In this letter, motivated by the superiority of continuous phase modulation (CPM) signals, a binary CPM with modulation index 0.5 is considered into downlink symbol-asynchronous non-orthogonal multiple access (ANOMA) to enhance power and spectral efficiency, especially for resource-limited wireless communications. According to the maximum likelihood (ML) criterion, a Viterbi-based block-by-block detector (VB-BBD) is first proposed. Considering the asymptotics of Toeplitz matrices, a DFT matrix diagonalization-based symbol-by-symbol detector (DFTD-SSD) is also given. Finally, the detection complexity analysis is provided. Numerical results reveal the optimal time offsets with different modulation formats for a two-user system, and show that time asynchrony can bring about 3dB and 6dB performance gains at a bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> . The relationship between BER performance and different power levels, frequency pulses, response lengths is also investigated.
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