Simplified Graphical Approaches for CDMA Multi-User Detection, Decoding and Power Control
The individual optimal detector for code-division multiple-access (CDMA) systems is based on the marginal a posteriori distribution of the transmitted bits. The marginalization is in general hard since a summation is required, which grows exponentially in scope with the number of active users. Based on graphical representations of probability distribution, message-passing schemes like the belief propagation algorithm (BP) have become efficient tools for computing approximate marginal distribution. It is, however, well-known that the BP algorithm does not always converge when the graphical representation has loops. Solving the Lagrangian dual problem of minimizing the Bethe free energy using simple block nonlinear Gauss-Seidel and Jacobi algorithms correspond to serial and parallel message updating, respectively, of the BP algorithm. Using the block nonlinear Gauss-Seidel iteration, corresponding to serial updating, convergence is guaranteed since the dual of the Bethe free energy is concave.
The parallel and serial BP algorithms provide low computational alternatives for approximating the individual optimum decision for both uncoded and coded CDMA systems. Using Gaussian approximation, the large system bit error rate (BER) performance of these algorithms is closely related to the replica analysis for the individual optimal detector. Moreover, it can be shown that the parallel and serial BP algorithms converge to the same estimated large system BER performance. From the analysis of the BP algorithms, we obtain functions describing approximately the large system BER performance for multiuser detection and iterative decoding. A power control problem is formulated using these functions, aiming to minimize the total power transmitted over a given discrete set of power levels, subject to maintaining an acceptable BER performance for each user. This problem is hard, so a suboptimal algorithm is proposed, which is of polynomial computational complexity.
code-division multiple access
large system analysis