A New Code for High-Rate Differential Space-Time Coding

In [1], a differential space-time modulation scheme (based on unitary matrices) are presented that can be used without knowledge of the Channel State Information (CSI) at the receiver. This is suitable for mobile communication applications where fading coefficients change rapidly with time. All previous differential space-time codes have been designed to produce full diversity. However, by sacrificing the diversity, one can increase the rate per channel use of the space-time modulation [2]. For very high values of Signal-to-Noise-Ratio (SNR), the performance of multiple-antenna systems is determined by diversity product. However, maximizing the diversity product is not the appropriate criterion for high-rate communications operating in practical ranges of SNR for the case of using multiple receive antennas. Indeed, for reasonable range of SNR values, when the number of receive antennas is greater than or equal to the number of transmit antennas, the diversity sum (minimum squared Euclidean distance) is more important than the diversity product. In this paper, we present a practical sub-optimum solution to the problem of high-rate non-coherent communication over a Multiple-Input Multiple-Output (MIMO) fading channel with M transmit antennas. We use a differential transmission scheme with unitary codewords in the form of V=D1AD2 where D1 and D2 are diagonal matrices with unit-norm elements and A is a fixed unitary matrix. To have a good distance distribution for the codewords, we show that A must have equal-norm elements [3], e.g., A can be selected as the Vandermonde matrix with M’th roots of unity, i.e.,