Some Goad Block PSK Real Number Codes for Rayleigh Fading Channels

Absmct- PSK real number codes for the Rayleigh fading channel were proposed in [I]. This paper tabulates the detailed mapping of sc*me simple full-diversity low-delay codes in the original and the manually refined forms. The performance is examined by simulation at various interleaving depths. For the codes considered, the manually refined ones are found to be easy to implement and offer very little performance loss compared with the original. I. INTRODUCrION Optimum coded modulation design for mobile wireless channels which typically experience severe RayleighRician fading is a topic of continued research. The lengthy burst errors caused due to the Occurrence of deep fades, particularly at slow mobile speeds, results in the performance of coded modulation schemes being worse than that of uncoded modulation, even when significant interleaving depths are employed. For Rayleigh fading channels, it has been shown that, using coherent maximum likelihood sequence estimation with known channel information, the pairwise error probability of the coded modulation schemes depends greatly on the degree of time-diversity [24] instead of squared Euclidean distance. Although many BCM codes for Rayleigh fading channels [e.g. 5-91 have Already been designed based on criteria such as increased diversity, their diversity length is still less than the codeword length. To achieve a given diversity length, longer channel codewords are used, which leads to increased interleaving delay. Block real number coding was introduced in [I] as a generalization of Block Coded Modulation (BCM). It uses a new design method and more accurate design criteria to search for the optimal code in the expanded code space. The codes so obtained are found to be able to provide full diversity for the Rayleigh fading channel. In this paper, we choose a few good full diversity low-delay low-complexity codes found in [l] for further investigation. The detailed mapping tables of the codes are presented; the manual refinements of the numerical solution are conducted; the performance of the codes are simulated for different interleaving depths in the Rayleigh faded channel