Bayesian turbo multiuser detection for nonlinearly modulated CDMA☆
Introduction
Direct sequence code-division multiple-access (DS-CDMA) is one of the most popular multiple-access schemes for multiuser wireless communications. A significant problem inherent to multiuser wireless communications is the fact that many users access the same physical channel simultaneously. The users’ signals interfere with each other, making their detection less reliable, particularly when the users’ received powers are severely unbalanced (near-far problem). That detrimental effect is known as multiple access interference (MAI).
The conventional detector ignores the structure inherent in MAI and treats it as ambient Gaussian noise. In practical wireless systems, power control is employed to maintain the interference at a certain level. When there is a big discrepancy among the users’ received powers, the performance of the conventional detector suffers a high degradation; that receiver is known to be interference-limited.
A large family of detectors, called multiuser detectors, can improve signal detection in the presence of MAI and near-far resistance. They treat the MAI as structured signals rather than ambient noise. An inventory of multiuser detectors for combating MAI is given in [29]. Most of the previous works on multiuser detection concentrate on linear modulation, and only a limited amount of work has been done on multiuser detection for nonlinear modulation.
When the channel parameters are known, the maximum a posteriori probability (MAP) detector is optimal, but it has a prohibitively high computational complexity. In practice, two kinds of detectors are considered for both linear and nonlinear modulation: namely, linear detectors such as the decorrelating detector or the minimum mean-squared error detector (MMSE) [11], as well as the subtractive interference cancelation detectors [7], [12]. Regarding specifically nonlinear modulation, the decorrelator was analyzed for non-coherent demodulation of Walsh-modulated signals in [10]. Non-orthogonal nonlinear modulation is considered in [23], [28]. In [19], adaptive interference suppression algorithms are proposed as an alternative to the interference cancelation detector.
Some solutions have been provided for linear modulation when the channel parameters are unknown, using the expectation-maximization algorithm [21] or a tree-search algorithm [33]. In [26], the problem of sequential multiuser amplitude estimation in the presence of unknown data is studied, where an approach based on stochastic approximation is considered.
The MAI is adding to the ambient channel noise, which follows different mathematical models according to the type of channel used in practice. Most of the previous works have assumed a Gaussian noise environment. However, in many wireless channels, such as urban and indoor channels [3], [4], [14], [15], [17], [18] or underwater acoustic channels [6], [16], the ambient noise is non-Gaussian in nature, due to impulsive phenomena. In [30], [31], a robust multiuser detection algorithm based on the Huber robust regression technique is proposed for non-Gaussian channels.
Data transmission in CDMA systems is usually protected by error control coding in order to combat the various channel impairment. In [32], a turbo (coupled iterative processing) multiuser detection scheme for coded CDMA systems is proposed, which iterates between multiuser detection and channel decoding to successively improve the receiver performance. Similar turbo processing techniques also appear in [2], [8], [20], [22]. Again, these works consider only linear modulation with known channel parameters.
In this paper, we introduce a blind iterative multiuser detection scheme for demodulating nonlinearly modulated CDMA signals in unknown channels, with Gaussian or non-Gaussian complex noise. The Bayesian inference is used to determine the joint estimates of channel gains, noise parameters and transmitted symbols. The numerical computation of those estimates is achieved by the Gibbs sampler. We then consider employing iterative joint multiuser detection and decoding, to improve the performance of the proposed receiver in a coded system.
The rest of this paper is organized as follows. In Section 2, a complete description of the multiuser communication system under consideration is given. The problems of Bayesian multiuser detection for nonlinear modulation in Gaussian and non-Gaussian noise are treated, respectively, in 3 Adaptive Bayesian multiuser detector in Gaussian noise, 4 Adaptive Bayesian multiuser detection in non-Gaussian noise. In Section 5, an adaptive turbo multiuser detection scheme is presented. Some simulation results and the performance analysis are found in Section 6. Finally, we draw some conclusions in Section 7.
Section snippets
System model
We consider a coded nonlinearly modulated synchronous CDMA system with K users. The ambient channel noise is assumed to be additive, white and complex.
For each user k, the information bits, {dk(n)}n=1Ni, dk(n)∈{0,1}, are encoded, using a convolutional code of rate R. The outputs of the encoder, {xk(m)}m=1Nc=Ni/R, xk(m)∈{0,1}, are then scrambled by a random interleaver to reduce the influence of error bursts at the input of the channel decoder. The resulting bits stream, {xπk(m)}m=1Nc=Ni/R, xπk(m
Adaptive Bayesian multiuser detector in Gaussian noise
Consider the signal model given by Eq. (5) for r(i) in Gaussian noise. The probability density function for the noise samples is given by Eq. (6). Our concern is to restore the transmitted bits, i.e., to reconstruct . Note that the spread Walsh code matrix carries no information, and is assumed to be known by the receiver. Therefore, it is equivalent to estimate the indicator vectors . Denote:as the
Adaptive Bayesian multiuser detection in non-Gaussian noise
Consider again the signal model given by Eq. (5) for r(i) in non-Gaussian noise. The probability density function of the noise samples is given by Eq. (7).
Iterative joint multiuser detection and decoding
In this section, we consider employing iterative joint multiuser detection and decoding to improve the performance of the system under study.
The multiuser detector gets the received signal r(i) as an input, and delivers the MAP estimates of for user k. Because the nonlinear modulator acts as a one-to-one mapper between blocks of q-bits and the symbols sk(i), each sequence of q-bits (xkπ(iq+1)…xkπ((i+1)q)) corresponds to a unique choice j such that 1k(i)=Ij. The role of the
Simulation results
In this section, we show the performance of the adaptive Bayesian multiuser detector through simulations. First, we observe the performance of the proposed multiuser detector for uncoded CDMA signals. Then we compare its performance with the receivers proposed in [19]. In the third subsection, we show the performance of the joint multiuser detection and decoding.
Conclusion
In this paper, we have presented a novel adaptive multiuser detection scheme based on the Bayesian inference, for demodulating nonlinearly modulated CDMA signals. The proposed receiver was derived under a Bayesian framework, for both Gaussian and non-Gaussian noise. The Bayesian estimates were computed using the Gibbs sampler, a Markov Chain Monte Carlo procedure. The performance of the Gibbs multiuser detector is compared with some other adaptive receivers implemented for the same
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This work was supported in part by the Interdisciplinary Research Initiatives Program, Texas A&M University, and in part by the US National Science Foundation (NSF) under grant CAREER CCR-9875314 and grant CCR-9980599.