Wireless-Powered Communication Assisted by Two-Way Relay with Interference Alignment Underlaying Cognitive Radio Network

Abstract

This study investigates the outage performance of an underlaying wireless-powered secondary system that reuses the primary users’ (PU) spectrum in a multiple-input multiple-output (MIMO) cognitive radio (CR) network. Each secondary user (SU) harvests energy and receives information simultaneously by applying power splitting (PS) protocol. The communication between SUs is aided by a two-way (TW) decode and forward (DF) relay. We formulate a problem to design the PS ratios at SUs, the power control factor at the secondary relay, and beamforming matrices at all nodes to minimize the secondary network’s outage probability. To address this problem, we propose a two-step solution. The first step establishes closed-form expressions for the PS ratios at each SU and secondary relay’s power control factor. Furthermore, in the second step, interference alignment (IA) is used to design proper precoding and decoding matrices for managing the interference between secondary and primary networks. We choose IA matrices based on the minimum mean square error iterative algorithm. The simulation results demonstrate a significant decrease in the outage probability for the proposed scheme compared to the benchmark schemes, with an average reduction of more than two orders of magnitude achieved.

Appendix

The optimization function in (23) is written by

$$\begin{aligned} F^{[j]}_{R_S}&=E\left\{ \Vert \textbf{f}_{\!_{R_S}}^{[j]}-\textbf{x}_{{i}}\Vert ^2\} \right. \\&=E\{Tr((\sqrt{p_{{i}}r_{\!_{{R_S}{i}}}^{-\tau }}\textbf{U}_{R_S}^{[j]H }\textbf{H}_{{R_S}{i}}\textbf{V}_{i}\textbf{x}_{i}\\&\quad +\sqrt{p_{\!_{P_j}}r_{\!_{{R_S}{P_j}}}^{-\tau }}\textbf{U}_{R_S}^{[j]H }\textbf{H}_{{R_S}{P_j}}\textbf{V}_{P_j}\textbf{x}_{\!_{P_j}} \\&\quad +\textbf{U}_{R_S}^{[j]H }\textbf{n}^{[j]}_{\!_{R_S}}-\textbf{x}_{{i}}) \\&\quad \quad (\sqrt{p_{{i}}r_{\!_{{R_S}{i}}}^{-\tau }}\textbf{U}_{R_S}^{[j]H }\textbf{H}_{{R_S}{i}}\textbf{V}_{i}\textbf{x}_{{i}} \\&\quad +\sqrt{p_{\!_{P_j}}r_{\!_{{R_S}{P_j}}}^{-\tau }}\textbf{U}_{R_S}^{[j]H }\textbf{H}_{{R_S}{P_j}}\textbf{V}_{P_j}\textbf{x}_{\!_{P_j}}\\&\quad \left. +\textbf{U}_{R_S}^{[j]H }\textbf{n}^{[j]}_{\!_{R_S}}-\textbf{x}_{{i}})^{H})\right\} , \end{aligned}$$

(29)

in which $i=A$ for $j=1$, and $i=B$ for $j=2$. To achieve the IA decoding matrix of the secondary relay at the first two time-slots ($\textbf{U}^{[j]}_{R_S}$, $j \in \{1,2\}$) the derivative of (29) with respect to $\textbf{U}^{[j]}_{R_S}$ should be set equal to zero. It is worth mentioning that because of the i.i.d. symbols, we have $E\{\textbf{x}_{\!_m}\textbf{x}_{\!_n}^H \}=\textbf{0}_{d_m \times d_n}$, for $m\ne n$, and $E\{\textbf{x}_{\!_m}\textbf{x}_{\!_m}^H \}=\textbf{I}_{N_m}$ for $m,n \in \{A,B,R_S,P_1,P_2,R_P\}$. Thus, we have

$$\begin{aligned} \frac{\delta F^{[j]}_{R_S}}{\delta \textbf{U}^{[j]}_{R_S}}&= \textbf{U}_{R_S}^{[j]H } \left( p_{{i}}r_{\!_{{R_S}{i}}}^{-\tau }\textbf{H}_{{R_S}{i}}\textbf{V}_{i}\textbf{V}^{H }_{i}\textbf{H}^{H }_{{R_S}{i}}\right. \\&\quad \left. +p_{\!_{P_j}}r_{\!_{{R_S}{P_j}}}^{-\tau }\textbf{H}_{{R_S}{P_j}}\textbf{V}_{P_j}{V^{H }_{P_j}}\textbf{H}^{H }_{{R_S}{P_j}}+\textbf{I}_{N_{R_S}}\right) \\&\quad -\sqrt{p_{{i}}r_{\!_{{R_S}{i}}}^{-\tau }}\textbf{V}^{H }_{i}\textbf{H}^{H }_{{R_S}{i}}=0. \end{aligned}$$

(30)

And in this way, (25) will be achieved.