LAUSR

To reduce the signal-to-interference-plus-noise ratio (SINR) loss of analog directional modulation (DM) with finite radio frequency (RF) phase shifters (PSs), a hybrid analog and digital (HAD) DM with mixed PSs is proposed. Using the law of large numbers, the closed-form expressions of SINR performance loss (PL), secrecy rate (SR), and bit error rate (BER) are derived. In accordance with the closed-form expression of SINR loss, it is clear that the SINR PL at desired receiver (Bob) gradually decreases as the fraction $\eta$ of the low-resolution phase shifter decreases, where $\eta$ is defined as the ratio of the number of low-resolution shifters to the total number of shifters. The simulation results show that the SINR PL, SR PL, and BER gradually decrease as the number of quantization bits increases. When the fraction of low-resolution shifters is equal to 50%, 2 bits is sufficient for low-resolution shifters to achieve a SINR PL less than 0.5 dB and a negligible BER degradation. Also, when the number of quantization bits of low-resolution shifters is equal to 2, the SR PL is about 0.3 bits/s/Hz. Thus, compared with analog DM, the HAD DM structure strikes a good balance between PL and circuit cost.