Separation of overlapping linear frequency modulated (LFM) signals using the fractional fourier transform

Abstract

Abstract-Linear frequency modulated (LFM) excitation combined with pulse compression provides an increase in signal to noise ratio (SNR) at the receiver. LFM signals are of longer duration than pulsed signals of the same bandwidth. Consequently, in many practical situations, maintaining temporal separation between echoes is not possible. Where analysis is performed on individual LFM signals, a separation technique is required. Time windowing is unable to separate signals overlapping in time. Frequency domain filtering is unable to separate signals with overlapping spectra. This paper describes a method to separate time overlapping LFM signals through the application of the fractional Fourier transform (FrFT), a transform operating in both time and frequency domains. A short introduction to the FrFT, its operation and calculation are presented. The proposed signal separation method is illustrated by application to a simulated ultrasound signal, created by the summation of multiple time overlapping LFM signals and the component signals recovered with ±0.6% spectral error. The results of an experimental investigation are presented where the proposed separation method is applied to time overlapping LFM signals, created by the transmission of a LFM signal through a stainless steel plate and water-filled pipe.

2-D DOA Estimation of LFM Signals Based on Sparse Representation in Fractional Fourier Domain

“…For calculating the azimuth i and elevation i , it is necessary to determine the corresponding relation between space angles  i and  i . From the analysis above, the same LFM signal received by sub-array X and Y will achieve the best energy concentration at the same order and the estimated value of initial frequencyˆi f and chirp rate i calculated by (10) are also the same. Therefore, the pair matching problem of space angles can be effectively solved byˆi f and i , which is respectively estimated by the received data from sub-array X and Y.…”

“…Utilizing the excellent energyconcentrated performance of LFM signal in the fractional Fourier domain [10][11], the received signals of sensor array are transformed into fractional Fourier domain, which changes the time-variant manifold matrices of LFM signals into timeinvariant one. Then, two 1-D dictionaries are established respectively based on the defined space angle.…”

Automatic Modulation Classification of LFM and Polyphase-coded Radar Signals

“…The SNR at the output of FrFT equals SNR o = SNR i + G, where SNR i is the signal to noise ratio at the input of the FrFT, and G =BT >> 1 is the pulse compression gain, therefore FrFT can be used to detect the input signal at low SNR. In the discrete domain the optimum transform angle α opt of the FrFT is given by [17], [7]:…”

Harmonic cancellation in switched mode Linear Frequency Modulated (LFM) excitation of ultrasound arrays

“…LFM signals and matched filtering techniques are commonly used in a wide range of applications to improve SNR of the received signals such as in [11] and [12]. An LFM signal can be expressed for time t as…”