Analytical approach to evaluate the effect of the spread of quantization noise through the cascade of decision operators for spherical decoding

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 un-smooth operators such as decision operators and especially when the quantization noise propagates through the cascade of decision operators. This problem is familiar in the case of spherical decoding algorithms. In this paper, we propose a generic analytical model allowing the evaluation of decision error probability for a case of spherical decoding which is SSFE algorithm. This algorithm contains an increasing decision operators cascade. Our model calculates the decision error probability taking into account the propagation of quantization noise from one decision operator to another. We have tested our generic approach described as an algorithm in the cases of BPSK, QPSK and 16-QAM constellations.