An Adaptive Filter Approach for Development in Performance of Chaotic Sequences

Abstract

Abstract-Pulse compression technique is the active research topic and widely used in various applications which requires sequences that has good correlation properties. In radar and spread spectrum systems random white noise is used that is similar to the sequence called chaotic sequence as it provides auto and cross-correlation properties similar to that of random white noise. The generation of good sequences which are applicable to radar systems are derived from chaotic maps. These sequences provide better performance in range resolution and detection range. The measures of performance are autocorrelation sidelobe peak (ASP), peak sidelobe ratio (PSR). This paper presents a novel method which improves these all performances. The sequence considered here is the four phase codes which are generated from chaotic map equations. Because the properties of these codes are same as that of random four phase codes. In this paper adaptive equalizer using least mean square (LMS) algorithm is adopted because of its simplicity in implementation and slow convergence. By using this novel method LMS algorithm superior performance can be achieved. However, the number of sequences is not limited by the length of the sequence. Simultaneously the improved performance of mean square error is also observed. Keywords-Chaotic maps, Peak Sidelobe Ratio, Autocorrelation Sidelobe Peak, Least Mean Square Algorithm, Mean square error I. INTRODUCTION Pulse compression technique has wide applications in various fields such as sonar, radar and spread spectrum and multiple access communication. A well-established radar technique is used in order to attain high transmit energy of a long pulse while keeping the range resolution of a short pulse. Pulse compression solves the practical problem of extending the operating range of radar while at the same time maintaining the required range accuracy along with the resolution. It is achieved by modulating the long transmitted pulse which will be correlated with its received reflection. Pulse compression technique has two different approaches. In the first approach the codes with small sidelobes in their auto correlation pattern are processed. In the second approach non recursive time invariant and recursive variant causal filters are used. In pulse compression technique the echo signal from the target passes through the matched filter and the output of the filter has spike like mainlobe and noise like sidelobes [1], [2]. These sidelobe masks the main lobe of weak target echo signals which are undesirable. The ratio of the peak sidelobe to the peak of the mainlobe is called as PSLR. In order to maximize the signal to noise ratio of the received signal at the output of the matched filter various pulse compressed waveforms have been used which includes linear frequency modulated signal and the nonlinear frequency modulated signal like biphase and polyphase sequences [3]. The radar performance depends on its range resolution which is obtained from the auto correlation pattern. Earlier it was reported that...