In this paper, we aim to obtain optimal space-time trellis codes and propose novel methods for reducing the highly growing full code search. We show that by exploiting the symmetry in the QAM and PSK constellations, the number combinations in the generator matrix of the encoder can be halved. We also show that for the same set of columns of the generator matrix, interchanging the columns give identical results hence reducing the full code search by the factorial of the number of transmit antennas. Using the suggested methods, we obtain novel space-time codes for slow Rayleigh fading environments and evaluate their performance by simulation, described by frame error probabilities. Furthermore, the performance of the obtained novel codes is evaluated in a multi-user code division multiple access (CDMA) system
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