由於多天線-多載波系統擁有優異的通道容量及錯誤機率，並且可提昇傳輸效率，已受到矚目許久。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。方向性向量是重要的通道資訊，可以有效的應用在預先編碼-多輸出多輸入的系統上，而一些通道資訊簡化及有效率回傳通道資訊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議題。而一般回傳方法為接收端利用向量量化方相性向量後，回傳至傳送端，但如果是同時具有方向性和能量分配等多功能的系統，接收端除了回傳方相性向量之外還須回傳額外的通道資訊至傳送端，勢必大幅提高回傳量。
為了更有效率的回傳通道資訊，我們基於Karhunen–Loève Expansion(KLE) ，提出回傳估測的通道響應至傳送端的方法。我們將KLE的係數當作通道響應重建的參數。而KLE係數的個數比起通道響應的數量少很多，這是很有效率的資料壓縮。這些係數為高斯分佈，在多輸入多輸出-正交分頻多工調變的系統下，為了有效率的回傳係數，我們使用高斯量化來減少量化誤差。模擬結果顯示了具有預先編碼的多輸入多輸出-正交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，並且有很好的錯誤率效能。

Multiple antennas -multiple carriers systems have been attracted many attention 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 beam forming 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. In general, we can use the vector quantization to feed back the beam-forming vectors to the transmitter. To implement a precoder which can be used not only the beam-forming but also the power allocation, we need to feed-back other channel information.
In order to feed-back CSI more efficiently, we propose an efficient method that feed-back the estimated channel responses (CRs) to the transmitter based on the Karhunen-Loève Expansion (KLE). The coefficients of the KLE are used as the parameters for rebuilding CRs. The number of coefficients of the KLE is much fewer than the size of than the block of CRs, and this leads to efficient compression. These coefficients are of Gaussian distribution. To efficiently return the coefficients for the MIMO with orthogonal frequency-division multiplexing (OFDM) systems, we use the Gaussian quantization (GQ) to reduce quantization error. The simulated results show that the proposed algorithms could attain outstanding error performance for precoded MIMO-OFDM systems with low feedback load in the time-varying and frequency-selective channel.

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