Further results on the sphere decoder

The fast development of digital communications hardware allows for the application of very powerful algorithms at the expense of a small increase in complexity compared to the traditionally implemented algorithms. In this paper we give further results on the sphere decoder (SD) algorithm, and its applications to a broad range of digital communications problems related to the separation of m independent sources by n sensors. First, we discuss practical implementation issues and propose an efficient method to initialize the SD parameters based on computing an estimate of the packing radius of the lattice. We relate the initializing method to the expected performance of the SD, and show that at high SNR, one obtains near optimum performance. The complexity of the SD is then shown to be much less than the upper bound on the complexity of the Fincke and Pohst (1985) algorithm for the problem of finding short length vectors in an m-dimensional lattice. Simulations show that the SD of an m-dimensional lattice needs at most O(m^4.5 ) arithmetic operations at low SNR, and O(m³) at high SNR. The obtained results offer a very powerful tool to reach near the maximum likelihood (ML) decoding performance in several cases such as lattice codes decoding over the Gaussian and Rayleigh fading channels, multiuser detection, uncoded multi-antenna systems detection and space-time codes decoding, and vector quantization