The study of sphere radius based on multiple symbol differential unitary space-time system

To solve the problem of high complexity for multiple symbol differential detection (MSDD), a series sub-superior detect algorithms have been proposed at present, wherein the depth-first sphere decoding is a classical algorithm whose performance approximates to the maximum likelihood detection. But it still has high computing complexity, and the pipeline and parallel operations are very difficult, so it is impossible to use widely in practice. At present the sphere decoding reduces complexity mainly by two ways: First, choosing the appropriate radius, second, combining with the K-Best algorithm, but the latter will cause some loss of performance. This paper focuses on the former, and researches two low-complexity radiuses based on the width-first tree detection. The performances of sphere decoding with two radiuses and maximum likelihood detection are compared. The simulation results show that the performances of the three are very similar at the low SNR, but as the SNR increased, the maximum likelihood is superior to the performance of nonlinear radius, nonlinear radius is better than linear radius, but the gap is smaller than 0.5dB. Complexity analysis shows that the complexity of sphere decoding with the appropriate radiuses can reduce a lot compared with maximum likelihood detection.