# Two Efficient Beamformers for Secure Precise Jamming and Communication with Phase Alignment

## TL;DR

This paper introduces two high-performance beamforming schemes, Min-TP and Min-RTP, for secure precise jamming and communication, significantly improving secrecy rate and bit-error-rate over existing methods by leveraging phase alignment and null-space projection.

## Contribution

The paper proposes two novel beamforming schemes, Min-TP and Min-RTP, that enhance secure precise jamming and communication using phase alignment and orthogonal constraints, outperforming existing methods.

## Key findings

- Min-TP and Min-RTP outperform equal amplitude methods in BER and secrecy rate.
- Both schemes effectively form peaks of artificial noise and confidential messages around Eve and Bob.
- Performance gap diminishes as the number of transmit antennas increases.

## Abstract

To achieve a better effect of interference on eavesdropper with an enhanced security, a secure precise jamming (PJ) and communication (SPJC) is proposed and its basic idea is to force the transmit energy of artificial noise (AN) and confidential message into the neighborhoods of Eve and Bob by using random subcarrier selection (RSS), directional modulation, and beamforming under phase alignment (PA) constraint (PAC). Here, we propose two high-performance beamforming schemes: minimum transmit power (Min-TP) and minimum regularized transmit power (Min-RTP) to achieve SPJC under PAC and orthogonal constraint (OC), where OC means that AN and CM are projected onto the null-spaces of the desired and eavesdropping channels, respectively. Simulation results show that the proposed Min-TP and Min-RTP methods perform much better than existing equal amplitude (EA) method in terms of both bit-error-rate (BER) and secrecy rate (SR) at medium and high signal-to-noise ratio regions. The SR performance difference between the proposed two methods becomes trivial as the number of transmit antennas approaches large-scale. More importantly, we also find the fact that all three schemes including EA, Min-TP, and Min-RTP can form two main peaks of AN and CM around Eve and Bob, respectively. This achieves both PJ and secure precise wireless transmission (SPWT), called SPJC.