Aerospace and Electronic Systems Magazine August 2016 - 24
Pioneer Award:
DOI. No. 10.1109/MAES.2016.160032
Statistical Antenna Theory: Formation and Extension
Yakov S. Shifrin, Kharkiv National University of Radio Electronics, Kharkiv, Ukraine
INTRODUCTION
In this article, I set forth the essence and contents of statistical antenna theory (SAT), a theory of antennas with random sources, and
I describe my activities elucidating and popularizing SAT ideas
and results, spending a considerable amount of space describing
my work with groups of scientists from different organizations of
the former Union of Soviet Socialist Republics (USSR), assisting
them in their investigations of SAT.
It is important to note that the presence of randomness in an antenna leads to randomness in the field radiated (or received) by the
antenna and in all associated antenna parameters; and this theory,
therefore, should be based on the theory of probability and the theory of random functions. The absence of a theory or set of principles
that would take into account randomness in antennas impelled me
in the early 1960s to create a new, statistical antenna theory with its
own procedures for antenna characteristics investigations, relevant
mathematical apparatus, terminology, and notions. Foundations of
the theory were developed as applied to the simplest antenna-a linear continuous antenna with a uniform amplitude distribution and
random phase errors. Three groups of statistical antenna characteristics are successively considered: mean, fluctuation, and correlation. Main attention is paid to studying a dependence of these characteristics on phase error's parameters - variance and correlation
radius at variations of the latter within wide limits.
The results obtained for the simplest system further are generalized
to many antenna types: linear and bidimensional, as well as continuous
and discrete. Along with this, in the article, new SAT issues are considered: the statistical antenna synthesis, transformation of the effect
of superdirectivity in SAT, and statistical antenna measurement theory
(SAMT), in addition to others. The article is completed by the consideration of a number of issues on introduction of the SAT results in practice.
DEFINING SAT
WHAT IS SAT AND HOW DID IT ARISE?
The SAT is the theory of antennas with random sources (currents
and fields). Randomness can apply to the source's amplitude,
Author's address: Kharkiv National University of Radio Electronics, 14 Prospekt Nauki, Kharkiv, 61166 Ukraine,. E-mail:
(max416@yandex.ua).
Manuscript received February 1, 2016; ready for publication
March 17, 2016.
Review handled by W. Walsh.
0885-8985/16/$26.00 © 2016 IEEE
24
phase, and/or polarization; to the number of sources and their
spatial location; to the shape and dimensions, etc. The specific
mechanisms, which give rise to the sources' fluctuations (errors)
can be diverse. In one case, the errors emerge inside the antenna.
In another case, the source's fluctuations are connected with external factors, such as may be caused by propagation conditions of a
wave impinging on the antenna. Correspondingly, we talk about
internal and/or external mechanisms of a fluctuations' origin.
When using a statistical approach to studying antenna characteristics, one should distinguish between the statistics taken over
the ensemble of similar antennas (ensemble statistics), and the statistics taken in time from an individual antenna (time statistics).
In the first case, one investigates the spread of the parameters
of antennas of the same type with respect to the ensemble of antennas. Such a spread can be caused by inaccuracies in their manufacturing or assembling, by inhomogeneities in the material of which
the antennas are made, etc. In the second case, one investigates the
spread of the parameters of one and the same antenna in time. This
spread can be caused by instabilities of parameters of the antenna
elements as well as by variations of parameters of the medium
through which a wave propagates. The presence of randomness in
the antenna deteriorates its characteristics, or restricts its attainable
values. This is especially undesirable for large and complicated
antennas that are very expensive (sometimes, their cost is greater
than 50 percent of the total cost of a large radio technical system
or radio telescope, quite often many millions of dollars). It is very
important therefore to know the causes of randomness and the
character of randomness in antennas, as well as how they influence
antenna parameters. When designing antennas, it is necessary to
be able to take into account randomness in them, to know how to
weaken the influence of randomness.
Solving these problems is one of the most important aspects of
SAT. However, the applicability of SAT is far from exhausted by
problems of antenna building and exploitation. Problems concerning and ways of studying the influence of a medium on antenna
parameters also constitute an important aspect of SAT.
FORMATION OF SAT
The SAT was born in the late 1950s and early 1960s at the Antenna
& Propagation Chair of the Artillery Radio Technical Academy
(ARTA) in Kharkov, in the USSR. At that time, I was Head of this
chair. Our chair was tasked with a government program that was
investigating the long-distance tropospheric propagation (LDTP)
of radio waves. A most important part of these investigations consisted in researching the characteristics of receiving antennas op-
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AUGUST 2016
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