Impact of Imperfect Angle Estimation on Spatial and Directional Modulation

In this paper, we investigate the impact of imperfect angle estimation (IAE) on spatial and directional modulation (SDM) systems, assuming that the signal experiences line of sight (LoS) propagation. In SDM systems with IAE, the variation is analyzed in detail, when there is a mismatch between the beamforming and precise channel matrices. Based on the union bound and statistics theory, the average bit error probabilities (ABEPs) for both the legitimate user and eavesdropper are derived. In addition, the ergodic rate is also quantified with IAE. Simulation results are presented to show that the achieved theoretical ABEPs are useful in quantifying the potential performance penalty. We also show that the mismatch between the beamforming and precise channel matrices will become greater with the increase in direction measurement error (DME), which affects the detection for both the legitimate user and eavesdropper. On the other hand, due to the effect of IAE, the SDM requires more signal-to-noise ratio (SNR) gain to achieve a stable ergodic secrecy rate.