Power Allocation Algorithm based on $N^{th}$ order Fibonacci Polynomial for Multi-User NOMA

Abstract

In this paper, we propose a novel empirical power allocation algorithm based on individual term normalization of N th order Fibonacci polynomial for multi user Non Orthogonal Multiple Access (NOMA), providing a characteristic solution to allocation problem for n-users. A deterministic mathematical expression for same predetermined power allocation scheme for both superposition coding (SC) at base station domain and successive interference cancellation (SIC) at user domain has been formulated. Fibonacci polynomial has been defined and linked to power allocation algorithm corresponding to radial distance of users from BS with sole requirement of second order statistics (SOS). Holistic analytical reasoning has been carried out for generic NOMA system and an exact closed-form expression for bit error rate (BER) has been derived using probabilistic models, which has been applied to proposed allocation algorithm. Detailed analysis validates that proposed power allocation algorithm is independent of user channel state information (CSI) which averts cumbersome computations and no prior information regarding allocation is required to be relayed to user domain for successful SIC. Numerical and simulation results (upto 7 user NOMA) have been provided to demonstrate superior performance in terms of reliability and latency of the proposed algorithm in comparison to channel inversion, a CSI based algorithm.