978-1-4244-4665-0/09/$25.00 ©2009 IEEE Improving Ambiguity Function of Costas Signal Khaola Kasas, Hassan Aboulnour. Dep. of Electronics and Communication Engineering, Faculty of Mechanical and Electrical Engineering Damascus University. Damascus, SYRIA. Email: khka@scs-net.org anruniv@gmail.com Osama Kawas Department of Telecommunications, Higher Institute of sciences and technology Damascus, SYRIA. Email: samkawas@gmail.com Abstract— This paper presents the effects of modifying Costas signal in time and frequency to improve Ambiguity Function (AF). The effect of adding frequency spacing, linear frequency modulation, constant space time, and variable space time between sub-pulses of Costas signal are presented and compared. It is shown that a considerable reduction of side-lobe and better Doppler resolution is achieved by using variable spacing between sub-pulses of Costas signal. Keywords: Ambiguity Function; Costas signal; Pulse Compression. INTRODUCTION For good detection of radar signal a ratio of a large peak signal power to average noise power is needed, at the time of the target's return signal. As we know the matched filter is the best of all possible filters which it produces the maximum ratio. This maximum ratio depends on the total transmitted energy and not on the presence of any frequency modulation on the transmitted signal. Thus for good detection many radars seek to transmit long-duration pulses to achieve high energy, since transmitters are typically operated near their peak power limitation. On the other hand, for good range measurement accuracy, radar needs short pulses. These divergent of the needs of long pulses for detection and short pulses for range accuracy in measurements prevented early radars from simultaneously performing both functions. Fortunately in the late 1950s and early 1960s a new concept was developed whereby both needs could be met. The concept is called “pulse compression” [5]. It makes use of the fact that a long-duration pulse's bandwidth can be made larger by use of modulation in frequency or phase. Large bandwidth implies narrow effective duration. With modulation a waveform can be designed to have both long pulse duration and short pulse effective duration (large bandwidth). The waveform with short pulse effective duration is produced when the long-duration waveform with modulation is applied to its matched filter. Thus, by use of modulation in frequency or phase over long transmitted pulses and a matched filter, a system can simultaneously obtain good detection performance and accurate range measurements Fig.1. The researchers develop many radar signals assisted by modern signal processing systems. Consequently, signals in different shapes have presented like Phase coded signals such as Barker Code, Frank Code, P1, P2, P3, Px Codes, as well as m-sequence code, Colombo code,… et, and frequency coding such as Linear Frequency modulation (LFM), non linear frequency modulation (NLFM), Stepped frequency modulation, and Costas signal [2,3,7,10]. Figure 1. Matched Filter Each of these signals has advantages and disadvantages. But the one of the most important one in the frequency coding is Costas signal. Costas signal, with pulse-width T, consists of N sub-pulses. Each sub-pulse has different frequency as shown in Fig.2 [2]. Each frequency is chosen from a series of frequencies within the Bandwidth B. We have N frequencies, and pulse width of each sub-pulse is given by N T t b /  . Costas has suggested algorithm to arrange the frequencies to enable us to control the side-lobes in such a way that these side-lobes will not exceed 1/N [6]. Then, the biggest side-lobe in ambiguity function (AF) is 1/N of its value in the main lobe Fig.3. Costas signal has a delay resolution of 2 / 1 N of pulse-width and the Doppler resolution is 1/T, and because of using matched filtering in the receiving system this signal has noise immunity. However, Costas signal is not an Ideal signal [1]. The objective of our research is studying the effects of the change of frequency spacing f  where b t f / 1   upon Costas Signal, adding LFM within each sub-pulse, and inserting a separate time between sub-pulses of Costas signal. This study has lead to improve ambiguity function by decreasing the side-lobes and increasing delay resolution and Doppler resolution without increasing the size of Costas array.