Performance of Reverse Link CDMA in a Multi-cell Environment with Moving Cells*

Transcription

1 Performance of Reverse Lnk CDMA n a Mult-cell Envronment wth Movng Cells* A. Chockalngam and Laurence. Mlsten Department of Electrcal and Computer Engneerng Unversty of Calforna, San Dego 9500 Glman Drve, La Jolla, CA E-mal: choks@ece.ucsd.edu Tel: (619) FAX: (619) Abstract We present the bt error performance and capacty of the reverse lnk of a DS-CDMA cellular system, takng nto account the effect of power-controlled nterferng users from other cells. A convolutonally encoded, PSK modulated, waveform s consdered. The channel s assumed to undergo flat Raylegh fadng, whch s typcal of narrowband CDMA systems. All the moble users are power-controlled by ther assgned base statons. A cellular CDMA system wth 25 cells n a square grd layout s smulated, and the performance n the center cell surrounded by 2-ters of nterferng cells s estmated. The effect of power control s accounted for by assumng the power control error to be log-normally dstrbuted. We present the performance results when the base staton of nterest moves relatve to other fxed base statons, resultng an overlappng cells, a stuaton possble n a battlefeld envronment where the base statons could be mounted on jeeps, tanks, UAVs, etc. 1 Introducton The rather well-known advantages of jammng resstance, low probablty of ntercept, smple frequency coordnaton, multple access, and ablty to combat multpath make spread spectrum technques combned wth cellular communcatons archtecture a natural choce for both commercal and battlefeld wreless communcatons [1],[2],[3]. In ths paper, we consder a drect sequence code dvson multple access (DS-CDMA) cellular system employng convolutonally encoded PSK modulaton. The base-temoble lnk (forward lnk) and the moble-tebase lnk (reverse lnk) operate on dfferent frequency bands. The capacty of the reverse lnk n a mult-cell envronment has been nvestgated 'Ths work was partally supported by TRW Mltary Electroncs & Avoncs Dvson under Grant N541VK2S, Artouch Communcatons, and by the MICRO Program of the State of Calforna. by many authors [2],[4],[5],[6]. Most of these studes, for analytcal smplcty, assume that a moble talks to a base staton whch s nearest to t, and further, that the base statons do not move. In ths paper, we study the reverse lnk performance n a mult-cell envronment adoptng two dfferent base staton assgnment models, and compare ther relatve performances. The frst model s based on a mnmum dstance crteron (dstance model), and the second on a maxmum receved power crteron (power model). Adaptve power control s essental to counteract the effects of the near-far problem and shadowng, so as to ensure an average equal performance to all the users n the system. We allow all the mobles to be power-controlled by ther assgned base statons. The power control error (PCE) resultng due to mperfect power control s assumed to have a log-normal dstrbuton, and the degradaton of the reverse lnk capacty as a functon of the standard devaton of the PCE s evaluated. Dynamc base staton moblty, n addton to user moblty, s a key ssue n hostle battlefeld envronments, where the base statons could be mounted on movng platforms (e.g., jeeps, tanks, UAVs) and can move along wth the solders as a cell [7]. We capture ths scenaro by allowng the cell-ofnterest to move wth respect to two ters of nterferng cells, and estmate the performance at the movng cell. In Secton 11, the system model, ncludng cell layout, channel characterstcs, and base staton assgnment models, s descrbed. In Secton 111, the capacty estmaton methodology s descrbed. Secton IV provdes the results and dscussons, and Secton V presents the conclusons. 2 System Model We consder a 25-cell square grd topology DS-CDMA cellular system wth base statons {l, 2,..., 25) as shown n Fgure 1. We are nterested n the performance at the test cell wth IZ as ts base staton. Ths test cell s surrounded $ IEEE

2 the desred user's base staton o, and b) the effect of power control to compensate for the attenuaton to the base staton of the out-of-cell nterferer,. That s, where d,, do are the dstances of the out-of-cell nterferng user to ts own base staton,, and the desred user's base staton O, respectvely. The varables (, and (0 are shadow parameters whch are assumed to be ndependent, Gaussan random varables wth zero means and equal standard devatons of U, d. Fgure 1: 25-cell square grd layout. by two ters of nterferng cells. Ter-I has nterferng cells and ter-i1 has 16 nterferng cells. Asynchronous moble users are assumed to be randomly located n the system wth a unform densty of K users-per-cell-area. Each user communcates wth ts base staton on the reverse lnk usng coherent PSK modulaton and drect sequence spreadng. The spreadng sequences have a common chp rate of &, where T, = 2. Tb and T, are the bt and chp duratons, repectvely, and N, s the processng gan. We consder the channel relevant to a narrowband CDMA system, whch s modelled by flat Raylegh fadng (.e., the coherence bandwdth of the channel s assumed to be larger than the bandwdth of the sgnal) and shadowng. The factors that affect the receved sgnal power are the dstance and shadow losses. We adopt a standard dstance loss model, namely, receved power s nversely proportonal to the dstance rased to the power U, where the propagaton exponent U vares n the range 2 to 5.5 dependng on the envronment. Apart from the attenuaton due to dstance, the sgnal also experences loss due to shadowng whch s caused by blockage (e.g., buldngs, hlls, folage, etc). It has been shown through measurements that shadow loss has a log-normal dstrbuton wth standard devaton us n the range 4 to 12 d []. Thus, the receved sgnal power s proportonal to the 10(c/lo)d-v, where d s the dstance between the moble and the base, and < s Gaussan random varable wth zero mean and standard devaton U, d. Each moble user's transmsson on the reverse lnk s power controlled by ts assgned base staton. Due to adaptve power control, the sgnals from all n-cell users arrve at the base staton wth nomnally equal power (except for the Raylegh fadng factor whch represents the resdual fadng that vares too rapdly to be tracked out by the adaptve power control). The nterferng sgnals from the out-of-cell users are compensated for dstance and shadow losses to ther own assgned base statons. Thus, the nterference due to an out-of-cell user (assgned to base staton,), at the desred user's base staton o, s proportonal to two factors, namely, a) attenuaton caused by dstance and shadowng to ase Staton Assgnment We consder two dfferent models for base staton assgnment, wz., 1) dstance model, and 2) power model. Dstance model In model 1, a moble user s assgned to the base staton, to whch the moble-tebase dstance s mnmzed,.e., 2 s the base staton ndex for whch d, = mn{dv}, y E {0,1,2,..., 24). Ths model s used n [7] for analytcal smplcty. In realty, due to fadng and shadowng, the base staton from whch a moble user receves the maxmum power need not be the closest one. Power model Model 2 consders both dstance and shadow losses for the base allocaton. Here, a moble user s assgned to a base staton, for whch the base-temoble receved power s mazmzed,.e., z s the base staton ndex for whch { d,-y1o(c"/lo) = max d,-yio(c~~lo)} y E {0,1,2,..., 24). In addton to the above two models, we also consder an approxmaton to the power model, used n [2]. The receved sgnal at the test base staton 12 s gven by r(t) = where yk = { 2SK k=l A~kakyk~k(t-7k)Ck(t-7k)COS(Wot + $k) + nw(t), 1 f k = n-cell user 10(c'2k-cmk)/20 f k = other-cell user. In (2), {Q} represents the random delays whch are ndependent and unformly dstrbuted n [o,tb], and {$E}, where $k = dk - w.,~, represents the ndependent dentcally dstrbuted random carrer phases unformly dstrbuted n [O, 24. The thermal nose term, nw(t), s addtve whte Gaussan wth two-sded power spectral densty 710/2, ak s a (2)

3 Raylegh random varable representng fadng due to multpath, and Ak s the power control error whch s a random varable log-normal1 dstrbuted wth standard devaton 36 ce d (.e., Ak = 10(.0), where the varable X follows a normal dstrbuton). At the recever, the sgnal s coherently despread and demodulated. 3 Capacty Estmaton A quas-analytc approach s adopted to estmate the bt error performance, and thus the capacty on the reverse lnk of the DS-CDMA system. We frst estmate the uncoded bt error performance of the system at dfferent system parameter settngs through large scale smulatons. We assume perfect nterleavng, and evaluate an upper bound on the coded bt error performance of the system usng convolutonal codes wth hard decson Vterb decodng. For convolutonal codes wth hard decson Vterb decodng, the ER transfer characterstc can be upper-bounded by the well known transfer functon bound m Po < pp(), (3) =xj where xf s the free dstance of the code, and {P} are the coeffcents n the expanson of the dervatve of T(D, N), the transfer functon (or generatng functon) of the code, evaluated at N = 1 [9]. P() s the probablty of selectng an ncorrect path, whch can be bounded by the expresson P() < [4p(l -p)]'/21 (4) where p s the uncoded ER. From the coded bt error performance, we then estmate the system capacty, whch s defned as the number of smultaneous users that can be supported whle mantanng an acceptable ER performance needed by the specfc applcaton (e.g., lo-' for voce). Smulaton The reverse lnk of the 25-cell DS-CDMA cellular system model descrbed above has been smulated, wth and wthout the test-cell moton. When there s no cell moton, all the base statons are kept statc. New, random, user 10- caton and shadow fadng processes are generated n each smulaton run and the average bt error performance at the test cell s computed. In the movng-cell case, a quas-statc model s assumed. That s, the base staton IZ and the mobles n the test cell area are moved nto an adjacent cell's boundares, and the ER s computed wth the test-cell statonary at dfferent postons n ts range of moton. Note that the cell geometres become dstorted and take random shapes when one accounts for base staton movement. A set of CDMA smulaton tools developed n C language has been used to synthesse the smulaton program ; t-i I ; j ; I! Nrube~ of users per cell (K) Fgure 2: Uncoded ER us number of moble users per cell (K) for dfferent base allocaton models. Statc base statons. NO AWGN. U# = 6 d. ue = 0 d. Random bnary sequences of length 127 are used as the spreadng codes for dfferent users. All the users transmt asynchronously wth dfferent tme delays 73.wth respect to the user-of-nterest assocated wth the test base staton 12, such that Tk s chosen randomly n the set (0, Tal 2T,,..., (NJ - l)t,], where T, s the samplng nterval, and J s the number of samples per chp. A samplng rate correspondng to 4 samples per chp s employed. Consstent wth the prevous studes [2],[7], the propagaton exponent Y s taken to be 4 n all the smulatons. System parameters such as the number of moble users per cell (K), the shadow loss parameter (us), the standard devaton of the power control error (ue), and the dstance and drecton of the test-cell moton, are vared n the smulaton program to study ther affect on the system performance. 4 Results and Dscusson Frst, we smulate the statc base statons scenaro to evaluate and compare the uncoded bt error performance of the system under the two dfferent base allocaton models. The smulaton results wth model 1 are compared wth the analytcal results of [7]. Fgure 2 shows the smulated bt error rate performance of the reverse lnk as a functon of number of moble users per cell (K) when there s no AWGN, no power control error (.e., ue = 0 d), and the shadow parameter ua s 6 d. The analytcal performance, as per [7], for the 25-cell square grd layout s also plotted. The analytcal and smulaton results for the dstance model (model 1) of base allocaton are n close agreement wth each other. In addton, use of base allocaton model 2 (power model) show

4 - ~ ; le-05 I II:I I I I I I I I. I!/! 1! 1!! &I I/ I I If d. : I I : le (15 rmber of usera per all (I() 5 4 le ! 1! I I I ao Ntx%ber of users per cell (K) Fgure 3: Upper bound of the coded ER vs number of moble users per cell (K). Statc base statons. No AWGN. U, = d. a) Sngle cell case; 6, = 0 d. b) 25-cell case; ue = 0 d, ld, 2 d. Fgure 4: Upper bound of the coded ER vs number of moble users per cell (K). Test cell movng n the horzontal drecton. Dstance moved, z = 0.0, 0.5, 0.707, 0.9. No AWGN. U, = d. ue = 0 d. better ER performance compared to model 1. Ths s b e cause an other-cell user, though nearest to ts assgned base staton, may have a small shadow loss to the base staton-ofnterest, causng severe multple access nterference. The nterference analyss presented n [2] uses an approxmaton to the power model of base allocaton to smplfy the analyss. The ER performance usng ths approxmaton (vz., dstance model wth addtonal power constrant) s also plotted and compared. The approxmaton s found to predct better performance than the dstance model. However, t provdes an under-estmate of the performance compared to the pure power model, as seen from Fgure 2. Snce the power model s closer to realty, and offers better performance than other models, we wll use ths model for the rest of the smulatons and dscusson. Next, we examne the effect of multple access nterference from adjacent cells, n conjuncton wth power control error, on the system capacty, agan, for the statc cell scenaro. In Fgure 3, we plot the upper bound of the coded ER as a functon of the number of users-per-cell, both for a sngle cell system and the 25-cell square grd layout. A rate-1/3 convolutonal code of constrant length 9 wth hard decson Vterb decodng s used. The {p) coeffcents n Equaton 3 ate taken from [lo]. It s seen that, when U, = 0 d, a sngle cell system (wthout any adjacent cell nterference) can support 33 smultaneous voce crcuts, meetng a ER requrement of However, for a 25cell system, the number of smultaneous voce calls reduces to 21, amountng to a 36 % reducton n capacty. Ths result s n consstent wth the results reported n [2]. Fgure 3 also shows the ER curves for a 25cell system when the standard devaton of the PCE, U,, s both 1 d and 2 d. It s found that the capacty reduces to 19 users (around 10 % degradaton compared to the no PCE case) when U, = 1 d, and further degrades to 17 users (around 19 % degradaton compared to the no PCE case) when Ue = 2 d. Fnally, we smulate a movng cell scenaro and estmate the capacty of the movng cell as a functon of the degree of cell overlap and the drecton of moton. Let z be the dstance moved by the test-cell normalzed wth respect to the cell wdth. ecause of the symmetry nvolved n the square grd layout, we evaluate the performance for the cases when the test-cell moves n both horzontal and dagonal drectons. Fgure 4 shows the ER performance at the test cell for varous degrees of cell overlap n the horzontal drecton. The varous values of z consdered are 0.0, 0.5, 0.707, and 0.9. Note that the value z = 0.0 corresponds to the statc base staton scenaro, and z = 0.5 corresponds to the test base staton beng at the mdpont between the statc locaton of 12 and that of 13. It s seen that even when the test-cell moves close to 2313 (e.g., z = 0.9), the capacty degradaton compared to the statc base statons scenaro s only around 15 %, when U, = 0 d. Ths result s n contrast to the results reported n [7], where the capacty was shown to degrade drastcally when the fractonal cell overlap ncreases beyond a certan pont. Ths dscrepancy s attrbuted to the dstance model of base allocaton used n [?I, whch gave pessmstc performance estmates. Fgure 5 gves the ER performance at the test-cell when t moves n a dagonal drecton towards lg between 13 and IT. Here, the value z = corresponds to the test base staton beng moved to the ntersecton of the cell boundares of 13, 17, and la. The values consdered for shadow loss and PCE parameters are us = d and ue = 0 d, respectvely. Note that agan, a gradual degradaton n capacty up to 15% s observed. Fgure 6 llustrates the varaton n

5 c j P le-05 la ao as 30 Nuber of user. per all (I() o dstance 3 (n dagonal drecton) Fgure 5: Upper bound of the coded ER us number of moble users per cell (K). Test cell movng n the dagonal drecton. Dstance moved, z = 0.0, 0.707, 1.0, No AWGN. US = d. = 0 d. the percentage degradaton n capacty as a functon of the dagonal dstance moved; the curves are parameterzed by be. As the test-cell moves too close to 1, the capacty s found to degrade up to around 20 % when ue s 1 d, and worsens to 30 % when U, s 2 d. 5 Conclusons We presented the reverse lnk capacty of a DS-CDMA system n a mult-cell envronment wth movng cells, whch s a lkely scenaro n emergency as well as battlefeld communcatons. Two dfferent base allocaton models were consdered. Under the statc base staton scenaro, usng the receved power crteron for base allocaton, the reverse lnk capacty estmates n a 25-cell square grd cell layout was found to be worse by 36 % compared to a sngle cell system devod of adjacent cell nterference. The power control error was found to degrade the capacty by 19 % when the standard devaton of PCE was 2 d. Capacty degradaton up to 30 % was observed when the test cell moves very close to the adjacent cells. Also, the degradaton as a functon of cell overlap was found to be much more gradual than what was predcted n [7], whch used the dstance crteron for base staton assgnment. References [l] R. L. Pckholtz, L.. Mlsten, and D. L. Schllng, Spread spectrum for moble communcatons, IEEE Trans. Veh. Tech., vol. VT-40, pp , May Fgure 6: % degradaton n capacty as a functon of dstance moved, t (n dagonal drecton), and the standard devaton of PCE. NO AWGN. U, = d. ue = 0 d, 1 d, 2 d. [2] K. S. Glhousen, I. M. Jacobs, R. Padovan, A. J. Vterb, and L. A. Weaver, On the capacty of a cellular CDMA system, IEEE Trans. Veh. Tech., vol. VT-40, pp , May [3] D. L. Schllng, G. R. Lomp, and T. Apelewcz, Propagaton loss and adaptve power control for a broadband CDMA communcaton system n a moble tactcal envronment, IEEE MILCOM, vol. 3, pp , October [4] G. L. Stuber, and C. Kchao, Analyss of a multple-cell drect-sequence CDMA cellular moble rado system, IEEE Jl. Sel. Areas Commun., vol. 10, no. 4, pp , May [5] L.. Mlsten, T. S. Rappaport, and R. arghout, Performance evaluaton for cellular CDMA, IEEE Jl. Sel. Areas Commun., vol. 10, no. 4, May [6] A. J. Vterb, A. J. Vterb, and E. Zehav, Othercell nterference n cellular power-controlled CDMA, IEEE Runs. Commun., vol. 42, No , pp , February/March/Aprl [7] A. M. Monk, and L.. Mlsten, A CDMA cellular system n a moble base staton envronment, IEEE GLOECOM 93, vol. 4, pp , November [] W. C. Jakes, Ed., Mcrowave moble communcaton, New York: Wley, [9] J. G. Proaks, Dgtal Communcatons, New York: McGraw-Hll, 199. [lo] J. Conan, The weght spectra of some short lowrate convolutonal codes, IEEE Trans. Commun., vol. COM-32, no.9, pp , September