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Nonlinear Radar for Finding RF Electronics:
System Design and Recent Advancements
Gregory J. Mazzaro, Senior Member, IEEE, Anthony F. Martone, Senior Member, IEEE,
Kenneth I. Ranney, Senior Member, IEEE, and Ram M. Narayanan, Fellow, IEEE
(Invited Paper)
Abstract— An extensive review of nonlinear radar systems is
performed. Emphasis is placed on designs relevant to detecting
RF electronics that were not intentionally manufactured as visible
radar targets. The state of the art in nonlinear radar is conveyed
by presenting high-level system architecture, explaining the
rationale behind design decisions pertaining to that architecture,
and listing the specifications that nonlinear radar designers have
achieved. The authors’ recent advancements in nonlinear radar
technology are summarized.
Index Terms— Nonlinear circuit analysis, nonlinear circuits,
nonlinear circuits and systems, radar systems, radar transceivers,
radars, radars and broadband systems, remote sensing,
RF circuits, RF front ends, RF transceiver architecture,
RF/microwaves, Schottky diodes, wireless RF components and
NE of the many decisions that a radar designer must
make is the selection of an appropriate transmit
waveform. This waveform, tailored to the target set and
its environment, will maximize signal-to-noise ratio (SNR),
generate the finest spatial resolution, minimize interference
with neighboring electronic systems, or achieve an acceptable
tradeoff between such metrics. Beyond choosing an
appropriate waveform, the radar designer must also select the
1) appropriate frequencies-of-operation;
2) minimum transmit power;
3) minimum receive sensitivity;
4) acceptable transmit and receive antennas;
5) an arrangement for the front-end architecture;
6) a technique for processing received waveforms into
information relevant to detection and ranging.
The authors are designing a radar to detect concealed targets in
environments densely occupied by naturally occurring clutter.
Manuscript received October 7, 2016; revised December 8, 2016;
accepted December 12, 2016. This work was supported in part by the
United States Army Research Laboratory of Adelphi, MD, USA, and in
part by General Technical Services, LLC of Wall Township, NJ, USA, under
Contract W911QX-15-R-0012 // TO 0001.
G. J. Mazzaro is with The Citadel, Department of Electrical and Computer
Engineering, The Military College of South Carolina, Charleston,
SC 29409 USA (e-mail: [email protected]).
A. F. Martone and K. I. Ranney are with the U.S. Army Research
Laboratory, Sensors and Electron Devices Directorate, Adelphi,
MD 20783 USA (e-mail: [email protected]).
R. M. Narayanan is with the Department of Electrical Engineering
and Computer Science, The Pennsylvania State University, State College,
PA 16801 USA (e-mail: [email protected]).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TMTT.2016.2640953
The radar to be implemented is nonlinear. Nonlinear radar
separates a particular type of target—man-made electronics—
from surrounding clutter by relying on the properties of the
target to convert a portion of the transmit wave into a reflection
at a different frequency. As part of designing a radar system
to detect and range radio frequency (RF) electronics, the
authors have advanced nonlinear radar technology by describing the electromagnetic behavior of relevant targets, evaluating
different waveforms for transmission, improving transmitter
linearity, tracking moving targets, and imaging targets using a
synthetic antenna aperture.
Presented in this paper is an extensive review of nonlinear
(often called “harmonic”) radar design principles and systems
published in the available literature. A generic architecture
used for the RF front-end of a nonlinear radar system is
illustrated, and the functionality achieved by many different
nonlinear radars which use the same (or a very similar)
architecture are highlighted. Emphasis is placed on those systems designed to detect passive electronic targets (as opposed
to powered tags or transceivers). This literature review thus
presents the current state of the art of nonlinear radar technology relevant to addressing electronic targets which are
not intentionally designed to behave as visible, identifiable
radar targets. Guided by the available literature and their own
investigations into target behavior and RF system design, the
authors of this paper have selected an ultrawideband linear
stepped-frequency waveform to exploit the harmonic behavior
of targets-of-interest. This paper culminates by summarizing
the authors’ recent advancements in nonlinear radar for finding
RF devices.
A. Applications of Nonlinear Radar
The design and implementation of nonlinear radars can
be traced at least as far back as 1976, for the purpose of
detecting metallic objects (such as vehicles) obscured by
foliage and located close to the ground [1]. Within the past
ten years, however, much of the research on nonlinear radar
has supported the following applications:
1) tracking insects and small amphibians [2]–[5];
2) detecting RF surveillance equipment [6], [7];
3) sensing temperature remotely [8], [9];
4) alerting a vehicle driver to the presence of people
crossing the path of the vehicle [10];
5) measuring the extent of corrosion [11];
6) monitoring human vital signs [12], [13].
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Fig. 1. Illustration of the nonlinear radar concept: the radar transmit (Tx)
antenna emits a wave (with an electric field denoted by E trans ) carrying a
known frequency (e.g., f 0 ) toward the nonlinear target. Upon reaching the
target, the wave (with an e-field denoted by E inc ) is incident upon the target.
The nonlinear target is illustrated as a diode with wire leads for its “antennas.”
A new wave (with an e-field denoted by E refl ) reflects from the target carrying
new frequencies (e.g., 2 f 0 and 3 f 0 ). The radar receive (Rx) antenna captures
the wave which arrives back at the radar (with an e-field denoted by E rec ).
The application of concern to the authors is the detection
and characterization of RF electronics such as cellular telephones and handheld radios [14], for the purpose of revealing
the presence and identity of such devices to law enforcement
officials or military personnel. Thus, the emphasis of this
paper will be on design principles relevant to detecting and
identifying man-portable electronics which are not explicitly
designed to be detected or identified by radar.
B. Principle of Operation of Nonlinear Radar
The operating principles of nonlinear radar may be summarized as follows.
1) Transmit a radar wave containing a known set of probe
frequencies into an environment where an electronic
device might be present.
2) If an electronic device is present, antennas-ofopportunity on its circuit board capture some of the
energy of this wave.
3) Some of this captured energy is modulated by the
semiconductor properties of the electronics connected
to these antennas, generating frequencies that were not
part of the original transmission.
4) Some of the new modulated waves are re-emitted
wirelessly from the device by these same antennas.
5) If new frequencies (i.e., not part of the original probe set)
are received by the radar, the presence of an electronic
device is detected.
Fig. 1 gives an example of a transmit waveform, a target
containing two antennas and a semiconductor junction
(illustrated as a diode with leads), and a nonlinear-target
reflection. The radar transmit (Tx) antenna emits a wave
which contains a single frequency in its electric and magnetic
fields, f 0 . An antenna within the device, often an unshielded
trace on its printed circuit board (PCB), captures some of the
transmit wave energy, converting it to a voltage and a current
along the conductors between the electronic components
within the device. This voltage/current wave oscillates at the
same frequency f 0 , and it eventually encounters a component
which conducts current nonlinearly with respect to applied
voltage, such as a transistor containing a semiconductor
junction. The semiconductor junction, as a consequence of
its design, modulates the sinusoid (e.g., a diode performs the
nonlinear operation of rectification). The modulation generates
harmonics of the original frequency, such as 2 f 0 and 3 f 0 .
As the antenna/junction network is generally not impedancematched at f 0 or its harmonics (because these frequencies are
generally not within the operating band of the device), some of
the harmonics reverberate within the device. Traveling backand-forth along conductors within the device (possibly along
the same trace as that which captured the original transmission
at f 0 ), harmonics ultimately radiate from the device. The
radar receive (Rx) antenna captures this radiated wave.
In this manner, it is possible to design a radar transmission to force electronic devices to radiate new signals
which give away the locations of (and possibly device signatures associated with) those electronics. Nonlinear radar is
used in place of traditional (linear) radar because traditional
radars have difficulty separating small handheld targets from
nearby clutter. Because only man-made electronics (with few
exceptions, such as ferromagnetics) re-emit waves at different
frequencies, such nonlinear targets are more easily discernible
from naturally occurring clutter.
C. High-Level System Architecture for a Nonlinear Radar
A generic architecture for the front-end of a harmonic
radar, which encompasses much of the system design
for nonlinear radars described in open literature, is given
in Fig. 2. The architecture is monostatic. It contains a transmit
chain and a receive chain which are fed by a common
clock signal but which are otherwise isolated from each
Along the transmit chain is at least one amplifier and
one filter, possibly multiple stages, here depicted as lowpass.
The transmitter broadcasts the original probe frequency set
{ f 1 , f 2 , f 3 , . . .}. The nonlinear target, illuminated by the
transmit probe, generates new frequencies { f a , f b , fc . . .}.
Along the receive chain is at least one amplifier and one filter,
possibly multiple stages, here depicted as highpass.
By carefully choosing transmit waveforms and frequencies
tailored to different targets, it is possible to generate new
frequencies from those different targets. Selection of filters and
amplifiers for the transmit and receive chains, corresponding
to the chosen frequencies, is critical so as not to mask
target responses which are typically weak compared to the
transmitted probe. Processing of the received waveforms, at
the new frequencies, reveals range-to-target. If the nonlinear
responses are received by a physical or synthetic aperture array
of antennas, location of the nonlinear target in two or three
dimensions becomes possible.
The design of a radar begins with some a priori knowledge
of the response of a target to illumination by an electromagnetic wave. Proceeding from a basic understanding of target
behavior, it is then appropriate to design a system to transmit
waves to the target, receive waves reflected from the target,
and process the received waves into information such as the
location of the target.
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Fig. 2. Generic nonlinear radar transceiver architecture: the transmit chain consists of a local oscillator, a mixer, two power amplifiers, two filters (here
depicted as lowpass), and an antenna; the receive chain consists of an antenna, two LNAs, two filters (here depicted as highpass), a mixer, and a detector;
both mixers are fed by a common clock frequency f clock (and the receive mixer is fed by a multiple of that clock, if the radar receives the Mth harmonic of
the transmit signal).
A. Memoryless Power-Series Model
A useful model for the behavior of an electromagnetically
nonlinear target under illumination by a wave is the memoryless power series [15]–[20]
E refl (t) =
am E inc
Other nonlinear targets that have been discussed in the
literature, though not as frequently as the Schottky diode, are
PCBs [30], mixers and other standalone integrated circuits [6],
RF identification tags [19], thumb drives [31], and cell
phones [32].
where E inc is the electric field incident on the target, E refl is the
electric field reflected from the target (observed at the target),
and am are complex power-series coefficients corresponding
to the amplitude and phase responses of the target at each
harmonic of the original wave E inc . The coefficient a1 is the
linear response of the target. The coefficients am for m > 1
depend upon the nonlinear properties of the target.
While a Volterra series model [21] would be a more
complete way to model a nonlinear element (since that model
accounts for memory effects), the power series expression that
neglects memory effects has, to date, been adequate to model
nonlinear targets-of-interest.
B. Targets-of-Interest
If there is one target that has appeared in the relevant
literature often enough to be considered a “canonical” target
for nonlinear radar, it is the Schottky diode [22]–[27].
Its characteristically low forward voltage drop and small junction capacitance (typically less than 1 pF) allow the diode to
switch very quickly between forward and reverse bias, which it
does under illumination by a sinusoidal field. As an element
which can change very quickly between carrying moderate
current for a given applied field and carrying essentially zero
current for an equal but opposite applied field, the Schottky
diode is highly nonlinear and nearly memoryless; thus, its
behavior is described well by (1), assuming that appropriate
values are substituted for am .
Because a typical Schottky diode weighs less than 1/4 of a
gram and requires no external power to be visible to nonlinear
radar, it is a frequent choice for the nonlinear element in
tags carried by insects, amphibians, and vulnerable road users
[2], [4], [10]. To increase the reflectivity of the target, the
Schottky diode is often attached to an antenna, usually no
longer than the standard leads attached to a two-terminal
through-hole component [22], [28], [29]. Often, the antenna
is shaped conformal to its carrier’s body.
C. Nonlinear Radar Equation
The entire channel between the transmitter and receiver,
including the nonlinear target, has been described mathematically in several references. Many derive some version of
the nonlinear radar range equation, which is a variant of the
Friis equation for a monostatic radar, extended to a nonlinear
receive mode.
Inside the nonlinear radar equation, as an alternative to am
coefficients, the nonlinear power reflected by a target has been
quantified in different ways: as a scaling of the target’s linear
radar cross section (RCS) [16], as a conversion gain/efficiency
from the original transmit frequency to each newly generated
frequency [6], [28], [33], as a harmonic RCS [15], [26],
[30], [34], or as the more general nonlinear RCS [1], [35], [36].
Adopting the notion of a nonlinear RCS, the nonlinear radar
range equation may be written [35] as
PR =
M!(PT G T /M) M G R λ2 σ M
(4π) M+2 R 2M+2
where PR is received (peak or instantaneous) power, M is the
order of the nonlinear interaction (e.g., M = 2 to receive 2 f 0 ),
PT is transmitted power, G T is the transmit antenna gain,
G R is the receive antenna gain, λ is the transmit wavelength,
σ M is the nonlinear RCS of the target for an Mth-order
interaction, and R is the distance from the radar to the
nonlinear target. Since values of σ M for electronic targets are
small, e.g., 10−8 to 10−5 m4 /W for M = 2 [15], generally a
much higher transmit power is required for nonlinear radar to
generate an SNR comparable to that of traditional linear radar
at a comparable distance R.
Although (2) is most readily applied to a continuouswave (CW) sinusoidal transmission, it has been applied
to more sophisticated waveforms, such as single-frequency
pulses, linear chirps, and stepped frequencies. These waveforms are described in greater detail in the following
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Fig. 3.
Illustration of popular transmit and receive waveforms for nonlinear radar. (a) CW transmission at f 0 and harmonic reception at M · f 0 ,
(b) single-frequency pulsed transmission with carrier frequency f 0 and single-frequency pulsed harmonic reception with carrier frequency M · f 0 , (c) steppedfrequency transmission at f 1 followed by f 2 and stepped-frequency harmonic reception at M · f 1 followed by M · f 2 , and (d) two-tone transmission
at f 1 and f 2 simultaneously, intermodulation received at P · f 1 + Q · f 2 .
The selection of an appropriate waveform is a key design
decision for nonlinear radar, as its selection greatly impacts
the overall architecture to be implemented. After an appropriate transmit waveform is selected and the target response
is assumed to follow (1), the received waveform may be
predicted. Around an intended transmission and an expected
reception, subsystems may be designed to achieve adequate
detection and ranging.
A. Target Response: Harmonic Versus Intermodulation
The choice of transmit waveform is intimately related to the
choice of nonlinear response to exploit from the target. By far,
the most commonly exploited nonlinear response is harmonic
[25]–[29], [31]–[35], [37]–[43]. In other words, only a single
frequency f 0 is active at any time within the transmission,
and the received response consists of only integer multiples
of this frequency M · f 0 where M is a positive whole number.
Mathematically, the transmit and received waveforms may be
written [14]
E trans (t) = E 0 cos(2π f 0 · t)
E refl (t) =
|E M | cos(2π · M f0 · t + φ{E M })
where E 0 is the amplitude of the transmitted electric field,
and |E M | and ϕ{E M } are the amplitude and phase of each
harmonic reflected from the nonlinear target. The initial phase
of the transmit waveform is assumed to be zero without
any loss of generality. For UHF-band transmission and
L-band reception, the phase reflected from the target may be
assumed constant with frequency, as recent experiments have
demonstrated that ϕ-versus- f 0 is flat over an ultrawide sweep
within these bands [44].
A CW version of the single-frequency transmission and
harmonic reception is shown in Fig. 3(a). Of those radars
that exploit a target’s harmonic response, CW transmission
and reception is the most popular [8], [11], [12], [19], [25],
[28], [39], [45]. For the purpose of illustration, M = 2 and
so a frequency doubling is evident from Transmit to Receive.
Although reception of a CW harmonic M · f 0 indicates that
a nonlinear target has been detected, this choice of waveform
contains little information that is useful for ranging.
Ranging becomes possible when the transmit (and consequently the receive) waveform varies with time. Behind
CW harmonic radar, the next most popular type of nonlinear
radar is one which pulses a single frequency ON and OFF
and receives a pulsed harmonic, as illustrated in Fig. 3(b).
Directional antennas and a time-of-arrival calculation are used
to determine range-to-target. Pulse widths reported in the literature are 10 ns [42], 100 ns [4], [33], 1 μs [26], and 50 μs [5].
To enable not only ranging but resolution (and ultimately
imaging) of nonlinear targets, waveforms containing wideband
spectra must be reflected from each target. It is possible
to generate a wideband spectrum by reducing the pulse to
a single cycle [46]. This approach has the advantage of
generating maximum peak power for a given total transmit power [47]. Another wideband waveform is steppedfrequency CW, illustrated in Fig. 3(c). The transmission
steps continuously through a sequence of frequencies, usually
increasing from a start frequency f start to an end frequency
f end with an even spacing f , which may be written [48]
E trans(t) = E 0 cos[2π · f (t) · t]
f start ,
0 ≤ t < t
⎪ f start + f, t ≤ t < 2t
f (t) = f start + 2 f, 2t ≤ t < 3t
⎩ f − f,
t ≤ t < T
where Nstep is the number of discrete frequency steps between
f start and f end , T is the full length of the stepped-frequency
pulse, and t = T /Nstep is the spacing in time between each
step. The received waveform is also stepped in time; it contains
a sequence of harmonics
E rec (t) = |E M | cos[2π · M · f (t) · (t − 2τ ) + φ{E M }] (5)
where 2τ is the time-of-flight from the radar transmitter, to the
target, and back to the receiver. The prime notation denotes
that the amplitudes and phases of each harmonic are described
at the radar receiver (instead of at the target). Bandwidths
for stepped-frequency transmissions ( f end – f start ) that have
been reported in the literature are 40 MHz [48], 100 MHz [6],
and 1.2 GHz [49].
A slight variation on the stepped-frequency waveform is
the linear chirp (frequency-modulated CW) [50]–[52]. For
this transmission, the frequency of E trans transitions smoothly
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from fstart to fend [53]
f end − f start
and the received waveform is a chirp which resembles (5),
smoothly transitioning from M · f start to M · f end for each
detectable harmonic M. Bandwidths for chirp transmissions
that have been reported in the literature are 150 MHz [2] and
200 MHz [53].
If the transmission contains multiple simultaneous frequencies (N “multitones”), the nonlinear target will generate a
wider set of frequencies than just harmonics. If, for example,
the transmission contains two frequencies (N = 2) with equal
amplitudes and equal (zero) initial phase, written
f (t) = f start +
E trans(t) = E 0 cos(2π f 1 · t) + E 0 cos(2π f 2 · t)
then the received waveform, by (1), will contain [14]
E refl (t) =
|E P Q | cos[2π(P f 1 + Q f 2 )t
P=−∞ Q=−∞
+ φ{E P Q }]
where P and Q are integers which allow (8) to span all
frequencies produced by mixing the original sinusoids in (7),
their harmonics, and their cross products. A two-tone transmit waveform (and its corresponding harmonic waveform at
M = 2 reflected from the target) is illustrated in Fig. 3(d).
For simultaneous transmit frequencies which are spaced
closely together ( f 2 – f 1 f 1 , f 2 ), a group of new frequencies
is generated close to the original transmitted frequencies,
such as 2 f 1 – f 2 and 2 f 2 – f 1 . These are intermodulation tones.
A handful of nonlinear radars are designed to receive intermodulation from their targets [10], [16], [17]. An advantage
of intermodulation radar is that a single antenna is more
easily implemented for both transmit and receive, since the
full set of transmit and receive frequencies falls within a
relatively narrow band. A disadvantage of this type of radar
is its relatively tight dynamic range; because the receive
frequencies are so close to the transmit frequencies, removal
of intermodulation frequencies generated by the radar itself by
filtering is generally not possible as it is when the frequencies
are widely separated (as in harmonic radar).
For a radar which transmits simultaneous frequencies, it is
also possible to design the receiver to capture not only the
harmonics of those frequencies but cross-modulation terms
near those harmonics (such as f 1 + f 2 ) which would not exist
if the transmit frequencies were not sent simultaneously [14].
The power received at each harmonic and cross-modulation
term may be used to extract the power-series coefficients am
which appear in (1). A unique set of am values for a given
target forms a signature associated with that target.
None of the aforementioned transmit waveforms contain
phase modulation, but this idea has been considered. Several
harmonic radars place pseudorandom noise (PRN) modulation
onto the (otherwise CW) transmit probe frequency f 0 . For
nonlinear targets-of-interest (whose phase response is constant
across frequency), the same PRN code is reflected from the
device at each harmonic. Integration of the target response
over time and matched-filtering this response using the original
transmit probe enables the radar to detect target responses
beneath the noise floor of the system. Chipping rates for PRN
codes that have been used for harmonic radar are 1 MHz [18],
20 MHz [54], and 25 MHz [3], [5].
Researchers working on nonlinear radar have overwhelmingly chosen to exploit the harmonic responses of targets
rather than intermodulation. Furthermore, most researchers
have chosen to exploit the second-harmonic (2 f 0 ) response
[25]–[29], [31]–[33], [37]–[43]rather than a higher harmonic
(e.g., 3 f 0 and 4 f 0 ) response [6], [8], [19], [20], [34], [35], [41]
because the second harmonic is usually the strongest harmonic
returned from the relevant target(s).
B. Transmit Frequency
Selecting a transmit frequency (and consequently a receive
frequency) requires all of the typical tradeoffs associated with
longer versus shorter wavelengths for radar, which include the
1) availability of components (e.g., amplifiers and filters)
which are efficient at those frequencies;
2) realization of an acceptable gain for the antennas to
achieve a sufficient SNR;
3) exploitation of the RCS associated with a particular set
of targets.
In the case of nonlinear radar, a frequency-dependent
(nonlinear) RCS is difficult to exploit because a typical electronic device will contain the following.
1) A variety of circuit elements, each of which possesses its
own set of am coefficients which governs its nonlinear
electromagnetic response.
2) A variety of traces and solder joints which connect each
component to its neighboring components; the lengths
of the traces depend upon the layout of the PCB by the
device manufacturer.
3) An unknown degree of shielding, as an unknown circuit
board layout implies an unknown arrangement of circuit
elements with respect to each other. With respect to
the path of an incoming radar wave, some components
and traces will lie behind other components and traces,
effectively shielding them from the transmit probe.
If it is assumed, as a very rough approximation, that the
length of a typical trace along a PCB is l = 2 cm, and the
effective dielectric constant of the board is close to εeff = 4,
the traces along the board become half-wave resonant dipoles
(l = λ/2) at a frequency of
c/ εeff
3 · 108 m/s/ 4
= 3.75 GHz
f0 =
2(0.02 m)
where c is the speed of propagation of a radar wave in air.
Thus, if the transmit probe is meant to couple electromagnetic
energy to nonlinear elements inside of a target by way of
unintentional antennas formed by traces on its PCB, it is
reasonable to expect that the nonlinear radar will transmit
frequencies in or near S-band.
The resonant dipole is a common field-circuit coupling
model for nonlinear tags [25], [28], [29], [33]. Consistent
with the approximation given by (9), all of the published
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harmonic radars relevant to addressing electronics transmit
frequencies between 750 MHz and 9.41 GHz (well within one
order of magnitude of 3.75 GHz). A summarized view of the
transmit frequencies reported in the literature at the time of
this publication is shown in Table I.
For the purpose of detecting and ranging electronics, the
systems developed are fairly evenly spread across the lower
UHF range up to X-band, though slightly more may be found
at the lower and upper ends of this range rather than in the
middle. As the radars on both ends of this frequency-ordered
list receive 2 f 0 , the lowest receive frequency is 1.50 GHz and
the highest is 18.82 GHz.
C. Transmit Power and Transmit Waveform Filtering
As is true for traditional (linear) radar, transmission of
higher power is generally best to produce a stronger target
response and achieve an adequate SNR. For nonlinear radar, an
additional complication arises, as generating high peak power
for transmission necessarily generates distortion in the transmit
waveform. For harmonic radar, this distortion manifests as
harmonics that (if they were absent from the transmit waveform) would otherwise be associated with the target reflection.
The harmonic distortion generated by the transmitter, if not
adequately filtered or canceled before transmission, either is
emitted from the transmit antenna and reflects from linear
clutter in the environment, generating false alarms, or couples
directly from the transmitter to the receiver and effectively
masks reflections from weaker (usually distant) targets.
Thus, a high-power radar applies a great degree of
filtering to the transmit signal before it leaves the radar. Many
researchers have implemented lowpass filtering as part of their
transmitter architecture [3], [22], [26], [34], [42]. Some have
reported splitting the filtering function across multiple filters
[11], [25], as illustrated in Fig. 2. For CW transmissions where
the bandwidth of the signal may be made arbitrarily narrow,
bandpass filtering may be implemented instead [28], [37],
[38], [40]. Those references which explicitly discuss filter
specifications report rejection of self-generated harmonics
(2 f 0 and above) by 50 dB or more [5], [6], [31], [54].
All of the transmit powers reported in the literature have
peak values between 10 mW and 200 kW. The lower power
radars are CW while the higher-power radars are pulsed.
A summary of the transmit powers reported in the literature
at the time of this publication is shown in Table II. Most of
these harmonic radars transmit a CW at 5 W or below.
D. Antennas for Transmit and Receive
Antenna selection for a nonlinear radar is not unlike antenna
selection for linear radar: transmit and receive gain must be
substantial to achieve an acceptable detection range and SNR.
One key difference is that, for harmonic reception, the transmit
and receive antennas must accommodate widely disparate
frequency bands. For example, a radar which transmits f0
inside of L-band would receive 2 f 0 inside of S-band. Another
key difference involves Tx/Rx isolation. Because nonlinear
reflections tend to be weak, transmit power tends to be high,
which generates distortion. Any distortion fed to the transmit
antenna will directly couple to the receive antenna if the two
antennas are not isolated from each other.
Because of the disparate frequency bands and the tendency
of distortion to couple from one antenna to another, the
transmit and receive antennas are usually physically separated
[31], [34], [37], [38], [55], as illustrated in Fig. 2. It is
possible, however, to design a single antenna to accomplish
both transmit and receive [7], [32]. In that case, the transmit
and receive signals to/from the antenna are separated by a
high-isolation diplexer [54], [56]. References [3] and [5],
which note diplexer specifications, report isolations greater
than 60 dB.
No one type of antenna seems to be best choice for
a harmonic radar transmitter, though the horn antenna
[22], [28], [40] is presently the most popular. Other antennas
that have been implemented are the dish [3], patch [46],
monopole [39], slotted waveguide [4], spiral [6], [37], and
Yagi [29], [45]. A list of transmit antenna gains reported in
the literature is given in Table III.
A variety of antennas have been used for the harmonic radar
receiver: dipole [37], dish [5], horn [22], patch [45], [46], [55],
and spiral [6]. A list of receive antenna gains reported in the
literature is given in Table IV.
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E. Target Reflectivity and Target Antenna
It should be noted that choices regarding transmit power
and antennas are also governed by factors such as distanceto-target, receiver sensitivity, and reflectivity of the target. For
a given distance-to-target and receiver sensitivity, traditional
radar calculations (using the Friis equation) may be performed
to predict the necessary SNR, if a reasonable assumption
may be made regarding target reflectivity. Unfortunately, target
reflectivity can vary wildly from one nonlinear target to
Several references which quantify, in different ways, the
amount of nonlinear power that a target reflects, for the
Schottky-diode/wire-antenna combinations are as follows:
1) a conversion loss, from f 0 to 2 f 0 , between and
40 dB, depending upon incident power [2], [3], [5],
[9], [38], [42];
2) a conversion efficiency, from f 0 to 2 f 0 , of 0.5%–1%,
depending on incident frequency [4], [33];
3) a harmonic RCS of under 10 mm4 /W [26], [30], [57].
Several researchers have studied nonlinear elements coupled
to different types of antennas, such as patches [8], [11], [24],
spirals [37], bowties [23], and circular loops [4]. Others have
noted that the signal received by the target and converted into
nonlinear power also depends upon its orientation (effectively,
the polarization of the target antenna) [4], [22], [37], [58], [59].
References [3], [9], [12], [27], [38], and [40], which discuss
specifications for the target antenna, list gains at f 0 or 2 f 0
between –5 and +6 dBi.
While this information may not be immediately useful for
the present application (because the radar designer will not
usually be able to alter the characteristics of the target), the
conversion-loss and antenna-gain data are summarized here to
give the reader a rudimentary quantified understanding of the
harmonic behavior of passive RF electronic targets.
F. Receive Waveform Filtering and Receiver Sensitivity
As evidenced by the aforementioned high conversion losses
and low antenna gains, nonlinear responses generated from
electronics are notoriously weak. Even at a relatively short
standoff distance of 3 m, a typical response received at 2 f 0
from a handheld radio, for a transmit power of 1 W, is less than
−80 dBm [14]. For this reason, a harmonic receiver requires
a high degree of amplification and a high sensitivity.
Often, the amplification is split across multiple lownoise amplifiers (LNAs) [12], [25], as shown in Fig. 2.
References [6], [22], and [40], which discuss LNA specifications, report a minimum total amplification of 45 dB in the
receive chain.
Because the amplification is very high and the detector
is very sensitive, filtering before each amplifier is necessary
to prevent the transmit signal from coupling further into the
receiver and causing saturation of its detector. For a signal
with an appreciable bandwidth (pulsed, stepped, chirped), the
receive filter is highpass [11], [26], [54]. Often, the filtering
is split across multiple filters [25], [40], as depicted in Fig. 2.
For CW transmission and reception, bandpass filtering is
permissible [2], [30], [31], [37], [42]. Filter specifications
for harmonic receivers have been reported with rejections
at f 0 equal to or greater than 76 dB [6], [12].
With extensive amplification and filtering, sensitivity high
enough to detect and range a nonlinear target may be achieved.
Typical sensitivities for nonlinear receivers have been reported
from −97 down to −106 dBm [3], [11], [25], [38], [40], [54].
References [5] and [31] report a sensitivity of −120 dBm.
To date, the weakest detectable signal for nonlinear radar was
reported to be −130 dBm [6].
G. Best Practices, Hardware, and Miscellaneous
Beyond waveform selection and choices for filters and
amplifiers to build the architecture of Fig. 2, there are very
few references which discuss best practices specifically for
constructing a nonlinear radar prototype (as distinct from
constructing a traditional radar prototype). Many practices are
as important to nonlinear radar as they are to linear radar, such
as the following:
1) physically separating the antennas away from the radar
chassis to avoid disturbing the patterns of each antenna;
2) minimizing trace lengths to reduce radiated emissions;
3) minimizing the area of circuit loops to reduce
susceptibility to external signals.
Some practices that are unique to nonlinear radar are as
1) minimizing the number of up- and down-conversion
stages, as each mixer in the transmit/receive path adds
distortion to the transmit/receive signal;
2) minimizing the number of attenuators used in the transmitter (and receiver) as any component which generates
heat also generates electrothermal distortion [60];
3) minimizing the number of dissimilar metals, connectors,
and ferroelectrics that are used, as metal–metal junctions
and magnetic materials are also common sources of
distortion [30];
4) shielding the transmitter from the receiver to improve
isolation between the two chains [26];
5) enclosing all components in a metal box (except for
the antennas) to further improve isolation between the
transmitter and the receiver [39].
As a high degree of linearity in the nonlinear radar is
critical to separating target responses from self-generated
harmonics/intermodulation, the best practices associated with
designing electronic components for minimal distortion are the
same practices to be followed for designing nonlinear radar.
Since the power carried by the transmitter will usually be
several orders of magnitude higher than the power carried
by the receiver, establishing high linearity is more critical
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to the transmitter than for the receiver. In general, though,
the radar designer should make every effort to avoid using
components/materials in the nonlinear radar which might
generate distortion.
H. Processing of the Received Waveform
For the purpose of generating high-resolution images of
harmonic targets, the authors have adopted the linear steppedfrequency waveform described by (4) resulting in a reflected
waveform described by (5). If the transmitted frequencies
are stepped across an ultrawide bandwidth, it is possible to
construct a nonlinear transfer function HNL [53]
H̃NL( f ) =
Ẽ rec
= |E M |e− j 2π f (2τ ) e j ·φ{E M } /E 0
Ẽ trans
which contains the amplitude and phase of the reflected
response of the nonlinear target due to its nonlinear behavior
modeled by (1), plus a phase shift which scales linearly with
frequency corresponding to the time-of-flight of the radar
signal out from the transmitter and back into the receiver.
If the response of the target (or equivalently the band of the
transmit signal) is limited to a width of B centered at f target ,
and the amplitude and phase of each target is assumed constant
over the received band, the inverse Fourier transform of (10)
sin{B(t − 2τ )} j (2π)( f target)(t −2τ ) j ·φ{E }
M .
h NL (t) =
|E M |e
E 0 π(t − 2τ )
Retaining only the real part of (11) and plotting against
distance d = c · t/2 instead of time, h NL indicates target
response versus range. A peak observed within this waveform
denotes the location of a nonlinear target.
A handful of researchers have either proposed [50], [61]
or implemented [2], [12] an inverse-transform technique such
as (11) to process received harmonic waveforms into radar
range plots. Alternative techniques include the following:
1) performing matched filtering of the received waveform
with a frequency-doubled (tripled, etc.) version of the
transmit waveform [52];
2) mixing the received waveform directly with the transmit
waveform and extracting d from a scaling of the phase
shift within the resultant mixed frequency [15], [31];
3) correlating the received waveform with the PRN code
modulated onto the transmit waveform [3].
By implementing such processing, researchers have not only
detected nonlinear targets; some have even resolved adjacent
nonlinear targets.
Prior to the work performed by the authors of this paper,
several researchers had demonstrated significant achievements
relevant to the authors’ application. Detection of a Schottky
diode using harmonic radar was demonstrated out to a distance
of 750 m by transmitting f 0 = 9.4 GHz at a peak power
of 25 kW [33]. Shorter standoff distances reported in the
literature at the time of this publication are shown in Fig. 4,
Fig. 4. Demonstrated standoff distances (between the radar and the target)
reported in the literature. The bistatic radar is at the center; the location of
the bracketed reference on the chart denotes the reported distance-to-target.
References are grouped logarithmically. The distance R reported by each
reference in the outer ring was between 100 m and 1 km.
drawn between radii spaced logarithmically away from the
bistatic radar. Resolution of multiple nearby targets has also
been demonstrated: 4 m [33], 1.5 m [4], and 1 m [3]. The narrowest resolution reported for nonlinear radar was 50 cm [2].
By pooling the knowledge available in open literature,
adopting many of the techniques used for addressing passive
radar tags, and performing their own investigations into the
behaviors of commercially available RF devices illuminated
by electromagnetic waves, the authors of this paper have
made several of their own advancements toward detecting and
locating handheld electronics using harmonic radar. Among
these advancements are as follows.
1) Validation of the nonlinear radar range equation for
RF electronic targets [62]; this result confirms the
authors’ understanding that targets relevant to the present
application, like Schottky-diode tags, follow (2).
2) Linearization of the harmonic radar transmitter by
adding a phase-shifted version of a harmonic (reflected
from one of the lowpass filters) to the high-power
probe [63]; this result shows that it is possible to reduce
self-generated harmonic distortion (for CW transmit and
receive) to a level that is well below the noise floor of
the receiver.
3) Demonstration of synthetic aperture imaging for targetsof-interest [64]; using the stepped-frequency waveform,
one log-periodic antenna (LPA) for transmit, and one
LPA for receive, a 32-ft-by-32-ft harmonic radar image
was generated by moving the LPA pair along a straight
10-ft track; also, a nonlinear target was clearly discerned
in the presence of a strong linear reflector,
4) Extension of a (traditional linear) range-Doppler technique to a harmonic response to accomplish movingtarget indication (MTI) for a nonlinearity [65]; again
using the stepped-frequency waveform and the same
experimental environment as [64], a nonlinear target
moving at 1 m/s was successfully tracked.
5) Application of the inverse Fourier transform exemplified
by (11) to a multitone stimulus [66]; demonstrated for
N = 20 simultaneous frequencies, this result indicates that it may be possible to perform ranging of
electronic targets by transmitting and receiving a set
of UWB frequencies simultaneously (rather than by
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sweeping through the frequencies in sequence, as in a
stepped-frequency waveform).
The authors are currently re-evaluating intermodulation
radar. By applying a linearization technique intended for
frequency-multiplexed communications [67] to nonlinear
radar, it is theoretically possible to generate a high-power
multi-tone transmission without the complexity introduced
by feedforward cancellation or pre-distortion. Whether the
intermodulation radar or the stepped-frequency architecture
is chosen for further development, the goals of this research
remain: 1) the generation of a high-quality radar image within
which multiple electronic targets are resolved and 2) the
classification, if not identification, of those same targets.
A review of nonlinear radar systems, developed since
1976 and published in open literature, was performed. Most
nonlinear radars are harmonic; thus “harmonic” radar is often
equated to “nonlinear” radar. For the purpose of finding
nonlinear targets amongst linear clutter, the radar requires a
high-power transmitter and a highly sensitive receiver. Many
designers of harmonic radars meet these criteria by lowpass
filtering in the transmitter, isolating the transmit and receive
antennas, and highpass filtering in the receiver. Processing
of the received waveform by an inverse Fourier transform or
by matched-filtering has enabled detection and location of
To date, harmonic radars have achieved detection of nonlinear targets out to 750 m and resolution of targets down
to 50 cm. Recently, the authors of this paper have improved
transmitter linearity for CW stimuli, demonstrated synthetic
aperture imaging and MTI of nonlinear targets using stepped
frequencies, and achieved ranging comparable to CW and
stepped-frequency techniques using multiple simultaneous
tones. Research continues in search of an optimal transmit,
receive, and processing scheme to generate high-resolution
radar images of RF electronic targets, leading to classification
and possible identification of those targets.
The authors would like to thank Dr. K. A. Gallagher for
the contributions that he has made to harmonic radar design,
development, construction, and evaluation as part of his graduate research at Pennsylvania State University and his collaboration with the United States Army Research Laboratory.
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Gregory J. Mazzaro (M’04–SM’15) received the
B.Sc. degree in electrical engineering from Boston
University, Boston, MA, USA, in 2004, the M.Sc.
degree from the State University of New York,
Binghamton, NY, USA, in 2006, and the Ph.D.
degree from North Carolina State University,
Raleigh, NC, USA, in 2009.
From 2009 to 2013, he was with the United States
Army Research Laboratory (ARL), Adelphi, MD,
USA, as an Electronics Engineer. With ARL, he
was also a member of the RF Signal Processing and
Modeling Branch of the Sensors and Electron Devices Directorate. In 2013,
he joined The Citadel, Charleston, SC, USA, as an Assistant Professor of
electrical engineering. At ARL, his primary responsibilities were to design,
prototype, and evaluate RF circuits for linear ultrawideband radar; to design
and conduct experiments to exploit the electronic properties of RF devices
using nonlinear radar; and to measure and catalog the electromagnetic properties of soils and energetic materials, in the laboratory as well as in situ. He
is currently the primary instructor and the course director of Electromagnetic
Fields, Antennas and Propagation, and Interference Control in Electronics at
The Citadel. He has authored more than 70 publications and holds four patents.
His current research interests include studying the unintended behaviors of RF
electronics illuminated by electromagnetic waves and developing experimental
radars for the remote detection and characterization of those electronics.
Dr. Mazzaro has served as a Technical Program Committee member and a
Session Chairman for the annual SPIE Defense and Commercial Sensing Symposium since 2011. He was the recipient of the Research and Development
Achievement Award from the U.S. Army for his ring-resonator technique,
which identifies the dielectric properties of explosive materials and soils
in 2012.
This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.
Anthony F. Martone (S’99–M’07–SM’13) received
the B.S. (summa cum laude) degree from the
Rensselaer Polytechnic Institute, Troy, NY, USA,
and the Ph.D. degree from Purdue University,
West Lafayette, IN, USA.
He joined the U.S. Army Research Laboratory,
Adelphi, MD, USA, as a Researcher with the RF
Signal Processing and Modeling Branch, in 2007.
Currently, he is the Sensors and Electron Devices
Directorate Lead for Cognitive Radar research. He
is overseeing, directing, and collaborating with multiple universities to address spectrum sharing for radar and communication
systems, software defined transceiver control, and adaptive processing techniques. He has authored over 70 publications.
Dr. Martone was the recipient of the Commanders Award for Civilian
Service for his research and development of sensing-through-the-wall signal
processing techniques.
Kenneth I. Ranney (M’04–SM’09) received the
B.S. degree in electrical engineering and computer science from The Johns Hopkins University,
Baltimore, MD, USA, and the M.S. degree in electrical engineering from the University of Maryland
at College Park, College Park, MD, USA.
He is currently a Senior Research Engineer with
the Army Research Laboratory, Adelphi, MD, USA,
focusing on problems related primarily to radar signal processing and automatic target detection. He has
authored or co-authored several journal articles and
holds multiple patents.
Mr. Ranney is currently a Planning Committee member of the
SPIE Defense and Commercial Sensing Symposium and serves as the
Co-Chair of the SPIE Radar Sensor Technology Conference.
Ram M. Narayanan (F’01) received the B.Tech.
degree in electrical engineering from IIT Madras,
Chennai, India, in 1976, and the Ph.D. degree
in electrical engineering from the University of
Massachusetts, Amherst, MA, USA, in 1988.
From 1976 to 1983, he was a Research and
Development Engineer with Bharat Electronics Ltd.,
Ghaziabad, India, where he developed microwave
communications equipment. In 1988, he joined the
Electrical Engineering Department, University of
Nebraska–Lincoln, Lincoln, NE, USA, where he
served as the Blackman and Lederer Professor. Since 2003, he has been
a Professor of electrical engineering with Pennsylvania State University,
State College, PA, USA. He has co-authored 125 journal papers and over
300 conference publications. His current research interests include harmonic
and nonlinear radar, noise radar, medical radar, quantum radar, radar networks,
and compressive sensing.
Dr. Narayanan currently serves as a member of the IEEE Committee on
Ultrawideband Radar Standards Development and an Associate Editor of
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