Channel Covariance Matrix Estimation via Dimension Reduction for Hybrid MIMO MmWave Communication Systems
Abstract
:1. Introduction
 We show that the mmWave MIMO channel covariance matrix follows a Kronecker product expansion model [18]. Following [18,19,20], we show that this model can be used for reducing the effective dimension of the largedimensional channel covariance matrices in mmWave MIMO systems. We further show that permutation can reduce the rank of the mmWave channel covariance matrix, which admits an expression of the summation of vector outer products. We thus formulate the channel covariance matrix estimation problem as a lowrank matrix sensing problem.
 Although the aforementioned lowrank matrix sensing problem has a smaller size than the original problem, the complexity can still be high when the numbers of the transmitter/receiver antennas are large. In order to reduce the complexity, we further exploit the structures of the ULA or USPA to reduce the dimensionality of the problem and formulate the problem as a structured lowrank matrix sensing problem. We adapt the recently proposed generalized conditional gradient and alternating minimization (GCGAlt) algorithm [21], which has low computational complexity, to find the solution. Numerical results with ULA and USPA suggest that our proposed estimator is effective in estimating the mmWave channel covariance matrix.
2. Spatial Channel Model
3. Structured LowRank Covariance Matrix Sensing
3.1. Rank Reduction By Permutation
3.2. Dimension Reduction by Exploiting the Toeplitz–Hermitian Structure
3.3. Training
3.4. LowRank Matrix Sensing Problem
Algorithm 1 The GCGAlt Algorithm for Estimating $\widehat{\mathbf{C}}$ of Equation (28) 

3.5. Computational Complexity
3.6. Extension to the USPA System
4. Simulations
4.1. The ULA System
4.2. The USPA System
5. Conclusions
Author Contributions
Conflicts of Interest
Abbreviations
mmWave  Millimeter wave 
MIMO  Multipleinput multipleoutput 
CSI  Channel state information 
CS  Compressive sensing 
AoA  Angle of arrival 
AoD  Angle of departure 
ULA  Uniform linear arrays 
USPA  Uniform squared planar arrays 
RF  Radio frequency 
NMSE  Normalized mean square error 
PNR  Pilottonoise ratio 
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Hu, R.; Tong, J.; Xi, J.; Guo, Q.; Yu, Y. Channel Covariance Matrix Estimation via Dimension Reduction for Hybrid MIMO MmWave Communication Systems. Sensors 2019, 19, 3368. https://doi.org/10.3390/s19153368
Hu R, Tong J, Xi J, Guo Q, Yu Y. Channel Covariance Matrix Estimation via Dimension Reduction for Hybrid MIMO MmWave Communication Systems. Sensors. 2019; 19(15):3368. https://doi.org/10.3390/s19153368
Chicago/Turabian StyleHu, Rui, Jun Tong, Jiangtao Xi, Qinghua Guo, and Yanguang Yu. 2019. "Channel Covariance Matrix Estimation via Dimension Reduction for Hybrid MIMO MmWave Communication Systems" Sensors 19, no. 15: 3368. https://doi.org/10.3390/s19153368