Adaptive Quadratic-Metric Parallel Subgradient Projection Algorithm and its Application to Acoustic Echo Cancellation

Publication in the conference proceedings of EUSIPCO, Florence, Italy, 200

QoS-Aware Precoder Optimization for Radar Sensing and Multiuser Communications Under Per-Antenna Power Constraints

In this work, we concentrate on designing the precoder for the multiple-input multiple-output (MIMO) dual functional radar-communication (DFRC) system, where the dual-functional waveform is designed for performing multiuser downlink transmission and radar sensing simultaneously. Specifically, considering the signal-independent interference and signal-dependent clutter, we investigate the optimization of transmit precoding for maximizing the sensing signal-to-interference-plus-noise ratio (SINR) at the radar receiver under the constraint of the minimum SINR received at multiple communication users and per-antenna power budget. The formulated problem is challenging to solve due to the nonconovex objective function and nonconvex per-antenna power constraint. In particular, for the signal-independent interference case, we propose a distance-majorization induced algorithm to approximate the nonconvex problem as a sequence of convex problems whose optima can be obtained in closed form. Subsequently, our complexity analysis shows that our proposed algorithm has a much lower computational complexity than the widely-adopted semidefinite relaxation (SDR)-based algorithm. For the signal-dependent clutter case, we employ the fractional programming to transform the nonconvex problem into a sequence of subproblems, and then we propose a distance-majorization based algorithm to obtain the solution of each subproblem in closed form. Finally, simulation results confirm the performance superiority of our proposed algorithms when compared with the SDR-based approach. In conclusion, the novelty of this work is to propose an efficient algorithm for handling the typical problem in designing the DFRC precoder, which achieves better performance with a much lower complexity than the state-of-the-art algorithm

Skaalattu harva lineaarinen regressio elastisella verkolla

Scaled linear regression is a form of penalized linear regression in which the penalty level is automatically scaled in proportion to the estimated noise level in the data. This makes the penalty parameter independent of the noise scale enabling an analytical approach for choosing an optimal penalty level for a given problem. In this thesis, we first review conventional penalized regression methods, such as ridge regression, lasso, and the elastic net. Then, we review some scaled sparse linear regression methods, the most relevant of which is the scaled lasso, also known as square-root lasso. As an original contribution, we propose two elastic net formulations, which extend the scaled lasso to the elastic net framework. We demonstrate by numerical examples that the proposed estimators improve upon the scaled lasso in the presence of high correlations in the feature space. As a real-world application example, we apply the proposed estimators in a simulated single snapshot direction-of-arrival (DOA) estimation problem, where we show that the proposed estimators perform better, especially when the angles of incidence of the DOAs are oblique with respect to the uniform linear array (ULA) axis.Skaalattu lineaarinen regressio käsittää regularisointimenetelmiä, joissa regularisointitermin painoa skaalataan datasta estimoidun kohinatason perusteella. Tämä poistaa optimaalisen regularisointitermin riippuvuuden tuntemattomasta kohinatasosta, mikä mahdollistaa analyyttisesti johdettujen regularisointitermien käytön. Diplomityössä tarkasteltiin ridge, lasso ja elastinen verkko -regressiomenetelmien ominaisuuksia sekä skaalattuja regressiomenetelmiä, kuten skaalattua lasso- eli neliöjuurilassomenetelmää. Diplomityössä kehitettiin täysin uudet estimaattorit: skaalattu elastinen verkko ja neliöjuuri elastinen verkko, jotka toimivat paremmin kuin skaalattu lasso multikollineaarisissa tilanteissa, mikä osoitettiin numeerisilla simulaatioilla. Esimerkkinä käytännön sovelluksesta, uusia estimaattoreita sovellettiin DOA-estimoinnissa, jossa pyritään antenniryhmän avulla määrittämään signaalin tulosuunta. Saatujen tulosten perusteella voitiin päätellä, että diplomityössä ehdotetut estimaattorit pystyivät määrittämään tulosuunnan paremmin kuin skaalattu lasso etenkin, kun signaalin tulokulma oli suuri antenniryhmän akselin suhteen

Efficient Robust Adaptive Beamforming Algorithms for Sensor Arrays

Sensor array processing techniques have been an important research area in recent years. By using a sensor array of a certain configuration, we can improve the parameter estimation accuracy from the observation data in the presence of interference and noise. In this thesis, we focus on sensor array processing techniques that use antenna arrays for beamforming, which is the key task in wireless communications, radar and sonar systems. Firstly, we propose a low-complexity robust adaptive beamforming (RAB) technique which estimates the steering vector using a Low-Complexity Shrinkage-Based Mismatch Estimation (LOCSME) algorithm. The proposed LOCSME algorithm estimates the covariance matrix of the input data and the interference-plus-noise covariance (INC) matrix by using the Oracle Approximating Shrinkage (OAS) method. Secondly, we present cost-effective low-rank techniques for designing robust adaptive beamforming (RAB) algorithms. The proposed algorithms are based on the exploitation of the cross-correlation between the array observation data and the output of the beamformer. Thirdly, we propose distributed beamforming techniques that are based on wireless relay systems. Algorithms that combine relay selections and SINR maximization or Minimum Mean-Square- Error (MMSE) consensus are developed, assuming the relay systems are under total relay transmit power constraint. Lastly, we look into the research area of robust distributed beamforming (RDB) and develop a novel RDB approach based on the exploitation of the cross-correlation between the received data at the relays and the destination and a subspace projection method to estimate the channel errors, namely, the cross-correlation and subspace projection (CCSP) RDB technique, which efficiently maximizes the output SINR and minimizes the channel errors. Simulation results show that the proposed techniques outperform existing techniques in various performance metrics

Non-convex Quadratically Constrained Quadratic Programming: Hidden Convexity, Scalable Approximation and Applications

University of Minnesota Ph.D. dissertation. September 2017. Major: Electrical Engineering. Advisor: Nicholas Sidiropoulos. 1 computer file (PDF); viii, 85 pages.Quadratically Constrained Quadratic Programming (QCQP) constitutes a class of computationally hard optimization problems that have a broad spectrum of applications in wireless communications, networking, signal processing, power systems, and other areas. The QCQP problem is known to be NP–hard in its general form; only in certain special cases can it be solved to global optimality in polynomial-time. Such cases are said to be convex in a hidden way, and the task of identifying them remains an active area of research. Meanwhile, relatively few methods are known to be effective for general QCQP problems. The prevailing approach of Semidefinite Relaxation (SDR) is computationally expensive, and often fails to work for general non-convex QCQP problems. Other methods based on Successive Convex Approximation (SCA) require initialization from a feasible point, which is NP-hard to compute in general. This dissertation focuses on both of the above mentioned aspects of non-convex QCQP. In the first part of this work, we consider the special case of QCQP with Toeplitz-Hermitian quadratic forms and establish that it possesses hidden convexity, which makes it possible to obtain globally optimal solutions in polynomial-time. The second part of this dissertation introduces a framework for efficiently computing feasible solutions of general quadratic feasibility problems. While an approximation framework known as Feasible Point Pursuit-Successive Convex Approximation (FPP-SCA) was recently proposed for this task, with considerable empirical success, it remains unsuitable for application on large-scale problems. This work is primarily focused on speeding and scaling up these approximation schemes to enable dealing with large-scale problems. For this purpose, we reformulate the feasibility criteria employed by FPP-SCA for minimizing constraint violations in the form of non-smooth, non-convex penalty functions. We demonstrate that by employing judicious approximation of the penalty functions, we obtain problem formulations which are well suited for the application of first-order methods (FOMs). The appeal of using FOMs lies in the fact that they are capable of efficiently exploiting various forms of problem structure while being computationally lightweight. This endows our approximation algorithms the ability to scale well with problem dimension. Specific applications in wireless communications and power grid system optimization considered to illustrate the efficacy of our FOM based approximation schemes. Our experimental results reveal the surprising effectiveness of FOMs for this class of hard optimization problems

Regularized Estimation of High-dimensional Covariance Matrices.

Many signal processing methods are fundamentally related to the estimation of covariance matrices. In cases where there are a large number of covariates the dimension of covariance matrices is much larger than the number of available data samples. This is especially true in applications where data acquisition is constrained by limited resources such as time, energy, storage and bandwidth. This dissertation attempts to develop necessary components for covariance estimation in the high-dimensional setting. The dissertation makes contributions in two main areas of covariance estimation: (1) high dimensional shrinkage regularized covariance estimation and (2) recursive online complexity regularized estimation with applications of anomaly detection, graph tracking, and compressive sensing. New shrinkage covariance estimation methods are proposed that significantly outperform previous approaches in terms of mean squared error. Two multivariate data scenarios are considered: (1) independently Gaussian distributed data; and (2) heavy tailed elliptically contoured data. For the former scenario we improve on the Ledoit-Wolf (LW) shrinkage estimator using the principle of Rao-Blackwell conditioning and iterative approximation of the clairvoyant estimator. In the latter scenario, we apply a variance normalizing transformation and propose an iterative robust LW shrinkage estimator that is distribution-free within the elliptical family. The proposed robustified estimator is implemented via fixed point iterations with provable convergence and unique limit. A recursive online covariance estimator is proposed for tracking changes in an underlying time-varying graphical model. Covariance estimation is decomposed into multiple decoupled adaptive regression problems. A recursive recursive group lasso is derived using a homotopy approach that generalizes online lasso methods to group sparse system identification. By reducing the memory of the objective function this leads to a group lasso regularized LMS that provably dominates standard LMS. Finally, we introduce a state-of-the-art sampling system, the Modulated Wideband Converter (MWC) which is based on recently developed analog compressive sensing theory. By inferring the block-sparse structures of the high-dimensional covariance matrix from a set of random projections, the MWC is capable of achieving sub-Nyquist sampling for multiband signals with arbitrary carrier frequency over a wide bandwidth.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/86396/1/yilun_1.pd