IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV - 97

IEEE AES Tutorials
challenges that exist in detection over SNs and the previously
proposed methods to deal with them are reviewed
and described in this tutorial.
A SURVEY OF CORRELATED WAVEFORM DESIGN FOR
MULTIFUNCTION SOFTWARE RADAR
SAJID AHMED
MOHAMED ALOUINI
King Abdullah University of Science and Technology
Thuwal, Saudi Arabia
To change the transmit beam pattern, single antenna radar
requires a change of antenna while multiple antenna array
radar, such as phased-array, require amplitude/phase
tapers, which are hardware components. Therefore, there
is a genuine demand that the parameters of future radar
systems be controlled through a software without changing
any hardware or using amplitude/phase tapers. It is
well known that the parameters of an antenna array radar
can be controlled by transmitting suitable correlated waveforms.
This approach provides more degree-of-freedom
and if constant-envelope (CE) or low peak-to-average
power ratio (PAPR) correlated waveforms are used, it
allows us to control the parameters of the radar without
changing any hardware. Therefore, this approach can be
considered as a step towards a software radar. The aim of
this article is to provide a survey of recent techniques used
to design CE and low PAPR correlated waveforms and
discuss the benefits and drawbacks of each.
GEOMETRY OF COMPLEX DATA
K. JAMES SANGSTON
Georgia Tech Research Institute
Atlanta, GA USA
Geometric algebra has been called a " unified language for
mathematics and physics. " Sometimes known as Clifford
algebra, it is based on the notion ofan invertible product of
vectors that captures the geometric relationship between
two vectors, i.e., their relative magnitudes and the angle
between them. This seemingly simple concept leads to a
rich system of algebra and calculus that encompasses the
diverse areas of complex numbers, quaternions, vectors,
tensors, spinors, and differential forms. This tutorial provides
a basic introduction to geometric algebra and presents
formulations of known electrical engineering and signal
processing concepts to illustrate some inherent advantages
ofgeometric algebra for formulating and solving problems
involving vectors. Being introductory, the goal of the tutorial
is to introduce this emerging area that, although old as
a mathematics discipline, has only recently started to garner
significant attention in engineering communities. Geometric
algebra should give another potentially powerful
tool for pursuing research in any area that uses vectors.
MAY 2022
RECURSIVE BAYESIAN FILTERING IN CIRCULAR STATE
SPACES
GERHARD KURZ
Karlsruhe Institute ofTechnology
Karlsruhe, Germany
IGOR GILITSCHENSKI
Swiss Federal Institute ofTechnology
Zurich, Switzerland
UWE D. HANEBECK
Karlsruhe Institute ofTechnology
Karlsruhe, Germany
To facilitate recursive state estimation in the circular domain
based on circular statistics, we introduce a general framework
for estimation ofa circular state based on different circular
distributions. Specifically, we consider the wrapped
normal (WN) distribution and the von Mises distribution.
We propose an estimation method for circular systems with
nonlinear system and measurement functions. This is
achieved by relying on efficient deterministic sampling techniques.
Furthermore, we show how the calculations can be
simplified in a variety ofimportant special cases, such as systems
with additive noise, as well as identity system or measurement
functions, which are illustrated using an example
from aeronautics. We introduce several novel key components,
particularly a distribution-free prediction algorithm, a
new and superior formula for the multiplication ofWN densities,
and the ability to deal with nonadditive system noise.
All proposed methods are thoroughly evaluated and compared
with several state-of-the-art approaches.
TUTORIAL X
OVERVIEW OF RADAR WAVEFORM DIVERSITY
SHANNON D. BLUNT
University ofKansa
Lawrence, KS, USA
ERIC L. MOKOLE
Private Consultant
Burke, VA, USA
Waveform Diversity (WD) is an exciting technology that
has sparked intense interest from the research community in
recent years because of advances in high-fidelity electronic
components and high-performance computing. WD is
expected to have a profound impact on radar spectrum management,
particularly in light of increasing competition for
spectrum usage, as well as to facilitate enhanced radar sensitivity
and discrimination and perhaps even to enable new
sensing modes. The definition of WD is clearly broad, but
such is to be expected for a topic that continues to evolve.
The purpose of this tutorial is to provide the reader with the
context in which WD has arisen, a sense of the tremendous
breadth of the subject, and a sufficient starting point from
which to exploreWDfurther.
IEEE A&E SYSTEMS MAGAZINE
97
IEEE - Aerospace and Electronic Systems - May 2022 - Tutorial XV

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