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In massive machine-type communications (mMTC), grant-free access is a key enabler for a massive number of users to be connected to a base station with low signaling overhead and low latency. In this paper, new Fourier-based sequence sets are proposed for user-specific, non-orthogonal, unimodular sequences for uplink grant-free access in multi-cell massive machine-type communications (mMTC). A design framework based on a partial Fourier matrix with masking operations is presented for multiple sets of non-orthogonal sequences, where the correlation matrix is defined to analyze the intra- and inter-cell correlations simultaneously. We use algorithms to find a subsampling index set for the partial Fourier matrix, in an effort to reduce the correlations of the resulting sequences of arbitrary length. Simulation results demonstrate that the Fourier-based non-orthogonal sequences achieve the excellent performance of sparse activity detection for uplink grant-free access in multi-cell mMTC. Compared to the Zadoff-Chu sequences, this design framework presents more sets of non-orthogonal sequences of arbitrary length, which can supply unique signatures for devices in more mMTC cells.

Design Framework of Fourier-Based Non-Orthogonal Sequences for Sparse Activity Detection in Multicell Massive Connectivity