**Optimization of Packet Length for Two Way Relaying with Energy Harvesting**

Ghassan Alnwaimi *,Hatem Boujemaa **, Kamran Arshad ***

(*) King Abdulaziz University, Kingdom of Saudi Arabia

(**) University of Carthage, Sup’Com, COSIM Laboratory, Tunisia

(***) College of Engineering, Ajman University

**Abstract**

In this article, we suggest optimizing packet length for two way relaying with energy harvesting. In the rst transmission phase, two source nodes N1 and N2 are transmitting data to each others through a selected relay R. In the second phase, the selected relay will amplify the sum of the signals received signals from N1 and N2. The selected relay amplies the received signals using the harvested energy from Radio Frequency (RF) signals transmitted by nodes N1 and N2. Finally, N1 will remove, from the relay’s signal, its own signal to be able to decode the symbol of N2. Similarly, N2 will remove, from the relay’s signal, its own signal to be able to decode the symbol of N1. We derive the outage probability, packet error probability and throughput at N1 and N2. We also optimize packet length to maximize the throughput at N1 or N2.

**Index Terms :**

Cooperative systems, Optimal packet length, Rayleigh fading channels.

**1. Introduction**

In Two-Way Relaying (TWR), two nodes N1 and N2 simultaneously transmit data to each other using a selected relay [1-5]. The communication process contains two phases. In the first one, N1 and N2 transmit data to some relays. Each relay will receive the sum of signals transmitted by N1 and N2. In the second phase, a selected relay amplifies the received signal. Then, N1 will remove, from the relay’s signal, its own signal to be able to decode the symbol of N2. Similarly, N2 will remove, from the relay’s signal, its own signal to be able to decode the symbol of N1.

Two way relaying for Multiple Input Multiple Output (MIMO) systems has been considered in [1-5]. Receive and transmit diversity improves the performance of TWR. At the receiver, the best antenna can be selected (Selection Combining SC). The corresponding Signal to Noise Ratio (SNR) is the maximum of SNRs over all antennas. It is also possible to combine the signals of all antennas using Maximum Ratio Combining (MRC). The SNR will be the sum of all SNRs [1-5]. TWR with Energy Harvesting (EH) consists to use the Radio Frequency (RF) signal to charge the battery of nodes [6-10]. Relays with EH capabilities has been studied in [6-10]. In order to enhance the throughput especially at low SNRs, channel coding is required in TWR [11-13]. Secure two way relaying has been suggested in [14-20]. Security aspects of TWR should be studied to avoid data recovery by a malicious node. The main contribution of the paper is to optimize packet length so that the throughput at node N1 or N2 is maximized. In all previous studies, a Fixed Packet Length (FPL) is used [1-20]. This is the first paper to suggest an Optimal Packet Length (OPL) for TWR with Energy Harvesting.

The system model is presented in section 2. Section 3 gives the Cumulative Distribution Function (CDF) of SNR. Section 4 derives the PEP while section 5 gives the expression of OPL. Some numerical results are given in section 6. Conclusions are presented in section 7.

**2. System model**

The system model is shown in Fig. 1. There are two nodes N1 and N2 communicating information to each other through a relay R. Node N1 transmits data to node N2 and at the same time node N2 is also communicating data to N1 through relay R. N1 and N2 transmit over the same channel.

**Figure 1**. Two way relaying with Energy harvesting.

The frame with duration T is decomposed in three parts :

– The first slot with duration T is dedicated to energy harvesting. Relay R harvests energy from RF signal transmitted by nodes N1 and N2.

The harvested energy is written as

where0< < 1 is harvesting duration percentage, Pi (resp. Ei) is the transmit power (resp. symbol energy) of node Ni and hN1R (respectively hN2R) is channel coefficient between nodes N1 (respectively N2) and R: p = T=Ts is the number of symbols per frame T. We have EX = TsPX

– During the second time slot with duration (1 − )T=2, N1 and N2 transmit data to node R over the same channel. This is the multiple access phase. The received signal at R is written as

**where Ei is the transmitted energy per symbol of node i with 1≤ i ≤ 2, xi(j) is the j-th transmitted symbol by node Ni and nR(j) is an Addivite White Gaussian Noise (AWGN)**

with variance N0. A Rayleigh block fading channel is assumed where the channel remains constant over all the time frame with duration T.

– During the third time slot with duration (1 − )T=2, R transmits amplifies the received signal to nodes N1 and N2. This is the broadcast phase.

Relay R uses the harvested energy E to amplify the received signal yR(j) to N1 and N2: The transmit symbol energy of R is equal to the harvested energy E devided by the number of transmitted symbols during (1−)T=2 seconds i.e. (1−)T=(2Ts) = (1−)p=2 with p = Ts=T :

Using (43), the amplification factor G used by relay R is written as

**2.1** **SNR at node N _{1}**

The received signal at N_{1} is written as

where n_{1}(j) is an AWGN with variance N_{0}. Using (43), we deduce

Node N_{1} removes the self interference,**since it knows the value of symbol x1(j): After removing self interference, we obtain**

The SNR at N_{1} is written as

Using the expression of amplification factor G (45), we deduce

We assume that channels are reciprocal i.e. h_{N1R} = h_{RN1} . By neglecting the term in N^{2}_{ 0} and using (44), the SNR at node N_{1} lower bounded by

This upper bound is tight at high average SNR as the term N2 0 can be neglected. We can write

**2.2 SNR at node N _{2}**

The received signal at N_{2} is written as

where n_{2}(j) is an AWGN with variance N_{0}. Using (43), we

Using the expression of amplification factor G (45), we deduce

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