Lv's Distribution: Principle, Implementation, Properties, and Performance

Abstract

This paper proposes a novel representation, known as Lv's distribution (LVD), of linear frequency modulated (LFM) signals. It has been well known that a monocomponent LFM signal can be uniquely determined by two important physical quantities, centroid frequency and chirp rate (CFCR). The basic reason for expressing a LFM signal in the CFCR domain is that these two quantities may not be apparent in the time or time-frequency (TF) domain. The goal of the LVD is to naturally and accurately represent a mono-or multicomponent LFM in the CFCR domain. The proposed LVD is simple and only requires a two-dimensional (2-D) Fourier transform of a parametric scaled symmetric instantaneous autocorrelation function. It can be easily implemented by using the complex multiplications and fast Fourier transforms (FFT) based on the scaling principle. The computational complexity, properties, detection performance and representation errors are analyzed for this new distribution. Comparisons with three other popular methods, Radon-Wigner transform (RWT), Radon-Ambiguity transform (RAT), and fractional Fourier transform (FRFT) are performed. With several numerical examples, our distribution is demonstrated to be a CFCR representationthat is computed without using any searching operation. The main significance of the LVD is to convert a 1-D LFM into a 2-D single-frequency signal. One of the most important applications of the LVD is to generate a new TF representation, called inverse LVD (ILVD), and a new ambiguity function, called Lv's ambiguity function (LVAF), both of which may break through the tradeoff between resolution and cross terms.

A Fast Motion Parameters Estimation Method Based on Cross-Correlation of Adjacent Echoes for Wideband LFM Radars

“…4. The acceleration and velocity are calculated using the estimated frequencies according to equations (23) and (24).…”

“…In [21], a novel estimation algorithm of motion parameters is proposed for ISAR imaging, based on KT and the adjacent cross-correlation function (ACCF). Then, a fast non-searching method based on ACCF is proposed for target motion estimation, target detection and ISAR imaging [22][23][24][25][26]. There are two differences between the two methods in [21] and in [22][23][24][25][26].…”

“…Then, a fast non-searching method based on ACCF is proposed for target motion estimation, target detection and ISAR imaging [22][23][24][25][26]. There are two differences between the two methods in [21] and in [22][23][24][25][26]. The first one is that the KT is not utilized in [22][23][24][25][26], and the other one is that the choice of the scaling factors is improved in [26], thus better performance is obtained under low SNR conditions.…”

“…There are two differences between the two methods in [21] and in [22][23][24][25][26]. The first one is that the KT is not utilized in [22][23][24][25][26], and the other one is that the choice of the scaling factors is improved in [26], thus better performance is obtained under low SNR conditions. Compared with the RFT method, the ACCF method [22,23] can achieve similar performance with much lower computational cost.…”

Systematic analysis of uncertainty principles of the local polynomial Fourier transform

“…These parameters can be estimated by using the polynomial time frequency transform [9] or the Lv's distribution [10]. The energy distribution of the LPFT is called the local polynomial periodogram (LPP) which is defined as |LPFT s (t, ω)| 2 .…”