Joint Beamforming Design of Physical Layer Security Transmission for IRS Assisted V2V Communication

Abstract

With the rapid development of Internet of Vehicles (IoV) technology, the data security transmission between vehicles has become particularly important. As a novel technology that can assist wireless communication, intelligent reflecting surface (IRS) can not only change the wireless signal propagation environment, but also has the advantages of easy deployment, low cost and low consumption. In this paper, an IRS is used to assist the physical layer security communication of vehicle to vehicle (V2V) in a multiple input single output (MISO) IoV system. The physical layer security rate maximization problem of V2V link is formulated while satisfying the total power constraint and the IRS phase-shift mode constraint. An alternating optimization algorithm based on the generalized Rayleigh entropy and semidefinite relaxation (SDR) is proposed. Simulation results show that IRS-assisted V2V communication can effectively enhance the physical layer security transmission rate.

Appendix

Detailed derivation of Eqs. 11 and 12 are as follows:

$\begin{gathered} |({\mathbf{h}}_{{{\text{TR}}}} + {\mathbf{f}}_{{{\text{IR}}}} {\mathbf{\Phi G}}){\mathbf{w}}|^{2} = |({\mathbf{h}}_{{{\text{TR}}}} + {\mathbf{p}}^{T} diag({\mathbf{f}}_{{{\text{IR}}}} ){\mathbf{G}}){\mathbf{w}}|^{2} \hfill \\ = ({\mathbf{h}}_{{{\text{TR}}}}^{*} + {\mathbf{p}}^{H} diag({\mathbf{f}}_{{{\text{IR}}}}^{*} ){\mathbf{G}}^{*} ){\mathbf{w}}^{*} {\mathbf{w}}^{T} ({\mathbf{h}}_{{{\text{TR}}}}^{T} + {\mathbf{G}}^{T} diag({\mathbf{f}}_{{{\text{IR}}}} ){\mathbf{p}}) \hfill \\ = {\mathbf{h}}_{{{\text{TR}}}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{h}}_{{{\text{TR}}}}^{T} + {\mathbf{p}}^{H} diag({\mathbf{f}}_{{{\text{IR}}}}^{*} ){\mathbf{G}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{G}}^{T} diag({\mathbf{f}}_{{{\text{IR}}}} ){\mathbf{p}} + \hfill \\ \, {\mathbf{p}}^{H} diag({\mathbf{f}}_{{{\text{IR}}}}^{*} ){\mathbf{G}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{h}}_{{{\text{TR}}}}^{T} + {\mathbf{h}}_{{{\text{TR}}}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{G}}^{T} diag({\mathbf{f}}_{{{\text{IR}}}} ){\mathbf{p}} \hfill \\ = {\mathbf{h}}_{{{\text{TR}}}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{h}}_{{{\text{TR}}}}^{T} + [{\mathbf{p}}^{H} ,1]\left[ {\begin{array}{*{20}c} {diag({\mathbf{f}}_{{{\text{IR}}}}^{*} ){\mathbf{G}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{G}}^{T} diag({\mathbf{f}}_{{{\text{IR}}}} )} & {diag({\mathbf{f}}_{{{\text{IR}}}}^{*} ){\mathbf{G}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{h}}_{{{\text{TR}}}}^{T} } \\ {{\mathbf{h}}_{{{\text{TR}}}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{G}}^{T} diag({\mathbf{f}}_{{{\text{IR}}}} )} & 0 \\ \end{array} } \right]\left[ {\begin{array}{*{20}c} {\mathbf{p}} \\ 1 \\ \end{array} } \right] \hfill \\ = h_{{\text{R}}} + {\mathbf{z}}^{H} {\mathbf{G}}_{{\text{R}}} {\mathbf{z}} \hfill \\ \end{gathered}$ where.

$h_{{\text{R}}} = {\mathbf{h}}_{{{\text{TR}}}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{h}}_{{{\text{TR}}}}^{T}$, ${\mathbf{z}} = [{\mathbf{p}}^{T} ,1]^{T}$, ${\mathbf{z}}^{H} = [{\mathbf{p}}^{H} ,1]$,

$${\mathbf{G}}_{{\text{R}}} = \left[ {\begin{array}{*{20}c} {diag({\mathbf{f}}_{{{\text{IR}}}}^{*} ){\mathbf{G}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{G}}^{T} diag({\mathbf{f}}_{{{\text{IR}}}} )} & {diag({\mathbf{f}}_{{{\text{IR}}}}^{*} ){\mathbf{G}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{h}}_{{{\text{TR}}}}^{T} } \\ {{\mathbf{h}}_{{{\text{TR}}}}^{*} {\mathbf{w}}^{*} {\mathbf{w}}^{T} {\mathbf{G}}^{T} diag({\mathbf{f}}_{{{\text{IR}}}} )} & 0 \\ \end{array} } \right]$$

Similarly, formula (12) can be derived as the $|({\mathbf{h}}_{{{\text{TE}}}} + {\mathbf{f}}_{{{\text{IE}}}} {\mathbf{\Phi G}}){\mathbf{w}}|^{2} = h_{{\text{E}}} + {\mathbf{z}}^{H} {\mathbf{G}}_{{\text{E}}} {\mathbf{z}}$.