Signal Processing in Radar Systems

Signal Processing in Radar Systems

The essential task in radar systems is to find an appropriate solution to the problems related to robust signal processing and definition of signal parameters. There are now a number of books and papers published in journals devoted to signal processing in noise in radar systems, but many key issues remain unsolved. New approaches to these problems allow us not only to summarize investigations but also to derive better quality of robust signal processing in noise in radar systems.

This book addresses the problems of robust signal processing in complex radar systems (CRSs) based on the generalized approach to signal processing in noise. The generalized approach to signal processing in noise is proposed based on a seemingly abstract idea: the introduction of an additional noise source that does not carry any information about the signal to improve the qualitative per­formance of CRSs. Theoretical and experimental studies lead to the conclusion that the proposed generalized approach to signal processing in noise in CRSs allows formulating a decision-making rule based on the determination of the jointly sufficient statistics of the mean and variance of the likelihood function. The use of classical and modern signal processing approaches allows us to define only the sufficient statistic of the mean of the likelihood function (or functional).

The presence of additional information about the statistical characteristics of the likelihood func­tion leads to better qualitative performances of robust signal processing in CRSs in comparison with optimal signal processing algorithms of classical and modern theories. The generalized approach to signal processing allows us to extend the well-known boundaries of potential noise immunity set up by classical and modern signal processing theories. The use of CRSs based on the generalized approach to signal processing in noise allows us to obtain better detection performances, particu­larly in comparison with CRSs constructed on the basis of optimal and asymptotic optimal signal processing algorithms of classical and modern signal processing theories.

To better understand the fundamental statements and concepts of the generalized approach, the reader is invited to consult my earlier books: Signal Processing in Noise: A New Methodology (IEC, Minsk, 1998), Signal Detection Theory (Springer-Verlag, New York, 2001), Signal Processing Noise (CRC Press, Boca Raton, FL, 2002), and Signal and Image Processing in Navigational Systems (CRC Press, Boca Raton, FL, 2005).

The radar system is an important element in the field of electrical engineering. In university engineering courses, in general, the emphasis is usually on the basic tools used by the electrical engineer, such as circuit design, signals, solid state, digital processing, electronic devices, electro­magnetics, automatic control, microwaves, and so on. In the real world of electrical engineering practice, however, these are only techniques, piece parts, or subsystems that make up some type of system employed for a useful purpose.

There are various aspects to radar system design. However, before a new radar system can be manufactured, a conceptual design has to be made to guide the actual development, taking into consideration the requirements of the radar system that must be customer- and user-friendly. Conceptual design involves identifying the characteristics of the radar system in accordance with the radar equation and related equations and the general characteristics of the subsystems such as transmitter, antenna, receiver, signal processing, etc., that might be used. A conceptual design can­not be formed without a systems approach. Another important procedure is to define the structure of computer subsystems used in the radar for the purpose of implementing modern robust signal processing algorithms.

It should be noted that there are at least two ways in which a new CRS might be produced. One method is based on exploiting the advantages of some new invention, new technique, new device, or new knowledge. The invention of the microwave magnetron early in World War II is an example. After the magnetron appeared, radar system design was different from what it had been before. The other, and probably more common, method for conceptual radar system design is to identify the function the new radar system has to perform, examine the various approaches available to achieve the desired capability, carefully evaluate each approach, and then select the one that best meets the needs within the operational and fiscal constraints imposed. This book discusses in detail these two methods that are based on a systems approach to design radar systems.

An important task in designing CRSs is to use robust signal processing algorithms and accurate definition of signal parameters. To this end, theory and methods of experimental investigations of stochastic processes are attracted to design the CRS. The theory of statistical estimates, for example, can be used for analyzing regularities to design and construct optimal and quasi-optimal meters of statistical parameters of stochastic processes. At the same time, significant attention is paid to investigation of systematic and random errors of statistical parameter definition as a function of considered time interval and noise level.

A detailed analysis of various procedures and methods to measure and estimate the main sta­tistical parameters of stochastic processes, such as mean (or mathematical expectation), variance, correlation (covariance) function, power spectral density, probability density functions, spikes of energy spectra, etc., is presented. Analog and discrete procedures and methods for measurements and errors, which are characteristic of these procedures and methods, are investigated. In addition, structural block diagrams of digital meters are considered. Structural block diagrams of optimal meters to define the mathematical expectation (mean), variance, and parameters of the correlation (covariance) function are discussed. The variance of estimations and biases of the earlier-mentioned parameters is measured. A procedure to measure the mathematical expectation (mean) and vari­ance of nonstationary stochastic process under robust signal processing used in CRSs is identified. General formulas for definition of biases and variances of statistical parameter estimations are also presented for direct analytical calculation.


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