近年來，超寬頻 (ultra-wideband，簡稱UWB) 通訊越來越受到各界的注意。超寬頻通訊主要是作為室內短距離的傳輸，並且具有高速率、低功率、超大頻寬的傳輸特性。
在這篇論文裡，我們提出一個使用時空碼 (space-time codes) 的超寬頻正交頻域多工 (orthogonal frequency division multiplexing， 簡稱OFDM ) 系統。在這個系統裡，所有可使用的頻寬被分割成數個較小的頻帶。每個頻帶上都使用OFDM的調變方式，並且同時使用所有的頻帶來傳輸資料。在傳輸端，我們在頻帶之間加上時空碼以獲得頻率分集( frequency diversity ) 與時間分集 ( time diversity )。在接收端，我們使用取樣頻率 ( sampling rate )小於奈奎斯特率 ( Nyquist rate ) 的類比數位轉換器(analog to digital converter，簡稱ADC)，於是接收端的功率消耗可以大為降低。這樣的系統將可視為一個多輸入、多輸出 ( multi-input multi-output，簡稱 MIMO) 系統。取樣頻率較低所造成頻譜上的失真類似在多輸入、多輸出系統中接收天線同時收到數個傳輸天線的訊號混雜加在一起。針對我們提出的系統在頻率選擇性衰變通道 ( frequency selective fading channel )中，我們導出成對錯誤機率 (pairwise error probability，簡稱PEP) 的上界。因此可以得到時空碼的設計準則 : 距離準則與乘積準則。依據這樣的準則，我們利用電腦做完全搜尋，得到具有最大分集增益 ( diversity gain ) 和編碼增益 ( coding gain ) 的時空籬柵碼 (space-time trellis codes，簡稱STTC)。模擬結果可以顯示我們所提出來的時空籬柵碼比之前所提出的編碼方式有更好的效能。

In this thesis, a ultra-wideband orthogonal frequency division multiplexing (UWB-OFDM) system with space-time coding is proposed. In this system, the total available bandwidth is divided into N smaller sub-bands. The OFDM modulation is adopted on each sub-band. All the sub-bands transmit data simultaneously. The transmitter encodes the sub-bands with the space-time codes to gain the frequency diversity and the time diversity. We consider a low-cost receiver with lower-sampling-rate, one N-th of the Nyquist rate. We will show that this system can be regarded as multi-input multi-output (MIMO) systems with N transmit
antennas and one receive antenna. The problem of recovering the aliased spectrum due to downsampling is similar to that of recovering the signals received simultaneously from
different transmit antennas in MIMO systems. The pairwise error probability (PEP) of the proposed system for quasi-static frequency selective channels is derived and two design criteria of the space-time codes are obtained: the distance criterion and the product criterion. The optimum space-time trellis codes (STTC) based on these criteria are found by computer search. We can see that the STTC can easily achieve the maximum diversity gain and large coding gain. Simulation results show that the proposed STTC have better performance than other codes proposed before.

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