Wei-Chiang Li

Wireless Information and Energy Transfer in Multi-Antenna Interference Channel

This paper considers the transmitter design for wireless information and energy transfer (WIET) in a multiple-input single-output (MISO) interference channel (IFC). The design problem is to maximize the system throughput subject to individual energy harvesting constraints and power constraints. It is observed that the ideal scheme, where the receivers simultaneously perform information detection (ID) and energy harvesting (EH) from the received signal, may not always achieve the best tradeoff between information transfer and energy harvesting, but simple practical schemes based on time splitting may perform better. We therefore propose two practical time splitting schemes, namely the time-division mode switching (TDMS) and time-division multiple access (TDMA), in addition to the existing power splitting (PS) scheme. In the two-user scenario, we show that beamforming is optimal to all the schemes. Moreover, the design problems associated with the TDMS and TDMA schemes admit semi-analytical solutions. In the general K-user scenario, a successive convex approximation method is proposed to handle the WIET problems associated with the ideal scheme, the PS scheme and the TDMA scheme, which are known NP-hard in general. Simulation results show that none of the schemes under consideration can always dominate another in terms of the sum rate performance. Specifically, it is observed that stronger cross-link channel power improves the achievable sum rate of time splitting schemes but degrades the sum rate performance of the ideal scheme and PS scheme. As a result, time splitting schemes can outperform the ideal scheme and the PS scheme in interference dominated scenarios.

Coordinated Beamforming for Multiuser MISO Interference Channel Under Rate Outage Constraints

This paper studies the coordinated beamforming design problem for the multiple-input single-output (MISO) interference channel, assuming only channel distribution information (CDI) known to the transmitters. Under a given requirement on the rate outage probability for receivers, we aim to maximize the system utility (e.g., the weighted sum rate, weighted geometric mean rate, and the weighed harmonic mean rate) subject to the rate outage constraints and individual power constraints. The outage constraints, however, lead to a complicated, nonconvex structure for the considered beamforming design problem and render the optimization problem difficult to handle. Although this nonconvex optimization problem can be solved in an exhaustive search manner, this brute-force approach is only feasible when the number of transmitter-receiver pairs is small. For a system with a large number of transmitter-receiver pairs, computationally efficient alternatives are necessary. Hence, the focus of this paper is the design of such efficient approximation methods. In particular, by employing semidefinite relaxation (SDR) and first-order approximation techniques, we propose an efficient successive convex approximation (SCA) algorithm that provides high-quality approximate beamforming solutions via solving a sequence of convex approximation problems. The solution thus obtained is further shown to be a stationary point for the SDR of the original outage constrained beamforming design problem. Furthermore, we propose a distributed SCA algorithm where each transmitter optimizes its own beamformer using local CDI and information obtained from limited message exchange with the other transmitters. Our simulation results demonstrate that the proposed SCA algorithm and its distributed counterpart indeed converge, and promising performance can be achieved for all the considered system utilities.

Simultaneous information and energy transfer: A Two-user MISO interference channel case

This paper considers the sum rate maximization problem of a two-user multiple-input single-output interference channel with receivers that can scavenge energy from the radio signals transmitted by the transmitters. We first study the optimal transmission strategy for an ideal scenario where the two receivers can simultaneously decode the information signal and harvest energy. Then, considering the limitations of the current circuit technology, we propose two practical schemes based on TDMA, where, at each time slot, the receiver either operates in the energy harvesting mode or in the information detection mode. Optimal transmission strategies for the two practical schemes are respectively investigated. Simulation results show that the three schemes exhibit interesting tradeoff between achievable sum rate and energy harvesting requirement, and do not dominate each other in terms of maximum achievable sum rate.

Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No-Pure-Pixel Case

In blind hyperspectral unmixing (HU), the pure-pixel assumption is well known to be powerful in enabling simple and effective blind HU solutions. However, the pure-pixel assumption is not always satisfied in an exact sense, especially for scenarios where pixels are heavily mixed. In the no-pure-pixel case, a good blind HU approach to consider is the minimum volume enclosing simplex (MVES). Empirical experience has suggested that MVES algorithms can perform well without pure pixels, although it was not totally clear why this is true from a theoretical viewpoint. This paper aims to address the latter issue. We develop an analysis framework wherein the perfect endmember identifiability of MVES is studied under the noiseless case. We prove that MVES is indeed robust against lack of pure pixels, as long as the pixels do not get too heavily mixed and too asymmetrically spread. The theoretical results are supported by numerical simulation results.

Coordinated Multicasting With Opportunistic User Selection in Multicell Wireless Systems

Physical layer multicasting with opportunistic user selection (OUS) is examined for multicell multi-antenna wireless systems. In multicast applications, a common message is to be sent by the base stations to all users in a multicast group. By adopting a two-layer encoding scheme, a rate-adaptive channel code is applied in each fading block to enable successful decoding by a chosen subset of users (which varies over different blocks) and an application layer erasure code is employed across multiple blocks to ensure that every user is able to recover the message after decoding successfully in a sufficient number of blocks. The transmit signal and code-rate in each block determine opportunistically the subset of users that are able to successfully decode and can be chosen to maximize the long-term multicast efficiency. The employment of OUS not only helps avoid rate-limitations caused by the user with the worst channel, but also helps coordinate interference among different cells and multicast groups. In this paper, efficient algorithms are proposed for the design of the transmit covariance matrices, the physical layer code-rates, and the target user subsets in each block. The system parameters are determined by maximizing the group-rate in the single-group scenario and by considering a group-rate balancing optimization problem in the multi-group scenario. To further reduce the feedback overhead, we also consider the case where only part of the users feed back their channel vectors in each block and propose a design based on the balancing of the expected group-rates.

A convex approximation approach to weighted sum rate maximization of multiuser MISO interference channel under outage constraints

This paper considers weighted sum rate maximization of multiuser multiple-input single-output interference channel (MISO-IFC) under outage constraints. The outage-constrained weighted sum rate maximization problem is a nonconvex optimization problem and is difficult to solve. While it is possible to optimally deal with this problem in an exhaustive search manner by finding all the Pareto-optimal rate tuples in the (discretized) outage-constrained achievable rate region, this approach, however, suffers from a prohibitive computational complexity and is feasible only when the number of transmitter-receive pairs is small. In this paper, we propose a convex optimization based approximation method for efficiently handling the outage-constrained weighted sum rate maximization problem. The proposed approximation method consists of solving a sequence of convex optimization problems, and thus can be efficiently implemented by interior-point methods. Simulation results show that the proposed method can yield near-optimal solutions.

Multicell Coordinated Beamforming With Rate Outage Constraint—Part II: Efficient Approximation Algorithms

This paper studies the coordinated beamforming (CoBF) design for the multiple-input single-output interference channel, provided that only channel distribution information is known to the transmitters. The problem under consideration is a probabilistically constrained optimization problem which maximizes a predefined system utility subject to constraints on rate outage probability and power budget of each transmitter. Our recent analysis has shown that the outage-constrained CoBF problem is intricately difficult, e.g., NP-hard. Therefore, the focus of this paper is on suboptimal but computationally efficient algorithms. Specifically, by leveraging on the block successive upper bound minimization (BSUM) method in optimization, we propose a Gauss-Seidel type algorithm, called distributed BSUM algorithm, which can handle differentiable, monotone and concave system utilities. By exploiting a weighted minimum mean-square error (WMMSE) reformulation, we further propose a Jocobi-type algorithm, called distributed WMMSE algorithm, which can optimize the weighted sum rate utility in a fully parallel manner. Both algorithms are shown to converge to the stationary points of the original NP-hard problems. To further provide a performance benchmark, a relaxed approximation method based on polyblock outer approximation is also proposed. Simulation results show that the proposed algorithms are significantly superior to the existing successive convex approximation method in both performance and computational efficiency, and can yield promising approximation performance by comparing with the performance benchmark.

On the endmember identifiability of Craig's criterion for hyperspectral unmixing: A statistical analysis for three-source case

Hyperspectral unmixing (HU) is a process to extract the underlying endmember signatures (or simply endmembers) and the corresponding proportions (abundances) from the observed hyperspectral data cloud. The Craigs criterion (minimum volume simplex enclosing the data cloud) and the Winters criterion (maximum volume simplex inside the data cloud) are widely used for HU. For perfect identifiability of the endmembers, we have recently shown in [1] that the presence of pure pixels (pixels fully contributed by a single endmember) for all endmembers is both necessary and sufficient condition for Winters criterion, and is a sufficient condition for Craigs criterion. A necessary condition for endmember identifiability (EI) when using Craigs criterion remains unsolved even for three-endmember case. In this work, considering a three-endmember scenario, we endeavor a statistical analysis to identify a necessary and statistically sufficient condition on the purity level (a measure of mixing levels of the endmembers) of the data, so that Craigs criterion can guarantee perfect identification of endmembers. Precisely, we prove that a purity level strictly greater than 1/√(2) is necessary for EI, while the same is sufficient for EI with probability-1. Since the presence of pure pixels is a very strong requirement which is seldom true in practice, the results of this analysis foster the practical applicability of Craigs criterion over Winters criterion, to real-world problems.

Outage constrained weighted sum rate maximization for MISO interference channel by pricing-based optimization

This paper considers beamforming designs for weighted sum rate maximization (WSRM) in a multiple-input single-output interference channel subject to probability constraints on the rate outage. We claim that the outage probability constrained WSRM problem is an NP-hard problem, and therefore focus on devising efficient approximation methods. In particular, inspired by an insightful problem reformulation, a pricing-based sequential optimization (PSO) algorithm is proposed for efficiently handling the considered outage constrained WSRM problem. We show that the proposed PSO algorithm has semi-analytical beamforming solutions in each iteration, and hence can be efficiently implemented. Moreover, the PSO algorithm upon convergence attains a point satisfying Karush-Kuhn-Tucker (KKT) conditions of the original outage constrained problem. Simulation results demonstrate that the proposed PSO algorithm not only yields competing weighted sum rate performance, but also is computationally more efficient than the existing method [1].

Multicell Coordinated Beamforming With Rate Outage Constraint—Part I: Complexity Analysis

This paper studies the coordinated beamforming (CoBF) design in the multiple-input single-output interference channel, assuming only channel distribution information given a priori at the transmitters. The CoBF design is formulated as an optimization problem that maximizes a predefined system utility, e.g., the weighted sum rate or the weighted max-min-fairness (MMF) rate, subject to constraints on the individual probability of rate outage and power budget. While the problem is non-convex and appears difficult to handle due to the intricate outage probability constraints, so far it is still unknown if this outage constrained problem is computationally tractable. To answer this, we conduct a computational complexity analysis of the outage constrained CoBF problem. Specifically, we show that the outage constrained CoBF problem with the weighted sum rate utility is intrinsically difficult, i.e., NP-hard. Moreover, the outage constrained CoBF problem with the weighted MMF rate utility is also NP-hard except the case when all the transmitters are equipped with single antenna. The presented analysis results confirm that efficient approximation methods are indispensable to the outage constrained CoBF problem.