Wreless Sensor Network,,, -6 do:.436/wsn.. Publshed Onlne January (http://www.scrp.org/journal/wsn/). Evaluaton of Downlnk Performance of a Multple-Cell, Rake Recever Asssted CDMA Moble System Ayodej J. BAMISAYE, Mchael O. KOLAWOLE Department of Electrcal and Electroncs Engneerng, The Federal Unversty of Technology, Akure, Ngera Emal: {ayobamsaye, kolawolm}@yahoo.com Receved August 5, 9; revsed September 7, 9; accepted September, 9 Abstract In wreless Code Dvson Multple Access (CDMA) system, the use of power control s ndspensable to combat near-far and fadng problems. Sgnals transmtted over a multpath propagaton channel whch exhbts nter-path nterference and fadng. The recever has to employ measures to mtgate these effects or t wll ncur severe performance degradaton. A classc approach n CDMA communcatons s the rake recever. In ths paper, the downlnk performance s estmated for a CDMA moble system at the vertex of multple adjacent cells. At the base staton the receved sgnal s coherently dspread and demodulated usng a rake recever. The effects of power control, error correcton and rake recever were also nvestgated on the assumpton that the receved sgnals undergo Raylegh fadng, lognormal shadowng, and frequency selectve fadng. The evaluaton of performance measures of base to moble lnk (downlnk) of a multple-cell CDMA moble system s presented. Ths study demonstrates that sgnfcant performance mprovements are achevable wth combned use of power control, rake recever and error correcton scheme. Keywords: DS-CDMA, Power Control, Rake Recever, Error Correcton, Probablty Densty Functon. Introducton In wreless communcaton, fadng s one of the problems that cause the sgnal fluctuaton so t may cause degradaton of sgnal level at the recever. CDMA as one of the wreless communcaton types also experences fadng. Although downlnk channels n CDMA are transmtted wth codes that are orthogonal to one another; that s, they are encoded for mnmal mutual nterference, multpath propagaton causes the downlnk sgnal to be smeared n tme, destroyng some of ths orthogonalty []. Another problem that CDMA suffers s sgnal nterference from other users because all users n CDMA system use the same frequency. One of the solutons to mtgate fadng s dversty. In a fadng envronment, the prncpal means for a drect-sequence (DS-CDMA) system to obtan the benefts of dversty combnng s by usng rake recever by coherently combnng resolvable fadng. Dversty can mprove the qualty of the receved sgnal at the recever. To combat other users nterference, power control s used to mprove the CDMA system performance because power control can mnmze the nterference between users. Spread-spectrum sgnals nherently exhbt frequency dversty. Due to the ncreased bandwdth, a spectral null s less lkely to affect the entre sgnal spectrum. For the same reason, however, the rado channel s lkely dspersve. In order to explot frequency dversty, the recever has to collect sgnal energy from several mult-paths. For ths purpose, a rake recever allocates so-called fngers to mult-paths; n whch each fnger dspreads the receve sgnal synchronzed to the correspondng path delay, whle the recever subsequently computes a weghted sum of the rake recever fngers output. The sgnal-to-nterference rato (SIR) n fadng channels vares accordng to the channels response, and the requred SIR to acheve a certan bt-error rate (BER) depends on the dstrbuton of SIR. To keep the SIR nearly constant at the desred level, power control can be used []. The reverse lnk of a CDMA system employs both open loop and closed loop power control. The open loop power control s performed at the moble staton based on the measurement of the downlnk sgnals and therefore, t can only compensate for the near far dstance problem. The closed loop power control s performed at the base staton based on measurements of the SIR experenced at the base staton and therefore requres nformaton to be fed back from the base staton to Copyrght ScRes.
A. J. BAMISAYE ET AL. the moble statons. The closed loop power control scheme ams at reducng the channel fadng effects and the mult user nterference experenced at the BS. In the past many papers have analyzed the performance of sngle cell CDMA systems. Ths s a useful and necessary step n the analyss of a complete CDMA system, as these analyses gve expressons for capacty and system performance measures under a varety of condtons. However, n order to evaluate the performance of a complete cellular system, the analyses performed for sngle cells have to be extended to multple cells. Ths paper analyses the performance of the base-to-moble lnk (downlnk) of a multple cell CDMA system. Ths paper s arranged as follows. Subsecton. descrbes the system analyss and outlnes the dervaton of the probablty densty functons (pdfs) of the sgnal varables. Approprate system performance measures are defned n Subsecton.. The role of error correcton s consdered n Subsecton.3, power control n Subsecton.4, rake recever concept n Subsecton.5 and the results from the analyses are presented n Subsecton.6. Fnally, the conclusons drawn from ths study are summarzed n Subsecton.7... System Model The qualty of rado recepton by a moble at the juncton of adjacent cells n a CDMA cellular system s estmated n ths analyss, whch s applcable to both two and three dmensonal cellular layouts and s ndependent of the cell shape. The sgnal from the base staton (BS) receved at the moble staton (MS) s assumed to suffer Raylegh fadng, lognormal shadowng and frequency selectve fadng [3]. In some cases the wde band nature of CDMA channels may result n fadng that s not Raylegh dstrbuted but s actually less severe. However [4] reported that sgnals occupyng a bandwdth of l MHz could suffer Raylegh lke fades exceedng -3 db. The sgnals from the dfferent base statons are assumed to be asynchronous and would fade ndependently of each other. III II I Base staton moble staton Fgure. Moble staton at the juncton of 3-cells. All the sgnals (ncludng those ntended for other users n the same cell) transmtted to by a partcular BS occupy the same frequency spectrum and propagate through the same multpath channel to arrve at an MS. Consequently, the CDMA sgnals from a partcular BS, arrvng at a gven MS, fade n unson. The frequency selectvty of the channel s modeled by the correlaton bandwdth of the channel. The tme delay correspondng to the correlaton bandwdth may be measured as a multple of the chp perod, T c, [3]. All the users n the system under analyss are assumed to employ coherent bnary phase shft key (BPSK) modulaton and drect-sequence (DS) spreadng [5]. All the base statons and moble antennas are assumed to be omndrectonal. The recever employed n ths CDMA system s assumed to reject all but one of the multpath components of the desred sgnal. Consder 3 cells: I, II and III,n Fgure, where t s assumed that the desred user s connected to the BS n cell I and all the other base statons act as nterferers. For smplcty t s assumed that there are k+ users n cell I and k users n the other nterferng cells (.e. there are k nterferers n each cell). The moble at the juncton of adjacent cells wll experence nterference from a number of cells, but the effect of the Interference from the adjacent cells wll domnate. Therefore n ths analyss only nterference from the adjacent cells II and III s consdered where the combned nterference s approxmated by a Gaussan random varable. When the user s at the juncton of adjacent cells the number of nterferers s generally large enough to make ths approxmaton vald. Havng approxmated the total nterference, the momentary bt error-rate pber can be approxmated by the complementary error functon of the sgnal-to-nterference rato erfcsir [5]. The SIR at the juncton of L-adjacent cells s gven by [5] o SIR L N ak () bk () o 3 L Eb () where a(k) represents the self-nterference from the desred BS. Ths comprses of unwanted multpath components of the desred user s sgnal and the nterference from sgnals ntended for other users n the same cell. b(k) represents the nterference from users n the other cells. N s the spectral densty of the double sded addtve whte Gaussan nose (AWGN). per bt. E b s the energy Copyrght ScRes.
A. J. BAMISAYE ET AL. 3 s the sgnal strength receved from BS I, s the sgnal strength receved from BS II, etc. It s assumed that,, 3,... L are each Raylegh dstrbuted, and the means of the Raylegh dstrbutons are assumed to be log-normally dstrbuted. β s the voce actvty factor. Ths factor s very mportant because although CDMA systems can reduce self-nterference by mutng transmsson durng pauses, n the downlnk much more s requred n terms of occasonal power control bts, to ensure effectve transmsson durng pauses, and δ represents the nterference reducton factor f power control s used. Hence, the momentary bt-error rate can be approxmated as: pber erfcsir () where the complementary error functon erfc(x) s the probablty that a normally dstrbuted random varable wll be x or more standard devatons from ts mean [6], and almost lnear for large nterference varance. By assumng the term n () to be neglgble, and N o Eb represent the -summaton term as ( a a 3 a ) L a, and substtutng n () n vew of (), then the expresson for the momentary BER reduces to pber erfc (3) ak ( ) bk ( ) In order to determne the actual probablty of error, the probablty densty functon of ;.e. pdf, must be determned usng the Laplace transforms and then evaluatng terms usng Melln convoluton [7]. Thus, pdf of the sgnal strength receved from BS A,.e., pdf of, s gven by [8] pdf e (4) where s the mean-square value of, whch agan s assumed to be log-normally dstrbuted. Often, the ratos of the mean-square values of the Raylegh varables are preferred;.e.,, 3,, L L n an attempt to study the relatve sgnal strength varaton as a consequence of adjacent cells nfluence. So the pdf of the ratos s expressed: ln 4 pdf exp,,, L (5) where s the mean area of the th cell (n dbm), s the standard devaton of the sgnal varablty (n db) and constant 4.349 ln()... Estmaton of System Performance Measures... Short-Term Average Bt-Error-Rate (Ber) The short-term average BER, P av (k), as a functon of k number of users, s defned as the momentary BER averaged over the Raylegh fadng and may be expressed by Pav k pberpdf d (6) And the short-term SIR average as a functon of k number of users, SIR av (k), can be defned as the momentary SIR averaged over the Raylegh fadng as SIRav k pdf d (7) ak ( ) bk ( )... Servce Relablty The servce relablty, P ser (k), may be defned as the percentage of tme the momentary BER s below a maxmum desred level BER max, whch alternatvely can be defned as the probablty of pber less than. Specfcally, BER max max P k prob p( BER) BER (8) ser For k users per cell, the servce relablty can also be expressed as P k prob SIR SIR (9) ser k SIR erfcsir where s gven by BERmax. For a gven value of SIR, a correspondng value of can be found. Hence the servce relablty can be estmated by evaluatng the probablty that averaged over the lognormal shadowng,.e. P k pdf pdf dd ser pdf pdf pdf dd d L L () Copyrght ScRes.
4 A. J. BAMISAYE ET AL...3. Lnk Avalablty The lnk avalablty, P (K) lnk_a v, s defned as the percentage of locatons that the short-term average BER s below a maxmum desred level BER short. The lnk avalablty can be calculated by ntegratng the pdfs of η, η L over all possble values for whch the short-term average BER defned n (6) s below the threshold BER ; that s, short Plnk _ av k pdf pdf,,, L dd () where,, 3,, L are values of,, 3,, L respectvely for whch the short-term BER s below the threshold BERsho rt. It should be noted that the values of,, 3,, L are functons of all the varables of the outer ntegrals..3. The Role of Error Correcton If we assume an lm, block code (.e. for every m data bts, l m error correctng bts are added) capable of correctng all combnatons of c and fewer errors, then the average BER, P, can be approxmated by [9] P e b l l c l l P Po Po b () where s the correspondng BER n the absence of error correcton. If the data s to be transmtted at a partcular rate then as error correctng codes are added to the data the bandwdth occuped by the composte (baseband sgnal) code ncreases. If only a lmted bandwdth s avalable for transmsson, then the processng gan has to be reduced to compensate for the greater bandwdth of the baseband sgnal..4. The Role of Power Control Power control s an essental requrement of CDMA systems. An effectve power control scheme where a power ncrease command s sent to all users before a new hgh data rate packet s transmtted could mprove the qualty of sgnal as well as the dstrbuton of sgnals to moble users wthn BS coverage [,]. A smple power control algorthm that could be mplemented requres that the power transmtted from the BS be proportonal to the dstance between the BS and the user, rased to the power of the path loss exponent []. If the users are assumed to be unformly dstrbuted wthn a crcular cell of radus R, the pdf of the dstrbuton of the moble system at a radus, r, from the BS may be expressed by r Pr r (3) R Thus the power control factor can be wrtten as R r R N Pr rdr N.5. The Role of Rake Recever (4) The rake recever conssts of a bank of L-correlators or matched flters (also called fngers) where each fnger s matched to a partcular multpath component to combne the receved multpaths coherently. In ths work, the rake recever s assumed to use the maxmal rato combnng (MRC) technque, where the ampltudes of the receved MPCs are estmated and used as weghtng vector l n each fnger. Each l matches the channel-fadng coeffcent l of the receved sgnal. Followng [3], and gven output sgnal-to-nose rato (SNR o ) per bt γ b, an approxmate expresson of bt error probablty, Pe b, condtoned on a partcular channel realzaton at the output of the rake, s wrtten thus: L Eb l l l Pe bq SNRo Q L no l l (5) where Q( ) s the standard Q functon, whch by defnton Q(x) s the probablty that a standard normal random varable (zero mean, unt varance) exceeds x; and no s the nose standard devaton. We assume that the channel fadng coeffcents l are random, so we average (5) over the probablty densty functon of γ b ; that pdf p to have s, b b P P p d (6) e e b b b A closed-form expresson of (6) s dffcult to obtan. A numercal method can be used to obtan a soluton. Often, some approxmatons are used n practce. For nstance, by estmatng across the fadng channel nstantaneous output SNR per symbol, an average bt-error probablty P e can be obtaned..6. Smulaton Results A smple three-cell system has been consdered n ths Copyrght ScRes.
A. J. BAMISAYE ET AL. 5 secton to nvestgate the mpact of error correcton and power control n rake recever asssted DS-CDMA system s performance. A (3,) Golay code for error correcton s assumed, for whch c = 3. In ths analyss, the system occupes the same bandwdth as the spread bandwdth of a sgnal. In order to mantan the same transmsson bandwdth of MHz, the error corrected data s assumed to have a processng gan of 66 and the uncorrected data processng gan of 8. A voce actvty factor of.5 and a path loss exponent of 4 are used. (a) Fgure presents two graphs of the short-term average BER: a) as a functon of the number of users per cell and b) as a functon of the short-term average SIR. In the fgure, curve A represents no error correcton, no power control and Rake Recever; curve B represents wth error correcton, no power control and rake recever; curve C represents wth power control, rake recever and no error correcton; and curve D represents wth error correcton, power control and rake recever. The results ndcate that for a small number of users, the system performs better than the system wth no error correcton, power control and Rake recever but as the number of users ncreases, the stuaton reverses, as n Fgure (a). As seen n Fgure (b), the combned effect of power control, rake recever and error correcton ncrease the capacty sgnfcantly dependng on the performance measure used n determnng the maxmum allowable number of users. A BER threshold of -3 and standard devaton values of 6dB were used n the estmaton of servce relablty and lnk avalablty. Fgure 3 presents the servce relablty and lnk avalablty as functons of the number of users per cell. The results ndcate that for a path-loss exponent of 4, power control ncreases the capacty by approxmately three fold. Generally, servce relablty and lnk avalablty decreases wth ncrease n number of users, but the performance wth error correcton, power control and rake recever has hgher servce relablty and lnk avalablty when compared wth other condtons. Consderng 7 users per cell, for nstance, the servce relablty and lnk avalablty of 7% s produced as compared wth less than 65% and 3% of servce relablty and lnk relablty respectvely of the remanng condtons, that s, A, B and C. (b) Fgure. Short term average BER as (a) a functon of number of users per cell and (b) short term average SIR.( A - wth no error correcton, no power control and Rake Recever; B - wth error correcton, no power control and Rake recever; C - wth power control, Rake recever and no error correcton; D - wth error correcton, power control and Rake Recever) (a) Copyrght ScRes.
6 A. J. BAMISAYE ET AL. (b) Fgure 3. (a) Servce relablty as a functon of number of users per cell and (b) lnk avalablty as a functon of number of users per cell..7. Conclusons Technques and expressons for estmatng the short term average Bt-error-rate (BER), servce relablty and lnk avalablty are developed. The downlnk performance s estmated for a CDMA moble system at the vertex of multple adjacent cells. The performance of rake recever asssted multple-cell CDMA moble system undergong Raylegh fadng, lognormal shadowng, and frequency selectve fadng was nvestgated where the system occupes the same bandwdth as the spread bandwdth of a sgnal. Ths study demonstrates that for rake recever asssted CDMA-system sgnfcant performance mprovements are achevable wth combned use of power control and error correcton scheme.. References [] ADC, CDMA Capacty and Coverage, Whte Paper, http://www.adc.com, 6. [] K. S. Glhousen, On the capacty of a cellular CDMA system, IEEE Transactons on Vehcular Technology, Vol. 4, pp. 33 3, 99. [3] D. E. Borth and M. B. Pursley, Analyss of drectsequence spread spectrum multple-access communcaton over Rcan fadng channels, IEEE Transactons of Communcatons, Vol. COM-7, pp. 566 577, 979. [4] D. L. Schllng, L. B. Mlsten, R. L. Pckholtz, F. Bruno, E. Kanteraks, M. Kullback, V. Erceg, W. Bederman, D. Fshman, and D. Salerno, Broadband CDMA for personal communcatons system, IEEE Communcatons Magazne, pp. 86 93, 99. [5] I. B. Mlsten, T. S. Rappaport, and R. Barghout, Performance evaluaton for cellular CDMA, IEEE Journal on Selected Areas n Communcatons, Vol., No. 4, pp. 68 689, 99. [6] A. N. Rosenberg and S. Kemp, CDMA capacty and qualty optmzaton, McGraw-Hll, 3 [7] M. D. Sprnger, The algebra of random varables, Wley, New York, 979. [8] K. W. Sowerby and A. G. Wllamson Outage probablty calculatons for a moble rado systems wth multple nterferers, Electronc Letters, Vol. 4, No. 4, pp. 5 53, 988. [9] D. J. Torrer, The nformaton bt-error-rate for block codes, Transactons of Communcatons, Vol. COM-3, pp. 474 476, 984. [] Y. Hara, K. Suzuk, K. Kaneko, and T. Sekguch, Rado Resource Management and Power Control for W-CDMA Uplnk wth Hgh Data Rate Packet Transmsson, IEICE Transactons on Communcatons, E88-B(5), pp. 9, 5. [] A. J. Bamsaye and M. O. Kolawole, Capacty and qualty optmzaton n CDMA 3G networks, Journal of Communcaton and Informaton Systems, 9, (accepted for publcaton). [] R. R. Gejj, Forward-lnk-power control n CDMA cellular systems, IEEE Transactons on Vehcular Technology, Vol. 4, pp. 53 536, 99. [3] J. G. Proaks, Dgtal communcatons, McGraw Hll, 995. Copyrght ScRes.