1.  Adaptive filter based on LMS Algorithm used in different fields  Equalization, Noise Cancellation, Channel Estimation...  Easy implementation in embedded systems (low complexity)  Fixed-Point implementation  Reduce the cost and the power consumption compared to floating-point arithmetic  Necessity to estimate the error due to fixed-point computation  Models ever developed by Caraiscos (1984) and Bellanger (1989)  Estimate the Mean Square Error in fixed-point implementation  Models only valid for convergent rounding  Development of a new model valid for all types of quantization  Evaluation by simulation of the model quality  Adaptive filter based on LMS Algorithm used in different fields  Equalization, Noise Cancellation, Channel Estimation...  Easy implementation in embedded systems (low complexity)  Fixed-Point implementation  Reduce the cost and the power consumption compared to floating-point arithmetic  Necessity to estimate the error due to fixed-point computation  Models ever developed by Caraiscos (1984) and Bellanger (1989)  Estimate the Mean Square Error in fixed-point implementation  Models only valid for convergent rounding  Development of a new model valid for all types of quantization  Evaluation by simulation of the model quality P n =E(ρ n ρ t n ), R=E(x n x t n ), Hypothesis b n =γ n ACCURACY EVALUATION OF FIXED-POINT LMS Romuald ROCHER, Daniel MENARD, Olivier SENTIEYS, Pascal SCALART R2D2 - IRISA, University of Rennes I 6 rue de Kérampont F-22300 Lannion, France Romuald.Rocher@enssat.fr Noise due to coefficient quantization Introduction Abstract : The implementation of adaptive filters with fixed-point arithmetic requires to evaluate the computation quality. The accuracy may be determined by calculating the global quantization noise power in the system output. In this paper, a new model for evaluating analytically the global noise power in the LMS algorithm and in the NLMS algorithm is developed. Two existing models are presented, then the model is detailed and compared with the ones before. The accuracy of our model is analyzed by simulations. At the steady state, P n+1 = P n ρnρn Input signal filtered by the coefficient error Signification Noise due to input signal quantization W* At the steady state, w n =w* α n white noise : m α et σ 2 α : mean and variance of α n I N : size N identity matrix Input noise filtered by optimal coefficients Signification Output quantization noise Fixed-point LMS x(n) w’ n µ Q Filter Q Q Z -1 Q y’(n) e’(n) nn γnγn  (n)  (n) y(n) Quantization equations Filter equations Adaptation part Noise due to filter computation. Simple precision multiplications. Double precision multiplications  Propagation noise models: Addition : z = u + v  Quantization noise model:  b g (n) : additive random variable  Stationary and uniformly distributed white noise  Uncorrelated with y(n)  First and second-order moments + Q Noise models Truncation Rounding Multiplication : z = u  v x(n) x(n-1) Z -1 QQQ x(n-N+1) w n (0) w n (1) w n (N-1) Q Evaluation of the relative error Filter size N :1-32 Adaptation step µ/µ max : 0 - 0.6 Quantization law : truncation  Relative error < 25% Comparaison with the existing models Model quality evaluation trough experimentations Truncation Model can be extended to NLMS Convergent rounding 16-tap filter  Our model has better results m η et σ 2 η : mean and variance of η n m γ and σ 2 γ : mean and variance of γ n I R I S A I R I S A Convergent rounding