Ergodic capacity in mmWave ad hoc network with imperfect beam alignment

Millimeter wave (mmWave) technology has several technical hurdles to overcome before becoming an integral next-generation wireless technology. One such hurdle is the alignment of the steerable mmWave antenna array. This paper quantifies both the ergodic capacity of a mmWave ad hoc network with perfect alignment and the loss in ergodic capacity when error is introduced. First, we leverage stochastic geometry to evaluate the ergodic capacity (bits/sec/Hz/area) in the network. Next, we compare two antenna models that are commonly used: sectored and Gaussian. Lastly, we derive expressions that quantify the loss in ergodic capacity per user when alignment error occurs at the receiver and transmitter. Our results show that even relatively small errors in alignment can lead to significant ergodic capacity reduction.