正交分頻多工系統中，用來實現載波頻率偏差與通道脈衝響應之聯合估計，最 常被用到的方法為最大似然估計。此方法主要的困難在於似然函數的高度非線性，造成 在估計載波頻率偏差與通道脈衝響應時有區域極值或多重解。最直接簡易的解決方法， 為採用最陡坡降法以逼近最大似然估計的解，但其參數大小之決定，譬如演算法初值與 步階大小之選定，造成在實際環境運用的阻礙。另一解決方為使用數學近似分析並配合 交替疊代以逼近最佳解。一些疊代求解的方法已被提出於文獻中，這些近似求解使用相 當於一階近似的精確度，不甚準確，效率不佳。 本計畫中將提出新的使用一階近似的疊代演算法，其估計載波頻率偏差與通道脈 衝響應較文獻中的方法為精確，估計區間也增大許多。此外，亦將提出使用二階近似 的疊代演算法，在增加一些計算量之餘，提供更精確之估計與更寬廣的估計區間。隔 年的計畫中，另一種新的估計方法將被探討。不使用最大似然估計，轉而採用最小平 方法，在犧牲一些傳輸效率之後，可在不需通道估測的情況下取得載波頻率偏差之估 計值。做完載波頻率偏差之估計後，再進行通道脈衝響應估計，期間並無用到疊代演 算法，因此節省疊代所需之額外計算花費。更重要的是，我們能預估精確度，提出數 學分析理論值，並與最大似然估計作比較。 To implement an algorithm for joint estimation of carrier frequency offset (CFO) and channel impulse response (CIR) in orthogonal frequency division multiplexing (OFDM) systems, the maximum-likelihood (ML) criterion is commonly adopted. A major difficulty arises from the highly nonlinear nature of the log- likelihood function which renders local extrema or multiple solutions for the CFO and CIR estimators. The most direct and straightforward method is the use of the steepest descent or gradient algorithm. But the implementing of the gradient algorithm is hampered by the starting point and the adaptive step size of the adaptive iteration process. An alternative is the use of mathematical approximation coupled with an adaptive iteration algorithm. Several iterative approximation algorithms have been proposed in the literature. The approximation methods used in those algorithms are of the first order level and are not very effective. Here, we shall propose a more effective first order approximation algorithm that will outperform existing algorithms in terms of estimation accuracies, tracking range, as well as algorithm convergence rate. In addition, we shall also propose a second order approximation algorithm that will offer even further improvement. Furthermore, by slightly sacrificing the data transfer rate, we seek another alternative in an attempt to gain more advantages. Rather than the ML criterion, we will use the method of least squares (LS) to track the CFO first. Our special LS formulation requires no channel knowledge and uses no approximations. Then, following the correction of CFO, channel estimation can be readily performed. This way, we also get rid of the adaptive iteration process and hence save a considerable amount of processing time. More importantly, we predict that the estimation accuracy can be further increased as compared to the ML techniques.
