Optimum step size of the LMS adaptive FIR filter with inadequate length for signal estimation

Step size is a key parameter that must be determined for the efficient use of the LMS algorithm in adaptive FIR filtering. The authors derive the optimum step size for the LMS adaptive FIR filter with inadequate length for signal estimation. The optimum step size yields the most rapid convergence for a given number of taps and a desired mean-square error. For white input data, it is a simple closed-form function of the number of taps, the input signal variance, the initial mean-square error, the desired mean-square error, and the squared norm of the truncated part of the optimum impulse response. This characteristic makes it easy to design in many practical applications. Based on the derived results, the optimum tap number for fastest convergence for a desired mean-square error is obtained via numerical evaluation. Computer simulations are given to support the derived results