Outage Performance Analysis and Code Design for Three-Stage MMSE Turbo Equalization in Frequency-Selective Rayleigh Fading Channels

This paper analyzes the outage performance of soft-cancellation frequency-domain minimum-mean-square error (SC FD-MMSE) turbo equalization in a serially concatenated coded modulation scheme over frequency-selective Rayleigh fading channels with exponential delay-power profile. The convergence behavior of this iterative three-stage system is evaluated with the aid of correlation charts. Based on the convergence characteristic of the equalizer and the inner and outer channel decoders, we derive a simple closed-form approximation on the outage probability of the turbo receiver. In particular, using a union-bounding technique and a specific central limit theorem, it is shown that the outage probability can be well approximated by a sum of complementary Gaussian error functions. A design criterion based on the resultant analytical expression is then proposed to construct outer encoders that minimize the outage probability of three-stage turbo systems employing irregular recursive convolutional (IRC) codes. We provide examples of optimized IRC-based outer encoders and investigate by simulation the performance improvement obtained by optimized IRC-coded turbo equalization over turbo equalization using regular recursive convolutional codes. Numerical results of outage performance simulations in channels with different delay-power profiles are presented to verify the analysis.