使用時限脈波成形之區塊調變

Abstract

為了達到最佳的功率效率，大多通訊系統採用符合奈奎斯零符元間干擾準則的有限頻寬脈衝進行傳輸。然而在實際的通訊系統中，有限頻寬脈衝在傳輸前必須在時間上先被截斷成時限脈衝，這無法避免得會產生符元間干擾。並且，在時域被截斷後的脈衝所使用的頻寬會超過奈奎斯頻寬，使得頻譜效率相對於奈奎斯脈衝下降。在本論文中，我們發展時限脈衝成形之區塊調變來達到能超過可實現的根餘弦脈衝的頻譜效率，甚至能逼近理想奈奎斯脈衝的頻譜效率，並且擁有和理想奈奎斯脈衝一樣的最佳功率效益，同時因為使用時限脈衝，所以能避免時間截斷所造成的符元間干擾。我們找出能達到功率頻譜旁波快速衰減的時限脈波限制並且設計出符合此限制的時限脈衝家族。同時，我們找出能在給定時限脈波下維持訊號正交性的預編碼條件，這能夠使系統達到最佳功率效率並且讓接收器的解碼維持在低複雜度。此外，我們也設計出能夠降低峰均功率比和壓抑特定頻帶功率且同時維持正交性的預編碼。根據我們的分析，設計出來的正交預編碼能夠在平均功率限制下達到最大通道容量。為了理論完整性，我們也考慮頻限脈波成形之區塊調變。為了幫助分析頻限脈波成形之區塊調變，我們提出了頻譜特徵值分布理論來連結脈衝成形和它對應的轉移矩陣的特徵值。

In order to achieve the optimal power efficiency, most communication systems adopt band-limited pulse shaping satisfying the Nyquist zero inter-symbol-interference (ISI) criterion. However, in practice, a band-limited pulse must be truncated in the time domain to a few symbol time duration before a transmission, which inevitably introduces ISI in the truncated transmitted waveform. Moreover, after the truncation, the pulse will occupy more than the Nyquist bandwidth and thus the spectral efficiency will degrade with respect to the Nyquist pulsed-modulation. In this thesis, block transmission of time-limited pulse shaping will be developed in order to achieve a high spectral efficiency which can be made arbitrary close to that offered by the ideal Nyquist-pulsed modulation and realizable RRC-pulsed modulation, and provide the same power efficiency (error performance) which is equivalent to that offered by the ideal Nyquist-pulsed modulation, while avoids ISI introduced by the truncation by adopting a time-limited pulse. Specifically, constraints on time-limited pulse are developed to provide desirable power spectrum with a fast sidelobe envelope decaying in the frequency domain and the corresponding pulse family are also proposed. Constraint on precoder of block transmission is developed in conjunction with the prescribed time-limited pulse to guarantee the orthogonality of signaling which is not only able to achieve the best power efficiency which is equivalent to that offered by the ideal Nyquist-pulsed modulation but also maintain decoding complexity low. Furthermore, precoder is designed to reduce peak-to-average power ratio(PAPR) and suppress specific band power while maintaining signaling orthogonal. Based on our analysis, the capacity achieved by the proposed orthogonal precoder is proved to be optimal in the sense that the capacity is maximized subject to an average power constraint. Additionally, block modulation system with band-limited pulse shaping is proposed for the theory completeness. To help the analysis of the block modulation system with band-limited pulse shaping, the spectrum eigenvalues distribution theorem is proposed to relate a pulse shaping to its eigenvalues distribution of the corresponding transfer matrix.