Closed-Form BER Expression for Multi-User Downlink NOMA

Massive machine-type communication (MMTC) is an essential element for realizing the Internet of Things (IoT). However, certain challenges arise because MMTC should support a massive number of users. Recently, non-orthogonal multiple access (NOMA) has been highlighted as a technology for MMTC in a limited frequency band. To design and operate a NOMA-based communication system for a massive number of users, an accurate performance analysis for an arbitrary number of users and a practical power assignment method for the channel condition of each user are required. In this study, the exact bit error rate (BER) expression for an arbitrary user number is derived in an explicit closed form for NOMA-based communication. In addition, for analytical purposes, an approximate expression with high accuracy is proposed. To achieve an extension to the fading channel, the average BER expressions for the Rayleigh and Nakagami-m fading channels are presented in closed forms. Based on the derived BER expression, a power assignment algorithm that can achieve the target performance is proposed when each user is associated with a different signal-to-noise ratio. The derived BER expressions and the power assignment algorithm were verified based on computer simulations.