Performance Analysis of Directional Modulation With Finite-Quantized RF Phase Shifters in Analog Beamforming Structure

The radio frequency (RF) phase shifter with finite quantization bits in analog beamforming (AB) structure forms quantization error (QE) and causes a performance loss of received signal to interference plus noise ratio (SINR) at the receiver (called Bob). By using the law of large numbers in probability theory, the closed-form expression of the SINR performance loss is derived to be inversely proportional to the square of Sinc (or sin(x)/x) function. Here, a phase alignment method is applied in the directional modulation transmitter with the AB structure. Also, the secrecy rate (SR) expression is derived with the QE. From the numerical simulation results, we find that the SINR performance loss gradually decreases as the number L of quantization bits increases. This loss is less than 0.3 dB when L is larger than or equal to three. As L exceeds five, the SINR performance loss at Bob can be approximately trivial. Similarly, the SR performance loss gradually reduces as L increases. In particular, the SR performance loss is about 0.1 bits/s/Hz for L = 3 at signal-to-noise ratio of 15 dB.