Constellations for good diversity performance

The case in which there are several channels available for transmission, and the additive noise on each channel may have different power, is treated. A signal constellation, called the coordinated code, for the signal space formed by the different channels is presented. The coordinated code has good performance when the noise powers are equal, while simultaneously providing diversity for good performance when the noise powers are unequal, and is relatively simple. The maximum-likelihood receiver is presented; it extracts information from the coded signal in inverse proportion to each channel´s noise power. The minimum distance of the code is found, and the coding gain over a system that transmits independent bit streams on each channel is derived as a function of the noise statistics. The gain of the code is also found relative to symbol splitting diversity, which transmits a copy of the same message on each channel; this gain is as high as 9 dB. The code is considered in detail for use with a high rate digital subscriber line (HDSL) comprised of two pairs of a local loop, each pair having different amounts of near end crosstalk (NEXT)