Signal Detection using the Correlation Coefficient in Fractal Geometry

Using the Fractal Geometry in Signal processing has been extended nowadays. They have found several applications in signal detection and recognitions. They use the chaotic feature of the noise and clutter and try to distinguish between the noise, clutter and the desired target. Recent works show that lots of clutters like sea and ground clutters have fractal behavior so this kind of approach to the signal detection has been extended these days. In this paper we have used the Box-Counts of a signal rather than the Fractal dimension of a signal as will be defined later in the text. By applying the new defined concept we have developed different methods of signal detection. We use the correlation coefficient of the Box-Count and the time domain range for different ranges. By using the difference in the behavior of these coefficients when we have or don't have a target, we can set statistics from these variables and set up some detectors to determine whether the received signal contains a target or not just by comparing the statistics with some thresholds. One of the applications of the method is in high resolution radars. The received signal contains the Range Profile of the target which is unknown in our point of view. So using matched filters cannot be such helpful. In this paper the proposed detectors can act much better the common detectors of these signals. We have shown the advantage of the new methods. They bring us about 3 db increases in SNR.