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 results in a performance loss of receive signal to interference and noise ratio (SINR)at Bob. By using the law of large numbers in probability theory, the closed-form expression of SINR performance loss is derived to be inversely proportional to the square of sinc function. Here, a phase alignment method is applied in directional modulation transmitter with AB structure. Also, the secrecy rate (SR) expression is derived with QE. From 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 0.3dB when L is larger than or equal to 3. As L exceeds 5, the SINR performance loss at Bob can be approximately trivial. Similarly, compared to the SR with infinite-precision phase quantizer, the corresponding SR performance loss gradually reduces as L increases. In particular, the SR performance loss is about 0.1 bits/s/Hz for $L\approx3$ at signal-to-noise ratio =15dB.