Grant-access based legacy networks are unable to deliver Uplink (UL) dominated sporadic transmission of short packets with low signalling overhead, which are the requirements of Massive Machine Type Communication (mMTC). Hence, grant-free Non-Orthogonal Multiple Access (NOMA) techniques are more suited for mMTC. Due to the inherent sparsity in the user activity pattern in an mMTC system, the existing literature revolves around Compressive Sensing based Multi User Detection (CS-MUD) algorithms, which employ random or Zadoff-Chu spreading sequences for NOMA. In this paper we explore the utility of sinusoidal spreading sequences, which allow some non-iterative algorithms to be employed in the context of active user detection, channel estimation and data detection in a UL grant-free mMTC system. These algorithms do not need prior knowledge about the user behaviour statistics, noise statistics, and the level of sparsity in the user activity, which might be difficult to obtain at the Base Station (BS). We present a comprehensive performance and complexity analysis to assess the feasibility of our proposal. Extensive numerical trials demonstrate the utility of sinusoidal codes for mMTC.

Sparse Code Multiple Access (SCMA) is considered to be one of the potential non-orthogonal multiple access (NOMA) techniques mainly targeting uplink transmission to support massive connectivity. In this work, an efficient high dimensional uplink SCMA codebook design is proposed using the Equiangular Tight Frames. Codebook design problem is posed as construction of generalized Equiangular Tight Frames where mutual coherence among codewords are minimized toward the optimal bound. The minimization problem is handled using gradient-based alternating projection technique under average symbol energy constraint. An important feature of the proposed design is monotonically improved Bit Error Rate (BER) performance with scaling of the proposed codebook.