Elsevier

Digital Signal Processing

Volume 68, September 2017, Pages 93-101
Digital Signal Processing

Inverse synthetic aperture radar phase adjustment and cross-range scaling based on sparsity

https://doi.org/10.1016/j.dsp.2017.05.004Get rights and content

Abstract

Due to inherent sparsity of ISAR images, compressive sensing theory has been used to obtain a high resolution image. However, before applying sparse recovery methods, the phase error due to the translational motion of target is compensated by autofocusing algorithms and the target rotation rate is estimated by cross-range scaling methods. In this paper, a comprehensive matrix model for a uniformly rotating target that includes the phase error and chirp-rate of the target is derived. Then by using sparsity and minimum entropy criterion, the estimation of residual phase error and the rotation rate is refined. In order to reduce the computational load, we simplify the model and by an iterative method based on adaptive dictionary, the phase error and chirp-rate are estimated separately. Actually, by exploiting a two-dimensional (2D) optimization method and the Nelder–Mead algorithm the phase adjustment is performed and the chirp-rate is estimated by solving a 1D optimization method for dominant range cells of the target. Finally, both simulation and practical data have been used to verify the validity of the proposed approach.

Introduction

Inverse synthetic aperture radar (ISAR) is a powerful signal processing tool for imaging moving targets usually on the two dimensional (2D) down-range cross-range plane [1]. ISAR imagery plays an important role especially in military applications such as target identification, recognition, and classification [1], [2]. In order to achieve a high resolution ISAR image, the radar transmits large bandwidth signal and integrates the received echoes of a moving target from different aspect angles coherently.

Recent results in signal processing have demonstrated the ability of Compressive Sensing (CS) to reconstruct a sparse or compressible signal from a limited number of measurements with a high probability by solving an optimization problem [3], [4]. Recently, CS has been adopted to obtain high-resolution ISAR images [5], [6], [7], [8], [9], [10], [11]. In [7], [8], [9], [10], [11] the authors assume that range alignment and phase adjustment have been completely done by conventional methods such as [12], [13], [14] and then a sparsity-driven algorithm is used to generate high-resolution ISAR images. Specifically, in [11], a high-resolution fully polarimetric ISAR imaging is proposed that images are constructed by means of the sparse recovery algorithm under the constraint of the joint sparsity. Actually, a 2D smoothed l0 norm (2D-SL0) reconstruction algorithm introduced in [15] is exploited by [11] to solve the sparsity-driven optimization problem. However, sparsity can be used to refine the phase adjustment, for example in [16] sparsity is exploited for joint SAR imaging and phase error correction. In [17] and[18] Bayesian compressive sensing (BCS) are developed for both ISAR imaging and phase adjustment for full aperture and sparse aperture (SA) conditions, respectively. Moreover, in [19] by utilizing sparse Bayesian learning, an autofocus technique is proposed to obtain a focused high-resolution radar image. On the other hand, in the above mentioned sparse based ISAR imaging the rotation rate is not estimated and therefore the obtained image cannot be scaled in the cross-range dimension. In [10] and [20] sparsity is applied to estimate the unknown rotation rate. Specifically, in [10] a parametric sparse representation method is exploited for both ISAR imaging and cross-range scaling of rotating targets.

In this paper, a comprehensive matrix model for a uniformly rotating target that includes both the phase error and chirp-rate of the target is derived. In order to simplify the sparse problem, the phase error and chirp-rate are estimated separately. Before solving the sparsity-driven algorithm the coarse motion compensation is performed by conventional methods introduced in [21], [22], [23], then by using joint constraint of sparsity and minimum entropy, the estimation of residual phase error is refined through an iterative method based on adaptive dictionary. Moreover, to speed up the reconstruction and reduce the memory usage, we exploit the dictionary so that the 2D-SL0 reconstruction algorithm can be used. In other words, by exploiting a two-dimensional (2D) optimization method and the Nelder–Mead algorithm [24] both phase adjustment and ISAR imaging are evaluated.

After fine motion compensation, the chirp-rate is estimated. In [25], the author proposed an algorithm for cross-range scaling. Therefore, we first estimate an initial value for chirp-rate using the method of [25], and then by an iterative approach, solve a 1D optimization method for dominant range cells of the target and search the best chirp rate around the initial value.

The remainder of this paper is organized as follows. Section 2 introduces the signal model. In section 3 the proposed sparse based algorithm is introduced. Sections 4 and 5 present some simulation and experimental results to validate the algorithm, respectively. Finally, Section 6 concludes this paper.

Section snippets

Signal model

In this section, we first describe the geometry of the target and the signal model and then simplify this model. The geometry of the uniformly rotating target is shown in Fig. 1. When the target is in the far field of the radar, the instantaneous distance from the scattering center P(x,y) to the radar can be approximated asR(t)Rt(t)+xcos(Ωt)ysin(Ωt) where Rt(t) is the target's translation range distance from the radar and Ω is the angular velocity of the target which is constant during the

Phase adjustment and cross-range scaling based on sparsity

The CS theory expresses that an unknown sparse signal can be recovered from a very limited number of measurements with high probability by solving a convex l0 or l1 optimization problem. However, to guarantee good reconstruction performance, three conditions should be satisfied. 1) the signal be sparse or compressible, 2) the sensing matrix satisfies restricted isometry property (RIP) and 3) an efficient reconstruction algorithm with low computational complexity be employed.

The ISAR image is

Simulation results

This section is to present some simulations and discussions for the proposed sparsity-based ISAR imaging. The ISAR geometry used in this simulation is shown in Fig. 1. Here we assume that P=2M and Q=2N, and as a consequence, the range and cross-range resolutions of the ISAR image would be two times that of the conventional range Doppler algorithm (RDA).

In the following simulations, the proposed phase adjustment and cross-range scaling algorithm will be compared with the conventional methods of

Experimental results

In this section we compare the performance of different methods for real data of a ship. The parameters of the radar are shown in Table 3. The ISAR images based on sparsity and different phase error estimation are shown in Fig. 6. In Table 4 a comparison based on IC and IE for different phase adjustment methods has been shown. The results prove the better performance of the proposed algorithm. The chirp-rate estimation based on different methods are depicted in Fig. 7.

Moreover, we compare the

Conclusion

In this paper we have proposed a comprehensive matrix model for a uniformly rotating target that includes the phase error and chirp-rate. Then by using sparsity and minimum entropy criterion, the estimation of residual phase error and the rotation rate were refined. In order to reduce the computational load, we simplified the model and by an iterative method based on adaptive dictionary, the phase error and chirp-rate were estimated separately. Actually, by exploiting a two-dimensional (2D)

Hamid Reza Hashempour was born in 1987. He received the B.S. and M.S. degrees in communication systems from Shiraz University, Shiraz, Iran in 2009 and 2011, respectievly. Currently, he is working toward the Ph.D. degree at the School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran.

His research interests include radar signal processing and ISAR imaging.

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    Hamid Reza Hashempour was born in 1987. He received the B.S. and M.S. degrees in communication systems from Shiraz University, Shiraz, Iran in 2009 and 2011, respectievly. Currently, he is working toward the Ph.D. degree at the School of Electrical and Computer Engineering, Shiraz University, Shiraz, Iran.

    His research interests include radar signal processing and ISAR imaging.

    Mohammad Ali Masnadi-Shirazi (M'92) received the B.S. and M.S. degrees in electrical engineering from Shiraz University, Shiraz, Iran, in 1974 and 1984, respectively, and the Ph.D. degree in electrical and computer engineering from the University of New Mexico, Albuquerque, in 1990.

    He taught at Shiraz college of Electronics from 1974 to 1984. He was a postdoctoral researcher at Scripps Institution of Oceanography, University of California San Diego from 1990 to 1992. In 1992 he joined the Department of Electrical Engineering at Shiraz University where he is now a professor. From 2001 to 2003 he was a visiting associate professor in the Department of Electrical Engineering of the University of Texas at Arlington. Dr. Masnadi-Shirazi was one of the recipients of the IET Premium Awards 2013, for the paper published in the IET Radar, Sonar and Navigation.

    His research interests are in the areas of statistical signal processing, adaptive and optimal digital filtering.

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