Joint Interference Cancellation and Viterbi Decoding in DS-CDMA M-Reza Koohrangpour
Arne Svensson
Royal Institute of Technology Department of Signal, Sensors and Systems Radio Communications Systems Group S-100 44 Stockholm Sweden phone: +46 8 790 93 64 fax: +46 8 790 93 70 e-mail:
[email protected] URL: http://www.s3.kth.se/radio/
Chalmers University of Technology Department of Information Theory S-412 96 Gothenburg Sweden phone: +46 31 772 17 51 fax: +46 31 772 17 48 e-mail:
[email protected] URL: http://www.it.chalmers.se/ArneSvensson/
ABSTRACT Direct-sequence code-division multiple access (DS-CDMA) is a popular wireless technology. In DS-CDMA communications, all of the users’ signals overlap in time and frequency and cause mutual interference. In this paper a novel multiuser decoding scheme for coded synchronous DS-CDMA is proposed. The decoder performs joint successive interference cancellation (SIC) and Viterbi decoding (VD) in each step of the interference cancellation. In a conventional SIC scheme, SIC is performed first, followed by VD that uses the outputs of the last stage of the SIC scheme for metric calculation. Simulated bit error probability for the proposed scheme is presented and compared with bit error probability of a conventional scheme. A capacity increase of at least 4 compared to SIC followed by VD is reported in one example. INTRODUCTION Wireless personal communications will soon be as common as the wireline telephone used today. It will provide reliable and affordable communications, anywhere and anytime: in the car, restaurant, park, home, or office, or on the slopes of the Swiss Alps. To bring this vision to fruition, major improvements in the current state of wireless technology are necessary. One type of wireless technology that has become increasingly popular over the last few years is directsequence code-division multiple access (DS-CDMA). In CDMA users are multiplexed by distinct codes rather than by orthogonal frequency bands as in frequency-division multiple access (FDMA), or by orthogonal time slots, as in timedivision multiple access (TDMA) [1]. In CDMA all users transmit at the same time and each are allocated to the entire available frequency spectrum. DS-CDMA is the most popular of CDMA techniques. The DS-CDMA transmitter multiplies each user’s signal by a distinct code waveform. The detector receives a signal composed of the sum of all users’ signals, which overlap in time and frequency. In a conventional DS-CDMA system, a particular user’s signal is detected by correlating the entire received signal with that user’s code waveform. More details on DS-CDMA in general may be found in [1] and [2].
There has been a substantial interest in DS-CDMA technology in recent years because of its many attractive properties for the wireless medium [3]-[6]. A DS-CDMA system has several unique features, that makes it a strong candidate for future generations of personal communication systems. Some of them are spectrum sharing, possibility to utilize multipath signal components for recombining and frequency reuse factor of one in a cellular scenario. The two major problems in DS-CDMA in a cellular system is the near-far effect and multiple access interference (MAI) [7]. The nearfar effect is caused by mobiles transmitting at different distances from the base station, such that mobiles far away experience a large path loss while nearby mobiles experience a small path loss. When all users transmit with equal power, a conventional matched filter (MF) receiver is unable to detect the weak signal from a distant user. For the MF receiver, this problem may be solved with stringent power control, whereby the base station instructs the mobiles to adjust their power such that all signals are received with almost equal power. Another way to solve this problem is to use more sophisticated multi-user detectors. A good overview of multi-user detection is given in [7]. The presence of a number of users in a DS-CDMA systems introduces MAI, since the signature sequence are not perfectly orthogonal at the receiver. The non-orthogonality may be both due to using non-orthogonal waveforms in the transmitters but also due to intersymbol interference on the channels. In the conventional MF receiver, MAI leads to a large irreducible error probability, which may be reduced by powerful channel coding but may not be avoided in practice. This major drawback can also be solved by using more sophisticated multi-user detectors. Many multi-user detectors have recently been proposed and analyzed. We will not try to describe them all here, but refer the interested reader to the overview given in [7]. One of the multi-users detectors is the successive interference canceller (SIC) [8], [9]. It was generalized to multi-code DS-CDMA [10] and to several stages in [11]-[13]. In this paper we consider multi-user detection of convolutionally coded DSCDMA, although the proposed technique may also be applied to block coded DS-CDMA. We propose a novel com-
complex envelope of received signal r( t)
IC1
IC1
IC1
IC2
IC2
IC2
ICK
ICK
ICK
Figure 1. A block diagram, showing the iterations in a multistage successive interference cancellation (SIC or JSICV) scheme.
bination of SIC and VD, which we refer to as JSICV (joint successive interference cancellation and Viterbi decoding), whereby the Viterbi decoding is performed within the SIC scheme and not after as conventionally done. A similar idea for parallel interference cancellation (PIC) which utilizes orthogonal convolutional codes was independently studied in [14]. They show that the user capacity is increased by 1.5 to 3 times for their scheme as compared to a conventional PIC scheme. In this paper, the performance of JSICV is simulated and compared with the performance of conventional schemes such as matched filtering followed by VD (MFV) and conventional SIC followed by VD (CSICV). The proposed scheme is based on the SIC scheme described in [8], [11][13]. The optimum detector for convolutionally encoded asynchronous DS-CDMA in additive white Gaussian noise (AWGN) is formulated and analyzed in [15]. The optimum detector is extremely complex.
N–1
∑ Cl, k pT ( t – lTc ) ,
l=0
c
(2)
where C l, k ∈ { – 1, 1 } , p T ( t ) is a rectangular pulse over c 0 ≤ t < T c , T c is the chip time and N = T ⁄ T c is the spreading ratio. The decision statistics used by all detectors considered in this paper as based on one or all of the outputs of a bank of filters matched to the code waveforms of all users. A matched filter output is given by ( n + 1 )T
∫
r ( t )c k ( t – nT ) dt .
(3)
nT
In this paper, for simplicity we consider synchronous DSCDMA on a flat Rayleigh fading channel with AWGN [1]. The proposed decoder may however be extended to asynchronous DS-CDMA and to frequency-selective fading channels in a way similar to [11]-[13]. The binary information is first convolutionally encoded, then interleaved and modulated by BPSK. The BPSK symbols are spread by binary spreading codes (here we consider random codes) of length equal to the bit period before being transmitted over the channel. A rectangular pulse shape is used in the transmitter. The complex baseband received signal over the interval nT ≤ t < ( n + 1 )T may therefore be given as K
∑ αk, n dk, n ck ( t – nT ) + w ( t ) ,
ck ( t ) =
y k, n =
SYSTEM DESCRIPTION
r( t) =
is the complex baseband Gaussian noise. The complex channel gain and the convolutionally encoded symbol (here assumed to be a BPSK symbol) for the kth user in the nth symbol interval, are referred to as α k, n and d k, n , respectively. The code waveform is given by
(1)
k=1
where T is the symbol time, K is the number of users, and
The set of MF outputs are then processed in different ways for the different schemes. Throughout this paper we assume ideal average power control. JOINT SIC AND VITERBI DECODING (JSICV) The new JSICV scheme that we propose here is quite similar to the traditional SIC scheme [11]-[13] with the main difference that decoding of the channel code is also done at each step of the cancellation in JSICV. This is the same idea as developed independently for PIC in [14]. The scheme is described in Figure 1 and Figure 2. The purpose of each cancellation unit (IC) in Figure 1 is to obtain an estimate of one user’s signal, which is then subtracted from the remaining composite signal. This is then repeated for all users’ signals in a first stage of interference cancellation. The signal remaining after these K steps of cancellation may be used in
final decision y k, n
αˆ k, n∗
αˆ k, n Deinterleaver
MF
VD
Encoder
ck ( t )
Interleaver
last stage soft output y k, n
MF
αˆ k, n∗
VD
decision
complex envelope of received signal
Figure 2. A block diagram of the contents of each cancellation unit in Figure 1 for the proposed JSICV scheme. The blocks in the shaded area are only used with hard decision decoding.
Figure 3. Conventional matched filter detector followed by a Viterbi detector (MFV). The blocks in the shaded rectangle are used with hard decision only.
the following stages to improve the cancellation efficiency and therefore to further reduce the bit error probability. These stages are quite similar except that the estimate obtained in the previous stage must be added to the remaining composite signal before the new estimate is obtained and subsequently subtracted. This is clearly shown in Figure 1. For a SIC scheme the best performance is obtained when the signal of the strongest (largest instantaneous received power) user is estimated first, followed by the signal of the second strongest user, etc. This does not cause any difficulty in a traditional SIC scheme since the signals may be estimated for one symbol interval after the other. In a coded and interleaved transmission scheme on the other hand the symbols appear in a different order on the channel as compared to the original data. Furthermore, when convolutional codes are used, there is always a delay between the metric calculation and the decisions. Since the purpose of JSICV is to include channel decoding in each step of the cancellation scheme, we have not found any other way to overcome this except using a block structure of the transmitted data and perform the cancellation block-wise (instead of symbol-wise). The chosen block length is equal to the number of symbols in the block interleaver and the last symbols are known tail bits in order to reset the memory of the encoder. Tail bits simplify the Viterbi decoding but could be exchanged with tailbiting Viterbi decoders [16]. However, by applying a block-wise cancellation scheme we loose most of the efficiency of power ranking, since only average (over the block-length) power ranking may be used and with blocks long enough for efficient interleaving the average power will be almost equal for different users (assuming average power control). The contents of each cancellation unit (IC) is shown in Figure 2, where a complete decoding of the encoded data is performed. The matched filter output of a given user is first multiplied by the complex conjugate of a channel estimate and then hard limited for hard decision Viterbi decoding. For
last stage hard output for VD
αˆ k, n∗
y k, n
αˆ k, n
ck ( t )
MF
Figure 4. A block diagram of the contents of each cancellation unit in Figure 1 for SIC. The blocks in the shaded area are not used for the linear SIC scheme (except for a final hard decision if necessary).
soft decision Viterbi decoding these two operations are omitted. The hard or soft decisions are then deinterleaved and Viterbi decoded. At the end of each transmitted block a decision of the whole block is obtained. These decisions are now reencoded, reinterleaved, multiplied by the estimated channel gain and finally spread by the code waveform of the user to give an estimate of that user’s signal over the whole block. This estimate is subsequently subtracted from the remaining composite signal as described above. In this paper, we have not studied channel estimation but assumed it to be perfectly done. For hard decision Viterbi decoding, Hamming distance have been used as a metric, while for soft decision decoding, Euclidean distance given by
∑
2
ˆ y k, n – αˆ k, n d k, n ,
(4)
n ∈ the block
where αˆ k, n denotes an estimate of the complex channel gain, dˆ k, n is a candidate symbol in the decoder and y k, n refers to the matched filter output at the corresponding step. REFERENCE DETECTORS For purpose of comparison we have also evaluated the performance of a single-user MF detector followed by a Viterbi detector (MFV) and a conventional SIC followed by a Viterbi detector (CSICV). The MFV scheme is shown in Figure 3. This is a conventional single-user scheme with hard or soft decoding VD. The metric used for soft decoding is Euclidean distance as given in Eq. (4) and in this paper we assume that a perfect channel estimate is available for the metric calculation. The CSICV scheme is described by Figure 1 with the details of each cancellation unit (IC) given by Figure 4. For a more detailed description, please refer to [11]-[13]. The CSICV scheme studied here consists of a linear SIC (no decision is made during the cancellation) followed by a
Legend for cancellation schemes, 10 users hard, 1-stage hard, 2-stage soft, 1-stage soft, 2-stage
Legend for cancellation schemes, 10 users hard, 1-stage hard, 2-stage soft, 1-stage soft, 2-stage
CSICV, symbol ranking JSICV
hard, MFV soft, MFV hard, single-user bound soft, single-user bound JSICV, 2 stages, soft, 40 users
hard, MFV soft, MFV hard, single-user bound soft, single-user bound 10-1
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10-2 bit error probability
10-2 bit error probability
CSICV, without ranking CSICV, symbol ranking CSICV, average ranking
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mean received Eb/N0 [dB] Figure 5. Bit error probability of JSICV and CSICV with instantaneous power ranking.
deinterleaver and a VD. The output from the SIC is either hard or soft decisions and these are in both cases obtained from the last stage of the cancellation. A SIC may use power ranking among users and here we consider instantaneous (per symbol), average (here over decoding block) and no power ranking. We assume ranking is based on perfect channel estimates. NUMERICAL RESULTS The performance of the considered schemes have been simulated on a flat Rayleigh fading channel with a Doppler frequency of 50 Hz. The bit rate of each user was assumed to be 20 kbps and the number of users were 10 in all simulations except one where 40 users were considered. The spreading ratio was 31 and random sequences were used. A convolutional code of rate 1/2 with constraint length 3 was employed and coded data were interleaved in a block interleaver with 10 columns and 20 rows (coded bits are written row-wise). This leads to a total delay of at most 15 ms for the considered data rate. Perfect channel estimation is assumed in ranking, hard decision and Euclidean distance calculation. In Figure 5, we show the bit error probability of each user in the system for JSICV, CSICV with instantaneous power ranking, MFV and the corresponding single-user bounds. After one
6
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mean received Eb/N0 [dB] Figure 6. Bit error probability of CSICV with different power ranking schemes.
stage of cancellation the performance of JSICV is worse than the performance of CSICV. The reason is that the gain of power ranking in CSICV is quite large in the first stage as seen in Figure 6, where the bit error probability of each user in a CSICV scheme is shown for the three considered power ranking schemes. The performance with instantaneous power ranking is in fact almost as good as the performance after 2 stages without power ranking. However, after 2 stages of cancellation the JSICV scheme outperforms all CSICVs with about 2 dB and performs almost equal to the single-user bound. We also see that soft decoding is much better than hard decoding which was of course expected. For the 2 stage JSICV with soft decoding we also show performance with 40 users in Figure 5 (only one result is shown due to very time consuming simulations). At a BER of 10-4 this detector performs only 1 dB worse than the single-user bound, and performs better that the best 2 stage CSICV for 10 users. Also noted is that a conventional MFV performs very poor under these conditions. We have also simulated the performance for hard decision decoding with a perfectly interleaved channel (obtained by generating random fading on the channel) but the obtained improvements is quite small for all considered scheme. We are therefore able to conclude that most of the available coding gain is obtained by the quite small interleaver.
DISCUSSION AND CONCLUSIONS In this paper we propose to perform channel decoding within each stage of successive interference cancellation, instead of performing interference cancellation succeeded by Viterbi decoding. Performance have been simulated for the proposed scheme and compared to the conventional schemes. The conclusion is that with 1 stage of cancellation, the improvement obtained by ranking in CSICV is larger than the improvement obtained in JSICV by decoding the channel code inside the cancellation loop. After 2 stages of cancellation, ranking does not change the performance in CSIVC significantly, while including the Viterbi decoder in the cancellation loop improves the performance significantly. Our results show that also with 40 users with spreading ratio of 31, the performance is within about 1 dB of the single-user bound down to 10-4. We also believe that the JSICV scheme can be slightly improved by using average power ranking and expect to see similar improvements as seen for CSICV. This has not been simulated since simulations are time consuming.
ify her computer programs. REFERENCES [1] [2] [3]
[4] [5] [6]
Based on the simulations that we have done, it is difficult to evaluate the capacity increase obtained by the proposed detector as compared to conventional detectors. This would require extensive simulations for many different values of the number of users such that bit error rate could be plotted versus number of users. However, since the required Eb/N0 at BER equal to 10-4 for a 2-stage detector is smaller for JSICV with 40 users than for the best CSICV with 10 users, we conclude that for this case the capacity increase is at least 4. The corresponding number in [14] for PIC is 1.5 to 3.
[7]
In this paper we assume that channel estimation is ideal. With practical channel estimation the performance will be degraded, but we do not expect any larger degradations as experienced for CSICV. For a decision directed MSE approach this means a degradation of the order of 1-2 dBs [13] and will appear also for CSICV.
[10]
Furthermore, multipath fading has not been taken into account. The JSICV scheme may however be generalized in the same way as CSICV [12], such that the different received paths are considered as different users in the first stages and then combined in a RAKE combiner in the latter stages. There is however one difference. For linear CSICV no channel estimates are needed until the RAKE combining is done, while in JSICV channel estimates are needed for the Viterbi decoding in all stages. This means that the channels estimates used in the first stages will not be that good since these are affected by uncancelled ISI and MAI. It is not clear how this will affect the performance of JSICV on multipath fading channels and this is a topic for further study. Complexity is a third issue that has not been taken into account here. The proposed detector is complex, since Viterbi decoding is done for each user at each stage. Less complex joint detectors is another topic for further study. One possibility which we will look into, is to replace Viterbi decoding by sequential decoding [17]. ACKNOWLEDGMENT We are grateful to Ann-Louise Johansson for many stimulating discussions on this topic and for letting us use and mod-
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