接收端的訊號雜訊比估測在很多現代無線通訊系統的運用上是很重要的一個議題，之前討論有關這個議題的文獻大多是只有考慮在經過有可加性白色高斯雜訊 (additive white Gaussian noise，簡稱AWGN)通道做傳輸，有的也有考慮在時間選擇性衰減 (time-selective fading) 通道做傳輸；然而這些討論都是針對單個傳輸載波來討論。近年來，正交頻域多工 (orthogonal frequency division multiplexing，簡稱OFDM)是一個非常熱門的研究主題。在這篇論文中，我們將考慮在正交頻域多工的傳輸當中去做訊號雜訊比估測。考慮經過有可加性白色高斯雜訊以及頻率選擇性衰減 (frequency-selective fading) 通道做傳輸。我們使用了三種方法來做估測，最大可能性估測　(maximum likelihood estimation)　，二階和四階動差估測　(second- and fourth-order moments estimation)　以及訊號變異比估測　(signal-to-variation ratio estimation)，並將模擬結果和推導出來的克拉默洛下限(Cramer-Rao Lower Bound)做比較。最後並考慮在頻率偏移(frequency offset)或是時間偏移(timing offset)的狀況之下，估測結果是否會受到影響。模擬的結果告訴我們，當用來做估測的訊號夠多的時候，最大可能性估測的表現結果十分良好，甚至可以逼近推導出來的克拉默洛下限。二階和四階動差估測在SNR值大的時候也有十分良好的表現，並且他不需要知道所傳送的訊號為何，這是它優於最大可能性估測的地方之一。當有頻率偏移的時候，最大可能性估測幾乎無法使用，但是二階和四階動差估測以及訊號變異比估測仍然表現十分良好，跟沒有偏移的時候效果一樣。若有時間偏移發生，並且量不大的時候，三種估測方法都不會受到太大的影響。若考慮兩種偏移同時發生的時候，最大可能性估測依然沒有辦法運作，不過二階和四階動差估測以及訊號變異比估測依然可以有良好表現。

Knowledge of the receiver signal-to-noise ratio (SNR) is often required in many modern wireless communication systems. For example, mobile-assisted handoff[1], selective combining [1], power control [1], data rate adaptation [2], dynamic channel assignment, and iterative MAP turbo code decoding [3], etc., require SNR as an important reference. In the past engineering practice, it usually used estimation of the total signal-plus-noise power instead of that of the SNR for convenience. However, performance can be improved if we use the real SNR estimate, which makes the investigation of SNR estimation techniques interesting and essential.
Most of the previous works [4]–[8] related to SNR estimation were considered in additive white Gaussian noise (AWGN) channels, while [9] considered the SNR estimation in time-selective fading channels for single carrier systems. Some considered the SNR estimation in generalized fading channels for single carrier system, too. Orthogonal frequency division multiplexing (OFDM) transmission is popular in various applications in recent years, which is a technique to transmit data over a number of subcarriers. In [10] a method for SNR estimation in OFDM system is proposed, yet, however, only AWGN and frequency non-selective channels are considered. In this thesis, we are going to discuss several SNR estimation techniques for OFDM transmission, and the channel model considered here is a frequency selective channel with AWGN. We modify several previously proposed SNR techniques [4] to our system, such as maximum-likelihood (ML) estimation, second- and fourth-order moments (M2M4) estimation, and signal-to-variation ratio (SVR) estimation. In addition, the Cramer-Rao Lower Bound (CRLB) [11], [12], which is a well known lower bound for the variance of any unbiased estimator, is derived for our system and compared to the simulated results. The simulation results show that the ML estimator performs best and its normalized mean-square error (NMSE) is close to the CRLB if the block size is large enough. However, the ML estimation has to be data-aided (DA) while the M2M4 and the SVR do not require knowledge of the transmitted data. This is the trade-off. Finally, we consider the estimators in the cases with frequency offset, timing offsets and the joint offset. The theoretical and simulation results show that the ML estimator suffers from the frequency offset but not the timing offset while the M2M4 and the SVR do not suffer from neither the frequency nor the timing offset. For the joint cases of timing and frequency offset, ML also degrades while the M2M4 and the SVR do not degrade, neither.

The thesis is organized as follows. In Chapter 2, we give an overview of OFDM. A review of some proposed techniques for SNR estimation is given in Chapter 3. In Chapter 4, we derive SNR estimators based on three techniques: ML, M2M4, and SVR, and derive the CRLB for our system. We then consider the situations with frequency offset and evaluate the impact on our estimators in Chapter 5 and discuss the timing offset effects for our estimators in Chapter 6. Finally, we give some simulation results in Chapter 7 and conclusion in Chapter 8.

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