Abstract
The exact symbol error probability (SEP) performance of M-ary cross quadrature amplitude modulation (QAM) in additive white Gaussian noise (AWGN) channel and fading channels, including Rayleigh, Nakagami-m, Rice, and Nakagami-q (Hoyt) channels, is analyzed. The obtained closed-form SEP expressions contain a finite (in proportion to √M) sum of single integrals with finite limits and an integrand composed of elementary (exponential, trigonometric, and/or power) functions, thus readily enabling numerical evaluation. Particularly, Gaussian Q-function is a special case of these integrals and is included in the SEP expressions. Simple and very precise approximations, which contain only Gaussian Q-function for AWGN channel and contain three terms of the single integrals mentioned above for fading channels, respectively, are also given. The analytical expressions show excellent agreement with the simulation results, and numerical evaluation with the proposed expressions reveals that cross QAM can obtain at least 1.1 dB gain compared to rectangular QAM when SEP < 0.3 in all the considered channels.
Highlights
Quadrature amplitude modulation (QAM) has been widely used in digital communication systems due to its high bandwidth efficiency
Smith shows that both the peak and average power can be reduced by using a cross-QAM constellation, and there is at least a 1-dB gain in the average signal-to-noise ratio
Cross-QAM has been found to be useful in adaptive modulation schemes wherein the constellation size is adjusted depending on the channel quality [2,3,4,5,6]
Summary
Quadrature amplitude modulation (QAM) has been widely used in digital communication systems due to its high bandwidth efficiency. By using the "preaveraging" technique [19], opposed to the customary and widely adopted "postaveraging" technique, the exact SEP of cross-QAM in Rayleigh fading channels has been derived in [20], where the closed-form SEP expression obtained contains only elemental functions (trigonometric). They use the moment generating function- (MGF-) based approach to obtain SEP expressions for various digitally modulated signals over fading channels Their basic technique is to rewrite the Gaussian -function into a preferred form of an integral with finite integration limits (many SEP expressions contain the Gaussian -function), so that the final average SEP expression can be numerically computed with more accuracy. In this paper, using the alternate representation of the two-dimensional joint Gaussian -function and the MGF-based method, the exact SEP expressions of arbitrary -ary cross-QAM in AWGN and fading channels, including Rayleigh, Nakagami-m, Rice, and Nakagami-q (Hoyt) channels, have been derived.
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