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Designing communication techniques for non-Gaussian impulsive noise has been attracting considerable attention from the research community. In this paper, we focus on the continuous phase frequency shift keying (CPFSK) signal detection for both white and bursty impulsive noises. The independent and identically distributed (i.i.d.) symmetric <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-stable (<inline-formula> <tex-math notation="LaTeX">${S\alpha S}$ </tex-math></inline-formula>) process and the stationary <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula>-order <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-sub-Gaussian [<inline-formula> <tex-math notation="LaTeX">${{\alpha \mathit {SG}}}(m)$ </tex-math></inline-formula>] model are adopted to model the white and the bursty impulsive noises, respectively. At first, both coherent and non-coherent detections of CPFSK signals are investigated for white <inline-formula> <tex-math notation="LaTeX">${S\alpha S}$ </tex-math></inline-formula> noises. For the coherent sequence detection, the Viterbi algorithm is used by replacing the maximum likelihood (ML) measure with the myriad measure. In non-coherent detection, a multiple symbol aided scheme is proposed, for which both the ML and myriad measures are considered. Subsequently, the detection of CPFSK signals is further addressed in <inline-formula> <tex-math notation="LaTeX">${{\alpha \mathit {SG}}}(m)$ </tex-math></inline-formula> noise. For coherent detection, based on the Markov property of <inline-formula> <tex-math notation="LaTeX">${{\alpha \mathit {SG}}}(m)$ </tex-math></inline-formula> noise, we first express the likelihood function as the sum of branch measures, and the myriad measure is also provided to replace the ML measure. The multiple symbol-aided methods are also applied to the non-coherent detection in <inline-formula> <tex-math notation="LaTeX">${{\alpha \mathit {SG}}}(m)$ </tex-math></inline-formula> noise, and the corresponding ML and myriad measure-based algorithms are given as well. For the sake of comparison, the Gaussian measure is also considered. The simulation results show that the performance of the myriad measure-based algorithms can closely approach that of the ML measure-based algorithms for both coherent and non-coherent detection, and is much better than that of the Gaussian measure-based algorithms.

CPFSK Signal Detection in White and Bursty Impulsive Noises