Maziar Sanjabi

Linear Transceiver Design for Interference Alignment: Complexity and Computation

Consider a multiple input-multiple output (MIMO) interference channel where each transmitter and receiver are equipped with multiple antennas. An effective approach to practically achieving high system throughput is to deploy linear transceivers (or beamformers) that can optimally exploit the spatial characteristics of the channel. The recent work of Cadambe and Jafar (IEEE Trans. Inf. Theory, vol. 54, no. 8) suggests that optimal beamformers should maximize the total degrees of freedom and achieve interference alignment in the high signal-to-noise ratio (SNR) regime. In this paper we first consider the interference alignment problem without channel extension and prove that the problem of maximizing the total achieved degrees of freedom for a given MIMO interference channel is NP-hard. Furthermore, we show that even checking the achievability of a given tuple of degrees of freedom for all receivers is NP-hard when each receiver is equipped with at least three antennas. Interestingly, the same problem becomes polynomial time solvable when each transmit/receive node is equipped with no more than two antennas. We also propose a distributed algorithm for transmit covariance matrix design that does not require the DoF tuple preassignment, under the assumption that each receiver uses a linear minimum mean square error (MMSE) beamformer. The simulation results show that the proposed algorithm outperforms the existing interference alignment algorithms in terms of system throughput.

Robust SINR-constrained MISO downlink beamforming: when is semidefinite programming relaxation tight?

We consider the multiuser beamforming problem for a multi-input single-output downlink channel that takes into account the errors in the channel state information at the transmitter side (CSIT). By modeling the CSIT errors as elliptically bounded uncertainty regions, this problem can be formulated as minimizing the transmission power subject to the worst-case signal-to-interference-plus-noise ratio constraints. Several methods have been proposed to solve this nonconvex optimization problem, but none can guarantee a global optimal solution. In this article, we consider a semidefinite relaxation (SDR) for this multiuser beamforming problem, and prove that the SDR method actually solves the robust beamforming problem to global optimality as long as the channel uncertainty bound is sufficiently small or when the transmitter is equipped with at most two antennas. Numerical examples show that the proposed SDR approach significantly outperforms the existing methods in terms of the average required power consumption at the transmitter.

A Stochastic Successive Minimization Method for Nonsmooth Nonconvex Optimization with Applications to Transceiver Design in Wireless Communication Networks

Consider the problem of minimizing the expected value of a cost function parameterized by a random variable. The classical sample average approximation method for solving this problem requires minimization of an ensemble average of the objective at each step, which can be expensive. In this paper, we propose a stochastic successive upper-bound minimization method (SSUM) which minimizes an approximate ensemble average at each iteration. To ensure convergence and to facilitate computation, we require the approximate ensemble average to be a locally tight upper-bound of the expected cost function and be easily optimized. The main contributions of this work include the development and analysis of the SSUM method as well as its applications in linear transceiver design for wireless communication networks and online dictionary learning. Moreover, using the SSUM framework, we extend the classical stochastic (sub-)gradient method to the case of minimizing a nonsmooth nonconvex objective function and establish its convergence.

Optimal Joint Base Station Assignment and Beamforming for Heterogeneous Networks

Consider a downlink MIMO heterogeneous wireless network with multiple cells, each containing many mobile users and a number of base stations with varying capabilities. A central task in the management of such a network is to assign each user to a base station and design a linear transmit strategy to ensure a satisfactory level of network performance. In this work, we propose a formulation for the joint base station assignment and linear transceiver design problem based on the maximization of a system wide utility. We first establish the NP-hardness of the resulting optimization problem for a large family of α-fairness utility functions. Then, we propose an efficient algorithm to approximately solve this problem for a variety of different utility functions. Our numerical experiments show that the proposed algorithm can achieve significantly higher levels of system throughput and user fairness than what is possible by optimizing the precoders alone.

Robust SINR-constrained MISO downlink beamforming: When is semidefinite programming relaxation tight?

We consider the robust beamforming problem under imperfect channel state information (CSI) subject to SINR constraints in a downlink multiuser MISO system. One popular approach to solve this nonconvex optimization problem is via semidefinite relaxation (SDR). In this paper, we prove that the SDR method is tight when the channel uncertainty bound is small or when the base station is equipped with two antennas.

Optimal joint base station assignment and downlink beamforming for heterogeneous networks

Consider a MIMO heterogeneous network with multiple transmitters (including macro, pico and femto base stations) and many receivers (mobile users). The users are to be assigned to the base stations which then optimize their linear transmit beamformers accordingly. In this work, we consider the problem of joint base station assignment and linear beamformer design to maximize a system wide utility. We first establish the NP-hardness of the resulting optimization problem for a large family of α-fairness utility functions. Then, we propose an efficient algorithm to approximately solve this problem for the special case of sum rate maximization. The simulation results show that the algorithm improves the sum rate.

Accelerated Alternating Direction Method of Multipliers

Recent years have seen a revival of interest in the Alternating Direction Method of Multipliers (ADMM), due to its simplicity, versatility, and scalability. As a first order method for general convex problems, the rate of convergence of ADMM is O(1=k) [4, 25]. Given the scale of modern data mining problems, an algorithm with similar properties as ADMM but faster convergence rate can make a big difference in real world applications. In this paper, we introduce the Accelerated Alternating Direction Method of Multipliers (A2DM2) which solves problems with the same structure as ADMM. When the objective function is strongly convex, we show that A2DM2 has a O(1=k2) convergence rate. Unlike related existing literature on trying to accelerate ADMM, our analysis does not need any additional restricting assumptions. Through experiments, we show that A2DM2 converges faster than ADMM on a variety of problems. Further, we illustrate the versatility of the general A2DM2 on the problem of learning to rank, where it is shown to be competitive with the state-of-the-art specialized algorithms for the problem on both scalability and accuracy.

Cross-Layer Provision of Future Cellular Networks: A WMMSE-based approach

To cope with the growing demand for wireless data and to extend service coverage, future fifth-generation (5G) networks will increasingly rely on the use of low-power nodes to support massive connectivity in a diverse set of applications and services. To this end, virtualized and mass-scale cloud architectures are proposed as promising technologies for 5G in which all the nodes are connected via a backhaul network and managed centrally by such cloud centers. The significant computing power made available by the cloud technologies has enabled the implementation of sophisticated signal processing algorithms, especially by way of parallel processing, for both interference management and network provision. The latter two are among the major signal processing tasks for 5G due to an increased level of frequency sharing, node density, interference, and network congestion. This article outlines several theoretical and practical aspects of joint interference management and network provisioning for future 5G networks. A cross-layer optimization framework is proposed for joint user admission, user-base station (BS) association, power control, user grouping, transceiver design, as well as routing and flow control. We show that many of these cross-layer tasks can be treated in a unified way and implemented in a parallel manner using an efficient algorithmic framework called weighted minimum mean squared error (WMMSE). Some recent developments in this area are highlighted and future research directions are identified.

Joint base station clustering and beamformer design for partial coordinated transmission using statistical channel state information

In this paper we consider the problem of partial coordinated transmission in the downlink of a wireless heterogeneous network (HetNet). The partial coordination is crucial in trading off system performance with backhaul overhead, and it is achieved through jointly optimizing the base station (BS) clustering and the downlink beamformers. Unlike many existing works, we focus on the practical scenario where the channel state information (CSI) is imperfect/incomplete at the transmitter. Mathematically, we formulate the problem into a penalized stochastic optimization problem, and propose an algorithm that converges almost surely to its stationary solution set. Interestingly, our method does not require any additional computational complexity or memory compared to the existing algorithms using perfect CSI. Effectiveness of our method is validated through numerical experiments.