Biconvex Problem Research Articles

VLSI Designs for Joint Channel Estimation and Data Detection in Large SIMO Wireless Systems

Channel estimation errors have a critical impact on the reliability of wireless communication systems. While virtually all existing wireless receivers separate channel estimation from data detection, it is well known that joint channel estimation and data detection (JED) significantly outperforms conventional methods at the cost of high computational complexity. In this paper, we propose a novel JED algorithm and corresponding VLSI designs for large single-input multiple-output (SIMO) wireless systems that use constant-modulus constellations. The proposed algorithm is referred to as PRojection Onto conveX hull (PrOX) and relies on biconvex relaxation (BCR), which enables us to efficiently compute an approximate solution of the maximum-likelihood JED problem. Since BCR solves a biconvex problem via alternating optimization, we provide a theoretical convergence analysis for PrOX. We design a scalable, high-throughput VLSI architecture that uses a linear array of processing elements to minimize hardware complexity. We develop corresponding field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) designs, and we demonstrate that PrOX significantly outperforms the only other existing JED design in terms of throughput, hardware-efficiency, and energy-efficiency.

Secrecy Sum Rate Optimization for Downlink MIMO Nonorthogonal Multiple Access Systems

Nonorthogonal multiple access (NOMA) is expected to be a promising technique for future wireless networks. In this letter, we investigate the secrecy sum rate optimization problem for a downlink multiple-input-multiple-output NOMA system that consists of a base station, multiple legitimate users, and an eavesdropper. Our objective is to maximize achievable secrecy sum rate subject to successful successive interference cancellation constraints and transmit power constraint. The formulated optimization problem is nonconvex. Motivated by the relationship between mutual information rate and minimum mean square error, we propose to transform the secrecy sum rate optimization problem into a biconvex problem. The biconvex problem is solved by alternating optimization method where in each iteration, we solve a second-order cone programming. Simulation results demonstrate that our proposed NOMA scheme outperforms conventional orthogonal multiple access scheme.

Cooperative Caching Placement in Cache-Enabled D2D Underlaid Cellular Network

In a cache-enabled D2D underlaid cellular network, cooperation of BS caching and D2D caching can further exploit the limited storage capacity and achieve more efficient wireless resource utilization. In this complex network scenario, the closed form expression for successful transmission probability is firstly derived using stochastic geometry, to measure the proportion of users satisfying the delay guarantee. On this basis, a cooperative caching placement problem is formulated to maximize the successful transmission probability. We prove it can be transformed equivalently into a biconvex problem and then a block coordinate descent based algorithm is proposed. Simulation results demonstrate the performance gain of the proposed cooperative caching placement.

Optimal Resource Allocation Policies for Multi-User Backscatter Communication Systems.

This paper considers a backscatter communication (BackCom) system including a reader and N tags, where each tag receives excitation signals transmitted by the reader and concurrently backscatters information to the reader in time-division-multiple-access (TDMA) mode. In this system, we aim to maximize the total system goodput by jointly optimizing reader transmission power, time allocation, and reflection ratio for the cases of passive and semi-passive tags. For each case, an optimization problem is formulated, which is non-convex and can be solved by being decomposed into at most N feasible sub-problems based on the priority of allocated reader transmission power. First, for the passive tags case, by solving the convex sub-problems sequentially and comparing their maximum total goodput, we derive the optimal resource allocation policy. Then, for the semi-passive tags case, we find a close-to-optimal solution, since each sub-problem can be reformulated as a biconvex problem, which is solved by a proposed block coordinate descent (BCD)-based optimization algorithm. Finally, simulation results demonstrate the superiority of the proposed resource allocation policies.

Rank constrained nuclear norm minimization with application to image denoising

In the low rank matrix approximation problem, the well known nuclear norm minimization (NNM) problem plays a crucial role and attracts significant interests in recent years. In NNM the regularization parameter λ plays a decisive part, λ controls both the rank of the solution and the extent of the thresholding. However, it is hard for a single λ to balance the two issuses, and meanwhile the solving method calls singular value decomposition (SVD), of which the computational complexity is impracticable when the scale of the problem becomes large. This paper presents a rank constrained nuclear norm minimization (RNNM) method, in which the rank and the extent of thresholding are controlled separately by an added parameter k. More importantly, by proving its equivalence with an unconstrained bi-convex optimization problem RNNM can be solved in SVD free manner. In this paper, a SOR (Successive Over Relaxation) algorithm is designed for the equivalent bi-convex problem and its convergence is proved. We show that RNNM has a unique global optimal solution although being non-convex. We explicitly analyse the structure of the solution for the bi-convex problem and show some interesting properties. Finally, we verify the effectiveness of RNNM in image denoising. Experimental results show that the proposed solving method works faster than SVD based method. Thanks to the well balance of rank and thresholding, RNNM achieves superior results than the state-of-the-art methods in image denoising such as BM3D, SAIST in terms of both quantity measure and visual quality.

Joint Robust Transmit/Receive Adaptive Beamforming for MIMO Radar Using Probability-Constrained Optimization

A joint robust transmit/receive adaptive beamforming for multiple-input multipleoutput (MIMO) radar based on probability-constrained optimization approach is developed in the case of Gaussian and arbitrary distributed mismatch present in both the transmit and receive signal steering vectors. A tight lower bound of the probability constraint is also derived by using duality theory. The formulated probability-constrained robust beamforming problem is nonconvex and NP-hard. However, we reformulate its cost function into a bi-quadratic function while the probability constraint splits into transmit and receive parts. Then, a block coordinate descent method based on second-order cone programming is developed to address the biconvex problem. Simulation results show an improved robustness of the proposed beamforming method as compared to the worst-case and other existing state-of-the-art joint transmit/receive robust adaptive beamforming methods for MIMO radar.

Multi-antenna Wireless Energy Transfer for Backscatter Communication Systems

We study RF-enabled wireless energy transfer (WET) via energy beamforming, from a multi-antenna energy transmitter (ET) to multiple energy receivers (ERs) in a backscatter communication system, such as RFID, where each ER (or RFID tag) reflects back a portion of the incident signal to the ET (or RFID reader). For such a system, the acquisition of the forward-channel (i.e., ET-to-ER) state information (F-CSI) at the ET is challenging, since the ERs are typically too energy-and-hardware-constrained to estimate or feed back the F-CSI. The ET leverages its observed backscatter signals to estimate the backscatter-channel (i.e., ET-to-ER-to-ET) state information (BS-CSI) directly. We first analyze the harvested energy obtained by using the estimated BS-CSI. Furthermore, we optimize the channel-training energy and the energy allocation weights for different energy beams, for weighted-sum-energy (WSE) maximization and proportional-fair-energy (PFE) maximization. For WET to single ER, we obtain the optimal channel-training energy in a semi-closed form. For WET to multiple ERs, the optimal WET scheme for WSE maximization is shown to use only one energy beam. For PFE maximization, we show it is a biconvex problem, and propose a block-coordinate-descent based algorithm to find the close-to-optimal solution. Numerical results show that with the optimized solutions, the harvested energy suffers slight reduction of less than 10%, compared to that obtained by using the perfect F-CSI. Hence, energy beamforming by using the estimated BS-CSI is promising, as the complexity and energy requirement is shifted from the ERs to the ET.

Penalized Classification using Fisher’s Linear Discriminant

We consider the supervised classification setting, in which the data consist of p features measured on n observations, each of which belongs to one of K classes. Linear discriminant analysis (LDA) is a classical method for this problem. However, in the high-dimensional setting where p ≫ n, LDA is not appropriate for two reasons. First, the standard estimate for the within-class covariance matrix is singular, and so the usual discriminant rule cannot be applied. Second, when p is large, it is difficult to interpret the classification rule obtained from LDA, since it involves all p features. We propose penalized LDA, a general approach for penalizing the discriminant vectors in Fisher's discriminant problem in a way that leads to greater interpretability. The discriminant problem is not convex, so we use a minorization-maximization approach in order to efficiently optimize it when convex penalties are applied to the discriminant vectors. In particular, we consider the use of L(1) and fused lasso penalties. Our proposal is equivalent to recasting Fisher's discriminant problem as a biconvex problem. We evaluate the performances of the resulting methods on a simulation study, and on three gene expression data sets. We also survey past methods for extending LDA to the high-dimensional setting, and explore their relationships with our proposal.

Biconvex programming approach to optimization over the weakly efficient set of a multiple objective affine fractional problem

We formulate the problem of optimizing a convex function over the weakly efficient set of a multicriteria affine fractional program as a special biconvex problem. We propose a decomposition algorithm for solving the latter problem. The proposed algorithm is a branch-and-bound procedure taking into account the affine fractionality of the criterion functions.