Nitin Jonathan Myers

Nitin Jonathan Myers

Recovering sparse signals from their subsampled Fourier representation is an important problem in communications, radar, and imaging. In this letter, we focus on reconstructing sparse 2D signals (matrices) under the constraint that only a fixed number of entries can be sampled from each channel, e.g., a row or a column in the Fourier domain. For a specified per-channel readout budget, we derive a lower bound on the mutual coherence of the corresponding compressed sensing matrix. We show that our bound is larger than the classical Welch bound, due to a limited readout budget. We also construct deterministic subsampling patterns that attain this bound for a class of matrix dimensions and readout budgets, and benchmark them against random subsampling through simulations.

Yuyang Wang, Nitin Jonathan Myers, Nuria González-Prelcic et al.

Millimeter wave vehicular channels exhibit structure that can be exploited for beam alignment with fewer channel measurements compared to exhaustive beam search. With fixed layouts of roadside buildings and regular vehicular moving trajectory, the dominant path directions of channels will likely be among a subset of beam directions instead of distributing randomly over the whole beamspace. In this paper, we propose a deep learning-based technique to design a structured compressed sensing (CS) matrix that is well suited to the underlying channel distribution for mmWave vehicular beam alignment. The proposed approach leverages both sparsity and the particular spatial structure that appears in vehicular channels. We model the compressive channel acquisition by a two-dimensional (2D) convolutional layer followed by dropout. We design fully-connected layers to optimize channel acquisition and beam alignment. We incorporate the low-resolution phase shifter constraint during neural network training by using projected gradient descent for weight updates. Furthermore, we exploit channel spectral structure to optimize the power allocated for different subcarriers. Simulations indicate that our deep learning-based approach achieves better beam alignment than standard CS techniques which use random phase shift-based design. Numerical experiments also show that one single subcarrier is sufficient to provide necessary information for beam alignment.