Aspects of Radar Imaging Using Frequency-Stepped Chirp Signals
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Institute for Parallel Processing Acad. G. Bonchev Str., 25-A, 1113 Sofia, BULGARIA email: [email protected] **
Sofia University “St Kliment Ohridski” J. Boucher Blvd. 5, 1164 Sofia, BULGARIA email: [email protected] Abstract: In this paper, a new convolution-based model for simulation of steppedfrequency GPR images is described. In contrary to the conventional convolution model, this model takes into account both the basic radar parameters and the basic parameters of multi-layered media and, therefore, it results in more accurate simulation of GPR images. The simulation results show that the algorithm presented can be successfully used for analysis and parameter optimization of the signal processing algorithms in stepped-frequency GPR.
1. Introduction In stepped-frequency GPR, the distance to subsurface objects is determined by constructing synthetic range profiles in the time domain. Two methods can be used for producing synthetic range profiles. These methods of the stepped-frequency processing construct a synthetic high-resolution range profile by transmission of a burst of narrowband LFM pulses with frequency bands separated by a fixed step [1, 2, 3]. At each transmission of a narrowband pulse, the EM wave radiated from a transmitter antenna travels through the multi-layered media with a velocity that depends on the electrical properties of the layers. If the EM wave encounters a boundary between two layers with different electrical properties, a part of the EM energy is reflected or scattered back to the surface, while the rest of the energy continues to travel downward. The radar receiver collects the return signal that contains several returns from various layers of different dielectric properties. There are a variety of methods for simulation of GPR return signals. For a basic first-order simulation, a simple convolution-based modeling technique can be used [4]. More accurate results, taking into account the effects of scattering due to random surfaces and the three dimensional antenna beam pattern can be obtained using advanced methods such as the Finite Difference Time Domain (FDTD) method, at the cost of complexity and computational time [5]. In this paper, we present a sophisticated convolution-based signal model for simulation of stepped-frequency GPR images. This model takes into account the basic radar parameters (energy potential, frequency, antenna beamwidth, number of transmitted chirps, wideband of transmitted chirps and so on) and the basic parameters of a multi-layered medium (number of layers, dielectric properties of layers, depth of layers, attenuation) and, therefore, it results in more accurate simulation of stepped-frequency GPR images.
2. Echo signal simulation The synthetic high-resolution range profile is constructed by transmission of narrowband LFM pulses with frequency bands separated by a fixed step. At the m-th transmission of a
narrowband LFM pulse, the signal reflected from a multi-layered medium with L layers can be mathematically described as: L
r (m, t ) = r0 (m,
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