Computational complexities of sphere decoding according to initial radius selection schemes and an efficient initial radius reduction scheme

We analyze the computational complexity of sphere decoding (SD) for maximum likelihood detection (MLD) according to initial radius selection schemes, and also propose an efficient initial radius reduction scheme that reduces further the initial radius. As the initial radius for SD, we use the Euclidean distance between the received signal vector and the lattice vector corresponding to a suboptimum initial estimate. The proposed initial radius reduction scheme selects a new lattice vector closer to the received signal vector than the initial lattice vector in order to reduce the initial radius further. From our analyses, the reduction in the overall complexity due to further reduction of initial radius gets more significant as the SNR decreases. The ZF-DFE scheme in a combination with the proposed radius reduction scheme has the fewest computations over practical SNR range for communications, and its computations are less than that of the vertical Bell-labs layered space-time (V-BLAST) detection scheme with optimal ordering, even at low SNR values achieving an uncoded bit error rate (BER) of 0.1