由於多天線-多載波系統可以增加通道容量及改善錯誤機率並且可提昇傳輸效率，已在學術上討論許久。藉由回傳的通道資訊，傳送端可使用預先編碼器改善系統的效能。方向性向量是通道資訊的部份重要資訊，可以有效的應用在具有預先編碼器的系統上，而一些通道資訊簡化及有效率回傳的演算法已經陸續被提出。然而，能量分配、選擇性天線及多型預先編碼也是可以增加通道容量及改善傳輸效能的重要課題。為了建構同時具有方向性和能量分配等多功能的預先編碼器，接收端需要回傳估測後的通道響應給傳送端。
在本篇論文，我們將通道響應參數化後達到通道資訊簡化的目的，此參數化過程中使用了退化的多項式模型，而多項式的係數被萃取出來當作通道響應的參數，並且發展了幾個有效率回傳多項式係數的演算法。在多輸入多輸出-正交分頻多工調變的系統下，為了有效的回傳大量的多項式係數，我們使用有效率的高斯量化和三角調變的量化器。同時，我們也提出一個低複雜度的前置處理器可以使得回傳的多項式係數大幅減少，稱為通道相位旋轉。並且也使用退化的多項式模型建構成的預測器，不僅可容許回傳延遲，而且可以更進一步減少回傳的負載。模擬結果也顯示了具有預先編碼的多輸入多輸出-正交分頻多工調變系統及時變且頻率選擇性的通道環境下，我們所提出的演算法擁有很低的回傳負載，並且幾乎可以達到最佳的通道容量和不錯的錯誤效能。

Multiple antennas multiple carriers systems have been attracted for a long time due to the outstanding capacity, error performance and throughput. The transmitter could apply the precoding based on the fed-back channel state information (CSI). The beamforming vectors, which are essential CSI, could be applied in precoded multiple-input multiple-output (MIMO) systems and some algorithms of CSI reduction and efficient feedback have been proposed. However, the power allocation, antenna selection and multi-mode precoding which can be applied in precoder are also important issues for increasing the channel capacity and improving the transmission performance. To implement a multi-function precoder which can exercise not only the beamforming but also the power allocation, antenna selection and so on, the receiver needs to feed back the estimated channel responses (CRs) to the transmitter.
In this thesis, we use the polynomial coefficients feedback algorithms based on the parameterization of CRs using the regression polynomial model. The polynomial coefficients are extracted as the parameters of CRs. To efficiently return the large amount of the polynomial coefficients for the multiple-input multiple-output with orthogonal frequency-division multiplexing (MIMO-OFDM) systems, we use efficient quantization algorithms based on the Gaussian quantization (GQ) and Delta modulation (DM). We also propose a low-complexity pre-processor based on channel phase rotation. The pre-processor operates before the parameterization to reduce the number of polynomial coefficients. We also consider the predictor in the transmitter based on the regression polynomial model. With prediction of the CSI in the transmitter could avoid the feedback delay in the feedback channel, and reduce the feedback load. The simulation results show that the proposed algorithms could attain the upper bound of channel capacity and result in outstanding error performance for the precoded MIMO-OFDM systems with low feedback load in time-varying and frequency-selective channel.

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