Fast communicationAdaptive step-size constant modulus algorithm for DS-CDMA receivers in nonstationary environments
Introduction
The performance and stability of a stochastic gradient algorithm used within a direct-sequence code division multiple access (DS-CDMA) receiver designed to mitigate multiple access interference (MAI) are dependent upon the choice of an appropriate step-size. In practice, such MAI is time-varying because users frequently enter and exit the channel. Therefore, the channel is far from being stationary and computation of a pre-determined step-size is difficult. In [3], the adaptive step-size strategy for tracking time-varying environments within DS-CDMA channels is successfully applied to the minimum mean output energy (MOE) detector. The effect of multipath distortion on the algorithm is, however, neglected in the derivation of the algorithm. This is because the MOE criterion is not designed to equalise the channel and tends to cancel the desired signal itself when the spreading waveform has a mismatch [2]. In reality, the multipath distortion, the cause of mismatch, must not be neglected especially when transmission at a high data rate is required. It should also be noted that there can be a substantial performance gap between the MOE detector and the minimum mean squared error (MMSE) receiver [2], even when there is no multipath distortion. On the other hand, the analyses in [6] show that the constant modulus algorithm (CMA) receiver can perform almost as well as the Wiener (MMSE) receiver provided that undesirable local minima can be avoided.
In this paper, we therefore propose a new adaptive step-size CMA (AS-CMA) algorithm for a DS-CDMA receiver for multipath fading channels. The algorithm adaptively varies the step-size in order to minimise the constant modulus (CM) criterion. The algorithm is blind in the sense that no training data are required. Simulations have confirmed the applicability of the algorithm for nonstationary multipath fading CDMA channels. The performance in terms of signal to interference plus noise ratio (SINR) of the proposed algorithm is shown to be superior to the existing adaptive step-size MOE (AS-MOE) and the fixed step-size CMA receivers.
Section snippets
Signal model
Consider the real signal model of an additive white Gaussian noise (AWGN) K-user synchronous DS-CDMA channel, the baseband received signal is defined aswhere Ak represents the received amplitude of the kth user. The data bits bk(i) are independent identically distributed (i.i.d.) and bk(i)∈{−1,+1}. The symbol period is denoted by T. The spreading waveform of the kth user ck(t) is N-dimensional and has unit energy property, i.e., ||ck||2=1. The AWGN w(t) has
Adaptive step-size CMA algorithm
The stochastic gradient adaptive gain strategy is introduced in [1] for the nonblind adaptive system to track nonstationary environments. We adopt the ordinary differential equation (ODE) approach suggested in [1] for the derivation of the adaptive step-size CMA algorithm. The CM criterion for real signals is given by JCM=E(zn2−γ)2, where is the output of the receiver. The dispersion constant γ is equal to unity for binary phase shift keying (BPSK) signals. By minimising JCM with
Numerical results
We considered a synchronous DS-CDMA system with spreading gain 31 (N=31). Without loss of generality, the first user was the desired user with unity power. The background noise was zero mean AWGN with referenced to the desired user. Six MAI users were in the channel at time zero. At time n=500, another four MAI users were added to the channel. At time n=1000, two of the MAI users and three of the MAI users exited the channel. We considered two test cases:
Conclusion
A new adaptive step-size CMA algorithm is proposed for a DS-CDMA receiver. The algorithm is designed to adapt the step-size in order to minimise the CM criterion. Simulation shows the effectiveness of the algorithm in both interference cancellation in a time-varying environment and channel equalisation for a multipath fading channel. Robustness against different initial settings of the step-size is also shown.
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2014, IEEE Signal Processing LettersElectromagnetism-like method tuned constant modulus algorithm for blind detector in multicarrier CDMA system
2014, International Journal of Communication SystemsLow-complexity variable forgetting factor mechanism for blind adaptive constrained constant modulus algorithms
2012, IEEE Transactions on Signal Processing
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This research is supported by the Mahanakorn University of Technology, Bangkok, Thailand.
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With effect from 1st February 2002, Prof. Chambers will be with the Centre for Digital Signal Processing Research, Division of Engineering, King's College London, Strand, London WC2R 2LS, UK.