高速移動單輸入單輸出/多輸入多輸出正交分頻多工系統的子載波間干擾消除:低複雜度演算法及效能分析

Abstract

在正交分頻多工系統中，一個基本的假設是在一個正交分頻多工符元時間內通道是靜止不變的。然而，在高速移動的環境下，這假設就不再成立了。因此會造成子載波間干擾且使系統效能降低。強制歸零(zero-forcing, ZF)及最小均方差(minimum mean square error, MMSE)等化器是兩個簡單的干擾消除方法。不幸的，強制歸零等化器需要執行NxN子載波間干擾矩陣的反矩陣運算，此處N是正交分頻多工系統的子載波數目。當子載波數目變大時，計算複雜度將會變得很高。對於最小均方差等化器，除了子載波間干擾矩陣的反矩陣運算之外，還需要一個矩陣與矩陣的乘法運算。這將使得最小均方差等化器的複雜度變得比強制歸零等化器還高。在本論文中，我們首先提出一個低複雜度的強制歸零等化器來解決單輸入單輸出正交分頻多工系統中的問題。主要的概念是探究子載波間干擾矩陣的特殊結構及應用牛頓反矩陣疊代法。依據我們的演算法結構，快速傅立葉轉換(fast Fourier transform, FFT)可以被結合到疊代過程中，進而使得複雜度從O(N^3) 降到 O(Nlog_2 N) 。此外，疊代次數約略為一或兩次。我們亦分析所提方法的收斂行為及推導其訊號干擾雜訊比(signal to interference noise ratio, SINR)。對於最小均方差方法，我們首先改寫其數學表示式，使矩陣與矩陣的乘法運算可以被避免。與先前提出的低複雜度強制歸零方法相似，我們也將探究子載波間干擾矩陣的特殊結構及應用牛頓反矩陣疊代法來降低最小均方差方法中反矩陣的高運算複雜度。在多輸入多輸出正交分頻多工系統中，強制歸零及最小均方差等化器所需的複雜度問題將變得更難以解決。有鑑於此，我們將延伸在單輸入單輸出正交分頻多工系統中所提出的演算法至多輸入多輸出正交分頻多工系統中。這樣的延伸應用，使得所降低的複雜度比在單輸入單輸出正交分頻多工系統中還大。模擬結果顯示，所提出的低複雜度強制歸零及最小均方差等化器效能跟直接強制歸零(direct ZF)及直接最小均方差(direct MMSE)等化器的效能相當，但是所需的複雜度卻是大幅降低。最後，我們也將所提的高速移動干擾消除方法再延伸應用到正交分頻多工存取(OFDMA)上傳系統中並將此概念進一步應用來消除子載波偏移所引起的干擾。模擬結果顯示，所提方法可以大幅降低所需複雜度。

In orthogonal frequency-division multiplexing (OFDM) systems, it is generally assumed that the channel response is static in an OFDM symbol period. However, the assumption does not hold in high-mobility environments. As a result, intercarrier interference (ICI) is induced and the system performance is degraded. A simple remedy for this problem is the application of the zero-forcing (ZF) and minimum mean square error (MMSE) equalizers. Unfortunately, the direct ZF method requires the inversion of an NxN ICI matrix, where N is the number of subcarriers. When N is large, the computational complexity can become prohibitively high. As for the direct MMSE method, in addition to an NxN matrix inverse, it requires an extra NxN matrix multiplication, making the required computational complexity higher compared to the direct ZF method. In this dissertation, we first propose a low-complexity ZF method to solve the problem in single-input-single-output (SISO) OFDM systems. The main idea is to explore the special structure inherent in the ICI matrix and to apply Newton's iteration for matrix inversion. With our formulation, fast Fourier transforms (FFTs) can be used in the iterative process, reducing the complexity from O(N^3) to O(Nlog_2 N) . Also, the required number of the iteration is typically one or two. We also analyze the convergence behavior of the proposed method and derive the theoretical output signal-to-interference-noise-ratio (SINR). For the MMSE method, we first reformulate the MMSE solution in a way that the extra matrix multiplication can be avoided. Similar to the ZF method, we then exploit the structure of the ICI matrix and apply Newton's iteration to reduce the complexity of the matrix inversion. For a multiple-input-multiple-output (MIMO) OFDM system, the required complexity of the ZF and MMSE methods becomes more intractable. We then manage to extend the proposed ZF and MMSE methods for SISO-OFDM systems to MIMO-OFDM systems. It turns out that the computational complexity can be reduced even more significantly. Simulation results show that the performance of the proposed methods is almost as good as that of the direct ZF and MMSE methods, while the required computational complexity is reduced dramatically. Finally, we explore the application of the proposed methods in mobility-induced ICI mitigation for OFDM multiple access (OFDMA) systems, and in carrier frequency offset (CFO) induced ICI mitigation for OFDMA uplink systems. As that in OFDM systems, the proposed methods can reduce the required computational complexity, effectively.