Abstract: In this paper, we regard as a coded transmission over a
frequency-selective channel. We plan to study analytically the
convergence of the turbo-detector using a maximum a posteriori
(MAP) equalizer and a MAP decoder. We demonstrate that the
densities of the maximum likelihood (ML) exchanged during the
iterations are e-symmetric and output-symmetric. Under the Gaussian
approximation, this property allows to execute a one-dimensional
scrutiny of the turbo-detector. By deriving the analytical terminology
of the ML distributions under the Gaussian approximation, we confirm
that the bit error rate (BER) performance of the turbo-detector
converges to the BER performance of the coded additive white
Gaussian noise (AWGN) channel at high signal to noise ratio (SNR),
for any frequency selective channel.