Maximum rank distance codes as space-time codes

The critical design criterion for space-time codes in asymptotically good channels is the minimum rank between codeword pairs. Rank codes are a two-dimensional matrix code construction where by the rank is the metric of merit. In the following, we look at the application of rank codes to space-time code design. In particular, we provide construction methods of full-rank codes over different complex signal constellations, for arbitrary numbers of antennas, and codeword periods. We also derive a Singleton-type bound on the rate of a code for the rank metric, and we show that rank codes satisfy this bound with equality.