Phase improvement algorithm for NLFM waveform design to reduction of sidelobe level in autocorrelation function

Abstract

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.

Sidelobe level reduction in ACF of NLFM waveform

“…Difference between and the amplitude of the Fourier transform of the desired signal is defined as the error. Since in NLFM signals, amplitude is constant, so our goal is to minimise the error with the constraint of being unit the amplitude of for , therefore we try to minimise the following equation: If two complex numbers come close to each other, then it can be concluded that the values of their amplitudes also close together, so if the following equation is reduced, then the error can be reduced, which is expressed in the phase matching problems [17–19]…”

“…If two complex numbers come close to each other, then it can be concluded that the values of their amplitudes also close together, so if the following equation is reduced, then the error can be reduced, which is expressed in the phase matching problems [18][19][20] min…”

Computationally efficient TDOA and FDOA estimation algorithm in passive emitter localisation

“…This negative influence will seriously decrease the estimation accuracy of TDOA and FDOA. Therefore, it is necessary to remove this migration before estimating parameters [20–22].…”

Conventional vs. Convolutional Windows for Reduction of Side Lobes

“…Basically window is a mathematically limited function which exists within given interval and is zero valued anywhere else and is used to reduce the well known Gibbs oscillations caused by the abrupt truncation of a Fourier series [1]. A window function is a basic signal processing tool that is needed in many signal processing fields such as radar/sonar [2]. In most of these applications window function is assumed to have all the spectral power into extremely narrow band with zero sidelobes which is impossible both theoretically and practically [3].…”