Performance of noncoherent turbo detection on Rayleigh fading channels

We are concerned with the performance of turbo codes on Rayleigh fading channels when noncoherent detection is employed. Performance of turbo codes with noncoherent detection on AWGN channels has been analyzed by E.K. Hall and S.G. Wilson (see Proc. IEEE Commun. Theory Mini-Conf, p.66-70, 1997). They compared the performance of turbo codes with the achievable information theoretic channel capacity for noncoherent detection on AWGN channels. We derive the information theoretic channel capacity for noncoherent detection on Rayleigh fading channels, and show that the noncoherent turbo decoder achieves performance close to this theoretical capacity (within 1.5 dB). We further show that the performance of noncoherent turbo decoder without the knowledge of channel fades is quite close (within 0.5 dB at 10^-5 BER) to that with perfect knowledge of the channel fades. Optimum decoding of turbo codes requires the knowledge of channel SNR. With this requirement in mind, we propose online SNR estimation schemes, based on the ratio of certain observables at the output of the noncoherent detector, which when used in the turbo decoder gives performance very close to that with perfect knowledge of channel SNR