The effect of LLR clipping to the complexity of list sphere detector algorithms

The optimal detection for coded system requires the use of a maximum a posteriori (MAP) detection. A list sphere detector (LSD) can be used to approximate the MAP detector. Depending on the used list size, LSD provides a tradeoff between the performance and the computational complexity. The LSD output candidate list is used to calculate the approximation of the probability log-likelihood ratio (LLR) of each transmitted bit. The list should be large enough and it should include at least one candidate for both possible bits for good approximation. The use of a small list size causes inaccurate and, especially, very large LLRs that prevent the decoder from correcting the falsely detected signals and, thus, degrades performance. We study the effect of the LLR clipping to the performance and complexity of the LSD algorithm. We show that by limiting the dynamic range of the LLR the required LSD list size can be decreased, and, thus, the complexity of the algorithms is decreased. The optimal dynamic range values for LLR clipping are determined and the effect of the clipping to the complexity of the LSD algorithms is analyzed.