全雙工中繼系統有限階數濾波器設計: 

關於全雙工中繼的傳收機設計議題雖然已被廣泛討論，但目前多數的方法都是將自我干擾視為有害訊號而希望能將其完全消除。實際上所謂的自我干擾其實是所需訊號構成，這個事實暗示著將自我干擾完全移除未必對整體效能是最好的策略。基於上述概念，我們試圖提出一個新穎的訊源端與中繼端濾波器設計，其中自我干擾訊號將被視為有用訊號而被部分保留在最後的訊號估測。本研究方法基本概念是先推導出訊源端與中繼端濾波器對應的最佳頻譜，由於在實際硬體上濾波器可能需要非常多的階數來實現最佳頻譜，因此我們再使用權重最小平方 (Weighted least-square) 準則來完成有限階數濾波器設計。首先從單天線且僅考慮單一中繼節點系統出發，然後延伸至單天線但具備多中繼節點之系統，最後完成多天線系統的設計。此部分研究成果豐碩，共計發表三篇 IEEE Transactions on Communications 期刊文章。

可調式智能反射面輔助之多天線傳收機設計: 

可調式智能反射面 (Reconfigurable intelligentsurface; RIS) 在近幾年受到廣泛討論，主因為RIS相對傳統中繼傳輸具有低佈建成本的優勢。本研究考慮RIS輔助空間多工傳輸之MIMO系統，接收端採用最大似然 (Maximumlikelihood; ML) 估測，設計目標是聯合最佳化前置編碼器以及反射器使得錯誤率最小化。目前文獻上的作法是採用梯度下降法來完成設計，然因為ML估測的錯誤率是一個相當複雜的函數，因此該文獻方法的實現成本非常高。為了解決這個問題，我們首先觀察ML估測的效能在高訊雜比的情況下會與接收訊號倆倆之間的最短距離有關，此距離亦稱為自由距離。然而即便如此，以自由距離最大化為設計準則仍是相當困難，原因為自由距離依舊是一個離散域的函數；此外由於反射器是由相位偏移器組成，因此其振幅限制會加深設計的困難度。本研究使用交替最佳化來解決這個難題，首先對於反射器部份我們透過矩陣特性來讓自由距離的梯度變得更容易計算，接著採用所謂的2-D前置編碼來讓移除梯度與通道的相關性，進而大幅降低運算複雜度。模擬結果顯示我們的演算法可以有效改善系統錯誤率表現，且複雜度遠比現有文獻低。目前研究結果已獲得 IEEE Communications Letters 接受刊登。

具直接路徑全雙工多天線中繼系統傳收機最佳化: 

全雙工多天線中繼是一個可以有效增加頻譜效率以及傳輸品質的通訊技術。有別於傳統半雙工中繼，當訊源端至目的地端的直接路徑存在於全雙工中繼系統時，會在接收訊號中引入符元向量間干擾，進而導致整體傳收機設計變得非常困難。為了解決此一問題，我們首先提出一個雙濾波 (Dual-filtering; DuF)接收機架構來移除符元向量間干擾，使得傳統的連續干擾消除 (Successive interference cancellation; SIC) 估測得以實現。接著我們再利用Primal分解將訊源端與中繼端前置編碼器設計拆解為主問題以及子問題。當接收機使用DuF-QR-SIC估測時，子問題中的訊源端前置編碼器可以用幾何平均分解方式求得。至於當接收機使用雙濾波最小均方誤差 (Minimum mean-squared error; MMSE) 連續干擾 (DuF-MMSE-SIC) 估測時，子問題的求解可以採用均勻通道分解來完成。在解完子問題之後，接下要處理的便是主問題中的中繼前置編碼器設計；由於其較為複雜，對此我們證明原本的主問題可以轉換成一個較容易處理的矩陣跡數 (Trace) 最小化問題，並透過疊代方式來求解。值得注意的是，我們所提出的主問題處理方式當系統使用DuF-QR-SIC以及DuF-MMSE-SIC兩種估測時均適用。模擬顯示本研究所提出的傳收機設計可以大幅改善系統錯誤率表現且複雜度維持在可接受的範圍內。此研究成果發表在頂級期刊 IEEE Transactions on Communications。

Joint Transceiver Designs in Full-Duplex MIMO Relay Systems:

Full-duplex (FD) MIMO relaying has been considered an effective scheme to increase the spectral efficiency for wireless communications. As known, the main problem for the FD system is the cancellation of loop interference (LI). In this work, we consider the joint source/relay precoding to reduce the influence of LI. An MMSE receiver is adopted at the destination. Note that the joint precoder design is more complicated when spatial multiplexing is exploited for signal transmission. To solve the problem, we propose an iterative method in which the original problem is split into two subproblems. With some matrix properties, we then show that each subproblem can be formulated as a convex optimization. A closed-form solution can be obtained with the Karush-Kuhn-Tucker (KKT) conditions. Using an MSE upper bound, we also propose a low-complexity method to reduce the computational complexity while the performance remains comparable.  In addition to linear transceiver, we alsor consider nonlinear transceiver design in FD-MIMO relaying. At the destination, QR-SIC and MMSE-SIC receivers are considered for signal detection. For SIC detection, the error-rate performance is a highly nonlinear function of the precoders. To overcome th difficuty, we propose using the primal decomposition, translating the original problem into a subproblem and a master problem. In the subproblem, the source precoder is first solved with the geometric mean decomposition (GMD) or uniform channel decomposition (UCD) method. Then, the master problem can be formulated as a convex optimization so that we can solve the relay precoder with KKT conditions. The proposed precoders have closed-form expressions, facilitating real-world implementations. Simulation results show that the proposed transceivers significantly improve the performance of FD-MIMO relay systems. 

Source/Relay Precoder Design in Amplify-and-Forward (AF) MIMO Relay Systems:

In addition to conventional MIMO, we also explore the problem of joint source/relay precoders design in two-hop AF MIMO relay systems. In this work, we start from the system with ML receivers. The problem is much more involved and a closed-form solution is intractable to find. To overcome the difficulty, we propose the use of X-structured precoding so that the problem can be reformulated as a simple scalar-valued optimization problem. Simulations show that the proposed method can significantly outperform existing joint design methods. Compared to ML receivers, successive interference-cancellation (SIC) detection can be of much lower computational complexity. Although the joint precoders design problem for SIC receivers has been investigated in literature, the optimality is still left unknown. In this subject, we consider QR-SIC and minimum mean-squared error (MMSE)-SIC receivers. We propose novel derivations for the precoders, and theoretically prove that the proposed schemes can achieve the optimum performance. 

The joint source/relay precoding relies on the knowledge of channel state information at the transmitter (CSIT). The acquisition of CSIT can be of severe feedback overhead. In this regard, the codebook-based limited-feedback precoding is widely exploited in practical systems since the feedback bits can be effectively limited. As known, the system performance strongly depends on the codewords selection criterion. In this work, we will explore how to design the selection criterion when SIC receivers are adopted at the destination. Starting from the QR-SIC receiver, we first propose a centralized selection scheme by maximizing the minimum post-processing signal-to-noise ratio. Next, a decentralized selection scheme is further developed to reduce the computational complexity. Furthermore, we demonstrate that our methods can be directly extended to the system with MMSE-SIC receivers. Simulation results show that the proposed designs can significantly improve the system performance. 

Low-Complexity ML Detectors for Generalized Spatial Modulation Systems:

Spatial modulation (SM) combined with spatial multiplexing is a newly developed transmission scheme in multiple-input multiple-output (MIMO) systems. The resultant system, referred to as generalized SM (GSM), can use the maximum-likelihood (ML) detector jointly detecting the antenna-subset (AS) index and symbol vector. As known, the ML detector can achieve optimum performance; however, its computational complexity can be prohibitively high when the dimension of the GSM system is large. In this work, we propose new methods to solve the problem. The main idea is to split the detection into two stages, one for the AS index and the other for the symbol vector. For the detection of the AS index, we develop two methods, referred to as Gaussian approximation and QR projection. Once the AS index is detected, conventional low-complexity ML detectors can be applied for the detection of the symbol vector. The diversity order for the proposed methods is further analyzed and an enhanced method is also proposed to achieve near-optimum performance. Finally, the proposed methods are extended to conduct soft detection of GSM systems. Simulations show that our methods significantly outperform existing ones while the detection complexity remains similar. Besides, this work also received the Postdoctoral Publication Award (Ministry of Science and Technology, Taiwan, 2016)。

Antenna Selection for Maximum-Likelihood MIMO Detection: 

Antenna selection is a simple but effective technique to enhance the performance of a spatial multiplexing MIMO system. For the ML detector, the criterion is to maximize the free distance. However, an exhaustive search is required to derive the distance, and the computational complexity can be prohibitively high. To avoid the exhaustive search, a lower bound of the free distance derived with the singular value decomposition (SVD) was then developed. This bound only involves the smallest singular value of the channel matrix and its maximization can be easily conducted. An alternative lower bound of the free distance with the QR decomposition (QRD) was also derived in the literature. In this work, we first propose a QRD-based selection method maximizing the 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 propose a basis-transformation method so that the lower bound yielded by the QRD can be further tightened.