Generalized APP Detection for Communication over Unknown Time-Dispersive Waveform Channels
The principle of transmitting time-equidistant pulses to carry discrete information is fundamental. When the pulses overlap, intersymbol interference occurs. Maximum-likelihood sequence detection of such signals observed in additive white Gaussian noise (AWGN) was known in the early 1970s. Due to distortion and multipath propagation, it is less artificial to assume that the received pulse shape is unknown to the receiver designer, and in this thesis, the channel is modeled as an unknown (and time-dispersive) linear filter with AWGN. First, we discuss how the conventional optimal front-end (based on the notion of a sufficient statistic and matched filtering) is inappropriate in this context. We revisit continuous time in order to derive an equivalent vector channel, and an alternative optimality criterion is reviewed. Moreover, we present an optimal sequence detector that performs joint estimation/detection by employing the generalized maximum-likelihood technique, and it is seen how such a detector relies on an exhaustive tree search. Pruning the optimal search tree leads to a suboptimal complexity-constrained algorithm, where only a subset of all sequences are evaluated as candidates. These elementary ideas are subsequently extended to the case of blind (or semiblind) soft decision detection, which also incorporates the concept of bi-directional estimation. The soft decisions are generated in the form of approximate a posteriori probabilities (APPs), and their soundness is evaluated by considering iterative detection of interleaved serially concatenated codes.