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This paper studies the effects of millimeter-wave (mm-wave) beam alignment errors on the downlink achievable rate of a heterogeneous network (HetNet), which consists of sub-6 GHz macro-cells and mm-wave small-cells. The alignment error is modeled as a function of the underlying mm-wave link parameters. The conventional maximum biased received power criterion, where the bias is used for mm-wave small-cells, is adopted for cell associations. By varying the value of the bias factor, we investigate the changes in the downlink rate coverage probability. Our simulation results indicate that high values (of the order of 30 dB) for the bias, while beneficial in the case of perfect alignment, are actually disadvantageous for the low-rate users in the case of imperfect beam alignment. The low-rate users are better served by a moderate value (of the order of 20 dB) of the bias when the beam alignment errors are accounted for. We also show that the above disparity can be narrowed down by increasing by mm-wave base station (BS) antennas and/or the mm-wave BS density. 

Beam alignment is a critical aspect in millimeter wave (mm-wave) cellular systems. However, the inherent limitations of channel estimation result in beam alignment errors, which degrade the system performance. For systems with a large number of antennas at the base station, downlink channel estimation is performed using uplink pilot signals. The beam alignment errors, thus, depend on the user equipment (UE) transmit power, which needs to be managed properly as the UEs are battery powered. This paper investigates how the use of uplink power control for the transmission of pilot signals in a mm-wave network affects the downlink beam alignment errors, which depend on various link parameters. We use stochastic geometry and statistics of the Student's t -distribution to develop an analytical model, which captures the interplay between the uplink power control and downlink signal-to-noise ratio (SNR) coverage probability. Our results indicate that using uplink power control significantly reduces UE power consumption without adversely affecting the downlink SNR coverage. 

The sensitivity to blockages at millimeter-wave (mm-wave) frequencies is very different from that at sub-6 GHz frequencies. The blockages affect the user-to-base station (BS) associations and the resulting association regions of the BSs in the network. This in turn alters the load, i.e., the total number of users associated to a BS. In this paper, we use a stochastic blockage model to analyze such effects. We characterize the variation in the load as a function of the blockage environment in a stochastic geometric setting. Our analysis indicates that in the extreme cases of total blocking and no blocking, the mean load on the tagged mm-wave BS is identical to that of a sub-6 GHz BS for a given BS and user density. For intermediate blockage environments, the mean load on the tagged mm-wave BS is found to be less than that on a sub-6 GHz BS. Using Monte-Carlo simulations, we establish that the existing analytical models for load characterization in mm-wave networks result in overestimation of the load per BS and underestimation of the achievable rate.