正交分頻多工系統之低複雜度同步設計與研究

Abstract

正交分頻多工技術可以有效處理頻率選擇性衰減的問題，且已廣泛使用於無線通訊上。由於此技術對頻率及時間偏移的敏感度高，同步設計便成為一個非常重要和值得討論的議題，但現有同步技術須要大量計算，因此本論文嘗試就IEEE 802.11a及 IEEE 802.16-2004 OFDM mode兩種系統，應用多解析度運算概念與技術來設計一套全面的同步方法希望其能達成低複雜度之同步計算，同時維持相當的效能。 多解析度運算的設計概念主要可以分成多解析度資料樣本次取樣方式、多解析度運算窗口長度方式、多解析度相關與匹配運算時間次取樣方式以及多解析度運算元長度方式；並將之應用於封包偵測、頻率偏移估測及符元時間估測等三種同步的設計。 在封包偵測的部份，本論文應用上述四種多解析度運算方式於傳統的功率比値法及延遲相關運算法，並應用漸進式的搜尋方式，在封包偵測起始時，先作低解析度運算，當運算結果大於一個特定的門檻值時，便提高運算解析度，進而達到細微的估測結果。在頻率偏移估測的部份，本論文嘗試用多解析度運算元長度方式來降低所須之運算複雜度，並增加樣本時間點以提高估測的效能。而在符元時間估測部分，本論文應用多解析度運算窗口長度方式及多解析度相關與匹配運算時間次取樣方式，將其運用於簡化直接時域符元時間(SDTDS)估測方法中。 經IEEE 802.11a和IEEE 802.16-2004 OFDM mode系統得知，低解析度資料樣本設定下先導訊號自相關的特性較不理想。而本論文發現若在低解析度匹配運算窗口長度減半的情況下，此兩種系統先導訊號的自相關特性仍會保持，但會降低對雜訊的容忍度，而在此兩種系統當中，IEEE 802.16-2004 OFDM mode系統在此方式下其對雜訊的容忍度會較差。多解析度相關與匹配運算時間次取樣方式則在其參數設定值小於3時才會有較好的效能。多解析度運算元長度方式則在資料位元長度6以上時有較好的表現。 封包偵測在IEEE 802.11a的規格設定下功率比值法使用多解析度運算約能降低15.3%左右的複數乘法量、20.53%的複數加減法量以及22%的實數乘法量，而在延遲相關運算法下使用多解析度運算約能降低19.73%左右的複數乘法量、23.08%的複數加減法量以及25.64%的實數乘法量及實數加減法量，兩種方式的效能平均約降低0.7dB。在IEEE 802.16-2004 OFDM mode的規格設定下功率比值法使用多解析度運算約能降低4.52%的複數乘法量、12.4%的複數加減法量以及21.43%的實數乘法量，而在延遲相關運算法下使用多解析度運算約能降低6.76%左右的複數乘法量、7.83%的複數加減法量以及18.52%實數乘法量及實數加減法量，兩種方式的效能平均約降低1.3dB。在頻率偏移估測上面，其運算複雜度會隨運算位元數的降低而下降，而效能會隨所取樣本點的增加而提高，然而礙於系統的考量，其樣本點並無法無止盡的增加，因此由模擬可以看出在此兩種系統下其效能的增加有限。在符元時間估測方面，在兩種系統規格下使用多解析度運算窗口長度方式能降低50%的複數乘法及複數加法運算，而在多解析度相關與匹配運算時間次取樣方式下大約能降低50%的複數乘法及複數加減法運算，且效能較多解析度運算窗口長度方式佳。

Orthogonal frequency division multiplexing (OFDM) technique is able to deal with the problem of frequency-selective fading channels and has become a widely used technique in wireless communication systems. A major drawback of OFDM is its high sensitivity to frequency and timing offsets. This thesis applies the concepts and techniques of multi-resolution computation to the design of an overall synchronization process for IEEE 802.11a and IEEE 802.16-2004 OFDM mode systems. The idea of multi-resolution can be divided into method of data multi-resolution, method of window multi-resolution, method of correlation and matching time multi-resolution and method of operand multi-resolution, which can be applied to correlation and matching operations required in OFDM synchronization processes including frame detection, frequency offset estimation and symbol timing estimation. In frame detection, the multi-resolution methods mentioned above are applied to conventional method of power ratio and method of delayed-correlation, combining with coarse-to-fine search method which employs low-resolution computation in the beginning of a frame detection process. When the computation result is lager than a proper threshold, we switch to high-resolution computation for fine estimation result. In frequency offset estimation, method of operand multi-resolution mentioned above is applied, and we add time samples to improve the estimation performance. In symbol timing estimation, this thesis applies methods of window multi-resolution and correlation and matching time multi-resolution to a simplified direct time-domain symbol timing estimation method to find the symbol time with less complexity. Owing to the features of IEEE 802.11a and IEEE 802.16-2004 OFDM mode, we can see that the low data resolution will cause the properties of preamble not ideal. However in applying the method of window multi-resolution, the properties of preamble will be maintained when window length is halved, but the tolerance of noise will decrease. Comparing these two systems, the noise tolerance of IEEE 802.16-2004 OFDM mode is worser than the noise tolerance of IEEE 802.11a. Method of correlation and matching time multi-resolution will perform well when the parameter is less than 3. Method of operand multi-resolution will perform well if the bit number is over and above 6. The proposed multi-resolution frame detection technique reduces about 15.3% complex multiplications, 20.53% complex additions and 22% real multiplications of overall computation in method of power ratio, and reduces about 19.73% complex multiplications, 23.08% complex additions and 25.64% real multiplications and real additions of overall computation in method of delayed-correlation with the setting of IEEE 802.11a system, and both at the cost of about 0.7dB performance loss. It can also reduce about 4.52% complex multiplications, 12.4% complex additions and 21.43% real multiplications of overall computation in method of power ratio, and reduce about 8.76% complex multiplications, 7.83% complex additions and 18.52% real multiplications and real additions of overall computation in method of delayed-correlation with the setting of IEEE 802.16-2004 OFDM mode system, and both at the cost of about 1.3dB performance loss. The complexity in carrier frequency offset estimation decreases when bit number decreases, and the performance will increase when the sample number increases. However, in according to system structures, the samples can not increase infinitely, and we can see that the performance increases slightly in our simulations of these two systems. In symbol timing estimation, methods of window multi-resolution and correlation and matching time multi-resolution which applied to the two systems mentioned above can reduce about 50% complex multiplications and complex additions. Of these two methods, the method of correlation and matching time multi-resolution performs better than method of window multi-resolution.