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2019 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Electronically Scanned Arrays (ESAs) and K-Space Gain Formulation

verfasst von: Roger A. Dana

Verlag: Springer International Publishing

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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SUCHEN

Über dieses Buch

This book fills in details that are often left out of modern books on the theory of antennas. The starting point is a discussion of some general principles that apply to all electronic systems and to antennas in particular. Just as time domain functions can be expanded in terms of sine waves using Fourier transforms, spatial domain functions can be expanded in terms of plane waves also using Fourier transforms, and K-space gain is the spatial Fourier transform of the aperture weighting function. Other topics discussed include the Discrete Fourier Transform (DFT) formulation of antenna gain and what is missing in this formulation, the effect of sky temperature on the often specified G/T ratio of antennas, sidelobe control using conventional and novel techniques, and ESA digital beamforming versus adaptive processing to limit interference.

Presents content the author derived when first asked to evaluate the performance of an electronically scanned array under design with manufacturing imperfections and design limitations;

Enables readers to understand the firm theoretical foundation of antenna gain even when they must start from well-known formulations rather than first principles;

Explains in a straightforward manner the relationship between antenna gain and aperture area;

Discusses the relationship between sidelobe control algorithms and aperture shape, how to take advantage of it, and what the penalties are;

Shows the equivalence of Minimum-Variance, Distortionless Response (MVDR) and Space-Time Adaptive Processing (STAP) and how these algorithms can be used with ESA subarrays to mitigate interference.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Introduction
Abstract
First the assumptions and limitations of the k-space gain formulation are enumerated. These include the assumption of observing the gain in the far field of the array, the demarcation of which is explained further in Appendix 1. Next are descriptions of antenna performance metrics used to evaluate performance: peak gain, maximum sidelobe level, beamwidths, and integrated sidelobe level (ISL). Then it is shown that plane waves are solutions of Maxwell’s equations (or more specifically, of the Helmholtz wave equation). This is a key result since the k-space gain formulation is based on two-dimensional (2-D) expansions of the ESA spatial weighting function into the summation of plane waves, each with its own amplitude and phase, through continuous or discrete 2-D Fourier transforms.
Roger A. Dana
Chapter 2. Some Basic Principles of RF Electronic Systems and Antennas
Abstract
Basic principles that apply to all electronic systems and to antennas in particular include: (1) Only signal plus noise can be measured, not signal by itself; (2) signals add coherently whereas noise adds incoherently; (3) signal-to-noise ratio (SNR) gain at the receiver is only accomplished by voltage integration; (4) radio performance goes as one over the square-root of the SNR. The keys to understanding the SNR in a receiver are Friis’ Link Margin Equation and Friis’ formula for the noise factor. These relationships are explained because they should be well-understood by electronic systems engineers.
Roger A. Dana
Chapter 3. K-Space Gain and Antenna Metrics
Abstract
This chapter starts with a derivation, in a straightforward manner, of the relationship between k-space gain G K and the more familiar angular-space gain G Ω. The two are not the same, for example, the latter is dimensionless but the former has units of area. From this relationship, the well-known formula is derived that the peak gain of an aperture antenna is related to its area A and the center frequency wavelength λ as G Ω,max = 4πA/λ 2. As part of this derivation, it is shown that the integral of G Ω over 4π steradians and the integral of G K over all K-space must both be equal to one, as this is required for conservation of energy. Next the discrete Fourier transform (DFT) implementation of ESA K-space gain is discussed, and important antenna effects that are not included in this formulation are pointed out. In particular, the affine transformation is used to incorporate the effects of aperture foreshortening in the DFT-based gain function. Other effects discussed in this chapter include the cosine taper of element gain, the frequency dependence of antenna gain, and the relationship between the number of elements of a transmit ESA and its effective isotropic radiated power (EIRP). This chapter also includes discussions on phase-comparison monopulse and on computing ESA directivity in angular space directly from power measurements recorded in k-space. It concludes with a derivation of the integrated sidelobe level (ISL) for 1-D and 2-D arrays and for uniformly weighted ESAs.
Roger A. Dana
Chapter 4. Effect of Sky Noise on Antenna Temperature
Abstract
The often used but rarely justified formula by Blake that the antenna temperature T A contribution from sky temperature T S is T A = 0.876T S+36°K. This equation is particularly mysterious when one considers the origin of the coefficients 0.876 and 36°K. In this chapter, the basic principles behind this expression are discussed, and it is shown to be valid for a 1950s type of antenna with high back or sidelobes. A general expression that applies to modern ESAs is developed.
Roger A. Dana
Chapter 5. Sidelobe Control and Monopulse Weighting
Abstract
Taylor weighting is often used in ESAs to control peak sidelobe levels below that resulting from uniform weighting. Examples of Taylor weights are given, and the effect of weighting on peak gain, maximum sidelobe level, beamwidth, and ISL performance metrics is shown. Octagonally shaped ESAs, possibly resulting from turning off corner elements of a square array, are discussed as a technique to reduce peak sidelobes. Another control technique is to rotate one of the sidelobe planes relative to the other of a square array with elements turned off to form a parallelogram. Finally, weighting schemes for phase-comparison monopulse are described, including Bayliss weights and a simpler to implement scheme referred to as split-Taylor.
Roger A. Dana
Chapter 6. Digital Beamforming and Adaptive Processing
Abstract
Modern ESAs present the opportunity to do digital processing on the outputs of multiple subarrays without having to digitally sample the output of each element, thereby greatly simplifying the design of the ESA while still achieving the benefits of adaptive processing. The principles behind two common techniques, minimum variance distortionless response (MVDR) and space-time adaptive processing (STAP), are described, and it is shown that under idealized conditions MVDR and STAP perform identically. An example of jammer nulling is discussed in detail when the interfering signal(s) is within the main beam of the ESA but outside of the full width at half maximum (FWHM) beamwidth. It is shown also that MVDR works better in this case when the jammers are distributed symmetrically about the desired signal, something that can be achieved in MVDR by simply modifying the subarray to subarray covariance matrix of the interference used to compute subarray weights.
Roger A. Dana
Backmatter
Metadaten
Titel
Electronically Scanned Arrays (ESAs) and K-Space Gain Formulation
verfasst von
Roger A. Dana
Copyright-Jahr
2019
Electronic ISBN
978-3-030-04678-1
Print ISBN
978-3-030-04677-4
DOI
https://doi.org/10.1007/978-3-030-04678-1

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