Hybrid Beamforming for Millimeter-Wave Massive Grant-Free Transmission

The increasing demands for spectral resources in emerging massive machine-type communication applications necessitate the implementation of massive grant-free transmission in the millimeter-wave (mmWave) band. This paper proposes two efficient receive analog beamforming design algorithms for mmWave massive grant-free transmission under hybrid beamforming architectures, intending to optimize spectral efficiency and access probability, respectively. Specifically, we first express the spectral efficiency of mmWave massive grant-free transmission systems and then derive an analytically tractable approximation using the random matrix theory. Following this, an alternating optimization method is employed to design the receive beamforming matrix efficiently. Additionally, we provide the formulation of access probability for mmWave massive grant-free transmission, whose explicit expression is approximately derived through the Gaussian approximation. Building upon this, we utilize a convex hull relaxation-based optimization method to optimize the beamforming matrix. The effectiveness of our proposed beamforming design algorithms in improving spectral efficiency and access probability is validated through extensive simulation experiments.