Adaptive Amplification forTwo-Way Amplify-and-Forward Relaying with Analog Network Coding over Flat-Fading Channels Basem M. ElHalawany, Maha ElSabrouty, Adel Abdelrahman Electronics & Communications Department, Egypt-Japan University of Science & Technology, EGYPT Abstract—This paper studies the application of a Zero- Forcing (ZF) concept for two-way amplify-and-forward adaptive gain relaying. The studied system uses the channels conditions to mitigate the effect of the interference and the multipath fading in the two-way cooperative communication with two-transmission phases Analog Network Coding. The system is studied and simulated for flat fading channel model. Keywords: Adaptive gain, ANC, Amplify-and-Forward. I. INTRODUCTION In practical systems, many wireless devices may not be able to support multiple antennas due to size and hardware limitations. However, cooperation in the networks can create a virtual antenna array. Cooperative communication can be traced back to [1] where some nodes help other nodes in intended way to get the information from the source to the destination. Cooperative communication (CC) can be seen as a virtual MIMO system which is more powerful in deployment flexibility and hardware feasibility [2]. A. Amplify-and-Forward Two-Way Relaying with Analog Network Coding Consider the two-way relaying system in Fig.1. In this scenario, where S and D want to exchange the data x s and x d respectively via the relay R. In classical half-duplex AF relaying networks, it is required to have four time slots to exchange data which reduces the spectral efficiency. Ahlswade in his seminal paper [3] proposed the concept of network coding which allows for efficient two-way transmission by reducing the required time slots from four to only two time slots. Fig. 1. Two-way Relaying with ANC B. Types of Relay node gains for AF protocols In Fixed-gain AF, the received signal is always multiplied with same gain no matter what the channel condition is between the source and the relay. On the other hand, using variable-gain AF is capable of compensating for the channels effect in such a way that the relay always transmits the signal with the same power. Adaptive amplification factor is investigated in [4] to counteract the effects of the multipath- fading channel in one-way relaying. In this paper, zero- forcing based adaptive gain is investigated for two-way relaying channel which can be considered as an extension of the work in [4] to the two-way relaying case in which analog network coding (ANC) is employed [5]. II. ZF ADAPTIVE GAIN FOR AF WITH ANC We consider the system model shown in Fig. 1 where h ୱ୰ and h ୰ are the channels coefficients of the source S-to-relay link and relay-to-source D link respectively. It is assumed that all nodes are using half-duplex mode. Assume that there is no direct link (DL) between the source (S) and the source (D). We also assume that channels are reciprocal. The transmission process is performed in two phases, in the first multiple access phase both sources transmit their data by transmit powers P ୱ and P  respectively, to the relay node. So the received signal at the relay node is given by: y ୰ ൌ h ୱ୰ ඥP ୱ x ୱ ൅h ୰ ඥP  x  ൅n ୰ (1) where n ୰ is the complex AWGN at the relay, n ୰ ~ CN(0, σ ଶ ሻ . In the second phase, broadcast phase, the relay node amplifies the received signal at the first phase, y r , as: y ୰୲ ൌ . ܩy ୰ ൌ ඥP r ܤ .y ୰ ሺʹሻ where y ୰୲ is the transmitted signal from the relay after amplification with the traditional variable-gain ( ඥP ౨ ஻ ), P ୰ is the average transmission power at the relay node, and the factor B is the normalization factor, ܤൌ ඥP ୱ . |h ୱ୰ | ଶ ൅ P  . |h ୰ | ଶ ൅σ ଶ ሺ͵ሻ The amplified analog network coded signal, y rt , can be broadcasted to both sources through the two links. The received signals at nodes S and D are given by: y ୱ ൌ h ୰ୱ ሺG y ୰ ሻ൅n ୱ ൌ h ୱ୰ ଶ G X ୱ ൅h ୱ୰ h ୰ G X  ൅ ሺh ୱ୰ G n ୰ ൅n ୱ ሻ (4) y  ൌ h ୰ ሺG y ୰ ሻ൅n  ൌ h ୰ ଶ G X  ൅h ୱ୰ h ୰ G X ୱ ൅ ሺh ୰ G n ୰ ൅n  ሻ (5) Where X ୱ ൌ ඥP ୱ x ୱ and X  ൌ ඥP  x  and n s and n d denote the AWGN noises at both S and D respectively, and it is assumed to be a zero-mean white Gaussian noise and equal variance of σ ଶ . Since each source know its own information, a self-interference cancellation technique could be used to get rid of the first term in (4) and (8) by assuming perfect CSI. The remaining signals at sources are given by: y ୱୱ ൌ h ୱ୰ h ୰ G X  ൅ ሺh ୱ୰ G n ୰ ൅n ୱ ሻ (6) y  ൌ h ୱ୰ h ୰ G X ୱ ൅ ሺh ୰ G n ୰ ൅n  ሻ (7) The signal to noise ratio (SNR) of the received signal at the node S (y ss ) and D (y dd ) can be calculated as SNR ୱ ൌ |ୋ ୦ ౩౨ ୦ ౨ౚ | మ P ౚ ஢ మ ሾ ଵ ା |ୋ ୦ ౩౨ | మ ሿ (8) SNR  ൌ |ୋ ୦ ౩౨ ୦ ౨ౚ | మ P ౩ ஢ మ ሾ ଵ ା |ୋ ୦ ౨ౚ | మ ሿ (9)