New Constructions of Binary Golay Spreading Sequences for Uplink Grant-Free NOMA

Non-orthogonal multiple access (NOMA) is a promising technology for massive machine-type communications (mMTC). This letter focuses on constructing spreading sequences with low coherence as well as low peak-to-average power ratio (PAPR) for uplink grant-free NOMA. Recently, a framework of spreading matrices from Boolean functions was provided by Yu. Exploiting this framework, we first show that optimum coherence of the constructed spreading matrices can be achieved if the difference of any two distinct Boolean functions is a bent (or almost bent) function. With this result, explicit constructions of Boolean functions are then developed, which lead to new binary Golay spreading matrices with optimum coherence and yielding PAPR of each spreading sequence at most 2. Simulation results demonstrate that such spreading sequences are suitable for uplink grant-free access. Moreover, the proposed Golay spreading sequences are capable of accommodating up to 400% overloaded devices, which can not be achieved from the existing algebraic methods.