Abstract-This paper will design non-linear frequency modulation (NLFM) signal for Chebyshev, Kaiser, Taylor, and raised-cosine power spectral densities (PSDs). Then, the variation of peak sidelobe level with regard to mainlobe width for these four different window functions are analyzed. It has been demonstrated that reduction of sidelobe level in NLFM signal can lead to increase in mainlobe width of autocorrelation function. Furthermore, the results of power spectral density obtained from the simulation and the desired PSD are compared. Finally, error percentage between simulated PSD and desired PSD for different peak sidelobe level are illustrated. The stationary phase concept is the possible source for this error.
In this paper, an iterative method is proposed for nonlinear frequency modulation (NLFM) waveform design based on a constrained optimization problem using Lagrangian method. To date, NLFM waveform design methods have been performed based on the stationary phase concept which we have already used it in a previous work. The proposed method has been implemented for six windows of Raised-Cosine, Taylor, Chebyshev, Gaussian, Poisson, and Kaiser. The results reveals that the peak sidelobe level of autocorrelation function reduces about an average of 5 dB in our proposed method compared with the stationary phase method, and an optimum peak sidelobe level is achieved. The minimum error of the proposed method decreases in each iteration which is demonstrated using mathematical relations and simulation. The trend decrement of minimum error guarantees convergence of the proposed method.
In this paper, a phase improvement algorithm has been developed to design the nonlinear frequency modulated (NLFM) signal for the four windows of Raised-Cosine, Taylor, Chebyshev, and Kaiser. We have already designed NLFM signal by stationary phase method. The simulation results for the peak sidelobe level of the autocorrelation function in the phase improvement algorithm reveal a significant average decrement of about 5 dB with respect to stationary phase method. Moreover, to evaluate the efficiency of the phase improvement algorithm, minimum error value for each iteration is calculated.Introduction: Goal of pulse compression is to increase bandwidth and improve range resolution [1]. There are several methods for pulse compression. For example, coding methods such as Barker, Huffman, Zadoff-Chu, etc. are utilized in pulse compression [2], but due to the phase discontinuity and the signal amplitude variability (such as the Huffman codes), they result in loss increment in the receiver (due to mismatching) [3]. The linear frequency modulation (LFM) method has received much attention since its phase continuity and the constant amplitude of the signal, but it suffers from relatively high sidelobes in autocorrelation function (ACF) [3].The NLFM method has been proposed to reduce the sidelobes level in ACF. In NLFM method, the signal amplitude is constant and the frequency variations with respect to time is nonlinear. Stationary phase concept (SPC) is commonly used in NLFM method. SPC explains that power spectral density (PSD) in a frequency is relatively high if the related frequency variation is low with regard to time [3]. Using this method leads to noticeable sidelobes level decrement in ACF. Additionally, it causes the main lobe width to increases slightly but negligible.The phase improvement algorithm (PIA) is proposed here to be used after the stationary phase method. This method is designed based on the phase matching techniques. To start the algorithm, an appropriate value for the phase is used which comes from stationary phase method. The algorithm is repeated several times in order to get closer to the optimal phase value where sidelobes level are significantly reduced compared to the stationary phase method.The remainder of the letter is organized as follows: Second section outlines the proposed phase improvement algorithm. In the third section, the simulation results of the proposed algorithm are discussed and a comparison between SPC and the proposed method is made. Finally, the fourth section concludes the paper.
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