Target parameter estimation and array features
1.10 Conclusions and final remarks
This chapter should provide a survey on the general methods of array signal pro- cessing and on the links to antenna design, hardware constraints and target detec- tion, parameter estimation and tracking. Specifically we have discussed the following features:
● Array signal processing is based on the availability of spatial samples of the incoming wavefront. Such samples can be conveniently obtained from arrays with digital sub-arrays. We have described how all the array processing methods can be extended to sub-array outputs, which problems arise for sub- array design, what the accuracy requirements are and how different sub-array features can be obtained by post-processing. In particular the concept of the super-array associated with every sub-array configuration provides a tool to
analyse the feature of the sub-array configuration. Sub-arrays are most important for large arrays, not only because of the requirement of cost, weight and processing time, but also because sub-array solutions for large arrays can be more flexible and efficient.
● Interference suppression by deterministic and adaptive pattern shaping are key techniques of array processing. Both approaches can be reasonably combined, where ABF should be applied against interference that can be learned in a training phase, while deterministic pattern shaping should counter all remain- ing surprise interference. Applying ABF after deterministic sidelobe reduction allows reducing the requirements on the low sidelobe level. So, a compromise between both techniques must be achieved. Special and effective techniques are available to make ABF preserve the low sidelobe level (e.g. CAPS method).
● General principles and relationships between ABF algorithms and super- resolution methods have been discussed, like dependency on the sample number, dependency on signal fluctuations, robustness, the benefits of sub- space methods, problems of determining the signal/interference sub-space, resolution limit.
● Array signal processing methods like ABF and super-resolution methods can be applied to sub-arrays generated from a large fully filled array. This means applying these methods to the sparse super-array formed by the sub-array centres. We have pointed out problems and solutions for this special array problem. Once a sub-array forming matrixThas been defined, the properties of the super-array and the sub-arrays can be analysed and from this perfor- mance features can be derived.
● A special technique of surprise interference suppression is side lobe blanking aiming at blanking impulsive interference. We have shown a general approach to combine side lobe blanking with adaptive interference suppression for the case of joint impulsive and continuous interference, where each of these techniques alone fails.
● ABF can be combined with super-resolution in a canonical way by applying the pre-whiten and match principle to the data and the signal model vector.
● All array signal processing methods can be extended to space-time processing (arrays) by defining a corresponding space-time plane wave model and a space-time sub-array transformation matrix. Again, this space-time sub-array transformation matrix defines the super-array pattern and the sub-array pat- terns and from these some features can be derived.
● Super-resolution is a joint detection-estimation problem. Many methods have been proposed for both aspects of the problem, but one must also consider the joint problem. One has to determine a multi-target model which contains the number, directions and powers of the targets and these parameters are strongly coupled. A practical iterative joint estimation and detection procedure has been presented. For a robust solution of the joint detection-estimation problem a sequence of criteria has been proposed which step-by-step refines the estimates.
● The problems of implementation in real system have been discussed, in par- ticular the effects of limited knowledge of the array manifold, effect of channel errors, eigenvalue leakage, unequal noise power in array channels and dynamic range of AD-converters.
● The problem of embedding signal processing into the whole radar system has been exemplarily studied for ABF. For achieving best performance an adap- tation of the processing subsequent to ABF is necessary. We have shown how improved performance can be achieved by modifying some subsequent pro- cessing blocks: direction estimation by ABF-monopulse, the detector by adaptive detection with ASLB, and the tracking algorithms by several adaptive tracking techniques and track management with jammer mapping.
With a single advanced array signal processing method alone a significant improvement of a radar system will often not be obtained. All functionalities have to be mutually tuned and balanced. This is an important task for future research. Of course, this tuning of functionalities depends strongly on the application of interest.
Therefore general rules cannot be given and the applications presented in the fol- lowing chapters will require additional special considerations. The approaches presented here constitute only first ad hoc steps providing examples of effects that have to be considered. Note that in most cases tuning the functionalities is often a software problem. So, there is the possibility to upgrade existing systems softly and step-wise. In many cases estimates of the limitations of the signal processing methods (of the antenna beamwidth, width of the jammer notch, admissible region for monopulse, convergence of super-resolution methods, dependency of bias values etc.) is already important information to be used for radar data processing and radar management.
In the future, radar systems will increasingly collect information about the environment in a background procedure, similar to the jammer mapping mode presented here. Using a clutter map together with a geographic map for supporting waveform selection, the detector and the tracking procedure is already an estab- lished technique. Multi-function radar may also operate in an electronic intelli- gence mode to collect information about its emitter environment. Information from other ‘sensors’ (e.g. weather data, GPS data, TV/IR data) together with data from big data bases may be fed into the radar system to improve signal or data processing and thus the overall performance. A meaningful model of the additional sensor data is the basis of successful processing of this information in the future.
This chapter is far from being exhaustive and a number of radar issues have not been considered, like clutter, passive radar, multistatic radar, or polarization. Still it is hoped that a set of useful tools has been provided.
Acknowledgements
This chapter summarizes some decades of experience and research in array radar collected in two research departments at the Fraunhofer institutes in Wachtberg, the department of Array Radar Imaging (ARB, formerly called ‘Electronics Dept’) of
Fraunhofer FHR (Fraunhofer Institute of High Frequency Physics and Radar) and the department of Sensor Data and Information Fusion (SDF) of Fraunhofer FKIE (Fraunhofer Institute of Communication, Information Processing and Ergonomics).
In FHR all viewpoints of radar signal processing with the associated hardware problems are studied while FKIE represents the associated tracking problems and system aspects. Together both perspectives offer a quite general view on radar technology and should be considered jointly in the future.
Without the continuing and stimulating spirit of the research groups in Wachtberg, the knowledge for writing this chapter would not be available. I am indebted to my colleagues in all these years, first of all to my former department head Wulf-Dieter Wirth, to the director of FHR Joachim Ender and to my current department head Wolfgang Koch. My special thanks also go to the excellent col- league scientists with whom I had the pleasure to work for many years: Richard Klemm, Christoph Gierull, Wolfram Bu¨rger and Helmut Wilden. As a con- sequence, this chapter includes work that has been published in many preceding papers as may be seen in the references. The most noteworthy works on radar research from Fraunhofer institutes in Wachtberg are concentrated in the excellent radar book of W.D. Wirth [1] and the books of R. Klemm on space-time adaptive processing [2,3]. The review paper [4] which appeared in 2013 is a kind of pre- cursor of this chapter, and it gave the motivation to write this extended view. For the preparation of this chapter, I had to rely on the generous support of my team colleagues. Of these, I want to thank especially Reda Zemmari and Michael Feld- mann, as well as Martina Bro¨tje and Alexander Charlish.
List of symbols and functions a/a/A Scalar/vector/matrix variable
|a| Magnitude of a (complex) variable
||a|| Norm of a vector
aT/a*/aH Transpose/complex-conjugate/complex-conjugate transpose (Hermitean operation) of a vector
diag{a} Diagonal matrix composed of the components of vectora diagM
k¼1f gak MMdiagonal matrix with diagonal elementsak
vec{A} Vector generated from matrixAby stacking all columns on top (ai)i¼1 . . .N Column vector with componentsai
(Aik)i,k¼1 . . .N Matrix with componentsAik
⊗ Kronecker matrix product
Schur–Hadamard (element wise) matrix product f,l Frequency of a signal and corresponding wavelength
B Bandwidth
c Velocity of light
N Number of array elements
K Number of time samples
L Number of sub-arrays
u¼(u, v, w) Direction vector of length one, for a planar arrayu¼(u, v) is also called direction cosines (for azimuth and elevation)
r¼(x, y, z) Co-ordinates of the array element positions
a(u,v) Plane wave array model vector for a plane wave from direction u¼(u, v)
s Signal vector
n Noise vector
z Array output data vector (data snapshot) 1,0 Vector containing only ones or zeros T The sub-array forming matrix
^
z Estimated quantity
~
z Vector at sub-array output level E{ . . . } Expectation operation
cov{ . . . } Covariance operation LP{ . . . } Low pass filtering operation Re{ . . . } Real part of a complex quantity sinc The function sincx¼(sinx)/x List of acronyms
ABF adaptive beamforming ACE adaptive cosine estimator ADC analogue-to-digital converter AIC Akaike information criterion AMF adaptive matched filter AP alternating projections AR auto-regressive
ASB adaptive sidelobe blanking BW 3 dB antenna beamwidth
CAPS constrained adaptive pattern synthesis CPI coherent processing interval
CRB Crame´r–Rao bound
DimSS dimension of jammer or interference sub-space Dof degrees of freedom
DSW direct sub-array weighting ELA equivalent linear array
ELRA electronically steerable radar (name of the experimental phased array radar of Fraunhofer FHR)
FHR Fraunhofer Institute for High Frequency Physics and Radar Technology FKIE Fraunhofer Institute for Communications, Information Processing and
Ergonomics
EM expectation maximization method EVP eigenvector projection
GLRT generalized likelihood ratio test GSLC generalized sidelobe canceller IMP incremental multi-parameter LMI lean matrix inversion
LSMI loaded sample matrix inversion MDL minimum description length ML maximum likelihood MUSIC multiple signal classification PRF pulse repetition frequency
SAGE space alternating generalized EM algorithm SLB sidelobe blanking
SLC sidelobe canceller Std standard deviation
SNIR signal-to-noise plus interference ratio STAP space-time adaptive processing ULA uniform linear array
WNT white noise test References
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