Communication over doubly selective channels: Efficient equalization and max-diversity precoding

We consider the problem of practical communication over a doubly selective (DS) channel, i.e., a time and frequency selective channel. The problem is approached in two different ways: coherent communication and noncoherent communication, and for each communication scheme we propose practical and near-optimal equalizers and maximum-diversity precoders. Toward these ends, we adopt (1) basis expansion (BE) modeling of the channel, which allows for an efficient and unified way of describing a DS channel in both time and frequency domain; and (2) tree-search algorithms (TSAs), which facilitate near-optimal performance with low complexity.;For practical coherent communication, we focus on the pulse-shaped (PS) multicarrier modulation (MCM), where controlled inter-symbol-interference (ISI) and intercarrier- interference (ICI) can be leveraged for computationally efficient receiver structures. Then, we propose a novel channel adaptive TSA with a novel fast minimum mean-squared error (MMSE) generalized decision-feedback equalizer (GDFE) preprocessing, and a rank-reduced channel estimation by using the BE channel model. Also, a new finding about optimality of MMSE-GDFE preprocessing is presented, which states that under constant modulus constellation the minimum distance property is preserved by the MMSE-GDFE preprocessing.;Then, two practically realizable noncoherent equalization schemes are proposed: a sequential algorithm and a Bayesian expectation maximization (EM)-based algorithm. The sequential algorithm is derived from the optimal noncoherent metric, and made practical by a fast algorithm and a TSA to evaluate and search over the metric. The Bayesian EM-based noncoherent algorithm is derived from optimal maximum a posteriori (MAP) estimation of the BE parameters, and efficiently implemented via iteration between soft coherent equalizer and soft channel estimator. Efficient operations are accomplished using fast algorithms whose overall complexities grow linearly in the block size and quadratically in the number of BE parameters. Also, we demonstrate that the noncoherent equalization can be readily applied to the communication problem in a highly spread underwater acoustic channel (UAC).;Finally, we establish maximum-diversity conditions for each affine and linear precoder, which imply that under some mild channel assumptions almost any random affine (linear) precoder facilitates the maximum-diversity noncoherent (coherent) reception.