Maximum rate of 3- and 4-real-symbol ML decodable unitary weight STBCs

It has been shown recently that the maximum rate of a 2-real-symbol (single-complex-symbol) maximum likelihood (ML) decodable, square space-time block codes (STBCs) with unitary weight matrices is 2a/2^a complex symbols per channel use (cspcu) for 2^a number of transmit antennas [1]. These STBCs are obtained from Unitary Weight Designs (UWDs). In this paper, we show that the maximum rates for 3- and 4-real-symbol (2-complex-symbol) ML decodable square STBCs from UWDs, for 2^a transmit antennas, are 3(a-1)/2^a and 4(a-1)/2^a cspcu, respectively. STBCs achieving this maximum rate are constructed. A set of sufficient conditions on the signal set, required for these codes to achieve full-diversity are derived along with expressions for their coding gain.