Design of space-time codes achieving generalized optimal diversity

In this paper, we propose a generalized structure for constructing space-time codes (STCs), which achieves generalized optimum diversity (GOD). A GOD class of STCs can achieve the full diversity and an optimized coding gain with minimum delay for any number of transmit antennas (N_t) and any rate (R), if the rate is less than or equal to the rank of the channel matrix. The structure combines mutually exclusive R data symbols with complex weights at each transmit antenna and the same set of data symbols is repeated at every time slot in a code block, but is transmitted through different transmit antennas with different sets of complex weights. In addition, it does not need any restrictions to the complex weights, thus the code can be designed with the maximum degrees of freedom. Optimized codes based on the proposed structure are obtained under the well-known rank and determinant criteria by applying two design constraints in order to reduce the design complexity. Even using two constraints, however, the proposed structure has an unaffordable design complexity when the number of complex weights gets larger. Hence, we provide some guidelines for code design, which can further reduce the design complexity by examining the characteristics of the determinant of codeword difference matrices