以迴歸模式為基礎的正交分頻多工系統之通道與信號估測

Abstract

正交分頻多工系統(OFDM)是一種在頻率選擇性衰退通道中的有效傳輸方式。如果應用於目前的行動通訊，則此時的通道衰退除了具有頻率選擇的特性之外，同時也是隨時間而變化的。因此接收端必須機動適應性地做通道效應估計。在本論文中我們提出一種以回歸模式為基礎的通道估計方法，並由此分別導出新的引導信號式與盲敝式通道估計與信號檢測演算法。同時，我們也對一般的引導信號式通道估計系統分析了其位元錯誤機率(BEP)。 我們提出的回歸模型式通道估計法可從兩種方式導出。第一種導出方式是將通道的自我關聯矩陣(autocorrelation matrix)之特徵向量(eigenvector)以多項式近似，然後帶入線性最小均方差(LMMSE)估計器並只保留一些較大之特徵值。另一種導出方式較為直觀：用多項式以最小方差來貼合一個區段內的試驗性估計值。我們分析其均方差(MSE)並在各種通道條件中與線性最小均方差估計器比較以驗證其效能。由此種估計原則導出的引導信號式通道估計法並不需要知道通道的關聯函數與雜訊能量，其複雜度也不高，一個時頻符元只需要約3個複數乘法即可完成。已曲面代替多項式並使用二維的區塊，我們可得到一種二維的估計器，使時間與頻率的相關性(correlation)均可被利用到。在另一方面，不使用引道信號，我們從回歸模型式估計原則導出一盲敝式聯合通道與信號估測準則，並將其化成一整數規劃問題。由此我們提出一種以分支界限(branch-and-bound)為基礎之盲蔽式估測法。利用回歸原則的特性，我們推導出一遞迴關係式來簡化計算量。我們討論其他設計上的議題並據以提出一種複雜度較低之半盲式(含有稀疏的引導信號)估測法。 對於引導信號式估計器在雷氏衰退(Rayleigh fading)通道下的位元錯誤率，我們提出一系統化的分析方法並對各種調變方式導出封閉式的分析結果，並與模擬的結果比較來驗證其正確性。我們發現一些已知的結果和我們的特例相吻合。我們的結果也可以應用到窄頻單載波的系統。

Orthogonal frequency division multiplexing (OFDM) has been proposed as an efficient transmission scheme in a frequency-selective fading environment. For a wideband mobile radio communication system, the channel is time-variant and has different fading effect on each ubchannel, hence we require real-time channel estimation to compensate channel effects. In this thesis, we propose a new channel estimation algorithm, from which pilot-assisted and blind schemes of channel estimation and data detection can be derived. Also the bit-error probability (BEP) of the OFDM systems with general pilot-assisted channel estimation in Rayleigh fading is analyzed. The proposed model-based (MB) channel estimator can be obtained by two approaches. The first approach is to use orthonormal polynomials to approximate the eigenvectors of the channel autocorrelation matrix in the linear minimum mean-squared error (LMMSE) estimation, which is theoretically optimal. By some further approximation, we can derive an estimation method which doesn't need the information about the channel statistics like channel correlation and signal-to-noise ratio (SNR). The second approach is more intuitive: using a polynomial of pre-determined degree to fit a block of tentative channel estimates in the least-squares sense. Both approaches lead to the same result. The mean-squared error (MSE) of the proposed estimator is analyzed and compared with the MSE of the LMMSE estimator in several channel conditions to validate its effectiveness. Based on the proposed estimation algorithm, we derive a new pilot-assisted channel estimator and a blind data detector, respectively. For the pilot-assisted channel estimation, our algorithm needs about only three complex multiplications in the equalization process for every symbol in each subchannel. A 2-dimensional scheme that makes full use of the time and frequency correlation of channel is also proposed. On the other hand, without resorting the pilot symbols, we derive a blind detection criterion and relate it to an integer-programming problem. We then proposed an algorithm based on the branch-and-bound principle. A recursive formula for fast metric update is derived by exploiting the intrinsic characteristics of the cost function. Some related design issues and modifications are addressed, which lead to much reduced complexity algorithms for both blind and semi-blind (low pilot density) data detections. A systematic approach for analyzing the bit-error probability (BEP) of equalized OFDM signals in Rayleigh fading is proposed. Closed-form expressions for BEP performance of various signal constellations (PSK, DPSK, QAM) are derived for receivers that use linear pilot-assisted channel estimation. The analytical and simulated BEPs are compared to validate our analysis. Some special cases of our results coincide with the previous known results. The results obtained here can be applied to single-carrier narrowband systems as well.