Linear dispersion code with an orthogonal row structure for simplifying sphere decoding

In this paper, we propose a family of full diversity fast decodable Linear Dispersion Codes (LDCs) for use in MIMO systems. These codes have as many as possible the orthogonal rows in the dispersion matrices of the LDC. One of the main advantages of this family of LDCs is that it can be used in MIMO systems with arbitrary numbers of transmitted and received antennas and arbitrary transmission rates. We also develop a simplified Sphere Decoding (SD) algorithm to significantly reduce the decoding complexity for this family of LDCs. Monte Carlo simulation shows that the optimum LDCs with or without this orthogonal structure have nearly identical bit-error rate (BER) performances, but the complexity can be significantly reduced. For a 2×4 MIMO system transmitting 8 QPSK symbols in a block length of 4, the reduction is about 28-52%, and for a 3×3 MIMO system transmitting 10 QPSK symbols in a block length of 6, the reduction is about 28-49%.