RAKE Receiver with Adaptive Interference Cancellers for a DS-CDMA System in Multipath Fading Channels JooHyun Yi, Student Member, IEEE, and JaeHong Lee, Member, IEEE School of Electrical Engineering, Seoul National University Shillim-dong Gwanak-gu, Seoul 151-742, Korea E-mail:
[email protected]
Abstract In this paper, an adaptive RAKE receiver with diversity combing is proposed for a DS-CDMA system in multipath fading channels. The proposed adaptive RAKE receiver exploits antenna diversity and adaptive interference cancellation (AIC) to mitigate the effect of both multipath fading and multiple-access interference (MAI). The LMS algorithm with variable step-size is used to update the tap-weight vector of AICs. The performance of the proposed receiver is evaluated by computer simulation for the various numbers of antennas and RAKE fingers. It is shown that the proposed receiver achieves significant performance improvement over a conventional RAKE receiver.
1. Introduction A direct-sequence code-division multiple-access (DSCDMA) system suffers from multiple-access interference (MAI) and near-far problem that degrade its link quality. To mitigate the effect of MAI and near-far problem, the advanced receivers commonly called as multiuser detectors have been proposed. As a multiuser detector an adaptive interference canceller (AIC) is based on the minimum mean-squared error (MMSE) criterion. It is known that the AIC achieves better performance than a conventional matched-filter (MF) detector without much increase of receiver complexity for both forward and reverse links [1]-[4]. Channel fading and multipath propagation also cause severe performance degradation in a DS-CDMA system. To mitigate the effect of channel fading and multipath propagation, RAKE reception and diversity combining have been used for a DS-CDMA system [7]. Recently, to mitigate the notorious effect of both multipath fading and MAI, incorporation of diversity combin-
ing and interference cancellation is received a great deal of attention. Using training sequence the AIC with diversity antennas achieves significant performance improvement over a matched filter receiver in a frequency flat Rayleigh fading channel [4]. Also, to increase effectiveness of transmission, the adaptive RAKE receiver without training sequence is possible in a 2-path Rayleigh fading channel when the decisions made by a RAKE receiver are used to train AICs [5]. Blind adaptation without training sequence degrades performance of AIC at low SNR or in sever multipath channel. Thus it is necessary to provide reliable decision for AICs. In this paper, a RAKE receiver with AICs combined with diversity antennas is proposed for a DS-CDMA system in multipath fading. The proposed receiver exploits both time and space diversity to guarantee the reliable adaptation of AICs. This paper is organized as follows. In section 2 the baseband system model is described. In section 3 a RAKE receiver with multiple receiver antenna and AICs is proposed. Numerical results are presented in section 4 and conclusions are drawn in section 5.
2. System Model Consider a DS-CDMA system with K simultaneous users. A binary data sequence of each user is multiplied by a unique signature waveform to produce a transmitted baseband signal. The signature waveform for the kth user is given by N −1
ak (t ) = ÿ ak ,nϕ (t − nTc )
(1)
n= 0
where Tc is the chip duration, ak,n is the nth element of a signature sequence, and ϕ(t) is a rectangular chip-pulse
with unit energy. The transmitted baseband signal of the kth user is given by s k (t ) =
∞
ÿb
m = −∞
k
ÿb
=
m = −∞
r j ,l (m) = 2 P1 c j ,1,l (m)b1 ( m)a1 +
(m)a k (t − mTb )
∞
(m)ÿ a k ,nϕ (t − mTb − nTc )
k =2
n =0
where bk(m) ∈ {+1, -1} is the mth data bit, Tb is the bit duration, and N = Tb/Tc is processing gain. Assume that the channel has multipath fading with the number of resolvable paths Lp each of which has i.i.d. Rayleigh fading. The channel is designed as the tappeddelay-line (TDL) model. When the receiver has J diversity antennas, the baseband impulse response of the channel from the kth user to the jth antenna at the receiver is given by c j ,k (t ) = =
LP −1
ÿc l =0
j ,k ,l
(t )δ (t − τ j ,k ,l ) (3)
LP −1
ÿα l =0
(6)
K
I j ,1,l (m) + ÿ I j ,k ,l (m) + n j ,l (m)
(2)
N −1
k
user is the desired user. Then the received signal vector for the lth finger of the jth antenna is given by
j ,k ,l
(t )e
j θ j , k ,l ( t )
δ (t − τ j ,k ,l ) jθ
where τj,k,l is time delay, and c j ,k ,l (t ) = α j ,k ,l (t )e j ,k ,l is a complex Rayleigh fading process of which amplitude and phase are αj,k,l(t) and θj,k,l(t), respectively, for the lth path of the kth user at the jth antenna. The received baseband signal at the jth antenna is given by (t )
where a1 = [a1,0, a1,1, …, a1,N-1]T is the signature sequence vector for the first user, Ij,1,l(m) is inter-symbol interference (ISI), Ij,k,l(m), k = 2, 3, …, K, is multiple-access interference (MAI) from the kth user, and nj,l(m) is a noise vector with N independent zero-mean complex Gaussian random variables of which real and imaginary parts have the variance of N0/2. Assume that the propagation delay for the first path of the kth user is dj,kTc for some integer dj,k and the relative time delay τj,k,l lies in the interval [0, Tb] for convenience of the performance evaluation. Define a kL (i ) and a kR (i ) as the leftshifted and the right-shifted signature sequence vectors by i chips for the kth user, respectively. The nth elements of those signature sequence vectors are given by [a kL ( i ) ] n = a k , n +i χ n ≤ N −1−i and [a kR (i ) ] n = a k ,n −i χ n >i , n = 0, 1, …, N-1, respectively, where χA is an indicator function for the event A. Then, ISI and MAI terms are given by
{
l −1
}
I j ,1,l (m) = ÿ 2 P1 c j ,1,i b1 (m)a1L ( l −i ) + b1 ( m + 1)a1R ( l −i ) + i =0
LP −1
{
ÿ
2 P1 c j ,1,i b1 (m − 1)a1L ( N −i +l ) + b1 (m)a1R ( N −i +l )
i =l +1
} (7a)
K
r j (t ) = ÿ 2 Pk k =1
LP −1
ÿα l =0
j , k ,l
(t )e
jθ j , k , l ( t )
s k (t − τ j ,k ,l ) + n j (t ) (4)
where Pk is the average signal power of the kth user and nj(t) is the complex Gaussian noise with the power spectral density of N0. Assume that each tap in the TDL model is delayed by one chip duration and the fading process is so slow that it is constant over one bit duration. Then the output sample of the chip matched-filter (MF) for the lth RAKE finger of the jth antenna is given by
r j ,l ,n (m) =
mTb + ( l + n+1)Tc mTb + ( l + n )Tc
rj (t )ϕ (t − mTb − (l + n)Tc ) dt . (5)
During each bit duration, N output samples make a received signal vector rj,l(m) = [rj,l,0(m), rj,l,1(m), …, rj,l,NT 1(m)] where N is processing gain. Suppose that the first
I j , k ,l ( m ) =
L ( l −i − d j , k )
l − d j , k −1
+
ÿ i =0
2 Pk c j ,k ,i (m)
i =l − d j , k
bk (m + 1)a
+
R ( l −i − d j , k ) k L ( N −i − d j , k +l )
LP −1
ÿ
bk (m)a k
2 Pk c j ,k ,i (m)
bk ( m − 1)a k bk ( m)a
R ( N −i − d j , k +l ) k
+
,
(7b) respectively.
3. Adaptive RAKE Receiver with Diversity Antennas In this paper, an adaptive RAKE receiver with AICs is proposed. Fig. 1 shows the overall structure of the proposed receiver having two diversity antennas, i.e. J = 2, and L RAKE fingers for the first user. Each finger consists of a diversity combiner and an adaptive interference canceller (AIC). When the channel is in deep fade, the error
probability of bit-decision increases in a decision-directed mode that causes a severe degradation in the performance of the AIC [5]. To produce a reliable input for the AIC the received signal vectors are maximal-ratio-combined in a diversity combiner of each finger. The input of the AIC for the lth finger at the mth bit is given by J
y1,l (m) = ÿ cˆ*j ,1,l (m)r j ,l (m)
(8)
j =1
where cˆ*j ,1,l (m) is the complex conjugate of the estimated channel gain and r j ,l (m) is the received signal vector at the jth antenna.
In the proposed receiver an adaptively chosen tap-weight vector for the lth AIC at the mth bit is given by [5]
w 1,l (m) = a1 + x1,l (m)
(10)
where a1 is the signature sequence for the first user and x1,l(m) is an adaptive component which is updated once every symbol by the LMS algorithm. In the LMS algorithm with variable step-size, the adaptive component is initially set to zero and there is no training mode. The proposed receiver uses an estimated bit bˆ1 (m) as a reference bit instead of a bit in training sequence for a regular LMS algorithm. In a decision-directed mode the adaptive component for the lth AIC at the (m+1)th bit is given by
Ant 1
x 1,l (m + 1) = x 1,l (m) +
Chip MF Tc
MRC
Re[ y1, 0 ]
. .. Tc
. .. Tc
Tc
1st finger
Adaptive Algorithm
MRC
Re[ y1, L −1 ]
Lth finger
Adaptive IC Adaptive Algorithm
e1,l (m) Re[y 1,l (m)]
e1, 0
(11) z1
bˆ1
z1, L −1
6 4
e1, L−1
Fig. 1. Overall structure of the adaptive RAKE receiver with two diversity antennas
where e1,l (m) = bˆ1 (m) − Re[y1T,l (m)] ⋅ w1,l (m) is the error signal and µ(m) is the variable step-size of the LMS algorithm. It is known that the value of 0 < µ < 2 guarantees the tap-weight vector to converge to the optimum vector [7], [8]. In the proposed receiver, the variable step-size is given by
µ max , µ min ,
µ (m + 1) = µ ini
If the estimate of the channel gain is accurate so that most of the phase variation is compensated, then the real part of y1,l(m) contains most of information on the transmitted real data bit. To reduce the complexity of computation, Re[y1,l(m)] instead of y1,l(m) is applied to the corresponding AIC. A decision variable of the lth finger at the mth bit is given by z1,l (m) = Re[y1T,l (m)] ⋅ w1,l (m)
|| y 1,l (m) || 2
6 4
...
Chip MF
Adaptive IC
z1, 0
...
Ant 2
µ (m )
(9)
where w1,l(m) is the tap-weight vector of the transversaltype AIC. From the Wiener-Hopf equation the optimum tap-weight vector minimizing MSE is obtained as R1−,1l (m)pl (m) where R 1,l (m) = E{Re[y 1,l (m)] Re[y 1T,l (m)]} is the autocorrelation matrix of the AIC’s input vector and p l (m) = E{b1 (m) Re[y1T,l (m)]} is the cross-correlation vector between the reference bit and the AIC’s input vector [8]. It is complicated to compute an opti-mum tap-weight vector for every symbol duration as R1−,1l (m) and p l (m) are not known at the receiver.
if MSE sh < µ ini / µ max if MSE sh > µ ini / µ min / MSE sh , otherwise (12)
where MSE sh is the short-term MSE which is given by MSE sh =
1 M
m
ÿ {e(m)}
2
(13)
i = m − M +1
and M is the summation interval for the short-term MSE. A final decision variable for the transmitted data bit is obtained by equally combining the outputs of all fingers. Taking the final decision variable z1(m) a slicer makes a decision on the transmitted data bit. The estimated data bit is given by bˆ1 (m) = sgn[ z1 (m)] = sgn
where sgn[ x] =
L −1
ÿz l =0
1, for x ≥ 0 , − 1, for x < 0 .
1, l
( m)
(14)
1.E+00
1.E-01
1.E-02 BER
Assume that perfect estimation is made on the channel gain of the desired user in the proposed adaptive RAKE receiver. The performance of the proposed receiver with processing gain N = 31 is computed by Monte-Carlo simulation in a forward link. The signature sequence for each user is randomly selected among a family of Gold sequence of which the generator polynomials are given by g1(D) = 1 + D2 + D5 and g2(D) = 1 + D2 + D3 + D4 + D5. The multipath fading process for the channel of each antenna has 4 paths with exponential intensity profile p(t) = 0.3499δ(t) + 0.2726δ(t - Tc) + 0.2122δ(t – 2Tc) + 0.1652δ(t - 3Tc) which satisfies the constraint of unit energy. Rayleigh fading process of each path is generated after the Jakes’ model for the normalized fading rate fDTb = 0.001 and 0.01 where fD is the maximum Doppler frequency [6]. Up to two receive antennas are considered and the receiver has up to four RAKE fingers for each antenna. Assume that relative time delay at a pair of finger corresponding two antennas is the same and the bit error rate (BER) in all the results is averaged for random delays in the interval [0, Tb]. The tap-weight vector of the AIC for each finger is updated by the LMS algorithm with the variable step-size of µini = 0.0005, µmax = 0.001, µmin = 0.0001. Fig. 2 shows the BER of the proposed adaptive RAKE receiver together with that of the conventional RAKE receiver for the number of users K = 5 in a slow fading channel, fDT = 0.001. Fig. 2 (a) shows the BER for the number of antennas, J = 1. It is shown that the adaptive RAKE receiver achieves lower BER than the conventional RAKE receiver having the same number of fingers in the region of moderately high SNR. As the number of RAKE fingers increases, the amount of performance improvement becomes more. Fig. 2 (b) shows the BER for the number of antennas, J = 2. It is shown that the proposed receiver with two antennas achieves lower BER than the conventional RAKE receiver having the same number of antennas and fingers even in the region of moderately low SNR, and the performance improvement of the proposed receiver with two antennas is more significant than that with one antenna. It is because antenna diversity combining provides a reliable reference bit for the AICs in relatively low Eb/N0. Fig. 3 shows the BER versus the number of users K for the number of antennas, J = 2 and Eb/N0 = 20 dB in a relatively fading channel, fDT = 0.001. If the maximum tolerable BER is 10-3, the proposed receiver with the number of RAKE finger of two and four can accommodate about 5 more users than the conventional RAKE receiver. These
are equivalent to 180 and 150% increases in the system capacity, respectively. Fig. 4 shows the BER versus the Eb/N0 for the number of users, K = 5 and the number of antennas, J = 1 as the normalized fading rate fDT varies.
Adap. RAKE 1 finger 2 finger 4 finger Conv. RAKE 1 finger 2 finger 4 finger
1.E-03
1.E-04
1.E-05 0
4
8 12 E b /N 0 (dB)
16
20
(a) Number of antennas, J = 1
1.E+00
1.E-01
1.E-02 BER
4. Numerical Results
1.E-03 Adap. RAKE 1 finger 2 finger 4 finger Conv. RAKE 1 finger 2 finger 4 finger
1.E-04
1.E-05
1.E-06 0
4
8 12 E b /N 0 (dB)
16
20
(b) Number of antennas, J = 2 Fig. 2. BER versus Eb/N0 as the number of RAKE fingers for the number of users, K = 5 in a relatively slow fading channel, fDT = 0.001.
5. Conclusion
1.E+00
In this paper, a RAKE receiver with adaptive interference cancellers and diversity antennas is proposed for a DSCDMA system. As the number of diversity antennas and RAKE fingers increases, the performance of the proposed receiver is evaluated by computer simulation in various fading rates. It is shown that the proposed RAKE receiver has better performance than a conventional RAKE receiver in multipath fading channels. The performance improvement becomes more significant by using antenna diversity. Also, the performance is more prominent in a slow fading environment than in a relatively fast fading one.
1.E-01
BER
1.E-02
1.E-03 Adap. RAKE 1 finger 2 finger 4 finger Conv. RAKE 1 finger 2 finger 4 finger
1.E-04
1.E-05
1.E-06 5
10
15 20 Number of users, K
25
30
Fig. 3. BER versus number of users K for the number of antennas, J = 2 and Eb/N0 = 20 dB in a slow fading channel, fDT = 0.001.
1.E+00
1.E-01
BER
1.E-02
f D T = 0 .01
1.E-03
1 finger 2 finger 4 finger
f D T = 0.001
1.E-04
1 finger 2 finger 4 finger
1.E-05 0
4
8 12 E b /N 0 (dB)
16
20
Fig. 4. BER versus Eb/N0 for the number of users, K = 5 and the number of antennas, J = 1 as the normalized fading rate fDT varies.
It is shown that, as the normalized fading rate fDT is incresed, the performance of the proposed degrades. It is because, as the rate of channel fading is fast, the LMS algorithm doesn’t keep to track in a variation of channel. This phenomenon is more prominent in the proposed receiver with single antenna than that with two antennas.
Reference [1] H. V. Poor and S. Verdú, “Probability of error in MMSE multiuser detection,” IEEE Trans. Inform. Theory, vol. 43, no. 3, pp. 858-871, May 1997. [2] S. L. Miller, “An adaptive direct-sequence codedivision multiple-access receiver for multiuser interference rejection,” IEEE Trans. Commun., vol. 43, no. 2/3/4, pp. 1746-1755, Feb./Mar./Apr. 1995. [3] P. B. Rapajic and B. S. Vucetic, “Adaptive receiver structures for asynchronous CDMA systems,” IEEE J. Select. Areas Commun., vol. 12, no. 4, pp. 685-697, May 1994. [4] Y. Cho, “Adaptive CDMA interference cancellation with diversity combining in a Rayleigh fading channel,” Ph.D. Dissertation, Seoul National Univ., Aug. 1999. [5] M. Latva-aho, M. Juntti, and I. Oppermann, “Reconfigurable adaptive RAKE receiver for wideband CDMA systems,” Proc. of the IEEE VTC ’98, pp. 1740-1744, Ottawa, Canada, May 18-21, 1998. [6] W. C. Jakes, Jr., et al., Microwave Mobile Communications. Wiley, 1974. [7] J. G. Proakis, Digital Communications. McGraw-Hill, 1995. [8] S. M. Kay, Fundamental of Statistical Signal Processing: Estimation Theory. Prentice-Hall, 1993.
