大型多天線通道及其估計之漸近行為分析

Abstract

多天線通道在轉換域（transform domain）的稀疏特性可用來而設計高效能的降秩（rank）通道估計法。在現有文獻中，此類通道估計方法的討論往往只侷限於傳送／接收端相關性是可拆的（separable）多輸入多輸出（multiple-input, multiple-output, MIMO）通道模型或擁有多用戶的單輸入多輸出系統。本論文一個探討重點便是分析降秩通道估計法在估計更具一般性的MIMO模型（例如：傳送／接收端相關性不可拆的通道）時的效能與它的其他性質。因為巨量天線陣列優良的空間解析能力與其通道有可被大幅降秩的潛力，系統若採用此天線陣列將能更顯著地降低運算複雜度、壓抑雜訊、過濾干擾而提升效能。基於上述考量，本論文將圍繞在探討具有巨量天線陣列的系統。根據最小平方（least-squares）和最小均方誤差（minimum mean-square error）準則，我們提出二種類型的降秩通道估計，並分析它們在系統天線數有限與漸近（趨近於無限大時）的行為表現。

我們首先探討具單一散射叢集（scattering cluster）的窄頻MIMO通道，再推廣至多叢集通道以至路徑延遲可區分的多散射叢集寬頻MIMO通道。為了估計此種類型的通道，我們同時也提出可最小化均方估計誤差的領航訊號（pilot）。我們所提出的降秩通道估計是自適式的，不需執行費時的空間搜索。它們不但擁有極佳的均方誤差效能，還適合混合式類比／數位傳收架構，這種架構能大幅降低產品的成本。我們證明了降秩通道估計的低變異數性質與漸近不偏性（unbiasedness）。另外，我們還求得在不同的訊號入射角／出射角分布下的空間關聯（spatial correlation）矩陣的漸近特徵值（eigenvalue），並且驗證前述的一般性的MIMO通道與其降秩估計的有利傳播（favorable propagation）性。我們更進一步探討這些漸近性質，求得資訊傳輸率在有完整通道資訊時與只有通道估計量時的確定性等價（deterministic equivalent），並利用這些確定性等價去解決向來複雜的多用戶巨量多天線系統總傳輸率最佳化問題。

此外，我們找到可以完全解決巨量天線系統中常見的領航訊號汙染（pilot contamination）問題的條件。在許多實際情境，只要傳送端能將信號集中載至適當的轉換域子空間、接收端又可將接收波束調整至所對應的方向，即可符合或幾乎符合上述的要求。增加傳送或接收端的天線數均能提供更多的自由度來避免領航訊號汙染。同樣的傳收兩端協調的概念也可運用於對抗無線蜂巢式網路中同巢或異巢間的干擾並增加系統容量。

Reduced-rank (RR) channel estimators that exploit the transmission channel's sparsity in transform domain, have been proposed but the discussions have been mostly limited to Kronecker-like multiple-input, multiple-output (MIMO) models or multiuser single-input, multiple-output (SIMO) systems. This work considers a general class of MIMO channels with non-separable spatial correlations. We focus on systems using large-scale arrays as they usually yield most impressive RR effect and spatial resolution that make possible significant complexity reduction, noise suppression, and interference filtering. We study both least-squares (LS)- and minimum mean-square error (MMSE)-based RR MIMO channel estimators and analyze their behaviors in finite as well as asymptotic regimes.

We begin our investigation with narrowband single-cluster channels and extend our analysis to multi-cluster and then wideband, multi-cluster, multi-delay MIMO channels. A mean-square error-minimizing pilot structure for estimating such channels is presented. The transform domain RR channel estimators are adaptive; they do not perform time-consuming spatial search and not only give excellent performance but also yield hybrid analog-digital implementation which is much desired for reducing the realization cost. We prove that our RR channel estimators are asymptotically unbiased and of low variances. We derive the exact asymptotic eigenvalues of the spatial correlation matrices for various angle-of-arrival/angle-of-departure distributions and verify that correlated MIMO channels and their RR estimates possess the favorable propagation property. Extending our asymptotic analysis, we derive the deterministic equivalent of per-stream ergodic rate and solve the computationally complex problem of the achievable sum rate of a multiuser massive MIMO system with either perfect or imperfect channel state information (CSI).

In addition, we find the condition of perfect pilot decontamination for a massive MIMO system. Based on the information extracted by our RR channel estimators, this condition can be met or nearly satisfied in many practical cases by placing the data streams in proper spatial modes and aligning the receive array toward only the right directions. Increasing the array size on either or both sides of the link offers extra degree-of-freedom to avoid pilot contamination. The same concept of transmission and reception coordination can be applied to mitigate the intra-cell/inter-cell interference and enhance the network capacity.