Non-orthogonal full rank space-time block codes over Eisenstein-Jacobi integers for MIMO systems

In this work we present a full rank Space Time Block Codes with Non-orthogonal designs designated as NSTBCs constructed from cyclic codes over GF(q
^m
). Rank-Preserving Eisenstein-Jacobi map is employed to map the codewords over finite field to codewords over complex field. A generalized procedure for designing NSTBCs for MIMO system containing N
_t
Transmit antennas and N
_r
receive antennas is obtained. The computational complexity of the MIMO system employing the presented NSTBC with ML detection has been derived and an upper bound on the average probability of error is presented. It is shown that under quasi-static Rayleigh flat fading channel conditions at an ABER of 10
^-4
the proposed NSTBC MIMO system provides a gain of approximately 3 dB in compared with C (4,2,4) code.