Energy Detection for M-QAM Signals

Abstract

Accurate threshold setting for energy detector is important for example in dynamic spectrum access. This requires accurate statistical distribution models of the observed energy. In this paper, we consider energy detection (ED) for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary quadrature amplitude modulation (QAM) signals. The derivation of the exact solution of the distribution model (ES) requires all combinations of QAM signals in the observed signals based on the brute-force search and it leads to a significant computational cost. For this issue, this paper proposes three statistical distribution models which assume <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M=\infty $ </tex-math></inline-formula> to avoid the brute-force search. Due to the assumption of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> , the proposed models are independent of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and can handle adaptive modulation where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> can be changed dynamically. In the numerical evaluations, we compare the three proposed models with the other typical approximation models under additive white Gaussian noise (AWGN) channel and Rayleigh fading channel. In addition, the proposed models are extended for more realistic scenario where imperfect synchronization is considered. The comprehensive numerical evaluations show that the first proposed model is most accurate among all considered models except ES but requires relatively high computational cost. The second proposed model where the observed energy is assumed to follow Gaussian distribution is the least complexity but can have reduced accuracy. The third proposed model based on skew-normal distribution can achieve comparable accuracy and less complexity compared to the first model.