Accurate approximations of BER for DQPSK transmission via Least Squares estimation of the Marcum Q-function

This paper proposes five new estimators for the Bit Error Rate (BER), which have no closed form expression. Here, in particular, we focus on the case for coherent Differential Quaternary Phase Shift Keying (DQPSK), with Gray coding, over an Additive White Gaussian Noise (AWGN) channel, where the instantaneous BER can be expressed in a form involving the standard Marcum Q-function. By exploiting several alternative finite-domain integral representations of the Marcum Q-function, new estimators for the BER can be constructed using the Least Squares approach. The key idea is to derive exponential approximations for the zeroth-order modified Bessel function, where the coefficients of the exponent are provided by Least Squares fit. The new estimators are shown to be more accurate and efficient than the tightest bounds and approximations in the literature.