  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 $\frac{2a}{2^a}$ complex
symbols per channel use (cspcu) for $2^a$ number of transmit antennas
\cite{KSR}. 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 $\frac{3(a-1)}{2^{a}}$ and $\frac{4(a-1)}{2^{a}}$ 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.
