Polynomial‐approximation‐based locally optimum detector for signals with symmetric alpha stable noise

Abstract

Rational approximation to the non-linear score function used in the locally optimum detector is derived for signals corrupted by the impulsive symmetric alpha stable noise. The new approximation uses a third-order polynomial in the numerator and a fourth-order polynomial in the denominator, compared with the existing approximation that uses a first-order polynomial in the numerator and a second-order polynomial in the denominator. The parameters of the polynomials are derived using non-linear least squares curve fitting. The relationships between the polynomial parameters and the value of the characteristic exponent are also obtained. Numerical results show that the proposed approximation has superior accuracy to the existing approximations. The proposed new approximation is then applied to the locally optimum detector by replacing the score function in the decision variable. Numerical results show that the proposed detector, optimised according to a curve-fitting approach, outperforms previous approximations of the locally optimum detector, also optimised according to a curve-fitting approach, for binary phase shift keying signals and in some cases for on–off keying signals.