Duals of linear binary space-time codes

For the quasi-static Rayleigh fading multiple-input/multiple output (MIMO) channel, we consider BPSK space-time (ST) codes with rates ≥ 1 and diversity ≤ L derived from linear binary codes where L is the number of transmit antennas. For L = 2,3 and 4, we derive conditions on both the generator matrix G and the parity-check matrix H for a code to achieve diversities 2, ..., L. we then introduce the concept of duals of linear binary-based ST codes, since a particular relationship between the conditions on G and on H shows that rate 1, diversity L and rate L - 1, diversity 2 codes are duals. Thus, a matrix G (or a matrix H) of a rate 1, diversity L BPSK ST code may also be used as the matrix H (or matrix G) of a rate L-1, diversity 2 code. Example codes for 3 and 4 antennas are given along with decoding results from simulations.