Complex elliptically symmetric (CES) distributions have been widely used in various engineering applications for which non-Gaussian models are needed. In this overview, circular CES distributions are surveyed, some new results are derived and their applications e.g., in radar and array signal processing are discussed and illustrated with theoretical examples, simulations and analysis of real radar data. The maximum likelihood (ML) estimator of the scatter matrix parameter is derived and general conditions for its existence and uniqueness, and for convergence of the iterative fixed point algorithm are established. Specific ML-estimators for several CES distributions that are widely used in the signal processing literature are discussed in depth, including the complex t -distribution, K-distribution, the generalized Gaussian distribution and the closely related angular central Gaussian distribution. A generalization of ML-estimators, the M-estimators of the scatter matrix, are also discussed and asymptotic analysis is provided. Applications of CES distributions and the adaptive signal processors based on ML- and M-estimators of the scatter matrix are illustrated in radar detection problems and in array signal processing applications for Direction-of-Arrival (DOA) estimation and beamforming. Furthermore, experimental validation of the usefulness of CES distributions for modelling real radar data is given.

Complex Elliptically Symmetric Distributions: Survey, New Results and Applications

One of the key problems in spectrum sensing is to design the test statistic. Existing methods generally exploit the model-based features as the test statistic, such as energies and eigenvalues. However, these features could not accurately characterize the real environment. Motivated by this, in this paper, we use a deep neural network (DNN) to intelligently explore the data-driven test statistic. Firstly, we introduce a DNN-based detection framework, where a DNN-based likelihood ratio test (DNN-LRT) is derived to guarantee the optimality of the designed test statistic. As a realization of the developed DNN-based framework, we use the sample covariance matrix as the input of a convolutional neural network (CNN), and propose a covariance matrix-aware CNN (CM-CNN)-based spectrum sensing algorithm, which further improves the performance. In addition, we also provide the theoretical analysis of the proposed method. To the best of our knowledge, it’s the first time to analyze the theoretical performance of CNN-based methods. Finally, simulation results demonstrate that the performance of the proposed method is close to that of the optimal detector. Particularly, the proposed method could achieve a detection probability of 96.7% with a false alarm probability of 1.9% at SNR = −18dB, which significantly outperforms the conventional methods.

Deep CM-CNN for Spectrum Sensing in Cognitive Radio

This paper describes a new technique for modeling and simulating the coherent returns from radar sea clutter, based on the compound K-distribution model for clutter amplitude statistics. Using observations of recorded Doppler spectra, a simple method is proposed for characterizing the temporal variations of the Doppler spectrum observed in a single-range cell. It is shown that simulations based on this model can reproduce the main statistical features observed in real measurements.

Modeling and Simulation of Coherent Sea Clutter

Recently it was discovered that the Pareto distribution is a good model for low-grazing-angle high-resolution radar sea clutter returns. Validation of it as a model for high-grazing-angle radar clutter is provided.

Assessing Pareto fit to high-resolution high-grazing-angle sea clutter

A radar pulse that impinges upon a radar resolution area of the sea surface produces backscattered returns which are called sea clutter. For low grazing angles and very fine radar cell resolution areas, the clutter intensity distribution departs significantly from the exponential distribution. In this case, the clutter is said to display spiky behavior and the distribution of the intensity develops a much longer tail relative to the exponential distribution. Statistical analysis of collected data near a grazing angle of 0.2° at X-band from the sea off the coast of Kauai, Hawaii are examined relative to the log-normal, Weibull and K distributions. Based on an analogy of sea clutter and other disciplines including computer networks and finance, we also apply the Pareto distribution to the collected data. We also compare the data to the WW and KK two-population mixture distributions. Maximum likelihood estimation of the parameters of the distributions are obtained from the measured data. In all cases, the two population mixture distributions and the Pareto distribution are more accurate than the three classical distributions. However the Pareto distribution has the advantage of being an analytically tractable two parameter distribution while having similar accuracy to the five parameter WW and KK at critical values.

The Pareto distribution for low grazing angle and high resolution X-band sea clutter

Sea Clutter: Scattering, the K Distribution and Radar Performance, 2nd Edition gives an authoritative account of our current understanding of radar sea clutter. Topics covered include the characteristics of radar sea clutter, modelling radar scattering by the ocean surface, statistical models of sea clutter, the simulation of clutter and other random processes, detection of small targets in sea clutter, imaging ocean surface features, radar detection performance calculations, CFAR detection, and the specification and measurement of radar performance. The calculation of the performance of practical radar systems is presented in sufficient detail for the reader to be able to tackle related problems with confidence. In this second edition the contents have been fully updated and reorganised to give better access to the different types of material in the book. Extensive new material has been added on the Doppler characteristics of sea clutter and detection processing; bistatic sea clutter measurements; electromagnetic scattering theory of littoral sea clutter and bistatic sea clutter; the use of models for predicting radar performance; and use of the K distribution in other fields.

Sea Clutter: Scattering, the K Distribution and Radar Performance

This paper first examines the physical source of sea clutter spikes from considerations of oceanographic principles and electromagnetic scattering; it is shown how electromagnetic scattering theory can be used to predict the characteristics of discrete spikes in backscatter from the sea. The spikes can also be modelled statistically as extensions to the standard K-distribution model for sea clutter, as proposed by K.D. Ward et al. (1990). In this paper, the work in K.D. Ward et al. (1990) is extended to include the addition of thermal noise and it is also shown how the parameters of this model can be matched to real data. Results are presented for recorded airborne radar data, showing how the model can accurately match the characteristics of real clutter-plus-spikes-plus-noise, including the effects of pulse-to-pulse integration with frequency agility.

The physics and modelling of discrete spikes in radar sea clutter

Presented is a statistical analysis of vertically-polarised bistatic sea clutter data, with bistatic angles ranging from 30° to 90°, compared with simultaneously-gathered monostatic clutter data. It is found that there is no significant change in the bistatic reflectivity compared to the monostatic except close to bistatic angles of 90°. It is found that the shape parameter of the K-distribution fitted to the clutter is significantly higher for the bistatic clutter than for the equivalent monostatic clutter.

/pdf/statistical-analysis-of-simultaneous-monostatic-and-bistatic-3bw7nmoler.pdf

Statistical analysis of simultaneous monostatic and bistatic sea clutter at low grazing angles

Setting the detection threshold in a radar operating in a maritime environment is critically dependent upon the characteristics of the sea clutter Analysis is presented in this paper of the performance of the cell-averaging CFAR in K-distributed sea clutter It is demonstrated that in spatially uncorrelated, spiky clutter the CFAR loss is very high, but may be reduced in some circumstances by increasing the radar system noise level It has previously been reported (Watts, 2000) that in spatially correlated clutter the CFAR loss may be reduced by optimising the cell average length, which is some cases leads to a 'CFAR gain' rather than a loss Here, it is shown how added thermal noise affects this performance (5 pages)

CFAR loss and gain in K-distributed sea-clutter and thermal noise

This paper describes a multistatic, sea clutter and vessel database, assembled using the three node, S Band radar, known as NetRAD (for, “Netted Radar”). This data was collected in the United Kingdom and South Africa during 2009-201. It is the intention of the investigators and sponsors of this work to make the raw data available to individuals and organisations interested in processing this multistatic data in support of the development of the understanding of sea clutter and vessel properties in the multistatic configuration.

Robert Tough

Papers

Sea Clutter: Scattering, the K Distribution and Radar Performance

The physics and modelling of discrete spikes in radar sea clutter

Statistical analysis of simultaneous monostatic and bistatic sea clutter at low grazing angles

CFAR loss and gain in K-distributed sea-clutter and thermal noise

NetRAD multistatic sea clutter database