Complexity analysis of MIMO sphere decoder using radius choice and increasing radius algorithms

Maximum Likelihood (ML) detection is the optimum method for decoding the received signal vector in communication systems. Its complexity increases with the number of antennas and the constellation size. Sphere Decoding (SD) is an alternate for ML detection. Although SD significantly reduces the complexity of MIMO-ML decoding, its complexity remains too high to apply it for practical systems. As the radius determines the volume of the hyper sphere, choosing a proper radius can be helpful in further reducing the complexity of SD. It provides optimal or suboptimal performance with reduced complexity, as it searches the points which are within the specified radius of the hypersphere. The complexity of the sphere decoder depends on the initial radius selection of the sphere to begin the search process and to update the radius, when no points are found in the specified radius. A look up table of initial search radius is generated using Radius Choice Algorithm. The SD uses this LUT to consider the initial search radius for further processing. The Increasing Radius Algorithm (IRA) is used for updating the radius. The radii of spheres in which expected number of points are some predefined values are obtained. Then using these radii the search begins with IRA. The simulations are performed for constellation size of 4-QAM and 16-QAM with antenna size of 4X4 and 8X8 MIMO. It is shown that the average number of floating point operations are reduced by an amount of 35% at lower SNR values till 5 dB by reducing the number of nodes visited, without degrading the performance.