Sphere-constrained ML detection for channels with memory

The maximum-likelihood (ML) detection problem for channels with memory is investigated. The Viterbi algorithm (VA) provides an exact solution. Its computational complexity is linear in the length of the transmitted sequence but exponential in the channel memory length. Hence, the VA can be computationally inefficient when employed for detection on long channels. On the other hand, the sphere decoding (SD) algorithm also solves the ML detection problem exactly and has expected complexity which is polynomial (often cubic) in the length of the transmitted sequence over a wide range of signal-to-noise ratios (SNR). We combine the sphere-constrained search strategy of SD with the dynamic programming principles of the VA. The resulting algorithm has the worst-case complexity of the VA, but often significantly lower expected complexity.