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Beamforming training or cell discovery (CD) is a fundamental procedure in millimeter wave communication systems in which the user detects the presence of a base station, acquires the identity of that base station, and finds suitable beamforming directions to establish the wireless link for the subsequent data transmission phase. We consider uniform planar array-based beamforming under both separable and non-separable configurations as it allows confined antenna placements and 3-D steering of beams. Our focus is to design the beamforming training phase and develop low-complexity receiver algorithms for the cell discovery procedure. By exploiting the sparse nature of the mm-wave channels and using an equivalent compressive sensing measurement model, we obtain analytical bounds for the cell detection probability in terms of the mutual coherence parameter of the resulting sensing matrix. Using mutually unbiased bases (MUB) from quantum information theory, we design CD schemes with low mutual coherence. Our design includes parameters that control the training phase duration, and we analytically characterize the relationship between the training duration and the corresponding mutual coherence value. We present detailed simulation studies using experimentally driven mm-wave channel simulators and show that our MUB based scheme gives superior detection performance when compared to the conventional beam sweeping based schemes and random beamforming schemes.

3-D Beamforming Training using Mutually Unbiased Bases for Cell Discovery in mm-wave Systems