Constructions of space-frequency codes for MIMO-OFDM systems

Constructions of space-frequency (SF) codes for MIMO-OFDM systems with n_t transmit antennas and Q subcarriers are considered in this paper. Arising from the pairwise-error-probability analysis, in addition to the rank distance criterion, the minimum column distance of (n_t times Q) SF codes serves as another benchmark in code design. Codes with larger minimum column distance are expected to have better performance. Following this observation, two code constructions are presented. The first construction is obtained by right-multiplying the code matrices in a maximal rank-distance (MRD) code by a fixed, (Q times Q) nonsingular matrix. Codes obtained from this construction are called linearly transformed MRD (LT-MRD) codes in this paper. Minimum column distance of the LT-MRD codes, when averaged over all code ensembles, is shown to meet the Gilbert-Varshamov bound. The second construction is reminiscent of the construction of the Reed-Solomon codes except that the code polynomials are now selected according to the cyclotomic cosets of the underlying field. Exact minimum rank distances and bounds on the minimal column distance of these codes are presented