Abstract
In this paper, we consider the beamspace ESPRIT algorithm for Millimeter-Wave (mmWave) channel sensing. We provide a non-asymptotic analysis of the beamspace ESPRIT algorithm. We derive a deterministic upper bound for the matching distance error between the true angle of arrival (AoA) of the channel paths and the estimated AoA considering a bounded noise model. Additionally, we leverage the insight obtained from our theoretical analysis to propose a novel max-min criterion for beamformer design which can enhance the performance of mmWave channel estimation algorithms, including beamspace ESPRIT. We consider a family of multi-resolution beamformers which can be implemented using phase shifters and introduce a design scheme for the optimal beamformers from this family with respect to the proposed max-min criteria. We can guarantee a minimum beamforming gain uniformly over a region of possible multipath directions, which can lead to more robust channel estimation. We provide several numerical experiments to verify our theoretical claims and demonstrate the superior performance of the proposed beamformers compared to existing beamformer design criteria.
Highlights
Millimeter wave communication has emerged as a key technology for the generation of wireless communication systems due to an abundance of spectrum availability in the mmWave bands, and the higher data rates enabled by larger bandwidths (Bai and Heath, 2014).1 at mmWave frequencies, the wireless channel is spatially sparse and suffers from severe path loss
We fix the AOAs of the channel paths to be F {0.21, 0.29, 0.36, 0.38}, which belong to the region of interest T [0.2, 0.4]
We compute the average matching distance error of beamspace estimating signal parameters via rotational invariance techniques (ESPRIT) for this channel configuration averaged over L 500 different noise realizations
Summary
Millimeter wave (mmWave) communication has emerged as a key technology for the generation of wireless communication systems due to an abundance of spectrum availability in the mmWave bands, and the higher data rates enabled by larger bandwidths (Bai and Heath, 2014). at mmWave frequencies, the wireless channel is spatially sparse and suffers from severe path loss. Due to the large number of antennas in a mmWave system, it is impractical to implement a fully digital beamforming scheme with a dedicated radio frequency (RF) chain for every antenna, which would incur high power consumption and cost. In order to overcome this challenge, mmWave systems typically utilize either analog (Junyi Wang et al, 2009; Hur et al, 2013) or hybrid beamforming approaches with a reduced number of RF chains (Alkhateeb et al, 2014a; Han et al, 2015). The problem of mmWave channel estimation becomes challenging, since a high-dimensional channel matrix (whose size is given by the large number of antennas) needs to be Beamspace ESPRIT and Beamformer Design estimated from only low-dimensional measurements acquired at the output of a reduced number of RF chains, especially with limited pilot overhead
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