This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.

/pdf/multi-cell-mimo-cooperative-networks-a-new-look-at-1e6uuxtyow.pdf

Multi-Cell MIMO Cooperative Networks: A New Look at Interference

Consider the MIMO interfering broadcast channel whereby multiple base stations in a cellular network simultaneously transmit signals to a group of users in their own cells while causing interference to the users in other cells. The basic problem is to design linear beamformers that can maximize the system throughput. In this paper we propose a linear transceiver design algorithm for weighted sum-rate maximization that is based on iterative minimization of weighted mean squared error (MSE). The proposed algorithm only needs local channel knowledge and converges to a stationary point of the weighted sum-rate maximization problem. Furthermore, we extend the algorithm to a general class of utility functions and establish its convergence. The resulting algorithm can be implemented in a distributed asynchronous manner. The effectiveness of the proposed algorithm is validated by numerical experiments.

An iteratively weighted MMSE approach to distributed sum-utility maximization for a MIMO interfering broadcast channel

Consider the multiple-input multiple-output (MIMO) interfering broadcast channel whereby multiple base stations in a cellular network simultaneously transmit signals to a group of users in their own cells while causing interference to each other. The basic problem is to design linear beamformers that can maximize the system throughput. In this paper, we propose a linear transceiver design algorithm for weighted sum-rate maximization that is based on iterative minimization of weighted mean-square error (MSE). The proposed algorithm only needs local channel knowledge and converges to a stationary point of the weighted sum-rate maximization problem. Furthermore, the algorithm and its convergence can be extended to a general class of sum-utility maximization problem. The effectiveness of the proposed algorithm is validated by numerical experiments.

An Iteratively Weighted MMSE Approach to Distributed Sum-Utility Maximization for a MIMO Interfering Broadcast Channel

The block coordinate descent (BCD) method is widely used for minimizing a continuous function $f$ of several block variables. At each iteration of this method, a single block of variables is optimized, while the remaining variables are held fixed. To ensure the convergence of the BCD method, the subproblem of each block variable needs to be solved to its unique global optimal. Unfortunately, this requirement is often too restrictive for many practical scenarios. In this paper, we study an alternative inexact BCD approach which updates the variable blocks by successively minimizing a sequence of approximations of $f$ which are either locally tight upper bounds of $f$ or strictly convex local approximations of $f$. The main contributions of this work include the characterizations of the convergence conditions for a fairly wide class of such methods, especially for the cases where the objective functions are either nondifferentiable or nonconvex. Our results unify and extend the existing convergence results ...

https://works.bepress.com/mingyi_hong/1/download/

A unified convergence analysis of block successive minimization methods for nonsmooth optimization

The block coordinate descent (BCD) method is widely used for minimizing a continuous function f of several block variables. At each iteration of this method, a single block of variables is optimized, while the remaining variables are held fixed. To ensure the convergence of the BCD method, the subproblem to be optimized in each iteration needs to be solved exactly to its unique optimal solution. Unfortunately, these requirements are often too restrictive for many practical scenarios. In this paper, we study an alternative inexact BCD approach which updates the variable blocks by successively minimizing a sequence of approximations of f which are either locally tight upper bounds of f or strictly convex local approximations of f. We focus on characterizing the convergence properties for a fairly wide class of such methods, especially for the cases where the objective functions are either non-differentiable or nonconvex. Our results unify and extend the existing convergence results for many classical algorithms such as the BCD method, the difference of convex functions (DC) method, the expectation maximization (EM) algorithm, as well as the alternating proximal minimization algorithm.

A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization

To achieve the full multiplexing gain of MIMO interference networks at high SNRs, the interference from different transmitters must be aligned in lower-dimensional subspaces at the receivers. Recently a distributed “max-SINR” algorithm for precoder optimization has been proposed that achieves interference alignment for sufficiently high SNRs. We show that this algorithm can be interpreted as a variation of an algorithm that minimizes the sum Mean Squared Error (MSE). To maximize sum utility, where the utility depends on rate or SINR, a weighted sum MSE objective is used to compute the beams, where the weights are updated according to the sum utility objective. We specify a class of utility functions for which convergence of the sum utility to a local optimum is guaranteed with asynchronous updates of beams, receiver filters, and utility weights. Numerical results are presented, which show that this method achieves interference alignment at high SNRs, and can achieve different points on the boundary of the achievable rate region by adjusting the MSE weights.

/pdf/minimum-mean-squared-error-interference-alignment-4zpm3e0i52.pdf

Minimum Mean Squared Error interference alignment

We study distributed algorithms for updating transmit precoding matrices for a two-user Multi-Input/Multi-Output (MIMO) interference channel. Our objective is to maximize the sum rate with linear Minimum Mean Squared Error (MMSE) receivers, treating the interference as additive Gaussian noise. An iterative approach is considered in which given a set of precoding matrices and powers, each receiver announces an interference price (marginal decrease in rate due to an increase in interference) for each received beam, corresponding to a column of the precoding matrix. Given the interference prices from the neighboring receiver, and also knowledge of the appropriate cross-channel matrices, the transmitter can then update the beams and powers to maximize the rate minus the interference cost. Variations on this approach are presented in which beams are added sequentially (and then fixed), and in which all beams and associated powers are adjusted at each iteration. Numerical results are presented, which compare these algorithms with iterative water-filling (which requires no information exchange), and a centralized optimization algorithm, which finds locally optimal solutions. Our results show that the distributed algorithms perform close to the centralized algorithm, and by adapting the rank of the precoder matrices, achieve the optimal high-SNR slope.

/pdf/distributed-interference-pricing-for-the-mimo-interference-1eior6qx9v.pdf

Distributed Interference Pricing for the MIMO Interference Channel

We study distributed algorithms for allocating powers and/or adjusting beamforming vectors in a peer-to-peer wireless network which may have multiple-input-single-output (MISO) links. The objective is to maximize the total utility summed over all users, where each user's utility is a function of the received signal-to-interference-plus-noise ratio (SINR). Each user (receiver) announces an interference price, representing the marginal cost of interference from other users. A particular user (transmitter) then updates its power and beamforming vector to maximize its utility minus the interference cost to other users, which is determined from their announced interference prices. We show that if each transmitter update is based on a current set of interference prices and the utility functions satisfy certain concavity conditions, then the total utility is non-decreasing with each update. The proof is based on the convexity of the utility functions with respect to received interference, and applies to rate utility functions, and an arbitrary number of interfering MISO links. The extension to multi-carrier links is discussed as well as algorithmic variations in which the prices are not immediately updated after power or beam updates.

/pdf/monotonic-convergence-of-distributed-interference-pricing-in-yea8n11qgd.pdf

Monotonic convergence of distributed interference pricing in wireless networks

This paper presents a comparative study of algorithms for jointly optimizing beamformers and receive filters in an interference network, where each node may have multiple antennas, each user transmits at most one data stream, and interference is treated as noise We focus on techniques that seek good suboptimal solutions by means of iterative and distributed updates Those include forward-backward iterative algorithms (max-signal-to-interference-plus-noise ratio (SINR) and interference leakage), weighted sum mean-squared error (MSE) algorithms, and interference pricing with incremental signal-to-noise ratio (SNR) adjustments We compare their properties in terms of convergence and information exchange requirements, and then numerically evaluate their sum rate performance averaged over random (stationary) channel realizations The numerical results show that the max-SINR algorithm achieves the maximum degrees of freedom (ie, supports the maximum number of users with near-zero interference) and exhibits better convergence behavior at high SNRs than the weighted sum MSE algorithms However, it assumes fixed power per user and achieves only a single point in the rate region whereas the weighted sum MSE criterion gives different points In contrast, the incremental SNR algorithm adjusts the beam powers and deactivates users when interference alignment is infeasible Furthermore, that algorithm can provide a slight increase in sum rate, relative to max-SINR, at the cost of additional iterations

Comparison of Distributed Beamforming Algorithms for MIMO Interference Networks

We present a distributed algorithm for allocating power among multiple interfering transmitters in a wireless network using orthogonal frequency division multiplexing (OFDM). The algorithm attempts to maximize the sum over user utilities, where each user's utility is a function of his total transmission rate. Users exchange interference prices reflecting the marginal cost of interference on each sub-channel, and then update their power allocations given the interference prices and their own channel conditions. A similar algorithm was studied earlier assuming that each user's utility function is a separable function of the user's rate per sub-channel. Here, we do not assume this separability. We give a different algorithm for updating each user's power allocation and show that this algorithm converges monotonically. Numerical results comparing this algorithm to several others are also presented.

/pdf/distributed-interference-pricing-for-ofdm-wireless-networks-5ecojkaazy.pdf

Changxin Shi

Papers

Minimum Mean Squared Error interference alignment

Distributed Interference Pricing for the MIMO Interference Channel

Monotonic convergence of distributed interference pricing in wireless networks

Comparison of Distributed Beamforming Algorithms for MIMO Interference Networks

Distributed interference pricing for OFDM wireless networks with non-separable utilities