Analytical approach to evaluate fixed point accuracy for an iteration of decision operators

The use of fixed point arithmetic for digital signal processing applications has several benefits in terms of cost, energy consumption and time to market. The existing analytical approaches for evaluating fixed-point systems performance are not able to evaluate the error caused by quantization noise in the case of special configuration of un-smooth operators such as decision operators and especially when the quantization noise propagates through an iteration of decision operators. This problem is familiar in the case of equalization algorithms such as decision feedback equalization (DFE). In this paper, we propose an analytical model allowing the evaluation of decision error probability in the case of decision operator iteration. This model calculates the decision error probability taking into account the propagation of quantization noise from one decision operator to another based on the Newton-Raphson algorithm for resolution of non linear system. We have tested the approach for the DFE algorithm in the cases of BPSK, QPSK and 16-QAM constellations.