Error Reduced Carry Prediction in Approximate Addition for Low-Frequency Sound Zones

Generation of personal listening spaces and sound zones is an emerging smart technology which requires multiple loudspeakers with individual pre-processing FIR control filters in order to establish separate sound experiences in enclosed spaces. Earlier studies have shown that for low frequencies, the acoustic contrast ratio between the individual sound zones is more sensitive to the word-length of the adder than to the word-length of the multiplier in a fixed-point implementation of the FIR filter operations. In this work, we investigate a possible hardware complexity reduction of the adder circuitry by replacing the normal accurate fixed-point adder with an approximate adder based on error reduced carry prediction. Compared to a total word-length of 12 bit for the adder, our study reveals that the hardware complexity can be reduced by 8% by replacing the two least significant bit of the accurate part of the addition with inexact computations. The resulting reduction in acoustic contrast ratio is less than 0.1 dB. For higher reference word-lengths such as 14 bit, the reduction in hardware complexity increases to 17% at a negligible reduction in acoustic contrast ratio of about 0.05 dB.