Equalization and multiuser interference cancellation in CDMA ... - DEI

Equalization and multiuser interference cancellation in CDMA systems Stefano Tomasin Dept. of Information Engineering, University of Padova via Gradenigo 6/B, Padova, Italy 35131 e-mail: [email protected]

Abstract In this paper we propose a parallel interference cancellation (PIC) architecture for code division multiple access (CDMA) transmission over broadband wireless channel, which makes use of a block decision feedback equalizer (DFE) to remove inter-symbol interference (ISI) and whose overall complexity is much lower than equivalent (in terms of performance) existing structures. At the receiver, after IC, a block DFE operating at the chip-rate is applied, with both feedforward and feedback filters implemented in the frequency domain. Indeed, the receiver iterates more times between cancellation, equalization, despreading and data detection. The DFE filters are designed at each iteration, according to the reliability of the detected data in the previous iteration. Moreover, to reduce error propagation in the block DFE, a chip interleaver is used before transmission.

Nevio Benvenuto Dept. of Information Engineering, University of Padova via Gradenigo 6/B, Padova, Italy 35131 e-mail: [email protected]

ture is denoted FD-IC. At the receiver, for each stage of the PIC process, a block DFE is iterated with detection. In particular, for each user, at the first iteration only the feedforward (FF) filter is active and a tentative decision on data is performed. At the next iterations, decisions of previous iterations are used to generate the feedback (FB) filter input signal, whose output is added to the FF filter output before the new data detection. Coefficients of both FF and FB filters are varied depending on the reliability of the detected data at the previous iteration. However, we have verified by simulations that for many channel conditions, the error propagation in the block DFE is significant, due to the CDMA spreading where an error on one symbol generates a burst of wrong chips. To reduce this phenomenon the chips of each block are interleaved before transmission, so that symbol errors, after interleaving, are allocated on nonadjacent chips in the FB filter input signal.

1. Introduction Multiuser access interference (MAI) limits the performance of code division multiple access (CDMA) in dispersive channels, since multipath propagation disrupts the orthogonality among codes of different users. Channel dispersion generates also self-replica of the signal of each user and consequently both interference among chips (i.e. interchip interference, ICI) and inter-symbol interference (ISI) arise. In these cases, a classical rake receiver based on a matched filter and a despreader is not effective in combating the various sources of interference. To improve performance, parallel interference cancellation (PIC) has been considered. In PIC, after a bank of rake receivers, data of all users are detected to obtain tentative decisions that are used to regenerate MAI, which in turn is canceled from the received signal. However, the performance of traditional PIC schemes with rake receivers is limited by both ICI and ISI. Additionally, since the rake receiver operates at the chip rate, computational complexity of these schemes may be significant for channels with more than just a few taps. In this paper we propose a new IC architecture which allows the use of a more elaborate equalizer at an affordable complexity. The efficient scheme is based on frequency domain (FD) implementation of filters, and the resulting struc-

2. System model Let us consider a wideband CDMA transmission in the uplink. For each user, the multipath propagation can be described by a filter whose impulse response is the sum of delayed paths with different attenuations and phases. To allow sampling at the rate 1/(T NS ), the received signal is filtered by a filter matched to the transmit pulse shape and then sampled, [1]. As a result, we denote the impulse response of the discretetime base-band equivalent model of the channel for the user k as h(k) (q), q = 0, 1, . . . , Nq − 1. Each of the K active users spreads the information data with codes having a spreading factor NS . In particular, the resulting data sequence (chips), for the user k is 1 0

s (k) (m + nNS ) = c(k) (m)d(k) (n),

(1)

where d(k) (n) is the data signal and c(k) (m), m = 0, 1, . . . , NS − 1 is the spreading code. The received discrete-time signal comprises the sum 1 Notation: a signal is denoted with a lowercase letter, while its DFT is denoted with the corresponding uppercase letter. Vectors and matrices are denoted with bold italics letters. * denotes complex conjugate.

of the signals of all users i.e. r0 (`)

=

K−1 X

0

r (k) (`) + w(`) =

k=0

q −1 K−1 X NX

0

h(k) (q)s (k) (` − q) + w(`) ,(2)

k=0 q=0

where w(`) is the complex additive white Gaussian noise (AWGN) term, having zero mean and variance N0 /2 per dimension. If despreading with code of the user k is directly applied to r0 (`), the obtained signal is affected by MAI and ISI. Thus, more elaborate receivers must be used. For example, in the rake receiver a filter matched to h(k) (q) is applied to the received signal before de-spreading. Also in this case, for highly dispersive channels, performance are limited by the various sources of interferences. In this paper we propose a receiver with joint IC and equalization where filtering is performed in the FD. A. Data transmission format The scheme proposed in this paper makes use of the efficient implementation of filters in the FD. This objective is chieved by a particular transmission format that forces the duality between time convolution and product of DFT of signal blocks. As shown in [2], the PN-extension method is a technique that forces circularity of blocks convolution. In particular, to each 0 block of M information data s (k) (m) a known PN sequence [p(0), p(1), . . . , p(L − 1)] is appended and the transmitted data block of length P = M + L is given by s

(k)

(m)

= =

(k)

[s

0

(k)

(mP ), . . . , s

(k)

0

X (k) = R −

K−1 X

V (`) ,

k = 0, 1, . . . , K − 1 .

`=0,`6=k

(mP + P − 1)] (3)

Now, under the hypothesis that the length L of the PN sequence is not lower than the channel length Nq , the DFT of the received signal can be written 0 as the product of the DFTs of s (k) and the channel impulse response. By denoting with R(m), S (k) (m), W (m) and H (k) the DFTs of r(m), s(k) (m), w(m) and h(k) , respectively and assuming that all users are quasi-synchronous, i.e. the impulse of each channel falls within the extension of length L, the received signal can be written in the frequency-domain as K−1 X

3. Equalization and PIC The FD implementation of parallel IC (FD-PIC) is shown in Fig. 1. In PIC all users are detected simultaneously and the cancellation of their reciprocal interfernce is performed in parallel. In the scheme of Fig. 1, the detection and the generation of the interference contribution of user k is performed by the interf erencek block. The following operations perform iteratively detection and IC of user signals for I times. We refer to PIC iterations in the parallel IC process to avoid confusion with term iteration which is reserved for the equalization-detection process. At the first PIC iteration (i = 1), all feedback signals of Fig. 1 are not active and the received signal is applied to a bank of interferencek blocks, performing parallel detection of all user data signals and generation of MAI. At PIC iterations i = 2, 3, . . . , I, the input to each interf erencek block is obtained by canceling from the received signal the MAI due to all other users, as shown in the efficient implementation of Fig. 1. In this case, the signal at the input of the interf erencek block is

(5)

(k)

[s (mM ), . . . , s (mM + M − 1), p(0), . . . , p(L − 1)] .

Rp (m) =

so that the burst of chip errors is spread among the different frequencies of the equalizer. Note that since data must be detected at each block to allow DFE, the interleaver must operate separately on each block of transmitted chips. In particular, we consider a row-column block interleaver where the M information chips are written in a matrix column-wise and read row-wise [1].

Hp(k) Sp(k) (m) + Wp (m) .

(4)

k=0

B. Error propagation The proposed equalization and IC scheme operates iteratively on blocks of the signal. As it will be seen in more detail, the potential error propagation for one iteration to the next may be significant, due to poor initial data estimates. In order to limit this effect, we propose here to interleave chips before transmission

As an alternative, cancellation could include also ISI [3] and in this case Xp(k)

= Rp − [Hp(k) − e−j2πp∆` /P h(k) (∆k )]Sˆp(k) − K−1 X

Vp(k) ,

k = 0, 1, . . . , K − 1 ,

(6)

`=0,`6=k

p = 0, 1, . . . , P −1, where ∆` is the delay corresponding to the coefficient with the largest amplitude of the channel impulse response of user `. The general scheme of the interf erencek block, is shown in Fig. 2. Note that, due to the CDMA transmission format, a time-domain DFE can not be applied directly on the received signal, since despreading must be performed on blocks of chips before the FB signal is available. Hence, we use a block DFE, where the FB data signal is generated in blocks. In FD-PIC both ISI and MAI are efficiently reduced. In particular, PIC allows to reduce MAI by detecting all users and canl their mutual interference. On the other hand, ISI is mitigated in the interf erencek block. This block has the double purpose of performing FD equalization for the mitigation of MAI and to

+

X (0)

interference

+ + X

r(n) S/P

R

. . .

(1)

+

DFT

V (0)

0

interference1

V (1)

− +

X (K−1) interference

K−1

+

Fig. 1.

V (K−1)

General architecture of FD-PIC.

^(k,l−1) S X

(k)

DFE k

Y

(k,l)

H (k) V

^(k, l)

IDFT

DS

DET

d

DFT

(k)

SP

interference generator Fig. 2.

The interf erencek block.

B p(k, l) ^ (k, l−1) Sp C p(k, l) X p(k) Fig. 3.

+ +

l) Y (k, p

Frequency domain implementation of DFEk .

regenerate the interference due to user k for PIC. To implement equalization a DFE is used, since it is well known that by performing cancellation of interference by the feedback, DFE achieves a better performance than linear equalizers. However, contrary to the DFE proposed in [6], where the FB signal was designed to cancel only the interference among contiguous CDMA symbols, here the DFE operates at the chip rate, hence it is more effective in equalizing. In block DFE equalization and detection are iterated ν times on the input signal X (k) . All operations are performend in the FD and the resulting DFE is made of simple operations, as shown in Fig. 3. The feedforward filter performs the elementwise complex multiplication of X (k) with the vector of the FF filter coefficients C (k,l) = (k,l) (k,l) (k,l) [C0 , C1 , . . . , CP −1 ], where l = 1, 2, . . . , ν denotes the iteration number. Similarly, also the FB filter is implemented as a vector product in the FD and its (k,l) (k,l) (k,l) coefficients are B (k,l) = [B0 , B1 , . . . , BP −1 ]. Special attention must be paid to the first iteration (l = 1), since initially no decision is available. In

this case the DFE becomes a linear equalizer, since FB filter has all zeros, so the no FB cancellation is performed. Y (k,1) is then transformed into the time domain by IDFT. After de-spreading (DS), detection (DET) yields ˆ (k,1) . the tentative decision vector d Fig. 4 shows a detailed description of the interf erencek block. In this scheme parallel to serial conversion is denoted with P/S. In this scheme, according to the PN-extension technique the last L symbols of each block are discarded after the IDFT of the vector signal Y (k,1) . To exploit the benefits of chip interleaving, a de-interleaver (DEINT) is applied before de-spreading. Detection follows. Once a detected signal is available, the FB filter can be applied and a new equalization iteration follows. The FB filter is fed by recreating the spread signal and performing a DFT to obtain the reconstructed ˆ (k,1) . In particular, the detected data data vector S (k,1) ˆ block d is spread (SP), interleaved (INT) and PN extension is inserted. After transformation in the FD by DFT equalization of the input signal is performed. In general, from the second iteration on (i.e. l > 1) the DF Ek generates the vector signal Y (k,l) with elements Yp(k,l) = Xp(k) Cp(k,l) + Bp(k,l) Sˆp(k,l−1) ,

(7)

where p = 0, 1, . . . , P − 1. The equalization and detection processes are iterated ˆ (k,ν) is ν times, until a reliable decision vector S available which is multiplied by the corresponding channel frequency response to obtain the interference

^ s 0

Y0

u0

Y1

u1 . . . uM−1

IDFT

DEINT DS

P/S

~ d

^

d

SP INT

insert ^ PN−sequ. s P−1

remove the last L samples

Fig. 4.

p = 0, 1, . . . , P − 1.

(8)

4. DFE design For the design of the DFE filters we propose the minimization of the MSE at the detection point which at iteration l = 1, 2, . . . , ν, can be written in the FD as P −1 1 X h (k,l) (k) E Cp Xp + Bp(k,l) Sˆp(k,l−1) − J (k,l) = P 2 p=0 2  Sp(k) . (9)

By assuming that both transmitted and detected data are i.i.d. random variables, with zero-mean, and statistically independent from the noise, the expectation in (9) with respect to data and noise signals, yields the MSE P −1 2 1 X (k,l) 2 J (k,l) = 2 Cp MW + Cp(k,l) Hp(k) − 1 MS P p=0 2 + Bp(k,l) MS + 2Re[Bp(k,l)∗ (Cp(k,l) Hp(k) − 1)r(k,l) ] ,

where MW = P N0 is the noise power in the FD, MS the power of each element of S (k) , and r(k,l) is the correlation between the transmitted data and the detected data at the previous iteration, [8] r(k,l) = E[d(k) (n)dˆ(k,l−1)∗ (n)] .

(10)

Now the correlation depends on the channel and on the noise level and it must be estimated at the receiver. Here we summarize a method, where an estimate of r(k,l) is obtained by X (k) and the FD detected signal ˆ (k,l−1) , at the previous iteration, S P −1 X

(k)

Xp

(k) p=0 Hp

Sˆp(k,l−1)∗ ,

^ S P−1

Operations of the interf erencek block.

contribution in the FD that must be canceled from the received signal

ˆr(k,l) = η

^ S1

S/P DFT

YP−1

Vp(k) = Hp(k) Sˆp(k,ν) ,

^ S0

(11)

with η a correction factor (η < 1) to reduce the DFE error propagation phenomena.

Indeed, in this design method, since the reliability of the detected signal at the feedback input is increasing with the number of iterations, the filters will be different at the various iterations. To derive the filters that minimize (4), we also impose the constraint that the FB filter removes preand post-cursors, but does not remove the desired PP −1 (k,l) component, i.e. it must be = 0. The p=0 Bp application of the gradient method to minimize (4), with respect to the FB filter coefficients, yields Bp(k,l) = −

ˆr(k,l) (k) (k,l) [Hp Cp − γ (k,l) ] , MS

(12)

p = 0, 1, . . . , P − 1, where γ (k,l) =

P −1 X

Hp(k) Cp(k,l) ,

(13)

p=0

and, for the FF filter coefficients (k)∗

Cp(k,l) =

Hp 

MW + MS 1 −

2

|ˆr(k,l) | M2S

 . (14) (k) 2 Hp

Special attention should be paid to the first iteration of the DFE-detector (l = 1). At the first PIC iteration (i = 1) no tentative decision is available at the first DFE iteration, hence ˆr(k,1) = 0 and B (k,1) = 0, for k = 0, 1, . . . , K −1. At the next PIC iterations (i > 1), a tentative decision of the previous PIC iteration is available also for l = 1 and a DFE can be used for each user.

5. Performance results Simulations have been performed in independent dispersive Rayleigh fading channels with an exponential power delay profile with root mean square delay spread rmsds = 2Tm , where Tm = T M/(NS P ) is the chip period of the transmitted PN-extended data block. BPSK symbols are spread with Walsh sequences of length NS = 16. The length of the DFTs is P = 256 and the length of the PN sequence is L = 16. For each PIC iteration the number of DFE-detector iterations is ν = 1.

−1

6. Conclusions

10

1 it. 2 it. 3 it. 4 it.

−2

BER

10

In this paper we have proposed an equalization and IC structure for CDMA wideband transmission. The use of efficient DFTs to implement filters yields a reduced complexity with respect to existing CDMA receivers using time-domain operations. Moreover, the integration of equalization and IC outperforms significantly rake receivers, due to the mitigation of both MAI and ISI. Simulations performed on a dispersive channels shows that a reliable communication is possible with the proposed scheme.

−3

10

−4

10

−5

10

2

4

6

8

K

10

12

14

16

Fig. 5. Average BER versus number of users (K) for a number of PIC iterations ranging from 1 to 4 and average Eb /N0 = 16 dB. Chip interleaving is used. Dashed lines: RAKE-FD-PIC. Continuous lines: DFE-FD-PIC.

7. Aknowledgments This research has been developed in the frame of the Italian national project on fundamental research (FIRB) ”Reconfigurable platforms for wideband wireless communications”.

References Fig. 5 shows the BER of a transmission as a function of the number of active users K, for DFE-FD-PIC and rake-based PIC (RAKE-FD-PIC). The average performance of a single user on 500 channel realizations with an average Eb /N0 of 16dB are plotted for a number of PIC iterations ranging from 1 to 4. As shown in Fig. 5, the equalizer is effective in reducing the ISI generated by the dispersive channel. The DFE-FDPIC outperforms the RAKE-FD-PIC by more than one order of magnitude in BER. Note also that the PIC iterations beyond the second one give a contribution to the reduction of BER, especially when a large number of users is active. We conclude that interleaving yields a significant advantage in terms of performance with a negligible impact on complexity.

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