Abstract
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.
Highlights
Directional modulation (DM), as one of the key technologies of wireless physical layer security, is attracting ever-increasing research interests and activities from both academia and industry world
In this paper, we have made an investigation of the impact of quantization error (QE) caused by finite-quantized phase shifters of analog beamforming (AB) structure on performance in DM systems
In the presence of QE, the expression of signal to interference plus noise ratio (SINR) performance loss has been derived to be inversely proportional to the square of sinc function by making use of the law of large numbers in probability theory
Summary
Directional modulation (DM), as one of the key technologies of wireless physical layer security, is attracting ever-increasing research interests and activities from both academia and industry world. Traditional technology for directional modulation was proposed on the radio frequency (RF) frontend [1]–[3] In these articles, the authors proposed an actively driven DM array of utilizing analog RF phase shifters or antenna elements, which did not deal with the flexibility of design process. The transmitter Alice is equipped with an AB structure, while the desired receiver at Bob works in full-duplex model and helps Alice by transmitting AN with FD beamforming structure to degrade the performance of the illegitimate receiver at Eve. The main contributions of this paper are summarized as follows: 1) In AB structure, the RF phase shifter with finite quantization bits will lead to degradation of the value of the received SINR at Bob. By using the law of large numbers in probability theory, the approximate closed-form expression of SINR performance loss is derived to be inversely proportional to the square of sinc (i.e., sin(x)/x) function.
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