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                              E. Oluremi BEJIDE and F. Takawira
              School of Electronic and Electrical Engineering, University of Natal,
                                   Durban 4041,South Africa.

          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)
             a (t) =      ∑
                          j = −∞
                                     aj   (k)
                                                 P(t - j Tc)                        (2)
                                                                                                       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
             h k (t) = ∑ β l δ (t - τ l )e l
                            (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                                                                           ^
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
                                                                                  + 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
                                                                                             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 =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)
                                                                                   (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
                                                                                                                                                                                φ m( j )
the data bit duration. For MRC ω m
                                                              is given as[8]
                                                                                                         jth user after the nth cancellation stage. The modified
                                                                                                         R(t) that serves as input into the nth stage’s RAKE
                                                                                                         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
                                                                                                                               k =1 l =1
                                                                                                                               k≠ j
                            U2Tentative               -
                  MF2            Dec ision
                                                                   E2                                                                                        (18)
                                                                                                         At the nth cancellation stage, R (n) (t) is then fed into
                            U3Tentative               -
                  MF3             Decision
                                                                   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
                                                     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)
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
                                                                                                       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 ) .
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                                       
                                                                                                                                                             −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 
                                                                                                                                                            + 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 )
                                                                                                                                                                             ( j)
                   C k, j (τ ) = ∫ a (t − τ )a (t )dt
                                              (k )                 ( j)
                                                                                                 (17a)                                                                                  (20)
                                                                                                         IV.PERFORMANCE INVESTIGATION.
                   C /k, j (τ ) = ∫ a ( k ) (t − τ )a ( j ) (t )dt                               (17b)
                                                                                                         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],

                                                 U1                         U1 (1)                        U1(2)                             U 1 (n)
                                                U2                          U2 (1)                         U2 (2)                           U 2 (n)
                               Bank                         PIC                                PIC                            PIC
                               Of                U3
                                                            Stage 1
                                                                                               Stage 2    U3 (2)
                                                                                                                              Stage n
                               Matched                                                                                                      U 3 (n)

                                                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
  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.



                                                                                                                                                                                                                                                              HD -
                                                                                                        HD-PIC2                                                                                                                                               Series2
             0.1                                                                                                                                                                                                                                              PIC3(gain)
                                                                                                                                                                                                                                                              HD -



                        6          9          12           15          18         21        24
           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

                                                                                                                                                                                                                                                                   HD-PIC 1
                                                                                                                                                                                                                                                                   HD-PIC 2
                                                                                                                                                                                                                                                                   HD-PIC 3
                                                                                                                                                                                                                                                                   SD-PIC 1
                                                                                                                                                                                                                                                                   SD-PIC 2
                                                                                                                  HD-PIC3                                                                                                                                          SD-PIC 3
                                                                                                                  SD-PIC3                                                                                                                                          RAKE

                                                                                                                                                       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 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


                                                                                                                                                                                                                                                                     HD-PIC 1
                                                                                                                                                                                                                                                                     HD-PIC 2
                                                                                                                                                                                                                                                                     HD-PIC 3
                                                                                                                                                                                                                                                                     SD-PIC 1
                                                                                                                                                                                                                                                                     SD-PIC 2
                                                                                                                                                                                                                                                                     SD-PIC 3



                                                                                                                                                          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
                   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.

[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-
[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