2011/05/13 by Hua Yu, Gang Wei, Fei Ji +1 · 1 citation
Engineering · Computer Science · #Advanced Wireless Communication Techniques #PAPR reduction in OFDM #Coding theory and cryptography
paper · doi:10.1109/tvt.2011.2154347
The closed-form expressions for the exact average symbol error probability (SEP) and bit error probability (BEP) of arbitrary <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">M</tex></formula> -ary cross quadrature amplitude modulation (XQAM) signaling with maximal-ratio combining (MRC) diversity reception over independent but not necessarily identical <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">η</tex></formula> - <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex> </formula> fading channels are derived. The results are presented in terms of a finite (in proportion to <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">√(M)</tex></formula> ) sum of Lauricella hypergeometric functions <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">FD(n)</tex></formula> , which can be numerically evaluated using its integral or converging series representation. For some special fading scenarios of interest, the formulas are expressed by some simpler functions, such as Gauss's single hypergeometric function <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">2F1</tex></formula> and Apell's double hypergeometric function <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"> F1</tex></formula> , both of which are available functions in standard numerical software. For Rayleigh channels and some special cases of Nakagami- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">m</tex></formula> channels, the results are presented in the form of a finite sum of trigonometric functions. The analytical expressions show excellent agreement with the simulation results. Numerical evaluation with the proposed expressions reveals that cross-QAM can obtain at least 1.1-dB gain, compared with rectangular QAM when SEP <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX"><</tex> </formula> 0.3.