International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 607563, 11 pages

http://dx.doi.org/10.1155/2015/607563

## Beamforming and Interference Cancellation in D2D Random Network

^{1}Beijing University of Posts and Telecommunications, Beijing 100876, China^{2}Anqing Normal University, Anqing 246011, China

Received 15 January 2015; Revised 3 March 2015; Accepted 4 March 2015

Academic Editor: Heng-Tung Hsu

Copyright © 2015 Langtao Hu and Chaowei Yuan. 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

Device-to-Device (D2D) communication is an important proximity communication technology. We model the hybrid network of cellular and D2D communication with stochastic geometry theory. In the network, cellular base stations are deployed with multiantennas. Two transmission strategies including beamforming and interference cancellation are proposed to boost system achievable rate in this paper. We derive analytical success probability and rate expression in these strategies. In interference cancellation strategy, we propose the partical BS transmission degrees of freedom (dofs) that can be used to cancel its D2D users (DUEs) interferences around the BS or to boost the desired signal power of associated cellular (CUE). In order to maximize the total area spectral efficiency (ASE), the BS transmission degrees of freedom are allocated according to proper interference cancellation radius around the BS. Monte Carlo simulations are performed to verify our analytical results, and two transmission strategies are compared.

#### 1. Introduction

Device-to-Device (D2D) communication is an important proximity communication technology, which has been in standard process of LTE-advanced system and it is a key technology for the future hybrid networks. With the development of mobile internet, the cellular network is not able to meet the requirements for the future localizing applications and D2D technology comes to an important complement for it [1–3]. The performance of wireless communication can be analyzed accurately by stochastic geometry theory. Traditional model has Wyner model or hexagonal grid [4]. The Wyner model or the hexagonal grid can be evaluated by system-level simulations. However, both the scalability and the accuracy of grid model were questionable in the context of network heterogeneity [4–6]. An alternative is to model the locations of sites as random and drawn from a spatial stochastic process, such as the Poisson point process (PPP), which has been confirmed as accurate as the grid model [5]. This stochastic model has been used recently in [7] to analyze success probability and average rate of heterogeneous network.

Reference [1] has studied spectrum sharing and derived analytical rate expressions for D2D communication in cellular networks by stochastic geometry theory and compared with signal to noise plus interference ratios (SINR) distribution using the hexagonal model by Monte Carlo. In [8], the spatial distribution of transmit powers and SINR are studied, and cumulative distribution function (CDF) of the transmit power and SINR have analytically been derived for a D2D network employing power control. In [9], mode selection and power control have been presented for underlay D2D communication in cellular networks, in which the proposed mode selection scheme for a user accounted for both the D2D link distance and cellular link distance (i.e., distance between the CUE and the BS). In [10], the small-scale fading experienced in the D2D direct link is modeled as Rician distribution.

Most of the previous works, for example [7–10], study results were based on single antenna deployed at BS in cellular network by stochastic geometry theory. Multiple antenna techniques are already relatively mature, and many standardization activities clearly indicate that multiantenna techniques and hybrid network will coexist and complement each other in the future wireless networks and should not be studied in isolation, as has been typically done in the literature [11]. Multiple antenna techniques have many significant features [12–14], such as using precoding design for interference cancellation or using beamforming design for boosting diversity gain. In random network, average achievable rate and reliability can be improved by the multiple antenna techniques [15–17]. In this paper, we model the hybrid network of cellular and D2D communication with stochastic geometry theory. In the network, cellular base stations are deployed with multiantennas. We analyze two primary performance measures: success probability and average achievable rate expression. The rate performance of beamforming and interference cancellation strategies is compared.

The rest of the paper is organised as follows. In Section 2, we introduce the system model. In Section 3, the success probability and average rate performance of beamforming strategy are investigated. In Section 4, the success probability and average rate performance of interference cancellation strategy are investigated. In Section 5, numerical simulation and analysis are discussed to verify these results. A conclusion is drawn in Section 6.

*Notation*. Let denote a vector. Transpose and conjugate transpose are denoted by and . The expectation of function with respect to is denoted as . The Laplace transform of is denoted by . A circularly symmetric complex Gaussian random variable with zero mean and variance is denoted as ~. A Chi-square distributed random variable with degree of freedom is denoted by ~. An exponential distributed random variable with mean 1 is denoted by ~. Let be a set and let be a subset of ; then denotes the set of elements of that do not belong to .

#### 2. System Model

We consider a downlink hybrid network of cellular and D2D communication [1], as shown in Figure 1. The locations of base stations (BSs) are deployed as a PPP [5] with intensity and constant transmission power . Similarly, the cellular users locations are modeled as a PPP with intensity . The locations of the D2D users are assumed to follow a PPP with intensity and constant transmission power . We assume the whole bandwidth is divided into subchannels. All the subchannels are available for BSs and D2D. Each D2D transmitter may randomly and independently access the subchannel. Each BS is configured with antennas. Each CUE and DUE is configured with single antenna. The downlink channel is composed of path large-scale attenuation and fading for both cellular networks and D2D communication. Large-scale attenuation is modeled as the standard pathloss propagation represented as , where is path-loss exponent and is distance between transmitter and receiver . may be BS or DUE transmitter, and may be DUE receiver or CUE receiver. Each CUE is associated with the nearest BS. Therefore, the probability density function (PDF) of the distance can be derived as according to the null probability of a 2D Poisson process [10]. Each DUE transmitter and its DUE receiver have a fixed distance of . Meanwhile, Rayleigh fading is assumed for the BS-CUE, DUE-CUE, BS-DUE, and DUE-DUE links. We consider the interference limited regime; that is, noise power is negligible compared to the interference power [10]. In the following, we will characterize the performance of beamforming and interference cancellation strategies.