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PERFORMANCE OF PARALLEL INTERFERENCE CANCELLATION RECEIVERS FOR DS-CDMA IN FREQUENCY- SELECTIVE FADING CHANNELS. E. Oluremi BEJIDE and F. Takawira School of Electronic and Electrical Engineering, University of Natal, Durban 4041,South Africa. bejideo@nu.ac.za, ftakaw@nu.ac.za Abstract-In this paper, we investigate the nullifying the effects of MAI. One such technique is Parallel Interference Cancellation (PIC). performance of Parallel Interference Cancellation (PIC) detectors in The Parallel interference cancellation (PIC) frequency selective fading channels detector was first proposed in [2] and was analysed considering situations where there are there for the AWGN channel. PIC receivers which channel estimation errors. We consider use the soft decision output of information from adjacent DS-CDMA signals to estimate the MAI a DS-CDMA system that employs a are referred to as soft decision PIC(SD-PIC) while RAKE receiver followed by PIC. Results detectors where a tentative hard decision is taken show that the performance of PIC on the adjacent user’s information is referred to as schemes are degraded much more by hard decision PIC(HD-PIC). The performance of channel gain estimation errors than by the HD-PIC was found to be better than that of the SD-PIC in the AWGN channel in [6][9]. The phase estimation errors. performance of HD-PIC in Rayleigh fading channel was investigated for BPSK modulated DS-CDMA I. INTRODUCTION signals in [5] and for QPSK modulated signals in [10] on the assumption of perfect channel Code Division Multiple Access (CDMA) has some parameter estimation. In [11], the LMS algorithm advantages over the conventional narrowband was used to adaptively estimate the weight of the modulation schemes. These advantages have estimated MAI to be subtracted from the received therefore projected CDMA as a ready candidate for signal in each cancellation stage for HD-PIC various third generation personal communication receiver operating in the AWGN, Rician fading and applications. A few of such advantages are its low Rayleigh fading channels. A perfect channel gain probability of interception, mitigation against and phase estimation was, however, assumed in multipath effects, interference rejection capability, these studies. multiple access capabilities and its antijam capabilities (which is of interest to military In this paper, therefore, we study the performances application) [1]. When the multiple access of both the SD-PIC and the HD-PIC in a frequency capabilities of the DS/CDMA technique is selective Rayleigh fading channel with imperfect exploited in a multiuser environment, however, the channel gain and phase estimation. A RAKE performance of the technique is found to be limited receiver using a maximum ratio-combining scheme by interference from co-located DS/CDMA signals, is used for diversity combining of signals on the a phenomenon known as the multiple access different paths interference (MAI), and interference from a time- delayed version of itself in a multipath II. SYSTEM MODEL. environment. There has, therefore, been an increased research interest in developing Consider a BPSK DS-CDMA system having K DS/CDMA receivers that incorporates schemes for active users with each user’s message bits spread with unique spreading sequences. Let the spreading sequences have common chip duration of Tc and let This work was partially supported by Alcatel the information duration of each user be T. Hence, Altech Telecoms and Telkom SA as part of the the processing gain of the CDMA system will be Centres of Excellence Programme N = T / Tc (1) Now let ^ ^ − i φ m( j ) ωm = 2Pj β m e ( j) ( j) ∞ (9) (k) a (t) = ∑ j = −∞ aj (k) P(t - j Tc) (2) where ^ β l ( k ) is the value of β l (k ) estimated at the represent the spreading sequence waveform of the ^ kth user and let receiver. Also, φ l ( k ) is the value of φ l (k ) estimated ∞ at the receiver. It will be observed from eqn. (9) b(k) (t) = ∑ j = −∞ bj (k) P (t – j T) (3) that a reliable detection of the received signal at the receiver depends on having accurate estimations of represent the transmitted binary data signal of the the channel parameters. Channel estimation kth user, where P(t) is a unit rectangular pulse techniques could either be decision directed(DD), function , aj(k) ∈ {-1,1} are the spreading sequence where estimation is made based on the decision elements and bj(k) ∈ { -1,1}, with –1 and 1 made on the received data, or data aided(DA), having equal probabilities, are the message bits. where a pilot signal is transmitted along with the data to aid the estimation. In either scheme there is Next, let the complex low-pass equivalent impulse still some estimation error that is made. Therefore, response of the channel be given by the estimated channel gain and phase can be Lk expressed as iθ h k (t) = ∑ β l δ (t - τ l )e l (k) (k) (k) ^ l =1 (4) β l (k ) = β l (k ) +∆ (10) βl(k ) where βl (k) , τ (k) and θ (k) are the lth path’s gain, l l ^ th delay and phase for the k user respectively, φ l (k ) = φ l (k ) +∆ (11) φl(k ) i ≡ − 1 and Lk is the number of paths for the kth user signal. Therefore, the received signal for a where ∆ and ∆ ( k ) are errors made in synchronous CDMA system, can be stated as βl(k ) φl K Lk estimating the channel gain and phase respectively. R(t) = ∑∑ 2Pk β l a ( k ) (t − τ l )b( k ) (t − τ l )eiφl (k) + N (t ) (k ) (k ) (k ) k =1 l =1 (5) In this work, we modeled ∆ and ∆ (k) as zero where N(t) is a white Gaussian noise with double- βl(k ) φl sided power spectral density No/2, Pk = Ek/T is the mean Gaussian random variables having variance kth user’s signal power and Ek is the kth user’s signal energy, ωc is the carrier frequency and of σ2 and σ2 respectively. This model has βl(k) φl(k) φl(k) =θ(k) + θl(k) - ωcτl(k) (6) θ being the phase of the kth user’s carrier with (k) been reported to be valid for both the DA and the the multipath delay of the kth user given by DD channel estimation techniques [12]. τl(k) = τ1(k) + ( l-1)Tc (7) U(j) can be expressed as composed of four τl ∈ { Tc, Tm} where Tm is the maximum delay (k) components [4][7][8]: spread of the channel U (j) = ∑ {U (j) s,m + U (j) mai,m + U (j) si,m + U (j) N,m } M (12) m =1 A RAKE receiver employing a Maximum Ratio Combining (MRC) scheme for diversity combining is considered to be used for reception. The jth user’s where U (j) s, m is the desired signal component, RAKE receiver output, after diversity combining, U(i), may be expressed as U (j) mai, m is the “multiple access” interference M component, U (j) si, m is the self interference (j) τ m +T U (j) = Re∑ (ω m ∫ R(t).a (j) (t - τ m )dt) (j) (8) component and U (j) N, m is the AWGN component. m =1 τm where M is the number of fingers in the RAKE Expressions for the decision statistics are given as: (j) ^ ω m (j) = 2Pj b o Tβ m β m cos ∆ (j) (j) (j) receiver, is the combining weight, and T is U s, m (13) φ m( j ) the data bit duration. For MRC ω m (j) is given as[8] jth user after the nth cancellation stage. The modified (t) R(t) that serves as input into the nth stage’s RAKE Re - receiver for the HD-PIC will be given by U1Tentative Spread E1 K Lk ^ (k ) ^ (k ) R (n) (t) = R(t) - ∑∑ 2Pk Yn(k) (t − τ l( k ) ) β l a ( k ) (t −τ l( k ) )ei φ l MF1 Decision Device j k =1 l =1 k≠ j U2Tentative - Re Spread MF2 Dec ision Device E2 (18) At the nth cancellation stage, R (n) (t) is then fed into Σ j U3Tentative - Re Spread MF3 Decision Device E3 a RAKE receiver to obtain the decision statistics for user j. The expression for this decision statistics is obtained by substituting (18) into (8) as given as ^ ( j ) ^ ( k ) Y −1 (n −1)Ckj (τ l −τ m ) (k ) (k ) ( j) M K Lk - Re U (j) (n) = U (j) − ∑∑∑ 2Pk β m β l ( k ) HD UkTentative + Yo (n −1)C / kj (τ l −τ m ) (k ) ( j) MFn Decision Device Spread En m=1 k =1 l =1 k≠ j ^ ^ . cos(φ l − φ l ) (k ) ( j) Figure 1: Functional diagram of a stage of Parallel Interference Cancellation. (19) K Lk b ( k ) C k j (τ l ( k ) − τ m ( j ) ) ( k ) −1 ^ U (j) is as expressed in (12). = ∑ 2Pk ∑ β m β . (j) ( j) Umai,m k =1 l =1 . Equation (19) gives the expression for HD-PIC and + bo C kj (τ l − τ m ) (k ) / (k ) ( j) k≠ j l includes the effects of the channel gain and phase cos(φ l − φm ) (k ) ( j) (14) estimation errors. A similar expression for the SD- (k ) ^ b−1 C jj (τ l − τ m ) ( j) ( j) ( j) PIC if the soft decision information, U n (n) , is = 2 P j ∑ β m j ) β l( j ) . (j) ( U si, m + bo C jj (τ l − τ m ) ( j) / ( j) ( j) used in equation (18) for estimating the MAI can be l =1 l ≠m obtained. In this case the expression for SD-PIC ^ . cos(φl ( j) −φ m ) ( j) (15) will then be given as in eqn. (20). T + nTc ^ ( j) ^ ( j) =∫ 2 Pj n(t ) β m a ( j ) (t − τ mj ) ) cos φ m dt (16) ^ ( j ) ^ ( k ) U (j) −1 (n − 1)C kj (τ l − τ m ) ( (k ) (k ) ( j) U N.m nTc M K Lk U SD ( n) = U (j) − ∑∑∑ 2 Pk β m β l (j) + U o (n − 1)C kj (τ l − τ m ) (k ) / (k ) ( j) where bo is the information bit to be detected and m =1 k =1 l =1 k≠ j ^ ^ b-1 is the proceeding bit. . cos(φ l (k ) −φl ( j) ) τ C k, j (τ ) = ∫ a (t − τ )a (t )dt (k ) ( j) (17a) (20) 0 T IV.PERFORMANCE INVESTIGATION. C /k, j (τ ) = ∫ a ( k ) (t − τ )a ( j ) (t )dt (17b) τ The performance of both the SD-PIC and the HD- PIC were studied through a computer simulation. A III. INTERFERENCE CANCELLATION. multiuser DS-CDMA system using Gold codes of length 63 was simulated for various channel For total interference cancellation, a reconstructed parameter estimation errors with 5 active users. We baseband signal of interfering users is subtracted define the Signal-to-Noise Ratio (SNR) as Ek/No in from R(t) ( see figure 1). The resultant statistics is dB. A Rayleigh frequency selective fading channel was implemented. The transmitting frequency of then processed in a RAKE receiver again. This the active users was taken to be 2GHz and the process is repeated iteratively for as many mobiles were modeled to be traveling at a velocity cancellation stages as desired. Figure 2 illustrate a of 80Km/h. Therefore, the maximum Doppler’s multistage simultaneous cancellation of estimated spread, fm, of the fading channel is 148.13Hz. The interference for all active users. For HD-PIC, the channel is modeled to be correlated. The filtered reconstruction is done using the tentative hard white Gaussian noise (WGN) method of generating decisions in each stage and for SD-PIC, the correlated variates was used in the simulation. The reconstruction is done using the soft output of the correlated Rayleigh variates were generated by RAKE receivers. Let’s define a parameter Y (j) (n) to filtering two independent zero-mean Gaussian noise represent the result of a hard tentative decision by an FIR filter of length 31 and response h[n] by taken on U (j) (n) where U (j) (n) is the statistic of the [3], R(t) U1 U1 (1) U1(2) U 1 (n) U2 U2 (1) U2 (2) U 2 (n) Bank PIC PIC PIC Of U3 Stage 1 U3 Stage 2 U3 (2) Stage n Matched U 3 (n) Filters. Uk U k(2) Uk(2) U k (n) Figure 2: Multistage Parallel Interference Cancellation Scheme. The simulation results are presented in figures 3 to 1/ 2 Γ (3 / 4) 8. We use notation like SD-PIC3 to represent the ( f m ) Γ(5 / 4) third stage of SD-PIC cancellation and so on. n = 15 Figure 3 compares the BER performance of the h[ n] = 1/ 4 ( 21) HD-PIC and the SD-PIC with variation in SNR in a f m Γ(3 / 4)[n − 15]−1 / 4 .J (2πf (n − 15)), π 1/ 4 m frequency selective fading channel when the variance of the channel gain estimation error is n = 0,1,2, ...14,16,.. 30. 0.06. The HD-PIC is observed to have a better performance than the SD-PIC. Our remaining The resulting Gaussian processes were then added simulation results are presented at 21dB SNR with in quadrature to form a Rayleigh process. A MRC variation in the variance of the channel estimation Rake receiver using 3 fingers was used both errors. From figures 4 and 5, we observed that between cancellation stages and at the front-end of although the HD-PIC has a better BER performance the receiver. The number of cancellation stages for than the SD-PIC, (as also earlier noted for the both the HD-PIC and the SD-PIC detection was 3. additive white Gaussian noise channel in [9]), the We optimized the estimated MAI by using HD-PIC is more sensitive to both the channel gain weighted sum of the estimate for each user for and phase estimation error than the SD-PIC. cancellation. In this situation eqn (18) is modified to be Figure 6 illustrates that the two PIC schemes are more sensitive to gain estimation errors than to K Lk ^ (k ) ^ (k ) phase estimation errors. From figures 7 and 8 we R (n) (t) = R(t) - ∑∑ λk,n 2Pk Yn(k) (t − τ l( k ) ) β l a ( k ) (t −τ l( k ) )e iφl j l k =1 l =1 observe that the sensitivity of the PIC schemes to k≠ j (22) channel estimation errors increases with increasing stages of cancellation as will be expected since the where λlk, n is the weight of the kth user on the lth decision statistics at a cancellation stage are path at the nth cancellation stage. λlk, n was selected dependent on those of the previous stages. This way the unreliability of the decision made at the adaptively using the LMS algorithm in [11]. In this previous stage is propagated to subsequent stages. work, we estimate λlk, n through a computer search With channel gain estimation error, the and we take λlk, n to be constant for all users on all performance of the third stage of HD-PIC fell paths at a given cancellation stage. For the HD-PIC, below that of its second stage when the variance of the estimation error was about 0.09. The same our optimal λlk, n are 0.4, 0.7, and 1 for the first, observation was made in the case of the SD-PIC at second and the third stage of cancellation the variance of 0.14 respectively. For the SD-PIC, our optimal λlk, n are The performance of the RAKE receiver with no 0.0003, 0.0006, and 0.0009 for the first, second and cancellation was mildly affected by channel the third stage of cancellation respectively. estimation errors. 1.00E+00 1 1.00E-01 HD - Series1 PIC3(gain) 1.00E-02 HD-PIC2 Series2 SD- 0.1 PIC3(gain) SD-PIC2 Series3 HD - PIC3(phase) Series4 SD- PIC3(phase). 1.00E-03 0.01 6 9 12 15 18 21 24 SNRdB. 1.00E-04 Figure 3:BER performance of PIC schemes with increasing SNR with variance of 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 gain estimation error of 0.06. Varianceof Channel Param stim eterE ationError. Figure 6: Performance of HD-PIC and SD-PIC with channel gain and phase estimation errors. 1.00E+00 1.00E+00 1.00E-01 1.00E-01 HD-PIC 1 HD-PIC 2 HD-PIC 3 SD-PIC 1 SD-PIC 2 HD-PIC3 SD-PIC 3 SD-PIC3 RAKE 1.00E-02 1.00E-02 1.00E-03 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 1.00E-03 Variance of Channel Gain Estimation Error. 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 VarianceofChannel GainEstimationError. Figure 7: BERperformance of PIC schemes with channel gain estimation error and increasing stages. Figure 4:BER performance of HD-PIC and SD-PIC with channel gain estimation error. 1.00E+00 1.00E+00 1.00E-01 1.00E-01 HD-PIC 1 HD-PIC 2 1.00E-02 HD-PIC 3 1.00E-02 SD-PIC 1 HD-PIC3 SD-PIC 2 SD-PIC3 SD-PIC 3 RAKE 1.00E-03 1.00E-03 1.00E-04 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 1.00E-04 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 Variance of Channel Phase Estimation Error. Varianceof Channel PhaseEstimationError. Figure 8: BER performance of PIC schemes with channel phase estimation error and increasing stages. Figure 5: BER performance of HD-PIC and SD-PIC with channel phase V. CONCLUSION. Channels”. IEEE JSAC, Vol. 17, No. 12, Dec. 1999. Pp 2162 – 2180. The performance of PIC schemes in a fading [11].G. Xue, J. Weng, T Le-Ngoc and S. Tahar, channel was evaluated. The performance of the “Adaptive Multistage Parallel Interference HD-PIC was observed to be better than that of the Cancellation for CDMA”. IEEE JSAC, Vol. 17, SD-PIC even with channel parameter estimation No. 10, Oct. 1999. Pp 1815-1827. errors. The PIC schemes are more sensitive to [12].P. Frenger,” Turbo decoding of Rayleigh channel gain estimation error than they are to fading channels with noisy channel estimates”. channel phase estimation error. Considering the Proceedings of VTC’99. Houston Texas, May 16- sensitivity of the HD-PIC scheme, in particular, to 19, 1999. Pp 884 –888. channel estimation errors, a robust channel estimation algorithm is required in order to have a good performance. REFERENCES. [1]. R.A. Scholtz, “ The Spread Spectrum Concept”. IEEE Trans Comms. Nol. COM-25, no.8, August 1977, pp. 748-755. [2]. M.K. Varanasi and B Aazhang ”Multistage Detection in Asynchronous Code-Division Multiple-Access Communications”, IEEE Trans. Comms Vol 38 no4, pp 509-519. [3]. D.J. Young and N.C. Beauliue, “ A quantitative evaluation of generation methods for correlated Rayleigh random Variates”. Globecom 1998, Sydney Austrialia, 8-12 November 1998. Pp 3332- 3337. [4]. G.P. Efthymoglou, V.A. Aalo, H. Helmken, “ Performance Analysis of Coherent DS-CDMA Systems in a Nakagami Fading Channel with Arbitrary Parameters”. IEEE Trans. On Vehicular Technology, Vol. 46, No. 2, May 1997,pp 289-297. [5]. L.C. Hui and K.B. Letaief, “ Successive Interference Cancellation for Multiuser Asynchronous DS/CDMA Detectors in Multipath Fading Links”, IEEE Trans. Comm, Vol. 40, No. 3, March 1998. Pp 384-391. [6]. S. Moshavi, “ Multi-User Detection for DS/CDMA Communications” IEEE Communication Mag. Oct. 1996. Pp 124-136. [7]. K Cheun, ”Performance of Direct-Sequence Spread Spectrum RAKE Receivers with Random Spreading Sequences”. IEEE Trans. Comms. Vol. 45. No.9, Sept. 1997, pp 1130-1143. [8]. T. Eng and L.B. Milstein,” Coherent DS- CDMA Performance in Nakagami Multipath Fading”. IEEE Trans. Comms. Vol. 43. No. 2/3/4, Feb/March/April 1995, pp 1134-1143. [9]. R.M. Buehrer and S.P. Nocoloso, “ Comments on “Partial Parallel Interference Cancellation for CDMA” “. IEEE Trans. Comms. May 1999, Vol 47 No 5. Pp 658-661. [10]. J. Weng, G. Xue, T Le-Ngoc and S. Tahar, ”Multistage Interference Cancellation with Diversity Reception for Asynchronous QPSK DS/CDMA Systems over Multipath Fading

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