CONSTELLATIONS FOR GOOD DIVERSITY PERFORMANCE

Consider the case where there are several channels available for transmission, and the additive noise on each channel may have different power. This paper presents a signal constellation, called the ''coordinated code,'' for the signal space formed by the different channels. 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. The code is also 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 steams 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 described in detail for use with a high rate digital subscriber line (HDSL), which is comprised of two pairs of a local loop, and each pair has different amounts of near end crosstalk (NEXT). The coding gain is derived for HDSL using a gamma probability distribution for NEXT loss.