On the use of semidefinite relaxation for uplink phase-only hybrid beamforming with blockers

Densification of mobile networks using small cells (SCs) is a promising approach to achieve the forecasted 1000x growth in capacity for next generation wireless communication systems. However, a major impediment of dense SC network is the low signal-to-interference-plus-noise ratio (SINR) regime, notably in uncoordinated time-division duplexing (TDD) systems in sub-6GHz bands. To circumvent this issue and to enhance the performance of the physical (PHY) layer, hybrid beamforming (HBF) solutions involving both analog and digital stages are necessary. HBF technologies provide interference rejection through analog filtering prior to quantization, spatial multiplexing and require lesser radio-frequency (RF) chains and analog-to-digital converters (ADCs). Conversely, digital beamforming (DBF) performance saturates because of high interferers (blockers) and restricted ADC dynamic range. Moreover, HBF RF circuitry could be further simplified by the use of phase-only weights in analog beamforming (ABF) stage. However, this would be at the cost of making the SINR optimization problem non-convex. Existing sumrate results amalgamating quantization noise consist of lower bounds obtained by distortion factor approximation and worst-case distribution assumption. In this paper, we propose a relaxation approach to phase-only beamforming which allows for a straightforward solution using off-the-shelf interior point algorithms. Rather than directly comparing it in terms of sumrate, we compare it first in terms of SINR, as a function of an algebraic angle between the interferer and the user, with a state-of-the-art local convergence method. Further to this, we include an ADC model to the existing lower bound sumrate results, and analyze various solutions in a sub-6GHz multi-user uplink scenario.