Space-time coding for the parametric fading channel

Error correction coding across multiple transmit and receive antennas has gained much attention, pioneered by the space-time coding techniques presented by Tarokh, Seshadri and Calderbank (see IEEE Trans. Information Theory, vol.44, no.2, p.3744-65, 1998). Coding gains obtained therein rely on the independence of fading of signals from different transmit antennas. In most cellular systems, fades from the closely spaced transmit antennas are highly correlated, thereby reducing coding gains. An alternative wireless channel model that takes fade correlations into account is the parametric model. Drawing upon this model we propose path coding, which is an error correction coding across multiple propagation paths. Since it is based on the physical channel, path coding is a more powerful method of exploiting naturally available diversity. We derive the exact average pair-wise error probability (PEP) for maximum likelihood decoding. The PEP is a function of the norms of error sequences on different paths. We provide an insight into minimization of the PEP subject to constraints on the total norm.