An iterative approximate MAP symbol estimator for uncoded synchronous CDMA

This paper proposes an iterative algorithm for multiuser detection in uncoded synchronous code division multiple access communication systems based upon an approximate maximum a posteriori (MAP) formulation. For symbol estimation in the continuous domain, direct use of the a priori symbol distribution in the estimation process is prohibited because it is not differentiable. The proposed algorithm approximates the discrete finite alphabet symbol distribution by a sum of continuous Gaussian distributions centered at the true values of the symbol constellation. This approximation allows the development of a gradient-based iterative MAP estimator that employs the structure of the particular symbol constellation to improve estimation accuracy. Although iterative, the proposed method does not use a tentative solution from another multiuser detector. Simplifications of the proposed algorithm for constant modulus modulation and its special forms for M-ary phase-shift keying are given. Also, an optimum step size is derived to achieve fast convergence. The performance of the proposed algorithm is shown to outperform other well-known multiuser detectors such as minimum mean square error, the decorrelator, and the multistage hard-decision parallel interference canceller, especially for the near/far scenario.