In this paper, a theoretical framework of divergence minimization (DM) is applied to derive iterative receiver algorithms for coded CDMA systems. The DM receiver obtained performs joint channel estimation, multiuser decoding, and noise- covariance estimation. While its structure is similar to that of many ad-hoc receivers in the literature, the DM receiver is the result of applying a formal framework for optimization without further simplifications, namely the DM approach with a factorizable auxiliary model distribution. The well-known expectation- maximization (EM) algorithm and space-alternating generalized expectation-maximization (SAGE) algorithm are special cases of degenerate model distributions within the DM framework. Furthermore, many ad-hoc receiver structures from literature are shown to represent approximations of the proposed DM receiver. The DM receiver has four interesting properties that all result directly from applying the formal framework: (i) The covariances of all estimates involved are taken into account, (ii) The residual interference after interference cancellation is handled by the noise-covariance estimation as opposed to by LMMSE filters in other receivers, (iii) Posterior probabilities of the code symbols are employed rather than extrinsic probabilities, (iv) The iterative receiver is guaranteed to converge in divergence. The theoretical insights are illustrated by simulation results.

This paper deals with a novel design approach for a converging iterative receiver for coded CDMA that estimates both the channel coefficients and the transmitted symbols. The receiver design is based on the variational Bayesian space-alternating generalized expectation-maximization (VB-SAGE) method. Conceptually, the probability distribution of each user's code sequence and the probability distribution of all channel coefficients are updated in an iterative fashion. The obtained receiver, which we refer to as VB-SAGE receiver, performs iterative channel estimation, interference cancellation and single-user decoding. Even though the design is based on code sequence probabilities, only the soft decisions (mean values) and the variances of the code symbols are required for channel estimation and interference cancellation; moreover, the variances are functions of the soft decisions. These soft decisions are computed by the single-user decoders based on the outputs of the interference cancellation device. The iterative process of the VB-SAGE receiver is guaranteed to converge in the free energy. The VB-SAGE method proposed in this paper may also be used for other applications.

In this paper, the space alternating generalized expectation-maximization (SAGE) method is applied to derive receivers for coded CDMA systems. In the so-called SAGE receiver, hard decision code symbols are fed back from the single user decoders to the joint channel estimator and interference canceler. Using multivariate Gaussian approximations, the SAGE receiver is then modified such that soft values of code symbols are fed back from the single user decoders. We refer to this modified receiver as SAGE-based receiver. Compared to the SAGE receiver, the SAGE-based receiver considers the statistical properties of the code symbols, thus the channel estimation and the interference cancellation take symbol estimation errors into account. A performance improvement in terms of bit error rate (BER) and system load of the SAGE-based receiver compared to the SAGE receiver and other receivers is shown by means of Monte Carlo simulations.