Abstract
Bello’s stochastic linear time-varying system theory has been widely used in the wireless communications literature to characterize multipath fading channel statistics. In the context of radar backscatter, this formulation allows for statistical characterization of distributed radar targets in range and Doppler using wide-sense stationary uncorrelated scattering (WSSUS) models. WSSUS models separate the channel from the effect of the waveform and receive filter, making it an ideal formulation for waveform design problems. Of particular interest in the radar waveform design community is the ability to suppress unwanted backscatter from the earth’s surface, known as clutter. Various methods for estimating WSSUS system functions have been studied in the literature, but to date no analytic expressions for radar surface clutter range-Doppler scattering functions exist. In this work we derive a frequency-selective generalization of the Jakes Doppler spectrum model, which is widely used in the wireless communications literature, adapt it for use in radar problems, and show how the maximum entropy method can be used to extend this model to account for internal clutter motion. Validation of the spectral and stationarity properties of the proposed model against a subset of the Australian Ingara sea clutter database is performed, and good agreement is shown.
Highlights
Random linear time-varying (LTV) system theory was first comprehensively described by Bello [2]and has widely been used in the wireless communications field ever since, to model the multipath fading of mobile radio channels [3,4]
In this work we derive a frequency-selective generalization of the Jakes Doppler spectrum model, which is widely used in the wireless communications literature, adapt it for use in radar problems, and show how the maximum entropy method can be used to extend this model to account for internal clutter motion
We demonstrate how an estimation of spatially-local internal clutter motion (ICM) spectra can be cast as a probability density estimation problem, for which solutions can be found using the Jaynes maximum entropy (MaxEnt) method [44] and directional statistics [45]
Summary
Random linear time-varying (LTV) system theory was first comprehensively described by Bello [2]. A separate set of models that are distinct, but can be related to Bello’s LTV theory are the Clarke/Jakes Doppler spectrum class of models [9,10], originally only applicable for flat fading (i.e., where the symbol time is much larger than the multipath delay spread) This model is ubiquitous in the wireless communications literature, and many extensions have been proposed, such as for varying geometries [11] and more accurate fading statistics [12]. In this work we derive such analytic expressions for the case when localized internal clutter motion (ICM) is small relative to radar platform motion using a frequency-selective version of the Jakes model Extensions to this model are proposed to connect previous work on Doppler spectrum modeling to random LTV theory. The spectrum prediction method is validated against a subset of the Australian Ingara medium grazing angle clutter dataset [46], and good agreement is shown
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