coordinates of the MS in theth cell. Then,

the mean value of the interference is

(15)

Thus, the total interference is given by

(16)

is given by a constant when perfect power control isincorporated. Hence, the outage probability is

(17)

Using the total probability law, is equal to

(18)

which can be rewritten as

(19)

where is the unit step function.4) Sectorization With Perfect Power Control:The same

analysis used for MB antennas with perfect power control isused here. However, the directive antenna must be modifiedas expressed in (12). Therefore, the expression of the outageprobability given by (19) is still valid here.

B. Uplink Analysis [15]

Fig. 2 illustrates the geometry of the problem of the uplinkinterference to the BS in cell 0. The uplink analysis is similar tothat of the downlink with some changes to consider the mobilityof the cochannel interferers.

1) MB Antennas Without Power Control:The interferencepower at the BS in cell 0 from an MS in theth cell is

(20)

This equation is similar to (2) in the downlink analysis, butis replaced with . It is worth noting that the definitions ofboth and are also changed as illustrated in Fig. 2. The meanvalue of the interference from the MS in theth is given by

(21)

where and are the interferer MS coordinates in the polarform and is the distance between the MS in theth cell and

Fig. 2. Uplink interference from the MS in thejth cell to the BS in cell 0. Thesolid arrows represent the desired signals, while the dashed arrow represents theinterference signal.

the BS in cell 0. Other variables and parameters are similar tothose used in the downlink analysis. Thus, the total interferenceis given by

(22)

which is similar to (5). However, unlike the downlink case,is no longer dependent on . The carrier power expressiongiven in (5) is still valid here. Consequently, the expression ofthe outage probability for the downlink case given by (11) is stillvalid for the uplink case taken into consideration the differencein the definition of .

2) Sectorization Without Power Control:The expression ofthe outage probability given by (11) is also valid in this case, butthe directive gain function should be modified as in (12).

3) MB Antennas With Perfect Power Control:As in thedownlink analysis, the received power is assumed to be constantand equal to . Therefore, the cochannel interference at the BSin cell 0 from the MS in the th cell is still given by (14). From(14) and Fig. 2 it can be easily shown that the mean value ofthe interference from the cochannel interferer MS in thethcell is given by

(23)

Then, the total interference is given by (22) and it is alsoa function of only. Thus, the outage probability is expressedas

(24)


(a) (b)

(c) (d)

Fig. 3. CDF(CIR) atLF = 40%. (a) Downlink without PC. (b) Downlink with PC. (c) Uplink without PC. (d) Uplink with PC.

4) Sectorization With Perfect Power Control:The outageanalysis of the MB antennas with perfect power control can beused here. However, the antenna directivity must be modifiedas defined in (12).

C. Results

In this subsection, results of the CIR analysis are presentedfor both the downlink and the uplink based on the simulationdescribed in Section IV and the analytical method discussed

in this section. The following numerical values are used inthe analysis:

— cell radius km;— DTXF ;— average user speed km/h.

is determined analytically from (11), (19), and (24) and bysimulation at different values of LF. Fig. 3 shows the CDF(CIR)with MB antennas and with sectorization (SC) both with andwithout power control at % for the downlink and uplinkas well. It is evident that there is a good agreement between the


Fig. 4. Downlink outage probability(P ) dependence on the LF.

simulation results and the analytical values particularly whenpower control is not used. The difference between the CIRvalues of the two methods does not exceed 1 dB for most of theresults. With perfect power control, less agreement between thesimulation and analytical results is achieved. The differencein CIR estimation exceeds 3 dB at high CDF values. Thisis because perfect power control, assumed in the analyticalsolution, is hard to fully attain in the simulation since powercontrol algorithms usually experience errors and delays. It isobvious that the power control changes the distribution ofthe CIR. Without PC, the CDF has a smooth monotonicallyincreasing shape as shown in Fig. 3(a) and (c). With PC, thehigh values of the CIR are emphasized while the low valuesare de-emphasized. Therefore, the CDF of the CIR takes verylow values (approaches zero) at low CIR values, while it takesvery high values (approaches one) at high CIR values. Anabrupt change from the low values to high values can beremarked in Fig. 3(b) and (d). Fig. 3 also demonstrates theconsiderable enhancement in the CIR due to MB antennas.A 2.5–4 dB enhancement in the CIR is achieved using MBantennas (without PC), as shown in Fig. 3(a) and (c). Forinstance when the CDF is equal to 10% without PC, the CIRis increased from 10 to 13 dB for the downlink and from 9 to12.5 for the uplink. With PC, A 4–6 dB enhancement in theCIR is achieved using MB antennas, as shown in Fig. 3(b)and (d). For example at 10% CDF, the CIR is increased from7.5 to 12.5 dB for the downlink and from 7.9 to 11.9 dBfor the uplink.

is determined for the four cases mentioned above(with/without MBs and with/without PC) and then plottedversus LF in Figs. 4 and 5 for the downlink and the uplink,respectively, as well. Both Figs. 4 and 5 show the significantenhancement in the performance due to MB antennas combinedwith power control. It is shown that the outage probability issubstantially reduced due to MB antennas and PC particularly

Fig. 5. Uplink outage probability(P ) dependence on the LF.

at low and medium LFs. For example at 60% LF without PC,is reduced due to MB from 0.11 to 0.067 in the downlink

and from 0.13 to 0.06 in the uplink. Also at 60% LF withPC, is decreased from 0.63 to 0.02 for the downlink andfrom 1 to less than 1 10 for the uplink. However, it isalso shown that beyond a certain threshold value of LF,with PC starts to increase rapidly. It is evident that withPC can be higher than that without PC at high LF values.For instance when MB is not used, with PC starts toexceed without PC at % for the downlink andat % for the uplink. When MB is employedwith PC starts to exceed without PC at % for thedownlink and at % for the uplink. This is becauseperfect power control degrades the system performance underheavy loading conditions.

Tables I and II list the maximum LF at different maximumoutage probability requirements . For example, in thedownlink when %, the maximum LF is increasedfrom 7% to 20% (which is more than 180% enhancement) byincluding MB antennas without power control. is in-creased to 18% (which is more than 150% enhancement) byemploying power control without MB. By combining both tech-niques, is increased up to 60%, which is more than 750%enhancement. However, the capacity gain in reality might beless than that because of the complexity of realizing perfectpower control. By comparing the maximum LF in these two ta-bles, we can conclude that the downlink is the limiting factorin most of the cases (except at % with PC and MB,

% with PC and MB, and % with no PCand SC). For instance, at % with MB and PC, the net-work can tolerate values up to 66% in the uplink whileit can tolerate up to 60% in the downlink. Hence, the admissioncontrol must consider the smaller value and limits the laodingfactor to 60% eventhough the uplink can accommodate higherloading.


TABLE IMAXIMUM LOADING FACTOR (LF ) OF THE DOWNLINK AT VARIOUS OUTAGE PROBABILITY REQUIREMENTS(p )

TABLE IIMAXIMUM LOADING FACTOR (LF ) OF THE UPLINK AT VARIOUS OUTAGE PROBABILITY REQUIREMENTS(p )

Fig. 6. A sample of the LF variation with time.

VI. CALL ADMISSION CONTROL

Conventional loading-basedcalladmissioncontrolalgorithmsuse the instantaneous LF as a criterion for call admission [2],[7]. Fig. 6 demonstrates a sample1 of the LF in cell 0. Sincethe average LF is less than , the carried trafficintensity, which is equal to is always less than

1This sample is obtained by the simulation tool discussed in Section IV.

the maximum capacity given by (1). Since in TDMAsystems with soft capacity depends on (as shown inthe previous section), it is possible to accept some overloadinginstants (when the instantaneous LF exceed ) providedthat does not exceed . This can only be donewith soft capacity since calls are blocked while a number ofchannels are still available in the cell (sector) and these channelscan be utilized if the outage probability constraint is not beviolated.


Fig. 7. A Markov chain representing the state transition model of the proposed call admission algorithm.

A. Proposed Algorithm

The proposed algorithm aims to increase the maximum car-ried traffic intensity to achieve the maximum soft capacity valuegiven by (1). Since the objective of this algorithm is to increasethe average LF up to , the admission algorithm toleratesthe overloading instants shown in Fig. 6. The permission forsuch overloading instants reduces the call blocking and drop-ping probabilities. Hence, higher loading can be accommodated.Since the LF is equal to , the average LF is limitedby restricting the exponential weighted moving average of thenumber of users per cell defined as

(25)

where is the number of users per cell, is the updatingparameter which ranges from zero (no updating) to one(memoryless updating) and is the frame duration. Theexponential weighted moving average is chosen since it has atunable gradual averaging window rather than an abrupt aver-aging window as in the truncated average. The call admissioncondition is simply presented by the following statement: “theBS in any cell can accept the arriving users (new or handovercalls) as long as and .”The overloading status is only permitted for some time instantswhen there is high traffic and the average value of the LF is lessthan or equal to . In the sequel, the argument will beomitted from and for simplicity. However,it should be kept in mind that both and arefunctions of time.

B. Performance Analysis of the Proposed Admission ControlAlgorithm

In order to study the performance of the proposed algorithmanalytically, a stochastic analysis based on the state transitionmodel has been developed. When the exponential weightingmoving average is not employed, it is enough to define thesystem (cell) state (ST) as the number of users .Then, the system can be modeled as alost call cleared systemorM/M/C/C queuing system; and the blocking probability is de-termined by the Erlang-B formula [9]. By including ,we have to redefine the cell state. Each state is determinedby a two-element vector . Therefore,the cell-state transition can be modeled as a two-dimensional(2-D) Markov chain. By rearranging the Markov chain, it canbe represented as a one-dimensional (1-D) chain as shown in

Fig. 7. It is assumed that the transition occurs at each timeinterval , which is so small that no more than one eventoccurs during this interval. At a state ,the possible events are as follows:

1) one user arrives at the cell;2) one user departs from the cell;3) no users arrive at or depart from the cell.

The probability of the first event is equal to , the proba-bility of the second event is equal to , while the proba-bility of the third event is . Assuming that theinitial state of the system is equal to (0, 0), we can studythe system evolution based on (25) in addition to the possibleevents listed above. The system move to statewith probability . The probability of the transition from

to state is also . While theprobability of the transition from to stateis and to is .Following this procedure, we can determine all the states transi-tion probabilities of the Markov chain. However, the chain sizeis too large to be determined manually. Thus, a software rou-tine has been developed to find all the possible states associatedwith its transition probability matrix (TPM). Obviously, isa discrete variable that takes nonnegative integer values, while

is a discrete variable, which takes nonnegative valuesbut not necessarily integers. In order to reduce the computa-tional burden is quantized with a quantization level

, which implies that some states are merged to re-duce the number of the states and, consequently, the size of theTPM. Nevertheless, should be chosen to reduce thecomputation burden without compromising the accuracy.

A new user is blocked if the number of active usersis already equal to the maximum number of channels per cell

or when is greater than or equal to a certainthreshold value . Therefore, the blocking probabilityis expressed as

or (26)

The total arrival rate per cell is equal to , whereis the new call arrival rate and is the handover call arrivalrate and it is a function of and as follows [16]:

(27)


where HOR is the handover rate. The average call residencetime is equal to , where is the averagedwelling time of the MS in the cell, which is a function of theaverage speed of the MSs and the cell size, while is theaverage call duration [16]. Since the TPM is a function of theblocking probability, it is possible to determine the state prob-abilities and then the blocking probability iteratively as fol-lows:

1) set an initial value for ;2) calculate and from the expressions given above and

substitute for with ;3) determine the transition probability from each state to the

other states as explained above;4) determine the state probabilities using the global balance

condition

(28)

subject to the condition

(29)

where is the probability of theth state;5) estimate the blocking probability using the state probabil-

ities as follows:

or

(30)

6) calculate the relative error of the estimated blocking prob-ability as follows:

(31)

7) if is greater than 1% let and go to step 2,otherwise stop and let .

C. Results

In order to reduce the problem size, is limited to threechannels. is assumed to equal 33.33%. Both the updatingparameter and the quantization level are chosen tobe equal to 0.01. This value is chosen as a compromise betweenthe results accuracy and the computation burden. Smaller valuescan enhance the results accuracy but leads to a huge problemsize (with millions of states). It then becomes too tedious tosolve the problem particularly with the iterative method dis-cussed above. Other parameters are identical to those used in theanalysis. Using these values, it is found that the chain consistsof 992 states. Figs. 8 and 9 showas a function of the offeredtraffic using the conventional and the proposed call admissioncontrol algorithms. is determined for both algorithms analyt-ically and by simulation as depicted in Fig. 8. Several remarks

Fig. 8. Blocking probability(P ) of the conventional and proposed admissionalgorithms atCH = 3 andN = 1.

Fig. 9. Blocking probability(P ) of the conventional and proposed admissionalgorithms atCH = 48 andN = 16.

can be realized in Fig. 8. First of all, a good agreement betweenthe simulation results and the analytical findings can be noticedin Fig. 8. The relative error in does not exceed 3% for both al-gorithms. In Fig. 9, CH cell is increased to 48 channels (whichis a more realistic number), but is estimated by simulationonly since the problem size is too large to be solved analyti-cally. Both Figs. 8 and 9 also show that the blocking probabilityis considerably reduced using the proposed algorithm. For in-stance, in Fig. 8 is reduced from 0.22 to 0.095 atErlang/cell. In Fig. 9 at Erlang/cell, is reducedfrom 0.08 with the conventional algorithm to 0.042 using the


Fig. 10. CDF (CIR) of the conventional and proposed admission algorithms.

proposed algorithm. Thus, more traffic can be accommodatedwithout violating the blocking rate restriction. For example at2% blocking rate, can be increased from 10.3 Erlang/cell to13 Erlang/cell, which is more than 25% enhancement.

This capacity enhancement is obtained by admitting moreusers to the system in such a way that the average number ofusers per cell does not exceed to maintain the quality ofservice in terms of the CIR. Fig. 10 depicts the CDF(CIR) for theproposed and the conventional algorithms. The reduction in CIRdue to the proposed algorithm is less than 0.4 dB. From Fig. 10,it is evident that the outage probability isslightly increased from to .

VII. SUMMARY AND CONCLUSION

It has been shown that the network capacity of SFH-TDMAsystems can be determined analytically with a high degree ofaccuracy. A simulation tool for wireless networks has been de-veloped and used for comparison purposes. It has been shownthat the analytical values and the simulation results agree well.Smart antennas in TDMA systems with soft capacity have beeninvestigated as an efficient technique for enhancing cellular net-work capacity. It has been demonstrated analytically and by sim-ulation that the system capacity can be increased many folds byusing MB antennas combined with SFH and power control.

A novel call admission control algorithm has been proposedto enhance the system capacity by reducing the blocking anddropping probabilities without causing a significant degradationto the QoS. The proposed algorithm makes use of the temporalloading averaging. The capacity gain of this algorithm is morethan 25%. However, higher capacity gain can be achieved if thistemporal loading averaging is combined with the spatial loadingaveraging proposed in [7].

In practice, it is difficult to realize the perfect power con-trol assumed in the analysis. However, the results reported here

can provide an upper bound to the performance, which may beachieved as better power control techniques become available.The results reported here demonstrate that smart antennas pro-vide a feasible and effective alternative to cell splitting and mul-tilayers in cellular radio networks.

REFERENCES

[1] T. Chebaro, “Capacity evaluation of a frequency hopped TDMA cellularradio system,”Annael des Telecommun., vol. 51, pp. 99–104, Mar.–Apr.1996.

[2] J. Johansen and B. Vejlgaard, “Capacity analysis of a frequency hoppingGSM system,” Masters’ thesis, Alborg Univ., Alborg, Denmark, 1995.

[3] G. Tunnicliffe, A. Sathyendran, and A. Murch, “Performance improve-ment in GSM networks due to slow frequency hopping,”Proc. IEEEVehicular Technology Conf., pp. 1857–1861, May 1997.

[4] M. Keller, “A comprehensive simulation approach to study FH in theGSM system regarding the physical layer level and the system level,”Proc. IEEE Vehicular Technology Conf., pp. 1852–1856, May 1997.

[5] S. Channakeshu, A. Hassan, J. Anderson, and B. Gudmundson,“Capacity analysis of a TDMA-based slow-frequency-hopped cellularsystem,”IEEE Trans. Veh. Technol., vol. 45, pp. 531–541, Aug. 1996.

[6] J. Dornstetter and D. Verhulst, “Cellular efficiency with slow frequencyhopping: Analysis of the digital SFH900 mobile system,”IEEE J. Select.Areas Commun., vol. 5, pp. 835–848, June 1987.

[7] P. Beming and M. Frodigh, “Admission control in frequency hoppingGSM systems,” inProc. Vehicular Technology Conf., May 1997, pp.1281–1286.

[8] M. Madforset al., “High capacity with limited spectrum in cellular sys-tems,”IEEE Commun. Mag., pp. 38–45, Aug. 1997.

[9] T. Rappaport, Wireless Communications Principles & Prac-tices. Englewood Cliffs, NJ: Prentice-Hall, 1996.

[10] L. Godara, “Applications of antenna arrays to mobile communications,Part I: Performance improvement, feasibility, and system considera-tions,” Proc. IEEE, vol. 85, pp. 1029–1059, July 1997.

[11] J. Winters, “Smart antennas for wireless systems,”IEEE PersonalCommun., pp. 23–27, Feb. 1998.

[12] M. Ho, G. Stuber, and M. Austin, “Performance of switched-beam smartantennas for cellular radio systems,”IEEE Trans. Veh. Technol., pp.10–19, Feb. 1998.

[13] M. Ahmed, W. Wang, and S. Mahmoud, “Downlink capacity enhance-ment in GSM systems with frequency hopping and multiple beam smartantennas,” inProc. Int. Communications Conf. (ICC)’00, New Orleans,LA, June 2000, pp. 1015–1019.

[14] C.-C. Lee and R. Steele, “Signal-to-interference calculations formodern TDMA cellular communication systems,”Proc. Inst. Elect.Eng. Commun., vol. 142, no. 1, pp. 21–30, Feb. 1995.

[15] M. Ahmed and S. Mahmoud, “Capacity analysis of GSM system usingfrequency hopping and smart antennas,” inProc. Vehicular TechnologyConf., Tokyo, Japan, May 2000, pp. 335–359.

[16] B. Jabbari, “Teletraffic aspects of evolving and next-generation wire-less communication networks,”IEEE Personal Commun. Mag., pp. 4–9,Dec. 1996.

Mohamed H. Ahmed (S’97-M’01) received theB.Sc. and M.Sc. degrees in electronics and commu-nications engineering from Ain Shams University,Cairo, Egypt, in 1990 and 1994, respectively, and thePh.D. degree in electrical engineering from CarletonUniversity, Ottawa, ON, Canada, in 2001.

From 1991 to 1996, he was a Teaching Assistant inthe Department of Electronics and Communications,Minia University, Minia, Egypt. From 1996 to 2000,he was a Teaching Assistant and Research Assistantin the Department of Systems and Computer Engi-

neering, Carleton University, where he is currently a Senior Research Associate.His research interests include wireless access techniques, resource managementin wireless networks, smart antennas, 3G and 4G wireless systems, wireless in-ternet and multimedia services, and fixed wireless networks.

Dr. Ahmed received the Ontario Graduate Scholarship for Science and Tech-nology (OGSST) in 1997 and the Ontario Graduate Scholarship (OGS) in 1998,1999, and 2000.


Samy A. Mahmoud (M’73-SM’83) received theM.Eng. and Ph.D. degrees in electrical engineeringfrom Carleton University, Ottawa, ON, Canada, in1971 and 1974, respectively.

In 1975, he joined the Faculty of Engineering, Car-leton University, where he served as the Chair of theDepartment of Systems and Computer Engineeringfrom 1988 to 1996. At present, he is the Dean of theFaculty of Engineering and Design. He has directedseveral large research and development projects inthese areas, involving joint university/industry col-

laborations. He has recently led a major initiative to establish the National Cap-ital Institute of Telecommunications (NCIT), a joint research organization in-volving several large international companies in the telecommunications andcomputer industries, leading university researchers, and scientists and engineersfrom two major Canadian Government research laboratories (CRC and NRC).The new institute has been launched with major financial contributions fromthe Government of Canada, the Province of Ontario, and the industrial partners.He holds senior consulting appointments with major international companies inthe field of telecommunications. In the past 20 years, he has he published morethan 150 archival and conference papes in the areas of wireless communicationsand broad-band networks and supervised over 80 Masters’ theses and doctoraldissertations. His main academic and professional interests are in the areas ofmobile and personal communication systems, broad-band networks, and dis-tributed computing systems.

Dr. Mahmoud was a Guest Editor of two issues of the IEEE JOURNAL OF

SELECTEDAREAS INCOMMUNICATIONS in the area of wireless and satellite com-munications. He has won several recognition awards in recent years for pio-neering research work leading to university/industry technology transfer. He isa corecipient of the Stentor 1993 National Telecommunications Award and core-cipient of IEEE TRANSACTIONS ONVEHICULAR COMMUNICATIONS Best PaperAward in 1994.

Documents

Soft capacity analysis of TDMA systems with slow …mhahmed/publications/ma02-j01.pdf636 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 4, JULY 2002 Soft Capacity Analysis