Open-Loop Channel Estimation Algorithms for Millimeter Wave Communication Systems


Student thesis: Doctoral Thesis

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Award date6 Sep 2019


Communication on millimeter wave (mmWave) bands will be one of the essential new technologies in the next generation mobile cellular network. In order to obtain the high spectrum efficiency, an accurate channel estimate is the key, which facilitates advanced mmWave hybrid multiple-input multiple-output (MIMO) precoding techniques. Compared to conventional multiple-input multiple-output (MIMO) systems, mmWave MIMO channel estimation requires high overhead due to large-scale antennas and limited radio frequency (RF) chains. Since open-loop channel estimation methods require no additional feedback during estimation procedure, they have the potential to reduce the high overhead of mmWave channel estimation. In this thesis, we study the open-loop channel estimation methods for the mmWave communication systems.

After introducing the backgrounds in Chapter 1, we present in chapter 2 a non-adaptive mmWave MIMO channel estimation technique based on the knowledge of low-rank matrix reconstruction. Taking the limited RF chains of mmWave systems into account, we propose a random design of channel sampling signals. We show that the random sampling signals obey the restricted isometry property (RIP) with high probability. We then formulate the channel estimation as a low-rank matrix reconstruction problem, and based on the established RIP, show an estimation error bound of the proposed framework, which reveals robust performance at low signal-to-noise (SNR). We also devise an iterative technique that effectively finds a suboptimal but stationary solution to the formulated problem. The proposed technique is shown to have improved channel estimation accuracy with a low channel use overhead as compared to that of previous closed-loop techniques.

In chapter 3, we investigate low-rank matrix reconstruction techniques by fully exploiting the subspace information. By the priori subspace information, we mean that certain partial knowledge of low-rank matrices, such as column or row subspace information, is priori available. How to exploit such information to improve the reconstruction accuracy has recently received considerable interests. Specifically, for the task of low-rank matrix reconstruction, the observations are generated by an affine map of this matrix. We provide the optimality condition for affine maps that achieve the minimum mean squared error (MSE). In addition, we derive an optimal representation of low-rank matrices, which optimizes the rank and subspace of the estimate by adapting them to the noise level in order to achieve the minimum MSE. The simulations verify that the optimized affine map achieves more accurate reconstruction than the randomly generated affine map.

In chapter 4, we extend the low-rank matrix reconstruction techniques proposed in chapter 3 into mmWave channel estimation. We propose a sequential two-stage subspace estimation method that resolves the overhead issues as well as obtains accurate subspace information. In the first stage, the proposed method samples the columns of the channel matrix to estimate its column subspace. Then, based on the obtained column subspace, it optimizes the training signals to estimate the row subspace. We show that the subspace estimation accuracy is linearly with the SNR, i.e., O(SNR), at high SNR while quadratically with SNR, i.e., O(SNR^2) at low SNR. We provide theoretical justification for the above claims and numerical results showing improved accuracy compared to the prior arts.

Unlike the formulation of low-rank matrix reconstruction in chapter 2 and chapter 4, by utilizing the fact that the mmWave channel has sparse support in angular domain, we propose a sequential method to estimate the angles of arrival (AoAs) and angles of departure (AoDs) in chapter 5. Specifically, in the first stage, the AoAs are estimated by solving a multiple measurement vector (MMV) problem, which aims to recover a common support shared by a set of sparse vectors. In the second stage, based on the estimated AoAs, the sampling signals are carefully designed to estimate AoDs. We show that the successful reconstruction probability of the proposed sequential method is much higher than that of the existing one-stage compressed sensing (CS)-based methods. Moreover, to eliminate the quantization error introduced by the angle dictionary, we apply the atomic norm minimization in each stage of estimation. The simulation results demonstrate the significantly improved performance of the proposed sequential method.

Finally, Chapter 6 concludes the thesis and outlines possible future research.