Performance of the locally optimum threshold receiver and several suboptimal nonlinear receivers for ELF noise

Abstract

Naturally occurring atmospheric noise encountered at the input to an extremely low frequency (ELF) receiver is non-Gaussian, consisting of the sum of a low-level Gaussian background and strong narrow pulses caused by single lightning strokes from nearby thunderstorms. It has been khown for a number of years that significant improvements in performance can be achieved if the non-Gaussian nature of the noise is considered when the ELF receiver is designed. The optimum receiver structure for detecting known threshold signals in additive white non-Gaussian noise is known to be the same as that which should be used if the noise were Gaussian, except that a zero-memory nonlinearity is placed between the receiver input and the Gaussian detector. The input-output characteristic of the nonlinearity is given by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-d/dx [In P_{n} (x)]</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P_{n} (x)</tex> is the first-order amplitude probability density function of the additive noise. In this paper, the performance of this receiver, as well as of those where the nonlinearity is replaced by either a clipper, hole puncher, or hard limiter, is analytically evaluated for Middleton's Class B Noise Model. Although this analytical approach is different than the earlier empirical approach taken by Evans and Griffiths, it reaches identical conclusions concerning the design choice of the nonlinear noise processor for use at ELF. Briefly, it confirms that the optimum nonlinearity can achieve an improvement of as much as 20 dB in effective signal-to-noise ratio. Moreover, it shows that the more practical clipper achieves an improvement typically within 0.5 dB of the optimum nonlinearity.