適用於多輸入多輸出與多輸入多輸出中繼系統中最大似然接收機之前置編碼器設計

Abstract

前置編碼已被認為是一種可以有效改善多輸入多輸出 (Multiple-input multiple-output；MIMO)系統中傳輸品質的技術。一般而言，前置編碼的設計與接收機的類型有關。對於最大似然 (Maximum-likelihood；ML)接收機而言，最佳的前置編碼設計準則是最大化系統的自由距離，然而最佳解的導出相當困難，因此目前多數文獻僅討論其次佳解，本論文旨在探討對應ML接收機的前置編碼器設計問題。在論文的第一部分，我們首先考慮簡化之前置編碼，也就是傳送端天線選擇，最佳的天線選擇準則必需透過高運算量的窮舉法才能得到，為了避免此問題，研究者利用奇異值分解(Singular value decomposition: SVD)以及QR分解 (QR decomposition； QRD)推導出自由距離的下界。我們提出以QRD為基礎之天線選擇方法，我們證明了QRD選擇法會優於傳統的SVD法，此外我們進一步提出基底轉換的方法使得QRD選擇法能夠更接近最佳解。除了傳送端天線選擇之外，我們提出的方法也可適用於其他應用，例如接收端天線選擇、傳送端與接收端聯合天線選擇、以及在MIMO中繼系統中天線選擇。模擬結果顯示，我們提出的方式在上述應用中均能提供接近最佳的表現。 除了天線選擇之外，最近有研究者提出一種基於X-架構之次佳前置編碼方式，此方法的概念在於先利用SVD 得到平行子通道，再利用兩兩配對的方式得到多個2□2的子系統，這樣的作法允許我們僅需設計2□2的子前置編碼器，因而得以在降低編碼的複雜度，此外X-架構前置編碼的方式同時可提供一個低複雜度的ML接收機。然而，目前現有文獻中所提出的X-架構前置編碼器的設計均仰賴數值法以及查表的方式，使得現有的方法在實際應用上困難度與複雜度均相對增加。在論文的第二部分我們提出一個簡單但有效的方法來解決此問題，我們的方法所得到的前置編碼矩陣具有解析解，另外，我們也探討如何將X-架構前置編碼延伸至MIMO中繼系統中聯合前置編碼器設計的問題。模擬結果顯示我們提出的方法比現有的前置編碼法可以更有效的改善系統效能。 前置編碼器的計算需要完整的通道資訊，因此一般都在接收端完成，在實際系統中，前置編碼的實現是透過從碼書中選取一個最佳的碼字，再經由迴授通道將該碼字的索引回傳至傳送端。在論文的最後一個部分，我們將討論如何建構X-架構前置編碼所需要的碼書，有別於傳統的前置編碼，X-架構前置編碼器需要兩種碼書，一種是用於一么正矩陣，另一種是用於子編碼器的矩陣，使用於么正矩陣的碼書所面臨的問題在於量化的矩陣不能讓系統保有X的架構，低複雜度ML接收機也因此不復存在，針對此問題，我們先證明我們所提出的X-架構前置編碼器仍然有效，接著我們提出一個低複雜的接收機架構來解決偵測的問題。模擬結果顯示，我們所提出的方法除了可以使用低複雜度的接收機外同時也可有效改善系統效能。

Precoding has been considered a promising technique in multiple-input multiple-output (MIMO) transmission. In general, the design criterion depends on the detector used at the receiver. For the maximum-likelihood (ML) detector, the criterion is known to maximize the free distance. Unfortunately, the derivation of the optimum solution is difficult, and suboptimum solutions have then been developed. In this dissertation, we study the precoder design for the ML detector in MIMO and MIMO relay systems. In the first part of this dissertation, we consider a simplified precoding scheme, namely, transmit antenna selection. To maximize the free distance, it is necessary to conduct exhaustive search for the selection pattern. To avoid the problem, lower bounds of the free distance derived with the singular value decomposition (SVD) or QR decomposition (QRD) were developed. We propose a QRD-based selection method maximizing the corresponding lower bound. With some matrix properties, we theoretically prove that the lower bound yielded by the QRD is tighter than that by the SVD. We then further propose a basis-transformation method so that the lower bound yielded by the QRD can be further tightened. The proposed method is also extended to antenna selection in amplify-and-forward (AF) MIMO relay systems, and other types of selections such as receive antenna selection, and joint transmit and receive antenna selection. Simulations show that the lower bound that the proposed methods evaluate can approach the true free distance closely.

As mentioned, the optimum precoder for the ML detector is difficult to derive. Recently, a simple design method, referred to as X-structured precoding, was proposed to solve the problem. This method first adopts the SVD to transform the MIMO channel into parallel subchannels. Then, the subchannels are paired to obtain a set of 2x2 subsystems and 2x2 subprecoders can be designed. Due to this special structure, the ML detection in the receiver can be conducted on 2x2 subsystems, reducing computational complexity significantly. Several methods have been developed to solve the X-structured precoder. However, most of them use numerical searches to find their solutions and require table look-ups during the run time. In the second part of this dissertation, we propose a simple but effective method to solve the problems. The proposed precoder has a simple closed-form expression and no numerical searches and table look-ups are required. We also extend the proposed method in joint source/relay precoders design in two-hop AF MIMO relay systems. With the proposed source subprecoder, the joint design problem can be significantly simplified. Simulations show that the proposed X-structured precoding for MIMO relay systems significantly outperforms other types of precoding methods.

Calculation of the precoder requires full channel state information and is conducted in the receiver in general. In real-world applications, a codebook is designed for the precoder, and only the index of the codeword is fed back. In the final part of this dissertation, we investigate the codebook design problem in X-structured precoding. Unlike the conventional precoding, X-structured precoding requires two codebooks, one for a unitary matrix and the other for 2x2 subprecoders. The challenges are that the quantized unitary matrix cannot yield the X-structure and the receiver cannot conduct ML detection on 2x2 subsystems. We show that the proposed X-structure precoding scheme can still be used, and propose low-complexity detection schemes to solve the detection problem. Simulation results show that the proposed method can effectively reduce the computational complexity of the receiver and at the same time improve the system performance.