A Simple and Optimum Geometric Decoding Algorithm for MIMO Systems

Geometric decoding (GD) is a newly proposed decoding technique for multiple-input multiple-output (MIMO) transmission over the fading channels. With a complete search on all symbol vectors in the lattice structure, GD requires about the same decoding complexity to achieve the same optimum block-error rates (BLERs) as that of ML decoding. In this paper, we propose a simple implementation of GD for optimum decoding of MIMO transmission. The GD decoder uses the channel matrix to construct a hyper paraboloid and the zero forcing solution to obtain a hyper ellipsoid projected from the hyper paraboloid. It then restricts the search among the symbol vectors within the hyper ellipsoid. Computer simulation studies on 2times2, 3times3 and 4times4 MIMO systems transmitting 8PAM and 16QAM show that the proposed GD algorithm can achieve the same BLERs as those of the ML decoders, yet having complexity reduction of more than 90%.