Noncoherent Coded Modulation for Fading Channels

| Coded modulation for noncoherent transmission over slowly time{variant at fading channels without channel state information is considered. We focus on di erentially encoded M{ary PSK with multiple{symbol di erential detection (MSDD). Interleaving of blocks of symbols is used as a compromise between the con icting requirements of exploiting the channel coherence time and providing diversity for decoding. We study multilevel coding (MLC) which is perfectly matched to the overall vector channel. As already well{known for coherent transmission, properly designed MLC is proved to be asymptotically optimum in the noncoherent case, too. A favorable strategy for labeling of signal points is given. As a promising alternative to MLC, bit{interleaved coded modulation (BICM) is addressed. But since no Gray labeling is possible, BICM can only marginally bene t from MSDD. Conversely, in case of strict decoding delay constraints, MLC su ers from component codes with very short code length. To overcome this drawback, we propose hybrid coded modulation schemes, which are able to combine the advantages of MLC and BICM, respectively. For performance assessment, we evaluate both the achievable channel capacity and the random coding exponent associated with noncoherent coded modulation. Moreover, we show that in multilevel coding and multistage decoding (MSD) the complexity of MSDD can be reduced signi cantly. Remarkably, the performance gain of MSDD can be exploited almost completely with practically no increase in computational complexity compared to conventional di erential detection.