EM-based soft noncoherent equalization of doubly selective channels using tree search and basis expansion

We propose a soft noncoherent equalizer for coded transmissions over unknown time- and frequency-selective, or doubly selective, channels. Such a soft equalizer can be used in conjunction with a soft decoder as part of a turbo reception scheme. Like a number of existing designs, ours is motivated by the use of the expectation maximization (EM) algorithm to estimate the unknown channel parameters, and manifests as an iteration between soft channel estimation and soft coherent equalization. As a departure from the existing designs, which assume a Gauss-Markov (i.e., autoregressive) channel and employ a trellis whose number-of-states grows exponentially in the channel length, we use a basis expansion (BE) model for the channel and a soft tree-search in place of the trellis, leveraging recent ideas from the MIMO literature. The complexity of our schemes grows only linearly in the block length and quadratically in the number of BE coefficients. Numerical experiments show performance that is close to genie-aided bounds and robust to mismatch in channel-fading rate.