On the Impact of Exponent Multipath and Branch Correlation on MC-CDMA System in Frequency-Selective Fading Environments

Transcription

1 IAENG International Journal of Coputer Science, 33:, IJCS_33 5 On the Ipact of Exponent Multipath and Branch Correlation on MC-CDMA Syste in Frequency-Selective Fading Environents Joy Iong-Zong Chen, Chieh Wen iou jchen@ail.dyu.edu.tw, david@s.chinin.edu.tw Dep. of Coun. Eng., Da-Yeh University, Chang-Hua, 55 aiwan (R.O.C.) E.: ex 53 Astract he ipact of existence with exponent ultipath MI (ultipath intensity profile) for an MC-CDMA (ulti-carrier coded-division ultiple access) syste, which is assued working over the frequency selective fading environents in this paper. We derived the average BER (it error rate) forulas for MC-CDMA syste with MRC (axial ratio coining) diversity were with an alternative ethod for the copleentary error function. he consideration included not only the correlated sucarriers and independent sucarriers were addressed in the nuerical analysis, ut the paraeter of user capacity is also analyzed. Keywords MC-CDMA systes, exponent MI, MRC diversity, Nakagai- fading Ⅰ.Introduction In order to reduce ISI (inter-syol interference) effect and overcoing the channel fading in a transission channel, ulti-carrier odulation schee has een adopted for high speed transission applications. A nuer of ulti-carrier odulation techniques have een proposed during the pass decade []. o support a wide area of services and high data rate y using a variety of techniques capale of achieving the highest possile spectru efficiency is the ain ojective for future generations of wideand wireless counication systes. he CDMA (coded-division ultiple-access) schee has een applied as an attractive ultiple access technology in oth G (second-generation) and 3G (third- generation) wireless radio systes. In general, the ulticarrier DS systes have already een proposed and can e categorized into two types: a parallel transission-schee of narrowand DS wavefors in the frequency doain, and a coination of OFDM (orthogonal frequency division ultiplexing) and CDMA []. he availale frequency spectru of carrier wave is divided into M equal and of sucarriers in the forer systes. hese sucarriers are used to carry a narrowand DS wavefor and the nuer of sucarriers is usually uch less than the processing gain. In the latter syste, each chip odulates a different carrier conveying a narrowand wavefor rather than a DS wavefor, and the nuer of carriers should e equal to the processing gain. On other hand, due to the advantages of spectru efficient, interference iune, high date rate, and insensitivity to frequency selective channel, etc. Such that ultiple access syste ases on direct sequence CDMA (coded-division ultiple-access) have drawn recent interest in the application of wireless radio systes []. Especially, ulti-carrier CDMA (MC-CDMA) appears to e a considerale candidate for future oile radio counication syste. he MC-CDMA syste ased on the spread spectru techniques. here are a lot of previous researches have een pulished for investigation aout the issues of MC-CDMA syste. Besides, the BER (it error rate) analysis of MC-CDMA ased on considering different kinds of assuptions, so far, have een dedicated in nuerous previously researches [,, 3]. In [] the authors analyzed the BER (it error rate) perforance of uplink MC-CDMA syste over frequency selective Nakagai- fading with MRC and EGC receptions. he perforance evaluation of MC-CDMA over ultipath fading channels was studied in [3]. he results presented in [4] are for uplink channel using MRC (axial ratio coining) with the assued frequency offsets condition in correlated fading. he perforance of MC-CDMA in non-independent Rayleigh fading was studied in [5]. In [6], which y use of the ethod of CF (characteristic function) and residue theore to calculate the perforance for downlink MC-CDMA syste. Both of the envelopes and phases correlation are considered in [7] to evaluate the perforance of a MC-CDMA syste operates in Rayleigh fading channel. he literature in [8] illustrated the error proaility for MC-CDMA systes assued that the transission channel is in Nakagai- (Advance online pulication: 3 Feruary 7)

2 fading, and the postdetection of EGC (equal gain coining) is considered. In this paper, soe expressions of BER perforance for uplink MC-CDMA syste working in correlated fading channels is evaluated. he general correlation of channels with Nakagai- fading distriution is assued. An average BER forula closed-for is otained via the su of Gaa variates to avoid the difficulty of explicitly otaining the pdf for the SNR (signal-to-noise ratio) at the MRC output. he results analyze and show that how does the channel correlation affects the syste perforance of a MC-CDMA systes. he rest of this paper is organized as follows: section II gives a description of the MC-CDMA syste odel. he correlated-nakagai- fading channel odel is given in section III. In section IV descries the receiver odel of MC-CDMA syste. he perforance of MC-CDMA operating in uncorrelated and correlated fading cannel is carried out in section V. here are nuerically results shown in section VI. Finally, section VII draws riefly conclusions. II. Syste Models We considered an uplink MC-CDMA syste odel for the study. Assuing that exist K siultaneous users are with N sucarriers within a signal cell. Any effect of correlation aong users is going to e ignored y assuing the nuer of users is unifored of distriution. As shown in Fig., a signal data syol is replicated into N parallel copies. he signature sequence chip with a spreading code of length is used to BSK (inary phase shift keying) odulated each of the N suscriers of the k-th user. Where the sucarrier has frequency F/ Hz, and where F is an integer nuer. [,3]. he technical descried aove is sae as to the perforance of OFDM (Orthogonal Frequency Division Multiplexing) on a direct sequence spread-spectru signal when set F. he larger values of F, the ore transit andwidth increase. he transitted signal the resulting transitted aseand signal S ( t) corresponding to the M data it size can e expressed as M jn t S ( t) a [ n] [ ] ( t) Re[ e ] () k k k N n where ak[ n] {,}; k [ ] {,} the sequencer ak[],..., ak[ ] and k [],..., k [ M ] represent the signature sequence and the data it of the k-th user, respectively. is the power of data it, M denotes the nuer of data it, N denotes the nuer of sucarriers, he (t) is defined as k an unit aplitude pulse that is non-zero in the interval of [, ], and Re [ ] denotes the real part of a coplex nuer, n ( fc nf ) is the angular frequency of the n-th sucarrier. III. Channel Model A frequency-selective channel with BW c F is addressed in this paper, where BWc is the coherence andwidth. his channel odel eans that each odulated sucarrier does not experience significant dispersion and with transission andwidth of, i.e. d, where d is the Doppler shift typically in the range of.3~6. Hz [] in the indoor environent, and the aplitude and phase reain constant even the syol duration. In addition to, the channel of interest has the transfer function of the continuous-tie fading channel assued for the k-th user can e represented as F H f i e () k[ c jk, i ] k, i where k, i and k, i are the rando aplitude and phase of the channel of the k-th user at frequency fc i( F ). In order to follow the real world case, the rando aplitude, k, i are assued to e a set of N correlated not necessarily identically distriuted in one of our scenarios. he equal fading severities are considered for all of the channels, naely,,,. he pdf of the fading aplitude for the k-th user with i-th channel, k,, are assued as r.v. (rando variale) with the Nakagai- distriution, and given as [] ( ) ( ) exp ( ), ( ) (3) where ( ) is the gaa function defined y x ( x) t t e dt, E [ ] denoting expectation, the paraeter of the aplitude distriution characterizes the severity of the fading, and it is defined as.5 E [( ) ] (4) It is well known that.5 (one-sided Gaussian fading) corresponds to worst case fading condition, and correspond to Rayleigh fading (purely diffusive scattering) and the non-fading condition, respectively. As what follows, we consider these two cases. Firstly, if the propagation channels are assued as i.i.d (identically independent distriuted), then y use of the variale changing, the variale is assigned as the fading power

3 of the channel, and let, then the pdf of is given follows as a gaa distriution, can e otained y the processing of rando stochastic as r r e r ( r) (5) ( ) et [ ],,, e a set of N correlated identically distriuted, and all the figure paraeters and the average power are assued equivalent, that is, i j, and i j, where i j, for i, j,,. he power at the output of the MRC is a function of the su of the squares of signal strengths, and is given as R. Hence following the results extended fro the [9] y M. S. Alouini, A. Adi, and M. Kavehthe [7]. he pdf of R can e expressed as q q R ( ) ( ) q q ( q ) r e (6) where the coefficients q can e otained recursively y the following forula q q q q j j, q,,,... (7) where in { }, and,,, are the eigenvalues of the atrix Z XY, where X is the diagonal atrix with the entries of average power i, i,,, when the sucarrier paths are correlated, the entries of i can e otained y taking the iniu value of. he atrix Y is the positive definite atrix defined y ( ) ( ) Y (8) ( ) where l denotes the correlation coefficient etween and,,,,,,, and can e expressed as Cov(, ), [ Var( ) Var ( )] (9) where Var( ) and Cov( ) are the variance and the covariance operators, respectively. IV. MC-CDMA Receiver Model A slowly varying fading channel is considered in this paper, that is, the channel paraeters are unchanged over one it duration. For K active transitters, the received signal r( t) can e written as r( t) [ ] [ ] N ( t ) cos( t ) n ( t) k K M n, nak n k () k n, n where n( t) is the AWGN (additive white Gaussian noise) with a doule-sided power spectral density of N. We can evaluate, the local-ean power, k, n, which is given as E[ ] () N k, n k, n he total-ean power of the k-th user is defined to e k N k, n, if the local-ean power of the sucarriers is assued equal. Assuing that acquisition has een accoplished for the user of interesting ( k ). In addition, the syste operates synchronously with each user having the sae clock is assued, and the MRC diversity reception technique is considered in this paper. For the reason of using MRC, it is assued that perfect phase correction can e otained, i.e.,, i i. Deodulating each sucarrier includes applying a phase correction,,i, and a gain correction factor d [ ], n, n a n is ultiplied y the n-th sucarrier signal as shown in Fig.. All the signals at the output of the correlators are coined with the MRC diversity schee, and the results can e written as () where is the SNR at every ranch. he ranch nuer is assued that equal to the sucarrier nuer, that is, =N, in this paper. With all the assuptions for MRC coining, the decision variale D of the -th data it reference user, and given y D ( ) r( t) a [ ] d ( t, ) Re[ e ] dt, =U I S MAI (3) where r( t) is the received signal shown in (), d,i is the gain factor for MRC diversity. he first ter in second equivalent last equation represents the desired signal, can e expressed as U S N, a [ ] (4), and the second ter, I MAI, is the MAI (ultiple access interference) contriuted fro all other users which can e written as I a [ ] [ ] a [ ] cos( ) K ' MAI k k k,, n k, n N k n (5) ' where k, n, n k, n and k, n are i.i.d uniforly distriuted over [, ), is the AWGN ter.

4 V. erforance Analysis A generalized average BER for the k-th user using coherent BSK (inary phase shift keying) odulation schee is derived in this section. For coherent deodulation in the presence of AWGN, the proaility of error conditioned on the instantaneously SNR can e expressed as [] ( ).5 e s Q SNR (6) where the Gaussian Q is defined y t Q( x) e dt, and the received instantaneously x SNR, which conditioned on, n, n, at output of the receiver is calculated as U N, n s N n I MAI (7) where I MAI is the variance of I MAI, which is shown in (4). In the liiting case of large N and y the ethods of central liit theory (C), the MAI can e approxiated y a Gaussian r.v. with zero ean and the variance, I MAI, can e deterined as [ ] E I ( k ) E [ ] E [ cos ] ( k ) 4 IMAI MAI k, n k, n k, n (8) where k, n E[ k, n], E[ cos k, n ]. On the other hand, the ackground noise ter is a rando variale with zero ean and the variance can e calculated as NN E [ ] (9) 4 By sustituting (7) and (8) into (6), which can e otained as S U N () s where S N, n k, n () n NN k N k, and k, n () where k, n N E k, n N is the SNR of each it, and E denotes the it energy. It is known that the decision variale in (3) has a Gaussian distriution conditioned on the uncorrelated and correlated channel power,n, respectively, and the AWGN,, and the MAI, MAI are utually independent. herefore, the proaility of error y eans of BSK odulation conditioned on the instantaneously SNR has een given in (6) can e evaluated as follows. If the conditions of correlated channels are considered as the ipact factors for MC-CDMA syste, then the average it error proaility for the case can e calculated y averaging (6) and (6), and yield as M e E e e M d B y ku y k y exp k ( k ) sin k B d y y ku y k exp k ( k ) sin k (3) where k d, S N f N E.Next, y using of the integral equivalent forula e d. he average BER can e siplified and expressed as K e i sin N ( v ) E f N o N,,,,... j j d (4) where is given in (7), and are shown in (6) and (), respectively, the syol F (, ; ; ) denotes the confluent hyper geoetric function [3], and f d, N, which represent that the exponential MI (ultipath intensity profile) is adopted in this derivation, and the d, e e. VI. Nuerical Results Soe of the nuerical results for validation of the derived forulas are shown in this section. he syste perforance BER versus d of each it of MC-CDMA syste working in fading channels are shown in Fig. 3, in which the user nuer is set K=, the fading paraeter is = and the intensity decay and the SNR of each it are set.5 and SNR=5dB, respectively. It is clearly that the uch higher value of sucarrier nuer N, the uch etter for the syste perforance is. his is the reason that the higher value of d represents the less of correlation etween ranches. here is another point definitely to say that the syste perforance will ecoe superior if the ranch nuer is increase gradually. In addition, the syste perforance evaluated the results of

5 BER versus SNR is shown in Fig. 4, in which the syste paraeters are set as, K,, d /.7, and the intensity decay values.,.5, and.9. Fro the results shown in Fig. 4, it is oviously to declare that the ranch nuer do sae as the affect siilar to the results shown in Fig. 3. However, the syste perforance is still ajor decided y the paraeter of sucarrier nuer. Fro the other view point of the syste perforance is shown in Fig. 5 where the different fading paraeters with, and 3 are presented. he results illustrated in Fig. 5 clearly said that the deterination of the ase station is one of the ost iportant factors which will turn the syste perforance of the MC-CDMA syste to RIGH side. In order to prove the accuracy of our derived forulas entioned aove, in Fig. 6 the user capacity (K) versus BER is also presented. It is reasonale to descrie that the syste perforance ecoe degraded after the nuer of active user increased. his fact prove validates the accuracy of the investigation in this paper. VII. Conclusion In this paper the SNR and the user nuer versus syste perforance error rate for MC-CDMA operating in correlated Nakagai- fading channels has evaluated. he syste paraeters with the sucarrier nuer, correlation coefficients, the ranch nuer, and the exponential MI are considered for deterination the syste perforance of an MC-CDMA syste. he results explicit illustrated that the phenoena of channel correlation and the ultipath fading do doinate the perforance of MC-CDMA counication systes. However, the ost iportant factors should e the fading paraeter of the fading odel, and the sucarrier nuer. Hence it is worthy not only to pay uch attention in the consideration of correlation coefficient for channel fading while designing the MC-CDMA systes, ut the chosen of sucarrier nuer and the environent of the ase station are iportant.. r( t) [ ] k Fig. a k [] a k [] ak[ ] cos( f ct, ) cos(f ct F t, ) BER cos( f t) c cos(f t Ft ) c cos(f t F ( ) t ) c he transitter odel of the MC-CDMA syste a [] a ( t [] cos f ct F,) E-4 E-5 E-6 E-7 E-8 E-9 E- E- E- E-3 E-4 E-5 E-6 E-7 E-8 E-9 E- E- Fig. N=6 a [ ] d d, d,, N he receiver odel of the MC-CDMA syste N=3 ( ) Sk ( ) ( t) D d/ K= = =.5 SNR=5dB Fig. 3 d vs BER with different N values

6 BER. E-3 E-4 E-5 E-6 E-7 E-8 E-9 E- N= E /N (db) N=3 K= = d/=.7 =. =.5 =.9 Fig. 4 SNR vs BER with different sucarrier nuer, N, MI values, and BER. E-3 E-4 E-5 E-6 E-7 E-8 E-9 E- E- E- E-3 E-4 E-5 E-6 E-7 E-8 E-9 E- E- E- N=6 N=3 N=6 N=3 k= = =. d/=. d/=.5 d/= E /N (db) Fig. 5 SNR vs BER with different sucarrier nuer, N, MI values, and 3 BER.. E-3 E-4 E-5 E-6 E-7 E-8 E-9 E- E- E- E-3 E-4 E-5 N=6 Fig. 6 N=3 = d/=.7 =.5 SNR=5dB Nuer of active users K User capacity, K, vs BER References [] N. Yee, J. -. innartz, and G. Fettweis, Multi-carrier CDMA in Indoor Wireless Radio Networks, IEICE trans. on Coun., Vol. E77-B, No.7, July 994, pp [] Zhengjiu Kang and Kung Yao, erforance Coparison of MC-CDMA over Frequency-Selective Nakagai- and Rayleigh Fading Channels, Vehicular echnology Conference, Vol. 6, Sep. 4pp [3] E. A. Sourour and M. Nakagai, erforance of Orthogonal Multicarrier CDMA in a Multipath Fading Channel, IEEE trans. on Coun., Vol. 44, Mar., 996, pp [4]. Ki, Y. Ki, J. ark, K. Ko, S. Choi, C. Kang, and D. Hong, erforance of an MC-CDMA Syste with Frequency Offsets in Correlated Fading, IEEE International Conference on ICC, Vol., June, pp [5] J. ark, J. Ki, S. Choi, N. Cho, and D. Hong, erforance of MC-CDMA Systes in Non-independent Rayleigh Fading, IEEE on ICC 99, Vol., June 999, pp. 56-5, 6-. [6] Q. (Rock) Shi and M. atva-aho, Exact Error Floor for Downlink MC-CDMA with Maxial Ratio Coining in Correlated Nakagai Fading Channels, International Zurich Seinar on Broadand Counications, Fe., pp [7] Q. Shi and M. atva-aho, erforance Analysis of MC-CDMA in Rayleigh Fading Channels with Correlated Envelopes and hases, IEE proc. Coun. Vol. 5, No. 3, Jun. 3, pp.4-. [8] Z. i, and M. atva-aho, Erroe roaility for MC-CDMA in Nakagai- Fading Channels Using Equal Gain Coining, IEEE International Conference on ICC, Vol., 8 April- May, pp [9] M. S. Alouini, A. Adi, and M. Kaveth, Su of Gaa Variates and erforance of Wireless Counication Systes over Nakagai-Fading Channels, IEEE trans. on V.., Vol. 5, No. 6, Nov., pp [] Nakagai, M., he -Distriution-A General Forula of Intensity Distriution of Rapid Fading, Statistic Methods of in Radio Wave ropagation, ergaon ress, New York, 96, pp [] M. Schwartz, W. R. Bennett, and S. Stein, Counication Systes and echniques, McGraw-Hill: New York, 966. [] M. K. Sion and M. S. Alouini, A Unified Approach to the erforance Analysis of Digital Counication over Generalized Fading Channel, roc. Of the IEEE, Vol. 86, Sept. 998, pp [3] I. S. Grodshteyn, and I. M. Ryzhik. ale of Integrals, series, and products, San Diego, CA: Acadeic ress, 5th Ed. 994.