Effects of SNR-Dependent Beam Alignment Errors on Millimeter-Wave Cellular Networks

At millimeter-wave (mm-wave) frequencies, narrow beamwidth and inaccurate channel estimation result in beam alignment errors, which degrade the achievable signal-to-noise ratio (SNR) and rate. The extent of beam misalignment depends on the various link parameters, however, prior works ignored such a dependence and considered oversimplified array patterns. This paper formulates beam alignment errors for the uniform linear array at the base station as a function of the link parameters by using the Cramer Rao lower bound of angle-of-arrival estimates and proposes a tractable array pattern approximation to better reflect the effects of such alignment errors. Utilizing stochastic geometry and the statistics of the Student's t-distribution, a novel and robust analytical technique is developed to obtain the downlink SNR and rate coverage probabilities due to beam misalignment, assuming a single antenna at the user. We show that beam alignment errors significantly affect the achievable SNR and rate for non line-of-sight (NLOS)/distant users whereas the effect is negligible for LOS/nearby users. It is also illustrated that the effects of alignment errors cannot be mitigated only by increasing the number of antennas. We also show that our proposed array pattern approximation better captures the effects of beam alignment errors as compared to the widely used flat-top pattern.