An efficient H∞ estimation approach to speed up the sphere decoder

Maximum-likelihood (ML) decoding often reduces to solving an integer least-squares problem, which is NP hard in the worst-case. On the other hand, it has recently been shown that, over a wide range of dimensions and signal-to-noise ratios (SNR), the sphere decoding algorithm finds the exact solution with an expected complexity that is roughly cubic in the dimension of the problem. However, the computational complexity of sphere decoding becomes prohibitive if the SNR is too low and/or if the dimension of the problem is too large. In this paper, we target these two regimes and attempt to find faster algorithms by pruning the search tree beyond what is done in the standard sphere decoder. The search tree is pruned by computing lower bounds on the possible optimal solution as we proceed to go down the tree. Using ideas from H^∞ estimation theory, we have developed a general framework to compute the lower bound on the integer least-squares. Several special cases of lower bounds were derived from this general framework. Clearly, the tighter the lower bound, the more branches can be eliminated from the tree. However, finding a tight lower bound requires significant computational effort that might diminish the savings obtained by additional pruning. In this paper, we propose the use of a lower bound which can be computed with only linear complexity. Its use for tree pruning results in significantly speeding up the basic sphere decoding algorithm.