A Frame-Theoretic Scheme for Robust Millimeter Wave Channel Estimation

Abstract

We propose a new scheme for the robust estimation of the millimeter wave (mmWave) channel. Our approach is based on a sparse formulation of the channel estimation problem coupled with a frame theoretic representation of the sensing dictionary. To clarify, under this approach, the combined effect of transmit precoders and receive beamformers is modeled by a single frame, whose design is optimized to improve the accuracy of the sparse reconstruction problem to which the channel estimation problem is ultimately reduced. The optimized sensing dictionary frame is then decomposed via a Kronecker decomposition back into the precoding and beamforming vectors used by the transmitter and receiver. Simulation results illustrate the significant gain in estimation accuracy obtained over state of the art alternatives. As a bonus, the work offers new insights onto the sparse mmWave-multiple-input multiple-output (MIMO) channel estimation problem by casting the trade-off between correlation and variation range in terms of frame coherence and tightness.Index Terms-mmWave channel estimation, Compressed Sensing, complex incoherent tight frames, basis pursuit denoising.

Frame Theory and Fractional Programming for Sparse Recovery-Based mmWave Channel Estimation

“…However, the latter approach is also unfortunately not feasible, since in practice the measurement matrix affecting the channel estimation must be constructed as a result of the Tx and Rx beamforming, as indicated in equation (9). We have shown in [2] that OPT can be decomposed into a pair of corresponding beamforming matrices U and V via a Kronecker decompoistion, but that approach yields results inferior to the one to be presented subsequently in this article, and therefore is omitted here.…”

“…Based on the previous assumptions and equations, a linear system plainly formulating the mmWave channel estimation problem is obtained by vectorizing equation (1) in light of equation (2), yielding…”

“…In response to the latter, we proposed in [1] a mmWave channel estimation algorithm employing 1 -reweighted BPDN method [25] for recovery, with sensing matrices optimized as Parseval tight frame (PTF) [26], which was shown to yield significant NMSE gains over the classic OMP-based alternatives. That work was later improved in [2], [3] by the integration of a more effective scheme to design low-coherence sensing matrices based on the extension of the method proposed in [27].…”

Grant-Free Access via Bilinear Inference for Cell-Free MIMO With Low-Coherence Pilots

“…We therefore consider instead a convex optimization based construction method recently proposed in [55], [56] and further developed in [57], [58]. Such a low-coherence unit-norm tight frame with arbitrary dimensions can be obtained by taking advantage of an iterative method, referred to as sequential iterative decorrelation via convex optimization (SIDCO) [55], whose extension to the complex space -dubbed as complex SIDCO (CSIDCO) [56] -has been studied, where the strategy to minimize the mutual coherence is to solve iteratively (i.e., for different τ) the following convex optimization problem:…”

“…Aiming at real-time processing of convex optimization problems, the authors in [62] have developed an automatic low-level code generator for conic programming problems, which solves convex problems with moderate size on the order of microseconds or milliseconds, although it is limited to quadratic program (QP)-representable convex problems. In light of the above, for the sake of completeness, equation (9) was transformed in [57], [58] into the following quadratic program.…”