Hybrid beamforming designs for frequency-selective mmWave MIMO systems with Per-RF chain or per-antenna power constraints

Configuring precoders and combiners is a major challenge to deploy practical multiple-input multiple-output (MIMO) millimeter wave (mmWave) communication systems with large antenna arrays. Most prior work addresses the problem focusing on a total transmit power constraint. In practical transmitters, however, power amplifiers must operate within their linear range, so that a power constraint applies to each one of the input signals to these devices. Therefore, precoder and combiner designs should incorporate per-antenna or per-radio frequency (RF) chain transmit power constraints. We focus on such problem for frequency-selective channels with multicarrier modulation, and assuming hybrid analog/digital architectures based on fully connected analog blocks implemented with finite-resolution phase shifters. We first derive an all-digital solution which aims to maximize spectral efficiency. Then, we develop hybrid precoders and combiners by approximately matching the corresponding all-digital matrices while still enforcing the power constraints. Numerical results show that the proposed all-digital design performs close to the upper bound given by the standard waterfilling-based solution with a total power constraint. Additionally, the hybrid designs exhibit a moderate loss even when low-resolution phase shifters are considered.Agencia Estatal de Investigación | Ref. PID2019-105717RB-C21Xunta de Galicia | Ref. ED431C 2021/4

Fast Orthonormal Sparsifying Transforms Based on Householder Reflectors

Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative algorithms. Furthermore, the resulting transforms obtained generally lack structure that permits their fast application to data. To address this issue, this paper develops a framework for learning orthonormal dictionaries which are built from products of a few Householder reflectors. Two algorithms are proposed to learn the reflector coefficients: one that considers a sequential update of the reflectors and one with a simultaneous update of all reflectors that imposes an additional internal orthogonal constraint. The proposed methods have low computational complexity and are shown to converge to local minimum points which can be described in terms of the spectral properties of the matrices involved. The resulting dictionaries balance between the computational complexity and the quality of the sparse representations by controlling the number of Householder reflectors in their product. Simulations of the proposed algorithms are shown in the image processing setting where well-known fast transforms are available for comparisons. The proposed algorithms have favorable reconstruction error and the advantage of a fast implementation relative to the classical, unstructured, dictionaries

Algorithms for the Construction of Incoherent Frames Under Various Design Constraints

Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low coherence frames are useful in compressed sensing applications. When used as measurement matrices, they successfully recover highly sparse solutions to linear inverse problems. This paper describes algorithms for the design of various low coherence frame types: real, complex, unital (constant magnitude) complex, sparse real and complex, nonnegative real and complex, and harmonic (selection of rows from Fourier matrices). The proposed methods are based on solving a sequence of convex optimization problems that update each vector of the frame. This update reduces the coherence with the other frame vectors, while other constraints on its entries are also imposed. Numerical experiments show the effectiveness of the methods compared to the Welch bound, as well as other competing algorithms, in compressed sensing applications

Beamformer Design and Optimization for Joint Communication and Full-Duplex Sensing at mm-Waves

In this article, we study the joint communication and sensing (JCAS) paradigm in the context of millimeter-wave (mm-wave) mobile communication networks. We specifically address the JCAS challenges stemming from the full-duplex operation in monostatic orthogonal frequency-division multiplexing (OFDM) radars and from the co-existence of multiple simultaneous beams for communications and sensing purposes. To this end, we first formulate and solve beamforming optimization problems for hybrid beamforming based multiuser multiple-input and multiple-output JCAS systems. The cost function to be maximized is the beamformed power at the sensing direction while constraining the beamformed power at the communications directions, suppressing interuser interference and cancelling full-duplexing related self-interference (SI). We then also propose new transmitter and receiver beamforming solutions for purely analog beamforming based JCAS systems that maximize the beamforming gain at the sensing direction while controlling the beamformed power at the communications direction(s), cancelling the SI as well as eliminating the potential reflection from the communication direction and optimizing the combined radar pattern (CRP). Both closed-form and numerical optimization based formulations are provided. We analyze and evaluate the performance through extensive numerical experiments, and show that substantial gains and benefits in terms of radar transmit gain, CRP, and SI suppression can be achieved with the proposed beamforming methods.publishedVersionPeer reviewe