Design of Low Power FIR Filter Coefficients Using Genetic Algorithm (Optimization)

With the explosive growth of wireless communication system and portable devices, the power reduction has become a major problem. Many of the communication system today utilize digital signal processors (DSP) to resolve the transmitted information. Finite impulse response (FIR) filters have been and continued to be important building blocks in many digital processing systems (DSP). Hamming distance is a measure of switching activity corresponding to the number of energy consuming transition in multiplier and accumulate (MAC) of filter while implementing on digital signal processors (DSP). The hamming distance between consecutive coefficient values and the number of signal toggling in opposite directions thus forms the measure of bus power dissipation. Genetic algorithms can implemented as a computer simulation in which a population of abstract representations (called chromosomes or the genotype or the genome) of candidate solutions (called individuals, creatures, or phenotypes) to an optimization problem evolves toward better solutions. In this paper the hamming distance of fir filter is minimized by minimizing the switching activity using “Genetic Algorithms” optimization technique to reduce the power dissipation and to increase the battery life of portable multimedia devices. An optimization or a mathematical programming problem can be stated as follows: Find X = [x1x2x3.......xn] Subjected to the constraints gj(X) £ 0. j = 1, 2............m hj(X) £ 0. j = 1, 2............p Where X is an n-dimensional design vector, f(X) is termed the objective function and gj(X) and hj(X) are known as inequality and equality constraints, respectively. 2. OBJECTIVE Finite Impulse Response (FIR) filter is implemented as a series of multiply and accumulate operations on a programmable Digital Signal Processor (DSP). The multiply and accumulate (MAC) unit of a digital signal processor experiences high switching activity due to signal transitions which results in higher power dissipation. Hamming Distance forms a measure of the switching activity during implementation of the filter. The Objective of the paper is to minimize the Hamming distance and reduce the signal toggle by using optimization technique, Genetic Algorithm (GA), so that its power dissipation is reduced while its implementation on a Digital Signal Processor. International Journal of Computer Science & Communication (IJCSC) 2 The purpose of the optimization is to choose the best one of many acceptable designs available. Thus a criterion has to be chosen for comparing the different alternative acceptable design and for selecting the one. The criterion, with respect to which the design is optimized, when expressed as a function of the design variables, is known as objective function. If f1(X) and f2(X) denote two objective functions, a new objective function for optimization is constructed as f(X) = a1 f1(X) + a2 f2(X) where f(X) is a new objective function, a1 and a2 are constants whose values indicate the relative importance of one objective function relative to the other. Description Genetic Algorithm is an emerging optimization algorithm for signal processing and considered a powerful optimizer in away areas. The GA has been demonstrated a powerful method for these multi objective problems, enabling to obtain the pareto optimal set instead of single solution. Genetic Algorithms (GAs) were invented by John Holland and developed by him and his students and colleagues. Search Space The space of all feasible solutions (the set of solutions among which the desired solution resides) is called search space (also state space). Each point in the search space represents one possible solution. Each possible solution can be “marked” by its value (or fitness) for the problem. With GA we look for the best solution among a number of possible solutions represented by one point in the search space. Fig 2: G.A. Search Space Working Principle To illustrate the working principle of GA consider a unconstrained optimization problem Maximize f(X) Xi L ≤ Xi ≤ Xi U for i = 1, 2 ....N If f(X), for f(X) > 0 is to be minimized, then the objective function is written as maximize 1 1 ( ) f x + Encoding: Since genetic algorithms search directly in the solution space, it needs a way to encode solutions in a way that can be manipulated by the genetic algorithm. Binary Encoding: In binary encoding, every chromosome is a string of bits 0 or 1. Table1 Chromosomes with Binary Encoding Chromosome A 101100101100101011100101 Chromosome B 111111100000110000011111 Permutation Encoding: In permutation encoding, every chromosome is a string of numbers that represent a position in a sequence. Table 2 Permutation Encoding Chromosome A 1 5 3 2 6 4 7 9 8 Chromosome B 8 5 6 7 2 3 1 4 9 3. RANK SELECTION Rank selection ranks the population first and then every chromosome receives fitness value determined by this ranking. The worst case will have the fitness 1, the second worst 2 etc. and the best will have fitness N (number of chromosomes in population). Fig 3: Situation before Ranking Fig4: Situations After Ranking (Graph Of Fitness) Hamming Distance Minim. Algorithm Problem Definition: The Hamming distance minimization problem using Steepest Decent approach stated as follows For a Given N-tap FIR filter with coefficient A, i = 0, N – 1 i that satisfy the filter response in terms of pass band ripples, stop band attenuation and linear phase, find a new set of coefficient A, i = 0, N – 1 i such that the total Hamming distance between successive coefficients is minimized while still satisfied the desired filter characteristics in terms of pass band ripple and stop band attenuation. Design of Low Power FIR Filter Coefficients Using Genetic Algorithm (Optimization) 3 Coefficient Sealing: The first phase of the algorithm involves uniformly scaling the coefficient so as to reduce the total Hamming distance between successive coefficients. For N-tap filter with N coefficients (A, i = 0, N – 1), the output Y (n) is given by equation.