Shaping probability density function of quantization noise in fixed point systems

Word-length optimization provides opportunities for minimization of implementation cost metrics such as power, area and delay. The constraints on cost in case of implementation on miniature embedded systems platforms continues to grow more stringent. Implementation of complex systems such as wireless communication transceivers is known to greatly benefit from optimal word-lengths. However, WL optimization of such complex systems poses a NP hard combinatorial problem. In line with a divide and conquer technique already explored, this paper proposes to study the probability density function of quantization noise at the output of an arithmetic operator based system. The proposed technique is based on clustering of noise sources according to their power using Kurtosis of the total noise as the clustering criteria. It is noted in this paper that the noise PDF becomes important only at the un-smooth boundaries in the system. The proposed technique is tested on a synthetic 32 tap FIR filter and on a MIMO algorithm. Results obtained show a marked improvement in the behavior of analytical model with the use of the proposed density distribution shaping algorithm.