本篇論文主要是架構在Multiple-Input/Multiple-Output(MIMO)多天線接收與Orthogonal Frequency Division Multiplexing(OFDM)的結合，MIMO提供可靠的通訊與高速率的資料傳輸，能有效在無線通訊系統中對抗通道衰弱(fading)的影響。OFDM將資料載在許多的次載波上，且彼次之間互相正交。MIMO-OFDM結合成為4G行動通訊系統的重要應用。
在MIMO-OFDM架構下，接收端使用偵測器(detection)與解碼器(decoder)的遞迴式架構，使用LSD(List Sphere Decoder)演算法當偵測器，利用較低的複雜度運算出位元的事後機率，接著傳送至解碼器，並與傳統複雜度較高的MAP演算法做比較。接著探討多天線展頻(MIMO-Spreading)，使用新式遞迴低複雜度LSD偵測器，與Minimum Mean Square Error-Soft Interference Cancellation(MMSE-SIC)在通道衰弱情況下比較。
利用特性曲線圖觀察LSD偵測器的特性，並選擇不同的Candidates數目探討位元錯誤率與通道容量的表現。

In this paper, we focus on MIMO-OFDM systems. MIMO techniques have ability to achieve reliable and high speed data rates over fading channels. OFDM techniques use many sub-carries to carry data, and they are perpendicular to each other. MIMO-OFDM were widespread communications technology in fourth generation mobile communications

In MIMO-OFDM systems, we use the receiver with iterative detection and decoding. By using List Sphere Decoder(LSD) for detection，we can compute the bit posterior probabilities with low complexity. Then the posterior probabilities become the a prior input to the decoder. We compare the simulation results with conventional MAP detectors. We propose a novel low-complexity LSD detector used for iterative detection in MIMO-Spreading systems, and compare the simulation results with Minimum Mean Square Error-Soft Interference Cancellation (MMSE-SIC) in fading channels.

Finally, EXIT analysis is used to observe LSD detection. Furthermore, we choose different number of candidates to analyze bit error rate performance and capacity.

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