多輸入多輸出正交分頻多工系統中通道、接收與發射角度之聯合估計:演算法與應用

Abstract

天線陣列的波束成型為無線通訊系統裡的重要技術，然而使用波束成型，傳送與接收端分別需知傳送角度及接收角度。本論文第一部分考慮使用數位陣列之領航訊號輔助多輸入多輸出 (MIMO)正交分頻多工 (orthogonal frequency division multiplexing; OFDM) 系統中，傳送角度、接收角度與通道之聯合估計問題。首先，利用無線通訊通道響應稀疏的特性，我們提出以壓縮感知 (compressive sensing; CS) 為基礎的通道估計方法。之後，利用多個使用波束成型傳送之OFDM訊號符元所估計的通道，我們提出傳送角與接收角度之最大似然 (maximum likelihood; ML) 聯合估計法，其中因通道路徑增益為一隱藏的未知參數，我們使用期望最大化 (expectation maximization; EM) 演算法解決此問題。並且進一步分析該估計方法的理論下限 (Cram r rao lower bound; CRLB)，並設計最小化一CRLB相關函數的傳送波束成型矩陣 (transmit beamforming matrix; TBM)。另外我們也考量有事前資訊情況下，提出最大事後似然 (maximum-a-posteriori; MAP) 估計方法。同樣地，因通道路徑增益為一隱藏的未知參數，我們提出兩階段 (two-stage) 貝氏EM (Bayesian expectation maximization; BEM) 演算法解決此問題。在此情況下，我們亦進一步分析該估計方法的理論下限 (Bayesian CRLB; BCRLB)，並設計最小化一BCRLB相關函數的TBM，結果顯示只需兩個OFDM訊號符元便可進行有效率的估計。模擬顯示所提出方法的效能在有/無事前資訊的情況中皆能逼近CRLB/BCRLB。 本論文第二部分考慮使用混合式陣列之領航訊號輔助的MIMO- OFDM系統中，傳送角度、接收角度與通道之聯合估計問題。在混合式陣列中，波束成型須分為類比波束成型及數位波束成型。另外，接收端亦須使用接收波束成型。在此架構下通道響應估計方式與第一部份相同，故此部分著重於TBM與接收波束成型矩陣 (receive beamforming matrix; RBM) 的設計方法。首先分析此架構下傳送角度與接收角度MAP估計方法的BCRLB，再提出最小化一BCRLB相關函數的TBM與RBM，稱之為UC-TBM與UC-RBM。在混合陣列中，TBM/RBM為其類比TBM/RBM (A-TBM/A-RBM) 與數位TBM/RBM (D-TBM/D-RBM) 的乘積，其中A-TBM/A-RBM的每一元素代表類比相位位移器的動作，有振幅及有限相位位移限制。針對此非線性最佳化問題，我們提出線性化此問題並遞迴地求解A-TBM/A-RBM與D-TBM/D-RBM來最小化誤差矩陣的大小 (Frobenius norm)。模擬結果顯示提出的方法能達到與UC-TBM/UC-RBM相似的效能。 本論文最後部分，提出一傳送角與通道之聯合估計方法，以改善3GPP長程演進系統 (Long Term Evolution; LTE) 的三維定位。傳統上，觀測到達時間差 (observed time difference of arrival; OTDOA) 能提供良好二維定位解析度。雖然其亦能延伸到三維定位，但需較多的基地台，並且在一般的蜂巢網路基地台的佈建方式下表現不佳。我們提出新的OTDOA定位方法解決此問題。首先利用無線通道稀疏的特性，提出以CS為基礎的通道估計方法來提高訊號到達時間的估計精度。接著設計TBM使接收端能精準地估計仰發射角。最後，結合到達時間與仰發射角，我們提出改良式OTDOA方法進行三維定位。在提出的方法中，所需的基地台個數及其佈建方式可維持與原本二維定位相同，可大幅降低佈建成本並改善效能。模擬結果顯示90%的定位誤差可以小於7公尺。

Beamforming with antenna arrays has been considered as an enabling technology for next-generation wireless communication systems. To conduct beamforming, one has to know the angle-of-departure (AoD) at the transmitter and the angle-of-arrival (AoA) at the receiver. In the first part of the dissertation, we consider joint AoD, AoA, and channel estimation problem for pilot-assisted MIMO-OFDM systems with digital arrays. First, new compressive-sensing (CS) based methods are proposed for channel estimation, exploiting the sparse property of wireless channels. With multiple beamformed OFDM symbols, AoA and AoD are then jointly estimated for each channel path by the maximum likelihood (ML) method. Since a hidden parameter is involved in the problem, the expectation-maximization (EM) algorithm is then employed. The Cramer-Rao lower bound (CRLB) is derived and a transmit-beamforming-matrix (TBM) design minimizing a CRLB-related function is proposed accordingly. For the scenario that prior information is available, we propose a maximum-a-posteriori estimation method. Similar to the ML method, a hidden variable is involved and a two-stage Bayesian EM algorithm is proposed to solve the problem. We also derive the Bayesian CRLB (BCRLB) and propose a TBM design minimizing a BCRLB-related function. It turns out that only two training OFDM symbols are required for the estimation. Simulation results show that the proposed methods can attain the CRLB/BCRLB in both scenarios.

In the second part of the dissertation, we consider the joint channel, AoD, and AoA estimation problem for systems with hybrid arrays. In hybrid arrays, beamforming is split into analog and digital beamforming. Different from digital arrays, receive beamforming is also required. In this scenario, the time-domain channel estimation remains the same as that in digital arrays. The main focus is to design both the TBM and the receive beamforming matrix (RBM). We first derive the BCRLB for AoD/AoA estimation from which TBM and RBM can be designed by minimizing a BCRLB-related function, referring to as unconstrained TBM (UC-TBM) and unconstrained RBM (UC-RBM), respectively. For a hybrid array, the TBM/RBM can be expressed as a product of an analog TBM/RBM (A-TBM/A-RBM) and a digital TBM/RBM (D-TBM/D-RBM). Each entry of the A-TBM/A-RBM represents the phase-rotation operation conducted in a phase-shifter, posing an amplitude constraint in the design problem. Then, we propose minimizing the Frobenius norm between the UC-TBM/UC-RBM and the product of the A-TBM/A-RBM and D-TBM/D-RBM. Since the optimization is nonlinear, we further propose an iterative algorithm to solve the A-TBM/A-RBM and D-TBM/D-RBM. Simulation results show that the proposed method significantly outperforms the existing in the BCRLB of the AoD/AoA estimation, and the performance with the proposed method is similar to that with the UC-TBM and the UC-RBM.

In the third part of the dissertation, we consider 3D-positioning in the 3GPP LTE system. It has been shown that the observed-time-difference-of-arrival (OTDOA) method can provide good result for 2D-positioning. Although the conventional OTDOA method can be used in 3D-positioning, it requires more base stations (BSs) in cooperation and often performs poorly in typical cellular network geometry. Here, we propose a novel OTDOA-based method to solve the problems. First, exploiting the sparsity of the wireless channel, we propose a CS based channel estimation method that greatly enhances the precision of time-of-arrival (TOA) estimation. Then, we propose a TBM design scheme such that the elevation AoD can be accurately estimated. Combining the estimated TOAs and the AoD, we finally propose a modified OTDOA algorithm to conduct 3D-positioning. With the proposed scheme, not only the number of BSs required for 3D-positioning remains the same as that of 2D-positioning, but also the positioning accuracy greatly outperforms that of the conventional OTDOA method. Simulations show that 90% of the position error can be less than 7 meters.