Channel reliability metrics for flat Rayleigh fading channels without channel state information

In this work, iterative decoding of block turbo codes (BTCs) over flat Rayleigh fading channels is considered. The signal is modulated using binary phase shift keying (BPSK) and coherently detected. An exact channel reliability metric that should be passed to the iterative decoder to achieve optimum performance, when no channel state information (CSI) is available at the receiver, is developed. A low complexity cubic approximation to the exact metric, which has no performance loss, is presented. The numerical results obtained using (10, 9)² single parity check (SPC) BTC, show that the conventional approach, which uses a linear approximation to the channel reliability metric, results in a 27 dB penalty at BER of 10^-5 compared to the case where perfect CSI is available. On the other hand, the use of the proposed reliability metric outperforms the existing metric and results in only a 1.1 dB performance loss at BER of 10^-5 compared to the use of the metric when the CSI is perfectly known.