In this two-part paper, we propose a general algorithmic framework for the minimization of a nonconvex smooth function subject to nonconvex smooth constraints, and also consider extensions to some structured, nonsmooth problems. The algorithm solves a sequence of (separable) strongly convex problems and maintains feasibility at each iteration. Convergence to a stationary solution of the original nonconvex optimization is established. Our framework is very general and flexible and unifies several existing successive convex approximation (SCA)-based algorithms. More importantly, and differently from current SCA approaches, it naturally leads to distributed and parallelizable implementations for a large class of nonconvex problems. This Part I is devoted to the description of the framework in its generality. In Part II, we customize our general methods to several (multiagent) optimization problems in communications, networking, and machine learning; the result is a new class of centralized and distributed algorithms that compare favorably to existing ad-hoc (centralized) schemes.

Parallel and Distributed Methods for Constrained Nonconvex Optimization—Part I: Theory

We consider a $K$ link multiple-input multiple-output (MIMO) interference channel, where each link consists of two full-duplex (FD) nodes exchanging information simultaneously in a bi-directional communication fashion. The nodes in each pair suffer from self-interference due to operating in FD mode, and inter-user interference from other links due to simultaneous transmission at each link. We consider the transmit and receive filter design for weighted sum-rate (WSR) maximization problem subject to sum-power constraint of the system or individual power constraints at each node of the system. Based on the relationship between WSR and weighted minimum-mean-squared-error (WMMSE) problems for FD MIMO interference channels, we propose a low complexity alternating algorithm which converges to a local WSR optimum point. Moreover, we show that the proposed algorithm is not only applicable to FD MIMO interference channels, but also applicable to FD cellular systems in which a base station (BS) operating in FD mode serves multiple uplink (UL) and downlink (DL) users operating in half-duplex (HD) mode, simultaneously. It is shown in simulations that the sum-rate achieved by FD mode is higher than the sum-rate achieved by baseline HD schemes.

Weighted Sum-Rate Maximization for Full-Duplex MIMO Interference Channels

The heterogeneous cloud radio access network (H-CRAN) is a promising paradigm that incorporates cloud computing into heterogeneous networks (HetNets), thereby taking full advantage of cloud radio access networks (C-RANs) and HetNets. Characterizing cooperative beamforming with fronthaul capacity and queue stability constraints is critical for multimedia applications to improve the energy efficiency (EE) in H-CRANs. An energy-efficient optimization objective function with individual fronthaul capacity and intertier interference constraints is presented in this paper for queue-aware multimedia H-CRANs. To solve this nonconvex objective function, a stochastic optimization problem is reformulated by introducing the general Lyapunov optimization framework. Under the Lyapunov framework, this optimization problem is equivalent to an optimal network-wide cooperative beamformer design algorithm with instantaneous power, average power, and intertier interference constraints, which can be regarded as a weighted sum EE maximization problem and solved by a generalized weighted minimum mean-square error approach. The mathematical analysis and simulation results demonstrate that a tradeoff between EE and queuing delay can be achieved, and this tradeoff strictly depends on the fronthaul constraint.

Energy-Efficient Resource Allocation Optimization for Multimedia Heterogeneous Cloud Radio Access Networks

We consider the design of a hybrid multiple-input multiple-output (MIMO) processor consisting of a radio frequency (RF) beamformer and a baseband MIMO processor for millimeter-wave communications over multiuser interference channels. Sparse approximation problems are formulated to design hybrid MIMO processors approximating the minimum-mean-square-error transmit/receive processors in MIMO interference channels. They are solved by orthogonal-matching-pursuit-based algorithms that successively select RF beamforming vectors from a set of candidate vectors and optimize the corresponding baseband processor in the least squares sense. It is shown that various beamformers can be designed by considering different types of candidate vector sets. Simulation results demonstrate the advantage of the proposed design over the conventional method that designs the baseband processor after steering the RF beams.

MSE-Based Hybrid RF/Baseband Processing for Millimeter-Wave Communication Systems in MIMO Interference Channels

Next-generation communication systems have to comply with very strict requirements for increased flexibility in heterogeneous environments, high spectral efficiency, and agility of carrier aggregation. This fact motivates research in advanced multicarrier modulation (MCM) schemes, such as filter bank-based multicarrier (FBMC) modulation. This paper focuses on the offset quadrature amplitude modulation (OQAM)-based FBMC variant, known as FBMC/OQAM, which presents outstanding spectral efficiency and confinement in a number of channels and applications. Its special nature, however, generates a number of new signal processing challenges that are not present in other MCM schemes, notably, in orthogonal-frequency-division multiplexing (OFDM). In multiple-input multiple-output (MIMO) architectures, which are expected to play a primary role in future communication systems, these challenges are intensified, creating new interesting research problems and calling for new ideas and methods that are adapted to the particularities of the MIMO-FBMC/OQAM system. The goal of this paper is to focus on these signal processing problems and provide a concise yet comprehensive overview of the recent advances in this area. Open problems and associated directions for future research are also discussed.

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MIMO Signal Processing in Offset-QAM Based Filter Bank Multicarrier Systems

Interference alignment (IA) has evolved as a powerful technique in the information theoretic framework for achieving the optimal degrees of freedom of interference channel. In practical systems, the design of specific interference alignment schemes is subject to various criteria and constraints. In this paper, we propose novel transceiver schemes for the MIMO interference channel based on the mean square error (MSE) criterion. Our objective is to optimize the system performance under a given and feasible degree of freedom. Both the total MSE and the maximum per-user MSE are chosen to be the objective functions to minimize. We show that the joint design of transmit precoding matrices and receiving filter matrices with both objectives can be realized through efficient iterative algorithms. The convergence of the proposed algorithms is proven as well. Simulation results show that the proposed schemes outperform the existing IA schemes in terms of BER performance. Considering the imperfection of channel state information (CSI), we also extend the MSE-based transceiver schemes for the MIMO interference channel with CSI estimation error. The robustness of the proposed algorithms is confirmed by simulations.

Hui Shen

Papers

MSE-Based Transceiver Designs for the MIMO Interference Channel