本篇論文中，我們提出”先平均法”推導正交時-空區塊碼使用任意長方QAM於雷利衰退通道的精確錯誤率，並假設叢集子通道間為獨立的，而其子通道的功率可為均相異、均相同以及前兩者之混合等三種情況。再者，常見之正方QAM、一維PAM與BPSK調變方法均是本篇所考慮任意長方QAM的特例。特別要強調者，乃所有推導結果的最終公式均由最基本之數學式組成，無特殊高階的超越函數或尚未求出解的積分式，並且在討論混合均相異、均相同功率之雷利衰退通道時，我們亦說明如何將推導結果延伸至Nakagami-m衰退通道。 我們推導的方法有別於文獻中所提供者，乃以估計誤差機率密度函數為基礎之分析法成功的得到精確錯誤率公式，並且在證明的過程中，得到多個新發現的性質與恆等式。我們亦將理論值模擬與蒙地卡羅電腦模擬比較，其結果顯示兩者非常契合。另外，從模擬曲線也得知均相同功率通道比均相異功率通道的錯誤率還低。又正方形QAM較長方形QAM有更佳之績效表現。另外，並深入討論一般化正交時空區塊碼的錯誤率特性，因為目前文獻中已提出或討論正交時空區塊碼的精確錯誤率分析，只限於一般化正交時空區塊碼的特例。我們發現，一般化正交時空區塊碼對於不同的字符，可能造成不等效錯誤率，這在已知的文獻中並未曾被提及與證明。雖然在公式推導的過程中，假設通道間為獨立的，我們亦說明如何將我們的方法應用於有關聯性的通道中。 In this work, a pre-averaging method is proposed for deriving theoretical symbol error probability (SEP) expressions for orthogonal space-time block code (OSTBC) diversity systems employing arbitrary rectangular M-QAM transmission over flat Rayleigh fading channels. Independent fading between diversity channels are assumed for simplicity as the technique of channel decorrelation has been proposed in the literature. Channel average powers may be distinctive, identical, or mixed with both. The rectangular M-QAM results are extended to square M-QAM, M-PAM, and binary antipodal signaling. All derived expressions are in elementary forms without complicated high order transcendental functions and/or unevaluated integrals and hence are strictly exact and can be readily simulated by the computer with good accuracy. We delve into the error probability performance by proposing a new derivation method, from which many new equations and properties are shown and proved. Moreover, we show that mixed Rayleigh fading results can be readily extended to various Nakagami-m fading results. We use a four transmit antenna system with a half-rate OSTBC for 16-QAM signaling as the example to demonstrate that our theoretical results are in excellent agreements with the Monte Carlo simulated results. From simulation curves, we show that, under the independent channel fading condition, channels with identical powers have better error rate performance than channels with distinctive powers. Moreover, we discuss the performance of OSTBC with generalized complex orthogonal design (GCOD) in a rather general scope, which has not been explored in depth in the literature. Thus far, the SEP expressions for OSTBC found in the literature are only restricted to complex orthogonal design (COD) or some special GCOD cases. An important discovery is that OSTBC can produce different SEP performances for different information symbols. Although our derivation is presented based on the assumption of independent fading channels, we also provide an outline for the derivation for correlative fading channels.
