The fourth generation wireless communication systems have already been deployed. However, there are still some challenges that cannot be overcome by 4G due to an explosion of wireless mobile devices and services, such as higher user data rates, enhanced coverage, reduced latency, and so on. Thus, wireless systems designers have been facing the continuously increasing demand for high data rates and coverage extension. In this thesis, we propose potential transmission techniques at the relay station and the base station for next generation wireless communication systems. This thesis consists of three parts. Contributions of each part are provided as follows. In Chapter 2, the Filter-and-Forward (FF) relay design for orthogonal frequency-division multiplexing OFDM) transmission systems is considered to improve the system performance over simple amplify-and-forward (AF) relaying. Recently, relay networks have drawn extensive interest from the research community because they play an important role in enlarging the network coverage and improving the system performance in current and future wireless networks. Indeed, LTE-Advanced adopts relays for coverage extension and performance improvement [2]. There are several well-known relaying schemes such as AF, decode-and-forward (DF), and compress-and-forward (CF) [3？5]. Among the relaying schemes, the AF scheme (i.e., simple repeater) is the simplest and is suitable for cheap relay deployment. there have been some efforts to extend this simple AF scheme to a linear filtering relaying scheme, i.e., an FF scheme, to obtain better performance than the AF scheme while keeping the benefit of low computational complexity of the AF scheme [6？11]. It has been shown that the FF scheme can outperform the AF scheme considerably. However, most of the previous works on the FF relay have been done for single-carrier transmission, whereas most of the current wireless standards adopt OFDM transmission. Thus, in this chapter, we propose direct FF relaying for OFDM transmission instead of using conventional OFDMrelays which OFDM-demodulate the incoming signal, amplify or decode the demodulated signal, OFDM-remodulate the processed signal and transmit the remodulated OFDM signal to the destination [12？15]. In the proposed scheme, the incoming signal to the relay is FIR filtered at the chip rate of the OFDMmodulations in time domain and the filtered signal is directly forwarded to the destination. In this way, the necessity of OFDM processing at the relay is eliminated, but the overall performance can still be improved over the AF scheme by a properly designed relay filter. Three design criteria are considered to optimize the relay filter. The first criterion is the minimization of the relay transmit power subject to per-subcarrier signal-to-noise ratio (SNR) constraints, the second is the maximization of the worst subcarrier channel SNR subject to source and relay transmit power constraints, and the third is the maximization of data rate subject to source and relay transmit power constraints. It is shown that the first problem reduces to a semi-definite programming (SDP) problem by semi-definite relaxation and the solution to the relaxed SDP problem has rank one under a mild condition. For the latter two problems, the problem of joint source power allocation and relay filter design is considered and an efficient algorithm is proposed for each problem based on alternating optimization and the projected gradient method (PGM). Numerical results show that the proposed FF relay significantly outperforms simple AF relays with insignificant increase in complexity. Thus, the proposed FF relay provides a practical alternative to the AF relaying scheme for OFDM transmission. In Chapter 3, the FF relay design for multiple-input multiple-output (MIMO) OFDMsystems is investigated. In the previous chapter, we introduced direct finite-impulse response (FIR) filtering without OFDM processing at the relay, proposed several FF relay design methods for OFDM systems based on worst subcarrier SNR maximization or direct rate maximization, and showed that such direct FIR filtering relays can yield comparable performance relative to OFDM-processing relays [16,17]. However, the limitation of the work is that we considered single-input single-output (SISO)-OFDM only and its approach based on worst subcarrier SNR maximization or direct rate maximization is not easily extended to the MIMO-OFDM. Due to the considered MIMO structure, the FF relay design is investigated in the framework of joint design together with the linear MIMO transceiver. As the design criterion, first the minimization of weighted sum mean-square-error (MSE) is considered. The joint design in this case is approached based on alternating optimization that iterates between optimal design of the FF relay for given MIMO precoding and decoding matrices and optimal design of MIMO precoding and decoding matrices for a given FF relay filter. Second, a more advanced problem of joint design for rate maximization is considered. The second problem is approached based on the obtained result regarding the first problem of weighted sum MSE minimization and the existing result regarding the relationship between weighted MSE minimization and rate maximization. Numerical results show the effectiveness of the proposed FF relay design method and significant performance improvement by the proposed FF relay over widely-considered simple AF relays for MIMO-OFDM systems.
In Chapter 4, the problem of outer beamformer design based only on channel statistic information is considered for two-stage beamforming for multi-user massive MIMO downlink. The multiple-input multiple-output (MIMO) technology has prevailed in wireless communications for more than a decade. The technology has been adopted in many wireless standards since it improves the spectral efficiency and reliability of wireless communication without requiring additional bandwidth. Recently, the MIMO technology based on large-scale antenna arrays at base stations, so-called massive MIMO, is considered to further improve the system performance for upcoming 5G wireless systems and vigorous research is going on on this topic. Massive MIMO can support high data rates and energy efficiency and simplify receiver processing based on the asymptotic orthogonality among user channels based on large antenna arrays [18, 19]. However, realizing the benefits of massive MIMO in practical systems faces several challenges especially in widely-used frequency division duplexing (FDD) scenarios. In contrast to current small-scale MIMO systems, downlink channel estimation is a difficult problem for FDD massive MIMO systems since the number of available training symbols required for downlink channel estimation is limited by the channel coherence time and the number of channel parameters to estimate is very large [20？23]. Furthermore, channel state information (CSI) feedback overhead for downlink user scheduling for massive FDD multi-user MIMO can be overwhelming without some smart structure on massive MIMO systems. To overcome these difficulties associated with massive MIMO, two-stage beamforming for massive MIMO under the name of “Joint Spatial Division and Multiplexing (JSDM)” has been studied in [1, 24？27]. The two-stage beamforming idea is basically a divide-and-conquer approach, and the key ideas of the two-stage beamforming strategy are 1) to partition the user population supported by the serving base station into multiple groups each with approximately the same channel covariance matrix (this can be viewed as virtual sectorization) and 2) to decompose the MIMO beamformer at the base station into two steps: an outer beamformer and an inner beamformer. The outer beamformer faces the antenna array and roughly distinguishes different groups by bolstering in-group transmit power and suppressing inter-group interference, and the inner beamformer views the product of the actual channel and the outer beamformer as an effective channel, separates the users within a group, and provides spatial multiplexing among in-group users [24]. Here, major complexity reduction results from the approach that the outer beamformer is properly designed based only on channel statistic information not on CSI. In this case, the actually required CSI for the inner beamformer adopting typical zero-forcing (ZF) or regularized ZF (RZF) beamforming is significantly reduced since it only requires the CSI of the effective channel with significantly reduced dimensions. In this chapter, we consider the outer beamformer design problem based only on channel statistic information for the aforementioned two-stage beamforming framework for massive MIMO. The problem is approached based on signal-to-leakageplus- noise ratio (SLNR). To eliminate the dependence on the instantaneous channel state information, a lower bound on the average SLNR is derived by assuming zero-forcing (ZF) inner beamforming, and an outer beamformer design method that maximizes the lower bound on the average SLNR is proposed. It is shown that the proposed SLNR-based outer beamformer design problem reduces to a trace quotient problem (TQP), which is often encountered in the field of machine learning. An iterative algorithm is presented to obtain an optimal solution to the proposed TQP. The proposed method has the capability of optimally controlling the weighting factor between the signal power to the desired user and the interference leakage power to undesired users according to different channel statistics. Numerical results show that the proposed outer beamformer design method yields significant performance gain over existing methods.
In Chapter 5, the outer beamformer design problem for two-stage beamforming for multi-user massive MIMO downlink is considered under the assumption that the base station has erroneous channel statistic information (CSI). The conventional multi-user (MU) MIMO beamforming [28？30] requires perfect channel state information, which is difficult for FDD massive MIMO systems since the number of available pilot symbols required for downlink channel estimation is limited by the channel coherence time and it may become much smaller than the number of large antenna arrays [20？23]. To overcome
these difficulties associated with massive MIMO, two-stage beamforming for massive MIMO has been studied in [1, 24？27, 31], which decomposes the MIMO beamformer at the base station into two steps: an outer beamformer and an inner beamformer. In these works, the outer beamformer is designed based on the perfect channel statistic information (CSI) adopting the inner beamformer as typical zero-forcing (ZF) or regularized ZF (RZF) beamforming. However, in practice, the CSI available at the base station is prone to errors caused by feedback quantization, estimation error, and so on, which significantly degrade the performance of the non-robust beamforming method [1,24？27,31]. Hence, we consider the outer beamformer design problem under imperfect CSI and propose a robust outer beamformer design method as an extension version of[31]. To tackle the uncertainty of the channel statistic information, the problem is formulated based on worst-case approach. By Lagrangian duality, the problem is equivalently reformulated and solved using the bisection method via a sequence of convex feasibility problems in the form of semidefinite programs (SDPs). Numerical results show that the proposed outer beamformer design method has the same performance as the conventional method with perfect CSI and yields better performance gain over the existing methods with imperfect CSI.
본 논문에서는 차세대 무선 통신 시스템에 적합한 필터링-후-전달 중계 방식과 기지국의 두 단계 빔 설계 방식을 다루었다. 논문은 각 무선 통신 환경에 적합한 중계기 및 기지국의 설계 방법에 따라 크게 네 부분으로 구성되어 있다. 논문의 첫 번째 부분과 두 번째 부분에서는 필터링-후-전달 중계기를 다루며, 논문의 세 번째 부분과 네 번째 부분에서는 기지국의 두 단계 빔 설계 방식에 대해 다룬다.
논문의 첫 번째 부분에서는 기존에 단일 반송파 환경에서만 국한되어 연구되었던 필터링-후-전달 중계기 방식을 SISO-OFDM 시스템에서 처음으로 제안하였고, 다양한 문제를 고려하였다. 중계기의 전력을 최소화하는 필터링-후-전달 중계기 설계 문제, 기지국과 중계기의 전력 제한이 있는 환경에서 반송파중가장낮은 신호대잡음비를 최대화하는 필터링-후-전달 중계기 설계및송신전력 할당 문제, 그리고 기지국과 중계기의 전력 제한이 있는 환경에서 데이터 전송량을 최대화하는 필터링-후-전달 중계기 설계 및 송신 전력 할당 문제를 다루었다. 각 문제는 최적화 이론과 행렬 이론에 근거하여 설계방안이제시되었으며, 기존의증폭-후-전달 중계기 대비 상당한 성능 향상을 보인다는 것을 밝혔다.
논문의 두 번째 부분에서는 앞서 연구되었던 필터링-후-전달 중계기를 MIMO-OFDM시스템으로 확장하여 실제 무선 통신 환경에 적합한 구조를 제안하고 설계 방법을 고려하였다. 먼저 데이터 전송량을 최대화하는 필터링-후-전달 중계기 및 송수신 행렬 설계 문제를 제안하였으며, 해당문제를 기존에 잘 알려진 최소 자승 오차와 데이터 전송량의 동등관계를 이용하여 최적화 문제로 변형하였다. 또한 최적화 이론과 행렬이론을 이용하여 데이터 전송량을 최대화하는 필터링-후-전달 중계기의 설계 방식을 제안하였고, 제안된 설계 방식이 기존의 증폭-후-전달중계기 대비 성능 향상을 보인다는 것을 보였다.
논문의 세 번째 부분에서는 초다수 다중 입력 다중 출력 안테나 (massive MIMO) 환경에서 기지국의 두 단계 빔 설계 방식에 대해 다루었다. 두 단계 빔 설계 방식은 기지국에서 빔을 형성할 때 내부 빔과 외부 빔으로 나누어 두 단계로 빔을 형성하는 것을 말한다. 여기서 외부 빔은 채널의 확률적 정보만을 가지고 설계되고 내부 빔은 외부빔과 실제 채널이 곱해진 채널 정보를 추정하여 이를 기반으로 제로포싱 기법으로 설계된다. 본 논문에서는 내부 빔은 간단한 제로포싱 빔이라 가정하고 확률적인 채널 정보만을 가지고 외부 빔을 설계하는 방법을 다룬다. 먼저, 평균적인 신호 대비 간섭누설 더하기 잡음비의 하한 경계를 유도하였고, 이를 최대화하는 문제가 기존의 기계 학습 및 선형구별 해석 분야에서 잘 알려진 Trace quotient problem (TQP) 문제로 귀결된다는 것을 보였다. 또한, 이 문제의 최적해를 구하는 알고리즘을 제시하고 수렴성을 증명하였으며 기존에 연구된 알고리즘들 대비 데이터 전송량 측면에서 성능을 향상시킬 수 있다는 것을 보였다.
논문의 네 번째 부분에서는 세 번째 부분에서 제안된 두 단계 빔설계 방법을 확률적 채널 정보의 오차가 존재하는 환경에서 고려하였다. 세 번째 부분에서 제안된 두 단계 빔 설계 방식을 무선 통신 시스템에 적용하려면 기지국에서 정확한 채널 공분산 행렬 정보를 요구한다. 따라서 채널 공분산 행렬의 추정 오차가 존재할 수 밖에 없는 실제 환경에서 성능저하가 발생할 가능성이 있다. 이에 논문의 네 번째 부분에서는 이를 보완하고자 최악의 경우를 고려한 Lagrangian duality 방법을 이용하여 채널 공분산 행렬의 추정 오차에 강인한 두 단계 빔 설계 방법을 제안하였다. 그리고 제안된 강인한 두 단계 빔 설계 방식이 채널 공분산 행렬을 정확하게 알고있을경우에는 논문의 세 번째 부분에서 제안된 방법과 동일한 성능을 보이고, 추정 오차가 존재하는 경우에는 더 좋은 성능을 나타냄을 보였다.
