Space-time constellation-rotating codes maximizing diversity and coding gains

We apply algebraic number theoretic tools to design linear space-time constellation-rotating (ST-CR) block codes. With an arbitrary number of M transmit- and N receive-antennas, our ST-CR designs achieve 1 symbol/second rate and enjoy maximum diversity gains MN over quasi-static fading channels. When M is an Euler number φ(P) for P ≢ 0 (mod 4), or, when M = 2^m for some positive integer m, the designed ST-CR precoders also maximize coding gains over QAM constellations. When M takes other integer values, we construct a method to design precoders with large coding gains that can be computed explicitly. Simulations corroborate our theoretical findings.