Achievable performance over the correlated Rician channel

The correlated Rician channel is a useful model for a slowly fading channel, in which the complex fading process is composed of two quadrature Gaussian processes with a given autocorrelation function. For slow fading the correlation between adjacent symbols is relatively high. The authors investigate the achievable error probabilities over the channel, employing coherent detection and ideal side information on the realization of the fading processes at the receiver. An underlying decoding delay constraint which precludes the use of (ideal) interleaving is assumed. Coded BPSK performance is addressed both with and without the piecewise constant approximation (according to which the fading value remains constant during the symbol duration). For the latter case, that is no piecewise constant approximation, the analysis relies on the Fredholm determinant associated with the fading process autocorrelation function. The authors focus on the exponentially correlated channel. The “worst case” pairs of codewords are identified. The exponential behavior of the error probability with random coding (and i.i.d. Gaussian inputs) is analyzed, and the behavior of the cut-off rate and capacity is addressed. The results enhance the insight to the effect of the basic parameters governing the performance and these are examined in view of previous works and compared to relevant performance results for the block-fading channel model