We next consider the system with the USPA at the transmitter and receiver. The parameters fc, K, L, φtkl, φrklare assumed the same as in the ULA system. The transmitter has an 8×8
USPA (i.e., Nt = 64) and Kt = 16 RF chains, and the receiver has a 4 × 4 USPA (i.e.,
Nr = 16) and Kr = 4RF chains. We assume the elevation AoD angular spread υtv = 0 ◦
and the elevation AoA angular spread υr v = 6
◦based on the measurement results in [56].
The elevation AoDs and AoAs are distributed as
θtkl∼ U (θt k− υ t v, θ t k+ υ t v), θrkl∼ U (θr k− υ r v, θ r k+ υ r v),
CHAPTER 5. PHASE SHIFTER-BASED FULLY-CONNECTED HYBRID LARGE-SCALE MIMO SYSTEMS: LOW-RANK MMWAVE CHANNEL COVARIANCE
ESTIMATOR T 4 8 12 16 20 24 28 32 36 40 η 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1 GCG-Alt - 1 cluster DCOMP - 1 cluster GCG-Alt - 2 clusters DCOMP - 2 clusters
Figure 5.6: Comparison of η of the GCG-Alt estimator and the DCOMP estimator under
the USPA system, where Nt= 64, Nr= 16, PNR = 10dB, and S = 32.
S 8 12 16 20 24 28 32 η 0.88 0.9 0.92 0.94 0.96 0.98 1 GCG-Alt- 1 cluster DCOMP - 1 cluster GCG-Alt - 2 clusters GCG-Alt - 2 clusters
Figure 5.7: Comparison of η of the GCG-Alt estimator and the DCOMP estimator under
CHAPTER 5. PHASE SHIFTER-BASED FULLY-CONNECTED HYBRID LARGE-SCALE MIMO SYSTEMS: LOW-RANK MMWAVE CHANNEL COVARIANCE
ESTIMATOR υt h 5 10 15 20 25 30 η 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 GCG-Alt - υr h= 15 ◦ GCG-Alt - υr h= 35 ◦ GCG-Alt - υr h= 50 ◦ DCOMP - υr h= 15 ◦ DCOMP - υr h= 35 ◦ DCOMP - υr h= 50 ◦
Figure 5.8: Comparison of η of the GCG-Alt estimator and the DCOMP estimator under
the USPA system, where Nt= 64, Nr = 16, K = 1, PNR = 10dB, S = 16, T = 16,
υt
v = 0◦, and υvr= 6◦.
with the elevation center angles θt
k and θkr being generated in the same manner as the
azimuth center angles in the ULA system. For the DCOMP estimator, we set Gt =
2√Nt× 2 √ Nt= 256and Gr= 2 √ Nr× 2 √
Nr = 64. The parameters Lp, µ, , afor the
GCG-Alt estimator and DCOMP estimator are the same as in the ULA system.
We set PNR = 10 dB. The performance comparison with S = 32 under different T is shown in Fig. 5.6 and the performance comparison with T = 40 under different S is shown in Fig. 5.7. We can see that both of the GCG-Alt estimator and the DCOMP estimator achieve higher η for the USPA system. One reason for this is that the USPA system has lower resolution than the ULA system in the azimuth direction even though they have the same number of transmitter and receiver antennas. For the USPA system, the azimuth AoD is resolved by an√Nt= 8-element antenna array and the azimuth AoA
CHAPTER 5. PHASE SHIFTER-BASED FULLY-CONNECTED HYBRID LARGE-SCALE MIMO SYSTEMS: LOW-RANK MMWAVE CHANNEL COVARIANCE
ESTIMATOR
AoD is resolved by a Nt = 64-element antenna array and the azimuth AoA is resolved
by a Nr = 16-element antenna array. Therefore, for the same angular spread, the USPA
system resolves fewer paths than the ULA system, which results in a lower rank.
We also show the effects of angular spreads on the performance of the estimators. We set υt
v = 0 ◦, υr
v = 6
◦, K = 1, PNR = 10 dB, S = 16, and T = 16. The estimators’
performance under different angular spreads for the azimuth AoD/AoA (i.e., different υt h
and υr
h) shown in Fig. 5.8 suggests that the estimators achieve lower η when υthand υhrare
larger.
5.5
Conclusions
In this chapter, we have formulated the channel covariance estimation problem for hybrid mmWave systems as a structured low-rank matrix sensing problem by exploiting Kronecker product expansion and the structures of the ULA/USPA. The formulated problem has a reduced dimensionality and is solved by using a low-complexity GCG-Alt algorithm. The computational complexity analysis and numerical results suggest that our proposed method is effective in estimating the mmWave channel covariance matrix. However, the knowledge of the array response is needed to formulate the channel covariance matrix problem as a structured low-rank matrix sensing problem, which indicates that our method is sensitive to array impairments. In future works, we need to adapt our method to scenarios where the array response is not perfectly known.
Chapter 6
Conclusions and Future Works
6.1
Conclusions
In this thesis, we have focused on the CSI acquisition with low training overhead for three types of large-scale MIMO systems: fully digital MIMO systems, switch-based hybrid mmWave MIMO systems, and phase shifter-based fully connected hybrid mmWave MIMO systems. Moreover, we also considered the impact of array-inherent impairments. The major contributions of this thesis are summarized below.
In Chapter 2, we have proposed low complexity linear shrinkage-based covariance matrix estimation methods. Linear shrinkage designs are effective in improving the performance of covariance matrix estimation when the sample support is low, which is of interest in large-scale MIMO systems. Since the choice of shrinkage coefficients would greatly influence the performance of linear shrinkage estimators, therefore, we firstly proposed LOOCV methods to automatically choose the linear shrinkage parameters. Our proposed parameter choosing methods have low computational complexity as analytical expressions of the optimal shrinkage coefficients are obtained by employing a quadratic loss as the prediction error. The proposed LOOCV methods do not rely on the distribution
CHAPTER 6. CONCLUSIONS AND FUTURE WORKS
of the data and can be used together with general shrinkage targets. We then applied our proposed methods to MMSE channel estimation for fully digital MIMO systems. Simulation results suggested that our proposed methods can improve MMSE channel estimation when the training overhead is low.
In Chapter 3, we have proposed an MC-based channel estimator and a training scheme for switch-based hybrid mmWave MIMO systems. The MC-based estimator does not need the knowledge of the array response. Therefore, for systems with uncalibrated arrays, the proposed estimator outperforms the existing CS-based estimators that have been intensively discussed recently. Also, the MC-based estimator is implemented by the SVP algorithm, which has lower computational complexity than the CS-based estimator implemented by the OMP algorithm. Simulation results suggested that our proposed MC-based channel estimator outperforms the CS-based estimator in terms of estimation performance and computational complexity.
In Chapter 4, we have considered phase shifter-based hybrid mmWave MIMO systems. Similar to Chapter 3, the MC technique is again used to design the mmWave channel estimator due to its basis-free nature. Different from Chapter 3, the GCG-Alt algorithm, which does not need the channel rank as prior knowledge, was used to implement the MC- based estimator. Therefore, the GCG-Alt channel estimator can be more practical than the SVP channel estimator. We also proposed two training schemes that are compatible with phase shifter-based fully connected hybrid systems. Simulation results suggested that our proposed MC-based channel estimator, which is robust against phase/gain errors, has better estimation performance and lower computational complexity than two most recently proposed channel estimators.
CHAPTER 6. CONCLUSIONS AND FUTURE WORKS
In Chapter 5, we have considered the channel covariance matrix estimation for phase shifter-based fully connected hybrid MIMO systems. By exploring the structure of the mmWave channel covariance matrix, we formulated the channel covariance estimation problem as a structured low-rank matrix sensing problem. Then the problem was solved by the GCG-Alt algorithm. The computational complexity analysis and simulation results suggested that our proposed matrix sensing-based channel covariance estimator has lower computational complexity and outperforms one of the state-of-the-art mmWave channel covariance estimators.