Mobile Information Systems

Volume 2016 (2016), Article ID 1901952, 11 pages

http://dx.doi.org/10.1155/2016/1901952

## Coordinated Precoding for D2D Communications Underlay Uplink MIMO Cellular Networks

College of Communications Engineering, PLA University of Science and Technology, Nanjing 210007, China

Received 8 November 2015; Accepted 13 March 2016

Academic Editor: Lin Gao

Copyright © 2016 Bing Fang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

We study the coordinated precoding problem for device-to-device (D2D) communications underlay multiple-input multiple-output (MIMO) cellular networks. The system model considered here constitutes multiple D2D user pairs attempting to share the uplink radio resources of a cellular network. We first formulate the coordinated precoding problem for the D2D user pairs as a sum-rate maximization (SRM) problem, which is subject to a total interference power constraint imposed to protect the base station (BS) and individual transmit power budgets available for each D2D user pair. Since the formulated SRM problem is nonconvex in general, we reformulate it as a difference convex- (DC-) type programming problem, which can be iteratively solved by employing the famous successive convex approximation (SCA) method. Moreover, a proximal-point-based regularization approach is also pursued here to ensure the convergence of the proposed algorithm. Interestingly, the centralized precoding algorithm can also lend itself to a distributed implementation. By introducing a price-based interference management mechanism, we reformulate the coordinated precoding problem as a Stackelberg game. Then, a distributed precoding algorithm is developed based on the concept of Stackelberg equilibrium (SE). Finally, numerical simulations are also provided to demonstrate the proposed algorithms. Results show that our algorithms can converge fast to a satisfactory solution with guaranteed convergence.

#### 1. Introduction

Recently, device-to-device (D2D) communications underlay cellular networks have received much attention due to their potential power to provide higher data rates and larger system capacity to meet the overwhelming demands of “Big Data” age [1, 2]. D2D communication in cellular networks is defined as direct communication between two mobile users and is likely to be a promising paradigm for the next generation cellular technologies (i.e., 5G). Introducing D2D communication in cellular networks will dramatically improve spectrum utilization, network throughput, and energy efficiency, while facilitating new peer-to-peer and location-based social networking applications at the same time. However, enabling the D2D communication mode in the traditional cellular networks will also bring many challenges to the long-standing cellular architectures; the main ones among them are radio resource allocation and interference management [3–5].

Through taking the advantage offered by multiple-input multiple-output (MIMO) technologies, the D2D user pairs and the regular cellular users can cooperate in the same time-frequency resource block, while keeping the interference between them to a tolerable level [5–8]. For example, the authors in [5] considered the resource allocation problem for D2D communications underlay MIMO cellular networks. With a goal to maximize the achievable sum-rate, they exploit the MIMO transmission advantages, that is, through joint beamforming and power control, to allocate the available radio resources and control the interference at the same time. Paper [8] utilizes the spatial freedom offered by MIMO to avoid interference from cellular downlink transmission to the underlay D2D users, with the aim of guaranteeing the D2D communication performance. As the works done in [9, 10], this issue has also been studied from a game-theoretic perspective for a distributed implementation. However, the coordinated precoding problem to allocate the available cellular radio resource to the D2D user pairs for the general case, that is, all nodes considered in the system employing multiple antennas, is of huge nonconvex complexity and deemed as extremely challenging, especially when the social performance criteria, such as the achievable sum-rate and the total mean square error (MSE), are considered.

A common model for studying the coordinated precoding problem for D2D communications underlaying MIMO cellular networks is the MIMO interference channel (IFC), where multiple transmitters simultaneously communicate with their respective receivers over a common frequency band [11–15]. Coordinated precoding for the MIMO IFCs has been recognized as a promising approach to improving the system performance. According to the level of cooperation, the coordinated precoding problems can be roughly classified into two categories, that is, MIMO cooperation and interference coordination. In the MIMO cooperation case, the transmitters cooperate in data transmission by sharing all the channel state information (CSI) and data signals. However, in the interference coordination case, the transmitters only need to coordinate in the transmission strategies for mitigating the interchannel interference. Compared with MIMO cooperation, interference coordination scheme requires the CSIs to be shared only and hence induces less information exchanges among the transmitters.

In this paper, we keep a focus on the coordinated precoding problem for D2D communications underlay uplink MIMO cellular networks, where an interference coordination scheme is adopted. The system model considered here consists of multiple D2D user pairs attempting to share the uplink radio resources of a cellular network, where all modes are assumed to be equipped with multiple antennas. The coordinated precoding problem for such a system is formulated as a sum-rate maximization (SRM) problem subject to individual transmit power constraints. At the same time, since the base station (BS) has the power to control all D2D user pairs, thus a maximum tolerable interference power constraint is further imposed to protect the signal received by itself. Hence, the SRM problem for the proposed system is subject to both individual transmit power constraints and a coupling interference power constraint.

Since the formulated SRM problem is nonconvex in general, we equivalently reformulate it as a difference convex- (DC-) type programming problem, which can be iteratively solved by employing a successive convex approximation (SCA) method [16, 17]. With the SCA method, the nonconvex part of the SRM problem is locally linearized to its first-order Taylor expansion. Thus, relying on solving a series of convexified optimization problems, a centralized iterative precoding algorithm is developed. In addition, a proximal-point-based regularization is also pursued in this work to ensure the convergence of the proposed algorithm without requiring any special restrictions on antenna configurations and the channel ranks. Interestingly, the centralized iterative precoding algorithm is naturally suitable for a distributed implementation, because the convexified problem has a separable objective function. Then, by introducing a price-based interference management mechanism to overcome the coupling interference power constraint, we reformulate the coordinated precoding problem as a Stackelberg game [18–21]. Then, a distributed precoding algorithm is further developed based on the concept of Stackelberg equilibrium (SE). Numerical simulations are also provided to demonstrate the proposed algorithms. Results show that our algorithms can converge fast to a satisfactory solution with guaranteed convergence. In summary, main contributions of the present paper can be listed as follows:(i)A coordinated precoding framework is established for the D2D communications underlay uplink MIMO cellular networks. Moreover, the coordinated precoding problem is formulated as a SRM problem, about which the compute complexity is analyzed.(ii)Based on the SCA method, a centralized iterative precoding algorithm is developed relying on solving a series of convexified optimization problems. In addition, a proximal-point-based regularized approach is also pursued to ensure the convergence of the proposed algorithm without requiring any special restrictions on antenna configurations and the channel ranks.(iii)By the aid of the price-based interference management mechanism to overcome the coupling interference power constraint, we reformulate the coordinated precoding problem as a Stackelberg game. Then, a distributed precoding algorithm is further developed based on the concept of SE.(iv)Numerical simulations are also provided to demonstrate the proposed algorithms. Results show that the proposed algorithms can converge fast to a satisfactory solution with guaranteed convergence.

The rest of this paper is organized as follows: in Section 2, we introduce the system model and formulate the SRM problem; in Section 3, a centralized iterative precoding algorithm is developed; and a distributed precoding algorithm is also designed in Section 4; in Section 5, we evaluate the proposed algorithms via computer simulations; the present paper is concluded in Section 6.

*Notations*. Bold uppercase letters denote matrices and bold lowercase letters denote vectors; defines the space of all complex matrices; means that matrix is positive semidefinite; Hermitian transpose of matrix is represented as ; , , and mean the determinant, the Frobenius norm, and the trace of matrix , respectively; and denotes the natural logarithm.

#### 2. System Model and Problem Statement

In this section, we first provide the system model and then formulate the coordinated precoding problem as a SRM problem, about which the compute complexity is analyzed.

##### 2.1. System Model

In this work, we study the coordinated precoding problem for the D2D communications underlay uplink MIMO cellular networks. As shown in Figure 1, the system model considered here consists of D2D user pairs attempting to share the uplink radio resources of a cellular BS. For simplicity, we assume that only one BS coexists with the D2D user pairs. However, this model can be easily extended to the scenarios where multiple BSs are present. We also assume each D2D user pair is comprised of a secondary transmitter (ST) and an intended secondary receiver (SR), where and the set of all D2D user pairs is defined as . As mentioned before, a general case where all nodes in the proposed system are equipped with multiple antennas is considered. Specifically, it is assumed that the BS is equipped with antennas, and D2D user pair is equipped with antennas at the receiver and antennas at the transmitter. In addition, a quasi-static frequency-flat fading environment for all communication links is assumed.