Abstract—The idea of adaptive state allocation (ASA) algorithm is used in this paper to substantially reduce the computational com- plexity of the maximum-likelihood sequence detection and estima- tion (MLSD/MLSDE) receiver without a significant degradation in its performance. In the ASA algorithm, the total number of states assigned to the trellis and the number of states selected from the entire set are changed adaptively based on the short-term power of the channel impulse response (CIR) or its estimate. The ASA algorithm is a combination of two methods: adaptive threshold (AT) and adaptive state partitioning (AP). In the AT method, a threshold value is formulated based on the probability of removing the correct state in the trellis diagram. At each time, only the paths whose costs are less than the minimum cost (corresponding to the best survivor path) plus the threshold value are retained and are extended to the next trellis stage. The AT method significantly reduces the computational complexity of the regular MLSDE mostly at high signal-to-noise ratio (SNR) with a negligible loss in performance. Simulation results for fading channels show that the AT method typically selects one trellis state (the minimum possible number of states) at high SNRs. In the AP method, the branch metrics are fused and diffused adaptively by using the Kullback–Leibler (KL) distance metric invoked for quantifying the differences between the probability density functions of the correct and incorrect branch metrics in the trellis. The adaptation is done such that the channel coefficients with short-term power less than a threshold are assumed to be zero in computing the branch metrics. The AP method decreases the computational complexity of the regular MLSDE at low SNRs.

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