Spatio-Temporal Wireless D2D Network With Imperfect Beam Alignment

In this paper, we investigate the beam misalignment impacts of a dynamic device-to-device (D2D) communication model, where both transmitters and receivers adopt beamforming (BF) by using uniform linear array (ULA). A time continuous dynamic model is adopted for this network. We use tools of stochastic geometry and the Miyazawa rate conversation law to analyse the stability condition of such a network. An analytical expression of the critical arrival rate is given under a uniform or truncated Gaussian alignment error assumption. In contrast to our previous result, where the beam alignment is perfect, our analytical and numerical results show that, if the beam alignment is not perfect, the critical arrival rate can no longer increase without limit as a function of the number of antenna elements. Closed-form expressions of the upper bounds for critical arrival rates are given for both the uniform and the truncated Gaussian misalignment models.