Karthick Parashar

A Hierarchical Methodology for Word-Length Optimization of Signal Processing Systems

The problem of converting floating point algorithms to implementation friendly fixed point formats is often solved as an optimization problem where the precision is traded to gain in the implementation cost. The complexity of the problem is known to grow exponentially with more optimizable variables. This paper proposes a divide and conquer technique to solve the growing size of the problem. The approach in this technique is original in the sense that it is formulated from a designers perspective rather than merely attempting to divide and conquer at the algorithmic level. This paper introduces the single noise source model based on which the proposed technique is built. A mixed approach for error propagation is also explained keeping in view of the elements in the circuit that cannot be handled analytically.

Fast performance evaluation of fixed-point systems with un-smooth operators

Fixed-point refinement of signal processing systems is an essential step performed before implementation of any signal processing system. Existing analytical techniques to evaluate performance of fixed-point systems are not applicable to the errors due to quantization in the presence of un-smooth operators. Thus, it is inevitable to use simulation to evaluate performance of fixed-point systems in the presence un-smooth operators. This paper proposes a hybrid technique which can be used in place of pure simulation to accelerate the performance evaluation. The principle idea in the proposed hybrid approach is to selectively simulate parts of the system only when un-smooth errors occur but use analytical results otherwise. The acceleration thus obtained reduces the performance evaluation time which can be used to explore a wider word-length design space or speedup the optimization process. This method has been tried on a complex MIMO sphere decoding algorithm and the results obtained show several orders of magnitude improvement in terms of evaluation time.

Analytical approach for analyzing quantization noise effects on decision operators

The presence of decision operators has proved to be a serious impediment for a fully analytical noise power estimation technique. This paper proposes a generalized decision operator which can potentially capture the behavior of all possible types of decision operators and provides a fully analytical technique to handle them while performing quantization noise power estimation. The proposed method is applied to BPSK and 16-QAM decision operators. The total error rate and the PDF of the error signal are found to follow the simulation to a great degree of accuracy.

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.

A polynomial time algorithm for solving the word-length optimization problem

Trading off accuracy to the system costs is popularly addressed as the word-length optimization (WLO) problem. Owing to its NP-hard nature, this problem is solved using combinatorial heuristics. In this paper, a novel approach is taken by relaxing the integer constraints on the optimization variables and obtain an alternate noise-budgeting problem. This approach uses the quantization noise power introduced into the system due to fixed-point word-lengths as optimization variables instead of using the actual integer valued fixed-point word-lengths. The noise-budgeting problem is proved to be convex in the rounding mode quantization case and can therefore be solved using analytical convex optimization solvers. An algorithm with linear time complexity is provided in order to realize the actual fixed-point word-lengths from the noise budgets obtained by solving the convex noise-budgeting problem.