Parameter estimation in multi-antenna system based on iterative adaptive approach

As one of the main means for remote sensing and detecting, synthetic aperture radar is playing more important role in many fields such as country reconnaissance, ocean observation, environment disaster monitoring and military reconnaissance. The synthetic aperture radar system based on multi-antenna technology can achieve high resolution of still image and estimate the motion parameter. The echo model of target is set up for motion parameter estimation and the performance of system parameter estimation is given according to the moving target velocity estimation method based on iterative adaptive approach.


Introduction
As one important feature of modern airborne/ spaceborne radar system, ground moving target indication is of significant value of applications in both military and civil fields. With the extensive application of synthetic aperture radar technology, ground moving target indication based on synthetic aperture radar platform is required to obtain high-resolution images of the static scene of ground, meanwhile to detect moving objects and estimate the motion parameters. In recent years, the ground moving target indication technology based on synthetic aperture radar has obtained prodigious evolvement, but still faces the following challenges [1] . Firstly, it is known that the performance of multi-channel clutter suppression depends on system space DOF. However, there are many constraints for space borne synthetic aperture radar system to be installed with more receive channels, such as size, power, load and cost of the platform, which lower the space DOF. Secondly, since the increasing complexity of imaging and moving target detection scenes, especially in cities, mountains and other complex terrain, moving target detection is in face of several practical issues like non-uniform clutter and multipath echoes. Thirdly, increasingly complex electromagnetic environment, including active/passive jamming from enemy, poses critical challenges to image and detect moving targets. Synthetic aperture radar system requires a higher degree of freedom in space to solve these problems. While the way of simply adding more receive channels with limited potential and exploring a new radar system is necessary. Multiple input multiple output is a new kind of radar system which transmits independent waveforms through multiple antennas and receives scene echoes with plurality of antennas independently in order to obtain more spatial sampling in the condition of the same number of antennas [2] .
In this article, a mathematical model was built for echoes of static scenes and moving targets in multiple input multiple output imaging mode, based on which a method of moving target parameter estimation was proposed and validated by numerical simulation.

Method of velocity estimation
During moving target detection process, a set of discrete doppler frequency cells are searched to indicate the presence of moving targets for each resolution cell. Once moving targets are detected within a doppler cell, the estimation of the radial velocity of targets can be acquired. However, the radial velocity estimation of target acquired by this method is rough due to the limited number of doppler detection channels. Accurate estimates need more precise processing method.

Rough estimate of radial velocity based on FFT method
Target's radial motion will cause the azimuth offset in synthetic aperture radar images. In order to correct to the real location, it is necessary to estimate the radial velocity [3] .
With the clutter suppression, echo of cell to be detected can be expressed as The expression of the target's spatial steering vector can be expanded to Obviously, the doppler frequency of the echo of target is equivalent to the spatial frequency of target with respect to multiple input multiple output array. When the radial velocity of target is zero, then 0 v f , which is similar to the situation that signal source is incident from the normal direction of the array. Overall, target's radial velocity estimation is equivalent to the spatial spectrum estimation of array signal, or DOA estimation.
The issue of estimation of target velocity is transformed to DOA estimation of the target with a virtual array. Regular Delay and Sum (DAS) method can be realized by FFT transform [4] .
Restricted by the number of spatial sampling points, velocity estimation method based on DAS is defective for the low resolution and higher side lobes. Undoubtedly a more accurate method is needed for the parameter estimation.

Accurate estimate of radial velocity based on an IAA method
Iterative Adaptive Approach (IAA) is a new kind of nonparametric adaptive spectral estimation algorithm, by which higher accuracy spectral estimation can be acquired with only less or even a single snapshot of data. Meanwhile, it offers better robustness for the array of amplitude / phase error and system sampling error [5] .
In the phases of adaptive moving target detection, velocity range of the moving target is able to be defined roughly. Then the range is divided into v K discrete values. More intensive velocity interval division means higher estimation accuracy, but also higher computational complexity. To simplify the notation i vi f v v and combine the spatial steering vectors of interests into vector in form as Assuming corresponding response function of velocity After clutter suppression procession, echo of the cell to be detected is expressed as z A n (5) IAA solves with weighted minimum variance method in which minimum cost function is The above estimation process is achieved with iteration. Generally, IAA use period spectrum estimation as the primary iteration .The process is shown in Table 1.

Simulation of scene echo
Verifying the validity of method of moving target detection requires the clutter data of ground scene. However, it is difficult to obtain measured data from multiple input multiple output system in practice.
Weighting scattering coefficient with two-dimensional impulse response of the synthetic aperture radar system by two-dimensional frequency domain method is able to be realized quickly with FFT in two-dimensional frequency domain [6] . Depending on the specific relationship of transmitting and receiving echo signals between different combinations, a method for the fast generation of frequency domain of scene data in multiple input multiple output synthetic aperture radar is proposed ,which is based on the traditional twodimensional FFT frequency domain simulation method with single-channel raw data [7] .

Method of Echo Fast Generation in 2D FFT
Ignoring constant factor, echo of scene is derived from coherent superposition of echo of all scatters [8] and represented as: Where, x and r is defined as the coverage area of azimuth and range of Multiple input multiple output beam in ground scene respectively.
By applying two-dimensional Fourier transform on slow time and fast time , two-dimensional frequency domain of signal is expressed as x r C through two-dimensional Fourier transform. Scene echo signals can be obtained by applying inverse fourier transform to formula (10) and expressed as: , , Integration of i and i is realized with 2D FFT and interpolation, that is Where, mn r r r mn c mn Where,

00
, r y f represents synthetic aperture radar echo of referenced phase center of multiple input multiple output array that transmitted and received with single antenna [9] .

Simulation and results
In the simulation scenario, assuming that the number of transmit antennas 2 T M , the number of receive There is a moving target with radial velocity of 5 m/s in the cell to be detected. Assuming the clutter is completely suppressed after adaptive moving target detection and the system SNR=20dB, Figure 1 shows the estimation results of moving target's radial velocity by DAS and IAA based methods. Figure 1(a) shows the linear representation of normalized amplitude, while Figure 1 (b) demonstrates the normalized amplitude in dB. The result of simulation indicates that radial velocity estimation algorithm based on IAA can offer higher resolution (narrower main lobe) and larger dynamic range (lower ratio of peak value side lobe) compared with radial velocity estimation method based on DAS. Assume that there are two moving target points with the same scattering intensity to be distinguished in the resolution cell. The radial velocity are 4.8 m/s and 5.2 m/s respectively. By using both DAS and IAA algorithm, the results of velocity estimation is shown in Figure 2. The estimation results of DAS in Figure 2 (a) failed to distinguish one target from each other, while estimation results of high resolution spectral estimation algorithm IAA in Figure 2  Assume that there are two moving target points with different scattering intensity to be distinguished in the resolution cell. For target 1, radial velocity is 4.0 m/s and the scattering intensity is normalized to 1. For target 2, radial velocity is 5.0 m/s, with -10dB lower of scattering intensity than target 1.
Results of velocity estimation from DAS and IAA algorithm is shown in Figure 3 respectively. Due to the higher side lobe of DAS estimation method, it is difficult to distinguish different targets by DAS estimation since target with higher scattering intensity suppresses target with lower scattering intensity in the same resolution cell. While the side lobe of IAA algorithm is lower and it is possible to distinguish targets with in relatively larger dynamic range of speed.

Conclusion
In this article, a mathematical model was built for echoes of moving targets in multiple input multiple output synthetic aperture radar imaging mode, based on which a method of moving target parameter estimation was proposed and validated by numerical simulation. Results of velocity estimation shows that the iterative adaptive approach is possible to distinguish relatively larger dynamic range of speed.