Innovations-based MAP detection for time-varying frequency-selective channels

By using the innovations process, this paper provides a unification and extension of the existing maximum a posteriori (MAP) detectors (MAPDs). The practically important topics of linear modulations, time-varying frequency-selective channels, differential phase detection, and fractional sampling are accounted for. The MAPDs are derived under different conditions of optimality and a priori knowledge as follows: when the MAP criterion is applied to the constellation mapper's input bits or output symbols, when all observations or only a fixed number of future observations (i.e., fixed-lag MAPDs) from a transmission are available, when the time-varying channel impulse response is perfectly known, and when only the Gaussian-distributed channel's mean and autocovariance and the noise variance are known. As these quantities are actually unknown, their estimation in the context of MAP detection is also discussed. The MAPDs are characterized through simulation and a novel, unified analysis. Although MAPDs are less suited to hardware implementation than the traditional maximum-likelihood sequence detectors, the MAPDs can accept nonuniform a priori bit or symbol probabilities and provide soft outputs. In this way, the MAPDs are well suited to iterative decoding, and so they will become increasing integral to high-performance receiver designs.