This paper studies linear transmit filter design for Weighted Sum-Rate (WSR) maximization in the multiple input multiple output broadcast channel (MIMO-BC). The problem of finding the optimal transmit filter is non-convex and intractable to solve using low complexity methods. Motivated by recent results highlighting the relationship between mutual information and minimum mean square error (MMSE), this paper establishes a relationship between weighted sum-rate and weighted MMSE in the MIMO-BC. The relationship is used to propose two low complexity algorithms for finding a local weighted sum-rate optimum based on alternating optimization. Numerical results studying sum-rate show that the proposed algorithms achieve high performance with few iterations.

/pdf/weighted-sum-rate-maximization-using-weighted-mmse-for-mimo-54pjebubbu.pdf

Weighted sum-rate maximization using weighted MMSE for MIMO-BC beamforming design

Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results

Random Matrix Methods for Wireless Communications

In this chapter we deal with the following nonlinear fractional programming problem: 

$$P:\mathop{{\max }}\limits_{{x \in s}} q(x) = (f(x) + \alpha )/((x) + \beta )$$

where f, g: R n → R, α, β ∈ R, S ⊆ R n . To simplify things, and without restricting the generality of the problem, it is usually assumed that, g(x) + β + 0 for all x ∈ S,S is non-empty and that the objective function has a finite optimal value.

Nonlinear Fractional Programming

In this paper, we study the sum rate performance of zero-forcing (ZF) and regularized ZF (RZF) precoding in large MISO broadcast systems under the assumptions of imperfect channel state information at the transmitter and per-user channel transmit correlation. Our analysis assumes that the number of transmit antennas M and the number of single-antenna users K are large while their ratio remains bounded. We derive deterministic approximations of the empirical signal-to-interference plus noise ratio (SINR) at the receivers, which are tight as M, K → ∞. In the course of this derivation, the per-user channel correlation model requires the development of a novel deterministic equivalent of the empirical Stieltjes transform of large dimensional random matrices with generalized variance profile. The deterministic SINR approximations enable us to solve various practical optimization problems. Under sum rate maximization, we derive 1) for RZF the optimal regularization parameter; 2) for ZF the optimal number of users; 3) for ZF and RZF the optimal power allocation scheme; and 4) the optimal amount of feedback in large FDD/TDD multiuser systems. Numerical simulations suggest that the deterministic approximations are accurate even for small M, K.

https://hal-supelec.archives-ouvertes.fr/hal-00769398/document

Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels Under Limited Feedback

We consider the problem of linear zero-forcing precoding design and discuss its relation to the theory of generalized inverses in linear algebra. Special attention is given to a specific generalized inverse known as the pseudo-inverse. We begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudo-inverse are optimal among the generalized inverses in this setting. Then, we proceed to examine individual per-antenna power constraints. In this case, the pseudo-inverse is not necessarily the optimal inverse. In fact, finding the optimal matrix is nontrivial and depends on the specific performance measure. We address two common criteria, fairness and throughput, and show that the optimal generalized inverses may be found using standard convex optimization methods. We demonstrate the improved performance offered by our approach using computer simulations.

/pdf/zero-forcing-precoding-and-generalized-inverses-abzmy1394y.pdf

Zero-Forcing Precoding and Generalized Inverses

We address the problem of minimum mean square error (MMSE) transceiver design for point-to-multipoint transmission in multiuser multiple-input-multiple-output (MIMO) systems. We focus on the problem of minimizing the downlink sum-MSE under a sum power constraint. It is shown that this problem can be solved efficiently by exploiting a duality between the downlink and uplink MSE feasible regions. We propose two different optimization frameworks for downlink MMSE transceiver design. The first one solves an equivalent uplink problem, then the result is transferred to the original downlink problem. Duality ensures that any uplink MMSE scheme, e.g., linear MMSE reception or MMSE-decision feedback equalization (DFE), has a downlink counterpart. We propose two globally optimum algorithms based on convex optimization. The basic idea of the second framework is to perform optimization in an alternating manner by switching between the virtual uplink and downlink channels. This strategy exploits that the same MSE can be achieved in both links for a given choice of transmit and receive filters. This iteration is proven to be convergent.

Downlink MMSE Transceiver Optimization for Multiuser MIMO Systems: Duality and Sum-MSE Minimization

This paper focuses on linear transceiver design for rate optimization in multiuser Gaussian multple-input multiple-output (MIMO) systems. We focus on two design criteria: 1) maximizing the weighted sum rate subject to a total power constraint; 2) maximizing the minimum user rate subject to a total power constraint. For these problems, new power allocation strategies are derived, which can be formulated as geometric programs (GPs) involving mean square errors (MSEs). Based on these solutions, we propose iterative algorithms, where each iteration contains the optimization of the uplink power, uplink receive filters, and downlink receive filters. Monotonic convergence of the algorithms is proved. Simulations show that the algorithms outperform existing linear schemes. Additionally, we extend the results to other variations of the problems, such as, the problem of sum-rate constrained or user-rate constrained power minimization, and the problem of sum-rate maximization subject to user-rate constraints and a total power constraint.

Rate Optimization for Multiuser MIMO Systems With Linear Processing

The problem of transceiver optimization in multiuser multiple-input multiple-output downlink wireless systems is considered. The base station is assumed to possess only estimated, erroneous values of channel coefficients. The exact channels lie in uncertainty regions, specified by the Frobenius norms of the error matrices. An iterative optimization of the transmit and receive filters is performed with the goal of minimizing the total transmit power, while satisfying the users' mean square error (MSE) targets for all channels from the uncertainty regions. Each iteration consists of two steps that can be equivalently rewritten as semidefinite programs with efficient numerical solutions. It is shown that the whole algorithm converges. The proposed framework can be applied for solving robust counterparts of several related MSE-optimization problems. The modifications of the proposed algorithms for accommodating box-like disturbances are analyzed, as well.

Robust Transceiver Optimization in Downlink Multiuser MIMO Systems with Channel Uncertainty

We study robust transceiver optimization in a downlink, multiuser, wireless system, where the transmitter and the receivers are equipped with antenna arrays. The robustness is defined with respect to imperfect knowledge of the channel at the transmitter. The errors in the channel state information are assumed to be bounded, and certain quality-of-service targets in terms of mean-square errors (MSEs) are guaranteed for all channels from the uncertainty regions. Iterative algorithms are proposed for the transceiver design. The iterations perform alternating optimization of the transmitter and the receivers and have equivalent semidefinite programming representations with efficient numerical solutions. The framework supports robust counterparts of several MSE-optimization problems, including transmit power minimization with per-user or per-stream MSE constraints, sum MSE minimization, min-max fairness, etc. Although the convergence to the global optimum cannot be claimed due to the intricacy of the problems, numerical examples show good practical performance of the presented methods. We also provide various possibilities for extensions in order to accommodate a broader set of scenarios regarding the precoder structure, the uncertainty modeling, and a multicellular setup.

Robust Transceiver Optimization in Downlink Multiuser MIMO Systems

We consider the problem of sum rate maximization with joint resource allocation and interference mitigation by multiantenna processing in wireless networks. The denominators in the users' signal-to-interference-plus-noise expressions are assumed to be representable in the form of matrix-based, concave interference functions. It is shown that the problem of interest for this system model can be readily rewritten as a minimization of a difference of convex functions. Based on this representation, an iterative algorithm with guaranteed convergence is employed to calculate possibly suboptimal solutions of the main problem, which is known to be NP-hard. The proposed technique enables achieving a large portion of the globally optimal sum rate. It is also very efficient and rather general in terms of allowing interesting extensions, compared with the related results from the literature.

https://hal.inria.fr/inria-00502213/document

Shuying Shi

Papers

Downlink MMSE Transceiver Optimization for Multiuser MIMO Systems: Duality and Sum-MSE Minimization

Rate Optimization for Multiuser MIMO Systems With Linear Processing

Robust Transceiver Optimization in Downlink Multiuser MIMO Systems with Channel Uncertainty

Robust Transceiver Optimization in Downlink Multiuser MIMO Systems

DC programming approach for resource allocation in wireless networks