Channel Estimation for mmWave Using the Convolutional Beamspace Approach

Large antenna arrays for mmWaves use hybrid analog/digital processing to reduce the number of RF-chains. For such systems, this paper proposes a new channel estimation paradigm based on convolutional beamspace (CBS). CBS, recently proposed for DOA estimation in passive arrays, has some demonstrated advantages. Since mmWave channel estimation problems can be formulated as 2-D DOD/DOA estimation, benefits of CBS are applicable here. CBS receivers use spatial filtering followed by downsampling, and are attractive for mmWaves, as downsampling reduces the number of RF-chains. The paper develops a hybrid implementation of CBS without need to restrict filter-taps even while physically using only unit-modulus coefficients. Another novelty is the use of appropriate counterpart of CBS at the transmitter - upsampler followed by filtering - to reduce RF-chains. While traditional CBS uses uniform downsampling at the receiver, this paper also develops nonuniform downsampling (although the physical arrays are ULAs). This creates a 'dilated' virtual sparse array, defined by spatial locations of retained samples where RF-chains are deployed. The so-called difference coarray of this dilated nonuniform sparse array has a large ULA segment, leading to accurate DOD/DOA estimation with very few RF-chains. CBS - uniform or coarray-based nonuniform - is such that high-resolution gridless subspace method (ESPRIT) can be deployed without any preparation unlike DFT-beamspace. Crucial to success of the coarray method is the introduction of filter delays to decorrelate path gains. With RF-chain constraints and fixed pilot overhead, the paper demonstrates more accurate channel estimation than traditional DFT-beamspace-ESPRIT.