A geometry based efficient decoder for underdetermined MIMO systems

In this paper, a geometry based decoder with low decoding complexity and exact maximum-likelihood (ML) performance is proposed for underdetermined multiple-input multiple-output (MIMO) systems. In the proposed decoder, an underdetermined MIMO system can be divided into a multiple-input single-output (MISO) sub-system and a regular MIMO sub-system in which numbers of transmit and receive antennas are equal. An efficient slab search algorithm (ESSA) is adopted to efficiently obtain valid candidate points in the MISO sub-system. By adopting ESSA in the MISO sub-system and sphere decoding algorithm (SDA) in the MIMO sub-system, ML solution of underdetermined MIMO system can be obtained with low computational complexity. To further reduce the computational complexity, a near-ML SDA is proposed to more efficiently find the candidate points in the MIMO sub-system. In addition, an optimal preprocessing technique is proposed from the geometrical perspective and the comprehensive analysis on the complexity reduction is also provided. Simulation results indicate that the proposed approach significantly reduces the complexity as compared to existing ML decoders, particularly for systems with large number of antennas and/or high-order constellations.