大型多天線系統之三維通道估計

Abstract

我們首先探討一裝有大型天線陣列的基地台(BS)來服務多個單天線用戶(UE)的多輸入多輸出(MIMO)分時多工單細胞系統。若此天線陣列為均勻線性陣列(uniform linear array)，我們將通道空間相關矩陣經由二維么正轉換(2D unitary transforms)如離散傅立葉轉換(DFT)或是離散餘弦轉換(DCT)來分析、估計接收信號之平均入射角(Angle of Arrival, AoA)及入射角擴散(Angle Spread, AS)。二維轉換的分析是導因於我們對空間通道的非參數回歸建模(nonparametric regression modeling)，將通道本身或其相關矩陣投影至已知的正交座標。 我們分析相對應的回歸係數特性來估計AOA和AS。對窄頻信號而言，此方法提供了最小秩(minimum rank)通道建模並解釋了為何在同時估計AOA和通道係數時，可以利用估計較少的建模參數來改善通道估計的均方誤差(mean squared error, MSE)效能。 除了非參數回歸建模之外，我們也由波束行塑(beamforming)或空間濾波(spatial filtering)的觀點來解釋通道估計和AOA與AS相關的演算法設計。此一觀點是將通道向量(矩陣)視為收到的信號波形，將通道向量(矩陣)做二維的轉換可以等效的看成利用多個波束成型矩陣(beamforming matrix)去搜尋在空間多叢集(multi-cluster)的訊號並決定其入射方向以及角度分佈。這個空間搜尋的觀點引申出關於波束的數量、搜尋範圍、角度解析度和搜尋方式，進而衍生出不同的估計 選項。 我們接著將二維通道以及角度的估計延伸至三維的情境，且考慮多細胞系統。因基地台會收到鄰近細胞用戶送出的訊息，而這些訊息多會以不同的三維角度抵達。我們透過三維角度估計來分離這些由不同細胞送達的訊號，可減少細胞間的干擾，包括引航(pilot)信號間的干擾(pilot contamination)。 我們在上述各種情境(單細胞、多細胞，二維、三維)的環境下，分析了通道估計的均方誤差(mean squared error, MSE)效能，且通過電腦模擬驗證我們的確提供了高準確的通道估計演算法以及有效地解決鄰近細胞的引航信號干擾。

We consider a single-cell time-division duplexing (TDD) multi-user (MU) multiple input multiple-output (MIMO) system with a base station (BS) equipped with a large number of antennas serving many single-antenna mobile users. Assuming a linear receiving array at BS, we decompose the spatial channel (correlation) matrix through two-dimensional unitary transforms such as discrete cosine transform (DCT) or discrete Fourier transform (DFT). The channel estimation and related mean angle-of-arrival (AoA) and angle spread (AS) information id extracted two different perspectives; both offer useful insights into the problem at hand while render accurate estimates. From a model-based viewpoint, the transform attempts to describe the channel matrix by a nonparametric regression model or equivalently, projecting it into a predetermined unitary coordinate. We analyze the behavior of the corresponding regressioncoefficients to determine the desired mean AoA and AS values. This approach gives a minimum rank channel representation and explains why a joint mean AoA and channel estimate requires less modeling parameters thus gives improved performance when the AS is not large. An alternate perspective that treats the channel vector (matrix) as the received waveform so the responsibility of the receiver is locating the AoA(s) and the associated AS (beamwidth). Applying a 2D transform on the channel vector (matrix) is equivalent to using a multibeam antenna (beamforming matrix) to search for the directions and spreads of the incoming wavefront which arrives at the receive array in spatial clusters.The spatial search viewpoint raises issues concerning the number of beams, the search range, resolution and the search method, resulting in a variety of estimation options. The 2D channel and AoA/AS estimation problem is extend to the 3D case and the single cell assumption is removed and extended to a multi-cell scenario. As signals from neighboring cells tend to arrive at a BS in different spatial directions, they are likely to be separable in angle domain by our estimate which is capable of identifying the received waveform in both azimuth and altitude (elevation) directions, thereby eliminating most inter-cell interference, pilot contamination included. We analyze the mean squared error (MSE) performance of the channel estimate in both single-cell and multi-cell (with pilot contamination) environments. Numerical results show that we are able to provide quite accurate estimates and suppress most co-channel interference resulted from neighboring pilots, if exists.