  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 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 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, 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 15dB.
