CONSTELLATIONS FOR GOOD DIVERSITY PERFORMANCE

Consider the case where there are several channels available for trans mission, and the additive noise on each channel may have different pow er. This paper presents a signal constellation, called the ''coordinat ed 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 th e noise powers are unequal. The code is also relatively simple. The ma ximum likelihood receiver is presented; it extracts information from t he coded signal in inverse proportion to each channel's noise power. T he minimum distance of the code is found and the coding gain over a sy stem that transmits independent bit steams on each channel is derived as a function of the noise statistics. The gain of the code is also fo und 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 co de 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 g ain is derived for HDSL using a gamma probability distribution for NEX T loss.