在非同步分碼多工(Code-Division Multiple Access, CDMA) 系統中，當使用滿秩最小化均方差組合器(Full-Rank MMSE Combiner) 來偵測信號時，必須計算通道互相關(Crosscorrelation) 矩陣的反矩陣。由於這個矩陣與展頻碼、通道衰減係數及使用者延遲有關, 所以每傳一個符元(Symbol) 便須重新計算一次, 因此計算複雜度並不理想。
後來有人利用最小化均方差準則和將信號投影到Krylov 子空間的觀念, 提出了降秩(Reduced-Rank) 最小化均方差組合器, 可降低計算反矩陣時所用的維度。但因組合器的係數依然與展頻碼及通道真實情況相關, 所以仍然必須不斷被重新計算, 並不能大幅降低複雜度。
為了解決複雜度的問題, 有人提出了漸進(Asymptotic) 降秩最小化均方誤差組合器。當使用者的數目K 及展頻碼長度N 均趨近無窮大時, 可以使用它來取代真實降秩最小化均方差組合器。前者不但在系統效能上的表現, 如錯誤率(Bit Error Rate, BER) 及信號訊雜比(Signal to Interference Plus Noise Ratio, SINR) 都非常接近後者, 更可以有效降低組合器的計算複雜度。
由於在直接序列-分碼多工(Direct Sequence- Code Division Multiple Access) 及多載波-分碼多工(Multi-carrier Code Division Multiple Access, MC-CDMA) 系統中, 上述的理論已經得到了驗證。所以本論文將在非同步多載波-直接序列-分碼多工(MC-DS-CDMA) 系統的架構下, 計算在不同 K/N 及不同通道衰減係數機率分布情況下之漸進降秩最小化均方差組合器的係數, 並比較其與滿秩最小化均方差組合器及真實通道情況下的降秩最小化均方差組合器的系統效能差異, 最後再提出結論。

When using full-rank MMSE combiner to detect signals in an asynchronous code-division multiple access(CDMA) system, the inverse of channel crosscorrelation matrix must be calculated. Because the matrix is related to spreading sequences, channel fading coefficients and user delay, it must be re-calculated each time a new symbol is transmitted. Due to this reason, the calculation complexity is not satisfactory.
Later on, someone proposed reduced-rank MMSE combiner which can reduce the dimension used when calculating the inverse matrix by using MMSE criterion and the idea about projecting the signals onto the Krylov subspace. However, the weights of the proposed combiner still relate tightly with spreading sequence and channel realizations. Thus, the calculation complexity can not be greatly decreased because the weights still need to update with time.
For further complexity reduction, asymptotic reduced-rank MMSE combiner is proposed.It has been shown that it can be used to replace real reduced-rank MMSE combiner when user number K and spreading gain N both tend to infinity. The performance measurements of the former, such as BER and Output SINR is close to the latter, and one important advantage of the former is that it can reduce the calculation complexity greatly.
Because the above statements has been shown in direct-sequence CDMA (DS-CDMA) and multi-carrier CDMA (MC-CDMA), we will calculate the weights of the asymptotic reduced-rank MMSE in asynchronous MC-DS-CDMA, and different
K/N and different channel fading distributions will be used in simulation. Finally, we will compare the performance of asymptotic reduced-rank MMSE combiner, real reduced-rank MMSE combiner and full-rank MMSE combiner, and then put forward the conclusion.

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