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Uplink Power Control and SNR-Dependent Beam Alignment Errors in MmWave Cellular Networks

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.