US 2023/0194589 Al

MAPPING PROBE FOR REAL-TIME SIGNAL
SAMPLING AND RECOVERY FROM
ENGINEERED ELECTROMAGNETIC

INTERFERENCE

CROSS REFERENCE TO RELATED,
APPLICATIONS

[0001] This patent application is a continuation of U.S.

patent application Ser. No. 16/418,202 (filed May 21, 2019),
which claims priority to U.S. Provisional Patent Application
Ser. No. 62/675,386 (filed May 23, 2018), the disclosure of
each of which is incorporated herein by reference in its
entirety.

STATEMENT REGARDING FEDERALLY
SPONSORED RESEARCH

[0002] This invention was made with United States Gov-
ermment support from the National Institute of Standards and
‘Technology (NIST), an agency of the United States Depart-
ment of Commerce. The Government has certain rights in
the invention. Licensing inquiries may be directed to the
‘Technology Partnerships Office, NIST, Gaithersburg, Md.,
20899; voice (301) 301-975-2573; email tpo@nist.gov; ref-
erence NIST Docket Number 18-033US1.

BRIEF DESCRIPTION

[0003] Disclosed is a mapping probe for real-time signal
sampling and recovery from engineered electromagnetic
interference, the mapping probe comprising: a trigger volt-
age source that produces a trigger voltage signal that syn-
chronizes transmission of primary electromagnetic waves; a
plurality of primary electromagnetic wave synthesizers in
communication with the trigger voltage source and that:
receives the trigger voltage signal from the trigger voltage
source; produces time-varying voltage signals in response to
receipt of the trigger voltage signal from the trigger voltage
source: and communicates the time-varying voltage signals:
a plurality of transmitters in communication with the pri-
mary electromagnetic wave synthesizers and that: receives
the time-varying voltage signals from the primary electro-
magnetic wave synthesizers; and synchronously transmits
the time-varying voltage signals as primary electromagnetic
waves in response to receipt of the trigger voltage signal
from trigger voltage source by the primary electromagnetic
wave synthesizers, such that the primary electromagnetic
waves are subjected to scattering by a structural entity to
produce scattered electromagnetic waves from the primary
electromagnetic waves; a plurality of receivers that: receives
the scattered electromagnetic waves; and produces a plural-
ity of receiver signals based on the scattered electromagnetic
waves; a conversion stage in communication with the
receivers and that: receives, from the receivers, the receiver
signals; receives, from the trigger voltage source, the trigger
voltage signal; and produces converted data from the
receiver signals and the trigger voltage signal; and a render
in communication with the conversion stage and that:
receives, from the conversion stage, the converted data; and
produces a map of the structural entity.

[0004] Disclosed is a process for mapping a structural
entity with a mapping probe, the process comprising: pro-
ducing, by the trigger voltage source, the trigger voltage
signal synchronizing transmission of primary electromag-
netic waves; receiving, by the primary electromagnetic wave

Jun. 22, 2023

synthesizers, the trigger voltage signal from the trigger
voltage source; producing, by the primary electromagnetic
wave synthesizers, time-varying voltage signals in response
to receiving the trigger voltage signal from the trigger
voltage source; communicating, by the primary electromag-
netic wave synthesizers, the time-varying voltage signals;
receiving, by the transmitters, the time-varying voltage
signals from the primary electromagnetic wave synthesizers;
synchronously transmitting, by the transmitters, the time-
varying voltage signals as primary electromagnetic waves in
response to receiving the trigger voltage signal from the
trigger voltage source by the primary electromagnetic wave
synthesizers, subjecting the primary electromagnetic waves
to scattering by the structural entity; producing scattered
electromagnetic waves from the primary electromagnetic
‘waves in response to scattering the primary electromagnetic
waves by the structural entity; receiving, by the receivers,
the scattered electromagnetic waves; producing, by the
receivers, the receiver signals based on the scattered elec-
tromagnetic waves; receiving, by the conversion stage, the
receiver signals from the receivers; receiving, by the con-
version stage, the trigger voltage signal from the trigger
voltage source; producing, by the conversion stage, con-
verted data from the receiver signals and the trigger voltage
signal; receiving, by render, the converted data from the
conversion stage: and producing the map of the structural
entity from the converted data to map the structural entity.

BRIEF DESCRIPTION OF THE DRAWINGS

[0005] The following description should not be considered
limiting in any way. With reference to the accompanying
drawing, like elements are numbered alike.

[0006] FIG. 1 shows a mapping probe:

[0007] FIG. 2 shows a mapping probe; and

[0008] FIG. 3 shows interfering waves in panels A, B,C,
D, B, and F.

DETAILED DESCRIPTION
[0009] A detailed description of one or more embodiments

is presented herein by way of exemplification and not
limitation.

[0010] Ithas been discovered that a mapping probe herein
recovers a map of a structural entity, e.g., a three-dimer
sional (3D) environment such as a room, a building, a c
and the like, by illuminating the structural entity with
electromagnetic radiation structured in space and time
according to an excitation signal referred to as a synthesized
voltage signal 216.k (k-1, . . ., n, wherein n is an integer
from 1 to a selected upper value) applied to transmitters and
detecting scattered electromagnetic waves with receivers
226, 0-1, ..., m, wherein m is an integer from 1 to a
selected upper value). Accordingly, the mapping probe per-
forms localization and imaging with electromagnetic wave
interference in real-time. It is contemplated that transmitters
and receivers can be positioned outside or around a probed
environment, ic., the structural entity, The trigger voltage
signal automatically and synchronously starts transmission
and acquisition. Transmitted waves, ie., primary electro-
magnetic waves, are generated by synthesizers as time-
varying voltage signals coupled, e.g. to an antenna or
transducer. The scattered waves can be received by antennas
or transducers coupled to a data acquisition system that
includes, e.g., a mixer, amplifier, analog to digital converter,



US 2023/0194589 Al

for t'-t,"20 and zero otherwise. Upon illumination, the
propagation medium, also referred to as the signal, becomes
a passive source described by its reflectivity function 0x(r’,
t)S1. The illuminating radiation samples the whole signal.
‘Assume changes of reflectivity in time are slow enough to
consider the medium stationary, i.e., x(r (r'). Neglect
higher-order reflections from the signal. The response to the
illuminating field measured at a point r and time t is thus
given by:

Y (DAG hr ECO Mr drldt! B)

where:

olf = @-Wr-r' fe] @)

Grn t= ral

is the Green’s function for a point source in space-time. By
substituting (4) in (3) and integrating over t', we obtain:

E(t Ir’ 5
wens [ee eeu. ©

[0059] Using (2) to replace the j-th component of E in (5)
redefines the domain of integration for each source by
requiring r' to satisfy the condition t-t,"<(r'+lr'=1,"I/e. This
means that phase fronts arriving at the detector at a time t
come from the volume inside an ellipsoid defined by:

rir! ") ©

[0060] If we now approximate the Diracs by gaussian
pulses of duration At, it is obvious that each transmitter T,
will have an emission pattern consisting of concentric
spherical shells centered at r," of polarity +1 according to the
corresponding pseudo-random code (FIG. 3, panels A, B,
and C). The pattern sensed by the detector can be ellipsoidal
shells defined by (6) as shown in FIG. 3, panels D and F.
Superposition of shells coming from different transmitters
and carrying their corresponding code is a randomized
spatial pattern A(r’, t)=E(r, t-r/e/I—1'| that evolves in space-
time (FIG. 3, panels B and E). Therefore, (5) now reads ¥ (r,
D=( A(er.HIx(r)) ,'i.e., the signal measured by the detector
is the inner product of the random matrix A(r’, t) and the
medium reflectivity function x(r') during a time interval At
around t.

[0061] FIG. 3 shows interfering waves, wherein panels A,
B, and C show patterns generated by two transmitters on the
lower left and right corners of panel A and C, respectively
and their interference patterns in panel B. Panels C, D, and
E show the patterns shown in panels A, B, and C that are
detected by a receiver disposed half-way between two
transmitters. Black and white tones correspond to —1/+1
amplitude, and gray corresponds to zero amplitude.

[0062] Each pattern formed during the time At around t
probes x(r’) and returns a corresponding inner product to the
detector. For microwave systems, At is of the order of tens
nanoseconds and uses a bandwidth BoI/At. Moreover,
because they propagate at the speed of light and can have a
variable aggregated width determined by the pseudo-ran-
dom codes, pattern components perform a translation or
scale operation equivalent to a wavelet transform. A maxi-
mum spatial sampling resolution Ar=cAt(c=299792458 m/s,
speed of light) can be enhanced by utilizing more band-

Jun. 22, 2023

width, phase or quadrature amplitude modulation, polariza-
tion modulation or a combination thereof. Together with the
sampled range R, the spatial resolution defines the number
of pixels to be N=(R/Ar)°. Compared to N,, sampling of the
signal undergoes a compression of the order (I-N,/N).
Signal recovery involves a sampling matrix A, more spe-
cally sequences C,(t,") that minimize a number of mea-
surements M and recovery error.

[0063] While one or more embodiments have been shown,
and described, modifications and substitutions may be made
thereto without departing from the spirit and scope of the
invention. Accordingly, it is to be understood that the present
invention has been described by way of illustrations and not
limitation. Embodiments herein can be used independently
or can be combined.

[0064] All ranges disclosed herein are inclusive of the
endpoints, and the endpoints are independently combinable
with each other. The ranges are continuous and thus contain
every value and subset thereof in the range. Unless other-
wise stated or contextually inapplicable, all percentages,
when expressing a quantity, are weight percentages. The
suffix “(s)” as used herein is intended to include both the
singular and the plural of the term that it modifies, thereby
including at least one of that term (e.g., the colorant(s)
includes at least one colorants). “Optional” or “optionally”
means that the subsequently described event or circumstance
can or cannot occur, and that the description includes
instances where the event occurs and instances where it does
not. As used herein, “combination” is inclusive of blends,
mixtures, alloys, reaction products, and the like.

[0065] As used herein, “a combination thereof” refers to a
combination comprising at least one of the named constitu-
ents, components, compounds, or elements, optionally
together with one or more of the same class of constituents,
components, compounds, or elements.

[0066] All references are incorporated herein by reference.
[0067] The use of the terms “a” and “an” and “the” and
similar referents in the context of describing the invention
(especially in the context of the following claims) are to be
construed to cover both the singular and the plural, unless
otherwise indicated herein or clearly contradicted by con-
text. “Or” means “and/or.” It should further be noted that the
terms “first,” “second,” “primary,” “secondary,” and the like
herein do not denote any order, quantity, or importance, but
rather are used to distinguish one element from another. The
modifier “about” used in connection with a quantity is
inclusive of the stated value and has the meaning dictated by
the context (e.g., it includes the degree of error associated
with measurement of the particular quantity). The conjunc-
tion “or” is used to link objects of a list or alternatives and
is not disjunctive; rather the elements can be used separately
or can be combined together under appropriate circum-
stances.

What is claimed is:

1. A process for real-time signal sampling and recovery
from engineered electromagnetic interference, the process
comprising:

constructing a sampling matrix A for sampling signals

from a detector:

driving an array of transmitters by Dirac pulses;

forming illuminating fields by the array of transmitters in

response to driving the array of transmitters;
amplitude modulating the Dirac pulses by pseudo-random
codes;



US 2023/0194589 Al

tural entities 222 include trees and foliage, human bodies,
walls, metal structures, homes, buildings, bridges, tunnels,
and the like.

[0020] Structural entity 222 scatters primary electromag-
netic waves 220 as scattered electromagnetic waves 224.
Scattered electromagnetic waves 224 can have temporal
pulse width that vary in accordance with specific details of
the structural entity. This variation includes a linear combi-
nation of time varying voltages proportional to synthesized
waves produced by transmitters.

[0021] Receivers 226 receive scattered electromagnetic
waves 224 and produce receiver signals 228 in response to
receipt of scattered electromagnetic waves 224. Receivers
226 can include an antenna (e.g., one or more) or transducer
(e.g., one or more) that converts the electromagnetic wave
fields into a time varying voltage. Exemplary receivers 226
include a horn antenna, omni-directional antenna, Vivaldi
antenna, log-periodic antenna, combinations thereof and the
like. A number of receivers 226 (e.g., 226.1, 226.2,...,
226.n, wherein n is an integer number of total receivers 226)
can be from 1 toa selected upper number. In an embodiment,
receivers 226 include an omni-directional antenna or horn
antenna.

[0022] Conversion stage 230 receives receiver signals 228
and produces converted data 232 in response to receipt of
receiver signals 228. Conversion stage 230 can include an
amplifier, mixer, analog-to-digital converter, and the like.
Exemplary conversion stage 230 includes the analog-to-
digital converter. A number of conversion stage 230 (e..,
230.1, 230.2, ... ,230.n, wherein n is an integer number of
total conversion stage 230) can be from | to greater than 10
to, specifically from 1 to 4.

[0023] Receiver signals 228 are time varying voltages
produced by the receivers 226 and carried by transmission
lines such as coaxial cables to the converters 230.

[0024] Render 234 receives converted data 232 and pro-
duces map 236 in response to receipt of converted data 232.
Render 234 can include a processor that performs an algo-
rithm such as a field programmable gate array (FPGA) or an
algorithm in a computer that processes data generated in the
conversion stage and outputs a map of the structural entity.
Exemplary render 234 includes an L2 algorithm also
referred to a least square minimizer; an L1 algorithm also
referred to as compressed sensing.

[0025] Map 236 is a representation of the structural entity
in a two-dimensional (2D) or three-dimensional (3D) image
format that can be updated in real-time and displayed, e.g..
on a monitor.

[0026] Mapping probe 200 can be made in various ways.
In an embodiment, a process for making mapping probe 200
includes disposing 212 by trigger voltage source 210 in
communication with primary electromagnetic wave synthe-
sizers 214 and conversion stage 230 by connecting a pulse
generator to the trigger input of the synthesizer
version stage; disposing primary electromagnetic wave syn-
thesizers 214 in communication with transmitters 218 by
connecting an output of the signal 216 to the transmitting
antennas; disposing transmitters 218 in communication with
structural entity 222 by arranging the transmitting antennas,
e.g., in a straight line and positioning the antenna array at a
distance from the structural entity; disposing structural
entity 222 in communication with receivers 226 by arrang-
ing the receivers, e.g.. ina straight line and, e.g. at a distance
from the transmitting array and the structural entity; dispos-

Jun. 22, 2023

ing receivers 226 in communication with conversion stage
230 by connecting receivers to, ¢.g., the analog-to-digital
converter; disposing conversion stage 230 in communica-
tion with render 234 by a digital communication cable such
as universal serial bus (USB) interface to the render situated
as a storage memory program in a digital computer; and
disposing render 234 in communication with trigger voltage
source 210 by a communication cable from the computer to
the pulse generator.

[0027] Mapping probe 200 has numerous advantageous
and unexpected benefits and uses. In an embodiment, a
process for mapping structural entity 222 with mapping
probe 200 includes: producing, by trigger voltage source
210, trigger voltage signal 212 that synchronizes transmis-
sion of primary electromagnetic waves 220 and conversion
stage 230; receiving, by primary electromagnetic wave
synthesizers 214, trigger voltage signal 212 from trigger
voltage source 210; producing, by primary electromagnetic
wave synthesizers 214, time-varying voltage signals 216 in
response to receiving trigger voltage signal 212 from trigger
voltage source 210; communicating, by primary electromag-
netic wave synthesizers 214, time-varying voltage signals
216; receiving, by transmitters 218, time-varying voltage
signals 216 from primary electromagnetic wave synthesizers
214; synchronously transmitting, by transmitters 218, time-
varying voltage signals 216 as primary electromagnetic
waves 220 in response to receiving trigger voltage signal
212 from trigger voltage source 210 by primary electromag-
netic wave synthesizers 214, subjecting primary electromag-
netic waves 220 to scattering by structural entity 222:
producing scattered electromagnetic waves 224 from pri-
mary electromagnetic waves 220 in response to scattering
primary electromagnetic waves 220 by structural entity 222:
receiving, by receivers 226, scattered electromagnetic waves
224; producing, by receivers 226, receiver signals 228 based
on scattered electromagnetic waves 224: receiving, by con-
version stage 230, receiver signals 228 from receivers 226;
receiving, by conversion stage 230, trigger voltage signal
212 from trigger voltage source 210; producing, by conver-
sion stage 230, converted data 232 from receiver signals 228
and trigger voltage signal 212; receiving, by render 234
converted data 232 from conversion stage 230; and produc-
ing map 236 of structural entity 222 from converted data 232
to map structural entity 222.

[0028] In the process for mapping structural entity 222,
producing trigger voltage signal 212 includes launching, by
pulse generator 210, pulse signal 212 that travels through the
coaxial cables and synchronously starts operation of syn-
thesizers 214 and analog-to-digital converters 230. Primary
electromagnetic wave synthesizers 214 produce primary
electromagnetic waves 220 that include a voltage signal in
the form of a pseudo-random binary sequence that energizes
transmitters 218 (e.g., an antenna) and that propagate pri-
mary electromagnetic waves 220 and which are scattered by
structural entity 222. Scattered electromagnetic waves 224
arrive at receivers 226 and receiver signals 228 are con-
verted by conversion stage 230, e.g., digital-to-analog con-
verters. Converted data 232 (c.g., digitized information) is
communicated as a digital signal to render 234 (e.g.
mapping program stored in a digital computer) and con-
verted into map 236 (¢.g., a digital image signal) that
optionally can be displayed in real-time by a display such as
a monitor.



US 2023/0194589 Al

and the like, Received data are combined with a knowledge
of the transmitted signal to produce a map, eg.. a digital
representation, of the structural entity 222. Advantageously,
the mapping probe overcomes technical limitations of con-
ventional instruments that involve localization, mapping,
and imaging of unknown, not line-of-sight environments
such as burning or collapsed buildings that can encase an
individual such as a firefighter or fire victim.

[0011] Unlike GPS localization, indoor localization and
mapping involve effects such as multipath, attenuation, and
delays, and transfer of large amounts of information to
reconstruct a geometry of a structural entity that can over-
load a communication channel. Beneficially, the mapping
probe can involve signal processing algorithms such as
compressive sensing to overcome these technological bar-
riers and deficiencies in conventional devices and processes.
Unexpectedly, the mapping probe directly provides real-
time compressive sensing indoor localization based on inter-
ference of radiofrequency signals.

[0012] Mapping probe 200 provides real-time signal sam-
pling and recovery from engineered electromagnetic inter-
ference. In an embodiment, with reference to FIG. 1, map-
ping probe 200 includes trigger voltage source 210. Trigger
voltage source 210 produces trigger voltage signal 212 that
synchronizes transmission of primary electromagnetic
waves 220. Primary electromagnetic wave synthesizers 214
are in communication with trigger voltage source 210.
Primary electromagnetic wave synthesizers 214 receive trig-
ger voltage signal 212 from trigger voltage source 210,
produce time-varying voltage signals 216 in response to
receipt of trigger voltage signal 212 from trigger voltage
source 210, and communicate time-varying voltage signals
216. Mapping probe 200 also includes transmitters 218 in
communication with primary electromagnetic wave synthe-
sizers 214. Transmitters 218 receive time-varying voltage
signals 216 from primary electromagnetic wave synthesizers
214 and synchronously transmit time-varying voltage sig-
nals 216 as primary electromagnetic waves 220 in response
to receipt of trigger voltage signal 212 from trigger voltage
source 210 by primary electromagnetic wave synthesizers
214, such that primary electromagnetic waves 220 are
subjected to scattering by structural entity 222 to produce
scattered electromagnetic waves 224 from primary electro-
magnetic waves 220. Receivers 226 receive scattered elec-
tromagnetic waves 224 and produce receiver signals 228
based on scattered electromagnetic waves 224. Conversion
stage 230 is in communication with receivers 226 and
receives receiver signals 228 from receivers 226, wherein
conversion stage 230 receives trigger voltage signal 212
from trigger voltage source 210 and produces converted data
232 from receiver signals 228 and trigger voltage signal 212
Render 234 is in communication with conversion stage 230
and receives converted data 232 from conversion stage 230
and produces map 236 of structural entity 222.

[0013] Mapping probe 200 maps structural entity 222
from converted data 232 produced from synchronizing
operation of mapping probe 200 with trigger voltage source
210. Trigger voltage source 210 can include a voltage source
such as a signal generator, signal synthesizer, arbitrary
waveform generator, square waveform generator, pulse gen-
erator, and the like to produce a time-varying voltage that
crosses a voltage threshold (trigger voltage) either in rising
or falling fashion to produce an accurate time stamp mark to
initiate transmission and reception, wherein trigger voltage

Jun. 22, 2023

source 210 can provide analog or digital output. In an
embodiment, trigger voltage source 210 includes a pulse
generator.

[0014] Trigger voltage source 210 produces trigger volt-
age signal 212 for syncing production of primary electro-
magnetic waves 220 and acquisition of receiver signals 228.
‘A temporal pulse rise or fall time of trigger voltage signal
212 can be less than 1 nanosecond (ns), specifically from 10
picoseconds (ps) to 100 ps. An amplitude of trigger voltage
signal 212 can be from —2 volts (V) to 5 V, specifically from
-1 V to 2.7 V. As used herein, “amplitude” refers to a value
of voltage corresponding to a beginning or end of the rising
or falling edge of the pulse. In an embodiment, trigger
voltage signal 212 includes a time varying signal produced
by the trigger voltage source 210 transmitted through a
medium that can be a transmission line such as a coaxial
cable or through free space.

[0015] Primary electromagnetic wave synthesizers 214
receives trigger voltage signal 212 and produces time-
varying voltage signals 216 in response to receipt of trigger
voltage signal 212. Primary electromagnetic wave synthe-
sizers 214 can include a signal generator, signal synthesizer,
arbitrary wave generator, pseudo-random binary sequence
generator, vector signal generator, and the like. Exemplary
primary electromagnetic wave synthesizers 214 include the
pseudo-random binary sequence generator. A number of
primary electromagnetic wave synthesizers 214 (e.g., 214.1,
214.2, ..., 214.n, wherein n is an integer number of total
primary electromagnetic wave synthesizers 214) can be
from different pseudo-random binary sequence generators.
In an embodiment, primary electromagnetic wave synthe-
sizers 214 include pseudo-random binary sequence genera-
tors.

[0016] A temporal pulse width of time-varying voltage
signals 216 can be from 1 ps to hundreds of ns depending on
a selected temporal or spatial resolution, An amplitude of
time-varying voltage signals 216 can be from millivolts
(mV) to hundreds or thousands of volts. In an embodiment,
time-varying voltage signals 216 includes time-varying volt-
ages carried by coaxial cables or free space.

[0017] Transmitters 218 receive time-varying voltage sig-
nals 216 and produce primary electromagnetic waves 220 in
response to receipt of time-varying voltage signals 216.
Transmitters 218 can include an antenna or transducer that
couples the voltage signal to free space such a horn antenna,
Vivaldi antenna, printed circuit, omni-directional, and the
like. Moreover, antennas provide bandwidth to accommo-
date time variations of the synthesized signal. A number of
transmitters 218 (e.g., 218.1, 218.2, ..., 218.n, wherein n
is an integer number of total transmitters 218) can be from
1 to hundreds or thousands, specifically from 2 to 100, and
more specifically from 12 to 32. In an embodiment, trans-
mitters 218 include an omni-directional antenna or log-
periodic antenna.

[0018] Primary electromagnetic waves 220 can have tem-
poral pulse width that can be from 100 ps to 10 ns,
specifically from 100 ps to 1 ns, and more specifically from
300 ps to 1 ns. A power of primary electromagnetic waves
220 can be from a few milliwatts (mW) to tens of kilowatts
(kw).

[0019] Structural entity 222 is subjected to primary elec-
tromagnetic waves 220 from transmitters 218. Structural
entity 222 can include a structure that is different from free
space to scatter the electromagnetic wave. Exemplary struc-



US 2023/0194589 Al

one receiver 228 transmitting at data rates compatible with
voice channels that overcomes technical limitations
involved with more bandwidth intensive means such as live
video feeds. Moreover, the mapping probe provides refresh
rates of tens to hundreds of milliseconds for real-time
updates.

Example

[0047] Real Time Signal Sampling and Recovery Using
Engineered Electromagnetic Interference with a Mapping
Probe.

[0048] A superposition, also referred to herein as interfer-
ence, of propagating electromagnetic waves is generated by
a set of transmitters to sample signals in real time. A signal
can be a structural entity in a propagation medium that
scatters electromagnetic waves. Data y, measured by detec-
tors, corresponds to an inner product of a dynamically-
generated interference-based sampling matrix A and signal
x. Sampling occurs at a propagation speed of the waves, i.e.,
in real time. The signal can be sparse so that recovery occurs
by aggregation and can include computational optimization,
eg., with compressive sensing.

[0049] Naturally occurring signals can be sparse so that
they carry little information as provided for in compression
used in digital cameras that operate in a visible band of the
electromagnetic spectrum. Even though signal sparsity
exists in other bands, detection thereof can be difficult and
expensive. Non-invasive imaging provides sparse data,
wherein a three-dimensional medium can be characterized
by a small number of parameters in addition to embedded
lower dimensional interfaces. Sampling of such media
occurs with penetrating radiation such as radiofrequency
(RF) waves, acoustic waves, infrared radiation, or x-rays.
Detection at such wavelengths is difficult with a large array.
[0050] Compressed sensing is a signal recovery algorithm
and technique that exploits a sparsity and inherent reciproc-
ity between illumination and detection to make imaging in
forbidden bands of the spectrum accessible. In signal analy-
sis, a matrix AER” samples signal x¢RTM and retain
sampling inner products in a measurement vector ye RTM,
ie.,

Ax=y. (O)

[0051] To recover x, provided M2N, take a pseudo inverse
of A and multiply it by y. This procedure becomes imprac-
tical if N is very large as in the case of discretized two- and
three-dimensional spaces. If M<N, the inversion problem is
ill-posed and is intractable in general. However, if x is
compressible or sparse, then recovery can be achieved by
computational imaging and further optimized by com-
pressed sensing methods with a small number of measure-
ments M such that K<M<<N, wherein K is a number of
non-zero components of x in a suitable basis such as discrete
cosines or wavelets where most signals of interest are
compressible or sparse. To ensure recovery with a small
number of measurements M c K log (N/K), a strategy is to
have the sampling matrix A contain incoherent random
entries following, e.g., a Gaussian or Bernoulli distribution.
Computational imaging methods recover x by simple aggre-
gation S=y"ATM, whereas compressed sensing methods
search for x by minimizing ||z||p, subject to A z=y, wherein
\2\, (OSpsi) is an &,, norm.

[0052] These methods involve compression at a sampling
stage instead of a conventional approach to compression

Jun. 22, 2023

where the signal is sampled at full resolution by an array of
detectors and subsequently compressed. This new method
provides a measurement apparatus to have as few as a single
detector while the illumination source retains full resolution
with the corresponding computational load transferred to the
recovery stage. The reversal of roles between sources and
detectors overcome limitations in regions of the electromag-
netic spectrum where the cost of high pixel count sensor
arrays is prohibitive. It reciprocally transfers a burden of
spatial resolution to the illumination system that now gen-
erates structured sampling patterns at full resolution. Fur-
thermore, regardless of three-dimensional imaging recovery
schemes at optical wavelengths, radar at radio frequencies,
and ultrasound, improvements in real-time penetrating spa-
tial reconstruction is provided by the mapping probe herein.
Conventional devices involve sampling that has static pat-
terns and lack full three-dimensional coverage.

(0053] ‘The mapping probe, e.g., shown in FIG. 2, provides
full-space three-dimensional sampling at the speed of the
propagating waves in the medium by manipulating interfer-
ence effects during propagation and compression of the
sampling patterns that reduces a number of transmitters in
the illumination system.

[0054] The mapping probe includes N, transmitters and N,
receivers placed in the space where the signal is embedded,
and the ensemble of transmitters, receivers, and signal are
referred to as a scene. An arrangement of transmitters and
receivers is arbitrary. Selection of a location occurs and
provides for knowing their location; synchronizing, by a
master clock, a transmission and reception process: and
knowing the excitation waveforms on each transmitter.

[0055] Each transmitter independently has a waveform
source connected to an antenna by a coaxial cable. The
source has limited bandwidth and typically contains an
oscillator connected to a quadrature-amplitude modulation
stage such as an I-Q mixer. Synchronization ensures that the
excitation waveforms exit the transmitters simultaneously
with the start of data acquisition by the receivers.

[0056] The waveforms are tailored to produce modula-
tions in the form of, amplitude modulation, frequency modu-
lation, polarization modulation, or phase modulation.
(0057] Each receiver has an antenna connected to a
demodulation stage, such as an I-Q mixer, by a coaxial
cable. The mixer output is then digitized and stored for the
recovery step.

[0058] A sampling matrix A according to Eqn. (1) is
obtained and based on a model of point sources as the
illumination system, a spatially dependent reflectivity func-
tion as the signal and small number of detectors. With regard
to recovery of signals, to construct A in (1), a random
intensity pattern is created by interference between fields
formed by an array of N; transmitters driven by Dirac
pulses. The pulses are amplitude modulated by pseudo-
random codes of polarity +1. We thus model each transmitter
N;) as point sources placed in space-time at (1
t" y polarized along the same direction a. The total illumi-
nation function is thus given by E=E, «E,, where:

let @)

Ex.) = Yi Cutthy



23019.
as) United States
a2) Patent Application Publication co) Pub. No.: US 2023/0194589 Al

da Silva (43) Pub. Date: Jun. 22, 2023
(54) MAPPING PROBE FOR REAL-TIME SIGNAL Publication Classification
SAMPLING AND RECOVERY FROM 61) Int. C1
ENGINEERED ELECTROMAGNETIC GOR 39/08 (2006.01)
INTERFERENCE GOIR 31/00 (2006.01)
ov ; (52) US. Cl
(71) Applicant: Government of the United States of GOIR 29/0878 (2013.01); GOIR 29/0892
America, as represented by the (2013.01); GOR 31/001 (2013.01)
Secretary of Commerce, Gaithersburg,
MD (US) (67) ABSTRACT
A mapping probe provides real-time signal sampling and
(72) Inventor: Fabio Cesar Siqueira da Silva, recovery from engineered electromagnetic interference and
Westminster, CO (US) includes: a trigger voltage source that synchronizes trans-

mission of primary electromagnetic waves; primary electro-
magnetic wave synthesizers that receive a trigger voltage
signal and produce time-varying voltage signals; transmit-
ters that receive time-varying voltage signals and synchro-
(22) Filed: Feb. 9, 2023 nously transmit primary electromagnetic waves, such that
the primary electromagnetic waves are subjected to scatter-

ing by a structural entity to produce scattered electromag-

Related U.S. Application Data netic waves; receivers that receive scattered electromagnetic

(63) Continuation of application No. 16/418,202, filed on Waves and produce receiver signals based on the scattered
May 21,2019, sevy abandoned, electromagnetic waves; a conversion stage that receives the
receiver signals and the trigger voltage signal and produces

(60) Provisional application No. 62/675,386, filed on May converted data; and a render that receives the converted data

(21) Appl. No.: 18/107,899

23, 2018. and produces a map of the structural entity.
200
22 210 212
( it \
214, 220.1 2281 280.1
bom 212 ( { H { ( 236
; dy! } , :
216.2 2182 2262 1
( { ( f
Ler,
} ) } } H }
( i ( (ot ( {
2i4n 2160 220.0 228n 280.0 282.n



US 2023/0194589 Al

a plurality of transmitters in electrical communication
with the primary electromagnetic wave synthesizers
and that:
electronically receives the time-varying voltage sig-
nals from the primary electromagnetic wave syn-
thesizers; and

synchronously transmits the time-varying voltage
signals as primary electromagnetic waves in
response to receipt of the trigger voltage signal
from trigger voltage source by the primary elec-
tromagnetic wave synthesizers,

such that the primary electromagnetic waves are
subjected to scattering by a structural entity to
produce scattered electromagnetic waves from the
primary electromagnetic waves;

a plurality of receivers that:
receives the scattered electromagnetic waves; and
produces a plurality of receiver signals based on the

scattered electromagnetic waves;

a conversion stage in communication with the receivers
and that:
receives, from the receivers, the receiver signals:
receives, from the trigger voltage source, the trigger

voltage signal; and
produces converted data from the receiver signals
and the trigger voltage signal; and

a render in communication with the conversion stage
and that:
receives, from the conversion stage, the converted

data; and
produces a map of the structural entity;
synchronizing transmission of primary electromagnetic
waves;
receiving, by the primary electromagnetic wave synthe-
sizers, the trigger voltage signal from the trigger volt-
age source;

Jun. 22, 2023

producing, by the primary electromagnetic wave synthe-
sizers, time-varying voltage signals in response to
receiving the trigger voltage signal from the trigger
voltage source:

communicating, by the primary electromagnetic wave
synthesizers, the time-varying voltage signals;

receiving, by the transmitters, the time-varying voltage
signals from the primary electromagnetic wave synthe-
sizers;

synchronously transmitting, by the transmitters, the time-
varying voltage signals as primary electromagnetic
waves in response to receiving the trigger voltage
signal from the trigger voltage source by the primary
electromagnetic wave synthesizers,

subjecting the primary electromagnetic waves to scatter-
ing by the structural entity;

producing scattered electromagnetic waves from the pri-
mary electromagnetic waves in response to scattering
the primary electromagnetic waves by the structural
entity;

receiving, by the receivers, the scattered electromagnetic
waves:

producing, by the receivers, the receiver signals based on
the scattered electromagnetic waves;

receiving, by the conversion stage, the receiver signals
from the receivers;

receiving, by the conversion stage, the trigger voltage
signal from the trigger voltage source:

producing, by the conversion stage, converted data from
the receiver signals and the trigger voltage signal;

receiving, by render, the converted data from the conver-
sion stage; and

producing the map of the structural entity from the
converted data to map the structural entity.

+e eee


US 2023/0194589 Al

creating a random intensity pattern from the illuminating

fields formed by the array of transmitters;

illuminating a three-dimensional medium with the ran-
dom intensity pattern of the illuminating fields, such
that a propagation medium of the random intensity
pattern is a passive source with reflectivity function
x(r', t);

detecting by a detector a reflected pattern from the three-
dimensional medium, the reflected pattern produced
from reflecting the random intensity pattern from the
three-dimensional medium; and

compressing sampling on the order of (1-N;/N), wherein

N; is the number of transmitters, and N is the number
of pixels of the detector.

2. The process of claim 1, wherein the pseudo-random
codes comprise a +1 polarity.

3. The process of claim 1, further comprising modelling
each transmitter as a point source disposed in space-time and
polarized along the same direction.

4. The process of claim 1, wherein a response to the
illuminating field measured at a point r and time t is given
by

Y edlGntr AE

son ddr’

5. The process of claim 4, wherein

rill such that.

6. The process of claim 1, wherein phase fronts of the
reflected pattern arriving at the detector at a time t come
from the volume inside an ellipsoid given by

relran"l=04;),

7. The process of claim 1, wherein an emission pattern of
each transmitter comprises concentric spherical shells cen-
tered at r," of polarity +1 and corresponds to the pseudo-
random code,

8. The process of claim 7. wherein the reflected pattern
detected by the detector is constrained to ellipsoidal shells.

9. The process of claim 8, wherein a superposition of
shells emitted from different transmitters and carrying a
corresponding pseudo-random code is a randomized spatial
pattern that evolves in space-time.

10. The process of claim 9, wherein the randomized
spatial pattern is

11. The process of claim 10, wherein the signal measured
by the detector is the inner product of the random matrix
A(t) and medium reflectivity function x(t’) during a time
interval At around t.

12. The process of claim 11, wherein the signal measured
by the detector is

yend=( AGer.0lx(v)

Jun. 22, 2023

13. A mapping probe for real-time signal sampling and
recovery from engineered electromagnetic interference, the
mapping probe comprising:
a trigger voltage source that produces a trigger voltage
signal that synchronizes transmission of primary elec-
tromagnetic waves;
a plurality of primary electromagnetic wave synthesizers
in communication with the trigger voltage source and
that:
receives the trigger voltage signal from the trigger
voltage source;
produces time-varying voltage signals in response to
receipt of the trigger voltage signal from the trigger
voltage source; and

communicates the time-varying voltage signals;

plurality of transmitters in electrical communication

with the primary electromagnetic wave synthesizers

and that:

electronically receives the time-varying voltage signals
from the primary electromagnetic wave synthesizers;
and

synchronously transmits the time-varying voltage sig-
nals as primary electromagnetic waves in response to
receipt of the trigger voltage signal from trigger
voltage source by the primary electromagnetic wave
synthesizers,

such that the primary electromagnetic waves are sub-
jected to scattering by a structural entity to produce
scattered electromagnetic waves from the primary
electromagnetic waves:

a plurality of receivers that:

receives the scattered electromagnetic waves; and

produces a plurality of receiver signals based on the
scattered electromagnetic waves;

a conversion stage in communication with the receivers
and that:

receives, from the receivers, the receiver signals;

receives, from the trigger voltage source, the trigger
voltage signal; and

produces converted data from the receiver signals and
the trigger voltage signal; and

a render in communication with the conversion stage and

p

receives, from the conversion stage, the converted data;
and

produces a map of the structural entity.

14. A process for mapping a structural entity with a
mapping probe, the process comprising:
producing, by the trigger voltage source of mapping
probe, a trigger voltage signal, the mapping probe
comprising:
a trigger voltage source that produces a trigger voltage
signal that synchronizes transmission of primary
electromagnetic waves:
a plurality of primary electromagnetic wave synthesiz-
ers in communication with the trigger voltage source
and that:
receives the trigger voltage signal from the trigger
voltage source;

produces time-varying voltage signals in response to
receipt of the trigger voltage signal from the
trigger voltage source: and

communicates the time-varying voltage signals:



US 2023/0194589 Al

[0029] In the process for mapping structural entity 222,
receiving, by primary electromagnetic wave synthesizers
214, trigger voltage signal 212 from trigger voltage source
210 includes voltage signals that include rise or fall edges
from -1 V to 2.7 V ina time from 10 ps to 1 ns connected
to coaxial cables from the trigger voltage source 210 to the
trigger input of each electromagnetic wave synthesizers 214
and the trigger input of each component of conversion stage
230.

[0030] In the process for mapping structural entity 222,
producing, by primary electromagnetic wave synthesizers
214, time-varying voltage signals 216 in response to receiv-
ing trigger voltage signal 212 from trigger voltage source
210 includes voltage signals in a form of pseudo-random
binary sequences that include a rising or falling edge from
-1 V to 2.7 V ina time from 10 ps to | ns.

[0031] In the process for mapping structural entity 222,
communicating, by primary electromagnetic wave synthe-
sizers 214, time-varying voltage signals 216 includes pro-
ducing voltage signals that are pseudo-random binary
sequences having an amplitude from a few mV to hundreds
of V peak-to-peak with each voltage transition rise and fall
edges in a time from 10 ps and 1 ns and each voltage level
corresponding to a binary number, | or 0, ina time from 100
ps to several ns.

[0032] In the process for mapping structural entity 222,
receiving, by transmitters 218, time-varying voltage signals
216 from primary electromagnetic wave synthesizers 214
includes producing voltage signals that are pseudo-random
binary sequences having an amplitude from a few mV to
hundreds of V peak-to-peak with each voltage transition rise
and fall edges in a time from 10 ps and 1 ns and each voltage
level corresponding to a binary number, 1 or 0, in a time
from 100 ps to several ns.

[0033] In the process for mapping structural entity 222,
synchronously transmitting, by transmitters 218, time-vary-
ing voltage signals 216 as primary electromagnetic waves
220 includes producing wave disturbances that propagate in
free space and mimic voltage signals that are pseudo-
random binary sequences having an amplitude from a few
mV to hundreds of V peak-to-peak with each voltage
transition rise and fall edges in a time from 10 ps and 1 ns
and each voltage level corresponding to a binary number, 1
or 0, in a time from 100 ps to several ns.

[0034] In the process for mapping structural entity 222,
subjecting primary electromagnetic waves 220 to scattering
by structural entity 222 includes the transmission, reflection,
deflection, refraction and other forms of scattering of elec-
tromagnetic waves by media other than free space.

[0035] In the process for mapping structural entity 222,
producing scattered electromagnetic waves 224 from pri-
mary electromagnetic waves 220 in response to scattering
primary electromagnetic waves 220 by structural entity 222
includes producing a wave by interaction of incident elec-
tromagnetic waves 220 with the structural entity.

[0036] In the process for mapping structural entity 222,
receiving, by receivers 226, scattered electromagnetic waves
224 includes detecting any wave communicated to the
receiver after being scattered by the structural entity,
[0037] In the process for mapping structural entity 222,
producing, by receivers 226, receiver signals 228 based on
scattered electromagnetic waves 224 includes making a time
varying signal that includes a linear combination of the
transmitted signal modulated by the structural entity.

Jun. 22, 2023

[0038] In the process for mapping structural entity 222,
receiving, by conversion stage 230, receiver signals 228
from receivers 226 includes converting, by modules, analog
signal 228 into a digital form that is processed by the render.
An exemplary module is an analog-to-digital converter, a
frontend amplifier, a mixer, filter, and the like.

[0039] In the process for mapping structural entity 222,
receiving, by conversion stage 230, trigger voltage signal
212 from trigger voltage source 210 includes receiving
voltage signals that pseudo-random binary sequences and
having rise or fall edges from -1 V to 2.7 V ina time from
10 ps to 1 ns.

[0040] In the process for mapping structural entity 222,
producing, by conversion stage 230, converted data 232
from receiver signals 228 and trigger voltage signal 212
includes producing numerical representations of analog sig-
nal 228 in a digital form such as 8-bit, 16-bit, 32-bit, or
64-bit integer or floating-point.

[0041] In the process for mapping structural entity 222,
receiving, by render 234, converted data 232 from conver-
sion stage 230 includes a program stored in hardware such
as a field-programmable gate array (FPGA) or in a digital
computer, The program contains a recovery algorithm that
uses the digital signal 232 and creates a digital representa-
tion of the structural entity 236. The algorithm can use a
variety of recovery techniques based on least squares (L2
minimization) or compressed sensing (L1 minimization).
[0042] In the process for mapping structural entity 222,
producing map 236 of structural entity 222 from converted
data 232 includes producing a 2D or 3D image to be
displayed in, e.g., a digital monitor.

[0043] The process for mapping structural entity 222 also
can use other computational means for the recovery algo-
rithm in 234 such as graphics processing units (GPUs).
Trigger voltage signal can be sent via coaxial cable or
wirelessly via any synchronization protocol used for
example in clock recovery. Transmitter 218 and receiver 228
can be mounted on mechanically rigid structures such as fire
trucks or in a dynamically configurable system such as a
drone.

[0044] Mapping probe 200 and processes disclosed herein
have numerous beneficial uses, including fast response times
(e.g.. in microseconds) for real-time monitoring of move-
ments; mapping 1D, 2D and 3D structural entities such as
tunnels, individual floors, or whole buildings; tagging struc-
tural features based on recovered image contrast; using
mapping probe as a metrology tool in identification and
characterization of different materials; accommodating sizes
of structural entities from a few centimeters to thousands of
kilometers. Advantageously, mapping probe 200 overcomes
limitations of technical deficiencies of conventional articles
such as multiple reflection signals (multipath), long image
recovery times, and dependence on prior knowledge of the
structural entity. Further, this process allows for dynamic
deployment in unknown scenarios and provides timely
answers for mission critical activities such as search and
rescue in a burning building.

[0045] Moreover, mapping probe 200 and processes
herein have numerous advantageous properties. In an aspect,
providing image recovery with the mapping probe can be
provided via cloud service access, remote sensing, and the
like.

[0046] Mapping probe 200 and processes herein unexpect-
edly involve small bandwidths for sensing with as few as



Patent Application Publication Jun. 22,2023 Sheet 3 of 3 US 2023/0194589 Al

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US 2023/0194589 Al

Jun. 22, 2023 Sheet 2 of 3

Patent Application Publication

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US 2023/0194589 Al

Jun. 22, 2023 Sheet 1 of 3

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