Iterative multiuser detection and error control code decoding in random CDMA

The combination of forward-error control (FEC) coding with code-division multiple access (CDMA) using random spreading sequences is considered. Such systems can be viewed as serially concatenated, and iterative (turbo) decoding principles can be applied. An analysis of the component systems is presented by studying variance input-output behaviors. Soft symbols are derived from the FEC decoders' extrinsic information outputs. A variance measure of the error of these soft symbols is used in a variance transfer (VT) analysis between component systems to give an accurate description of the convergence properties of the iterative joint decoder. This VT analysis is applied to three CDMA interference resolution component-systems: 1) simple interference cancellation; 2) per-user minimum-mean-square-error (MMSE) cancellation; and 3) a low-complexity multistage method that is proposed to approximate the complex MMSE filter. Closed-form equations for large-scale systems are presented for all three filters as the number of users K→∞. It is shown that per-user MMSE filtering has a spectral advantage of 1+1/α over simple matched filtering, where α is the system load supported by the latter, and the multistage filter can approach the MMSE performance with a few stages. Moreover, the number of filter stages to achieve a certain performance is independent of the number of users. The impact of the FEC systems is studied, and it is shown that for low signal-to-noise ratios (SNRs) powerful concatenated codes are required, while for higher SNRs, simple single-error control codes support higher system loads. FEC code examples and simulation results are presented and put in contrast with the capacity limits of the random CDMA channel.