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This paper addresses non-coherent detection and performance of weak M-ary chirp spread-spectrum (MCSS) signals in non-Gaussian impulsive noise. The structure of the locally optimum Bayes detector (LOBD) is derived and consists of a zero-memory nonlinearity (ZMNL), a function of first-order noise density, followed by the non-coherent Gaussian envelope detector for MCSS signals. The performance of this receiver has been evaluated and closed-form expressions for symbol error rate (SER) and bit error rate (BER) have been derived. It has been shown that the SER and BER performances are functions of the signal-to-noise ratio (SNR), the sample size per symbol interval, the input data size, and the modulation parameters of MCSS signals. A comparison between the coherent and non-coherent detection for weak MCSS signals is also given.