International Journal of Antennas and Propagation

Volume 2015 (2015), Article ID 563737, 9 pages

http://dx.doi.org/10.1155/2015/563737

## Asynchronous Two-Way Relaying Networks Using Distributed Differential Space-Time Coding

Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200072, China

Received 25 June 2014; Revised 19 August 2014; Accepted 27 August 2014

Academic Editor: Lingyang Song

Copyright © 2015 Minjie Qian 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

A signal detection scheme is proposed for two-way relaying network (TWRN) using distributed differential space-time coding (DDSTC) under imperfect synchronization. Unlike most of existing work, which assumed perfect synchronization and channel state information (CSI) at all nodes, a more realistic scenario is investigated here by considering the signals transmitted from the two source nodes arriving at the relay not exactly at the same time due to the distributed nature of the nodes, and no CSI is available at any node. The proposed signal detection scheme is then demonstrated to remove the imperfect synchronization effect significantly through simulation results. Furthermore, pairwise error probability (PEP) of the asynchronous TWRN is analyzed and derived for both source nodes. Based on the simplified PEP expression, an optimum power allocation (OPA) scheme is then determined to further improve the whole system performance, when neither the source nor the relay has any knowledge of the CSI.

#### 1. Introduction

Cooperative communications have attracted much attention nowadays, by allowing nodes in the network to cooperate and form a virtual antenna array [1, 2]. Compared with one-way relaying, two-way relaying networks (TWRNs) [3] have the advantage of high spectral efficiency, where two source nodes exchange information via the help of the relay nodes located between them. Recently, distributed space-time coding (DSTC) for TWRNs was extensively investigated [4–6] due to the diversity and multiplexing gain of multiple-input and multiple-output (MIMO) technology. Most of the existing studies on DSTC consider coherent detection by assuming that the channel state information (CSI) is known at the receiver. However, in fast-fading scenario, accurate CSI is hard to acquire, and training symbols required for channel estimation will decrease the spectrum efficiency and increase computation complexity, especially when there are multiple relays in wireless networks. Therefore, differential modulation has been considered to address this problem since it does not require the knowledge of CSI at either the transmitter or the receiver [7, 8].

Similar to the coherent detection scenario [9, 10], several protocols have been proposed for TWRNs using differential detection. One of the most commonly used protocols is the amplify-and-forward (AF) scheme [11, 12]. In this scheme, both source nodes transmit information to the relay node at the same time, the relay then amplifies the received superimposed signal and broadcasts to both sources. For multiple relay nodes, space-time coding is used before amplifying the signals. This AF based bidirectional relaying is also referred to as analog network coding (ANC), which is very useful in wireless networks since the wireless channel acts as a natural fulfillment of network coding by superimposing the wireless signals over the air. In [11], distributed differential space-time coding by AF was applied to TWRNs for the first time. However, the correctness of the currently detected symbol significantly affects the decoding of next symbols, resulting in severe error propagation. To solve this problem, Huo et al. [12] presented a differential space-time coding with distributed ANC (DDSTC-ANC) scheme for TWRNs with multiple relays. The DDSTC-ANC scheme has been proved to achieve the same diversity order as the coherent detection scheme, but the performance of which is 3 dB away compared with that of the coherent detection due to the differential modulation.

So far, almost all work on DDSTC with TWRNs has assumed that the transmission is perfectly synchronized by assuming that the relay nodes receive the signals from both source nodes at the same time, which can be difficult to achieve in practical systems due to the distributed nature of the nodes, and the channels may become dispersive with imperfect synchronization even under flat fading [13–16]. In [15], a signal detection scheme for differential bidirectional relaying with ANC under imperfect synchronization was put forward, but it only considers a single relay node. In [16], the authors proposed a simple detection scheme for distributed space-time block coding under imperfect synchronization for TWRNs. However, perfect CSI is required at all nodes. To the best of our knowledge, little has been reported for TWRNs with multiple relays using DSTC under imperfect synchronization, when neither the sources nor the relays have any knowledge of the CSI.

Therefore, a differential signal detection scheme for asynchronous TWRNs with multiple relays using DDSTC is proposed in this paper. Due to imperfect synchronization, the symbols that relays broadcast back to sources are not symmetrical, signal detection will not be the same at the two sources, which will be described in detail thereafter. Due to the importance of resource allocation for the TWRN system [17, 18], the performance of the proposed detection schemes is analyzed and PEP for both sides is derived. Moreover, an optimum power allocation (OPA) scheme is presented to further improve the system performance, based on the simplified PEP expression.

The rest of this paper is organized as follows. Section 2 introduces the system model. In Section 3, the detection schemes of the different sides are proposed, respectively, by two subsections. Section 4 presents the performance analysis and OPA for the system. The simulation results and corresponding conclusions are provided in Section 5. Section 6 summarizes the paper.

*Notation*. Throughout this paper, capital and boldface lower-case letters denote matrices and vectors, respectively. , , , and stand for complex conjugate, transpose, conjugate transpose, and inverse, respectively, for both matrix and vector. denotes the expectation. represents matrix whose th diagonal entry is .

#### 2. System Model

A TWRN with two source nodes and two relay nodes is considered in this paper, all equipped with a single antenna and working in the half-duplex mode. The source nodes, and , exchange information through relay nodes and , using two phases, the multiple access (MA) phase and the broadcast (BC) phase, as shown in Figure 1. In the MA phase, both sources transmit signals to and simultaneously, while in the BC phase, the relays broadcast the amplified superimposed signal back to the source nodes. Let and () denote the fading coefficients of the channels and , respectively. In the MA phase, both relays receive a superposition of the signals transmitted from and . The number of symbols in a distributed differential space-time coding block is normally assumed to be equal to the number of relay nodes. Since two relay nodes are considered in this TWRN, the signals transmitted from and can be represented as two-dimensional vectors , normalized as . Considering that and are imperfectly synchronized during the first phase, therefore they arrive at the relay nodes at different time with a relative time delay. In the distributed TWRNs, there are two nodes in the relay, the relative relay time of and at two relay nodes are different, and they are assumed as and corresponding to nodes and , respectively. Since the effort of synchronization is always required, and are assumed no greater than the symbol period . Such a relative time delay will still cause “intersymbol interference (ISI)” from neighboring symbols at the receiver. Without loss of generality, we assume that the signal from is perfectly synchronized to and . The received signals at relay node can then be expressed as where and are the transmitted power of and . represents the noise in the MA phase, which follows a zero-mean white Gaussian distribution, that is, . stands for the imperfect coefficient of channel fading between and , which reflects the effect of timing delay . Normally, we have for , which means the synchronization situation, and for , which means the power of delay signal is equal to that of current signal. The fading coefficients and , denoting the Rayleigh channel fading from source to Relay and source to Relay , that is, and , are assumed to be constant over one frame and change independently from one frame to another for simplicity [15, 17, 18]. So, let , , and can be expressed as