This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 1 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 systems. I. I NTRODUCTION O 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 following: 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. II. BACKGROUND 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]. 0018-9480 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 2 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 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 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 other. 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. III. N ONLINEAR TARGETS 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. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. MAZZARO et al.: NONLINEAR RADAR FOR FINDING RF ELECTRONICS 3 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) = M m am E inc (t) 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]. (1) m=1 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 (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 section. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 4 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 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 . IV. N ONLINEAR R ADAR S YSTEM D ESIGN 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 }) (3) M=1 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 < T end (4) 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 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. MAZZARO et al.: NONLINEAR RADAR FOR FINDING RF ELECTRONICS 5 from fstart to fend [53] f end − f start t (6) T 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) (7) 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 }] (8) 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 following: 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 (9) f0 = λ 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 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 6 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES TABLE I TABLE II T RANSMIT F REQUENCIES FOR P UBLISHED H ARMONIC R ADARS T RANSMIT P OWERS FOR P UBLISHED H ARMONIC R ADARS 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. TABLE III T RANSMIT A NTENNA G AINS FOR P UBLISHED H ARMONIC R ADARS 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. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. MAZZARO et al.: NONLINEAR RADAR FOR FINDING RF ELECTRONICS TABLE IV R ECEIVE A NTENNA G AINS FOR P UBLISHED H ARMONIC R ADARS 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 another. 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. 7 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 follows: 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 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 8 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES 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 (10) 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) becomes sin{B(t − 2τ )} j (2π)( f target)(t −2τ ) j ·φ{E } M . e h NL (t) = |E M |e E 0 π(t − 2τ ) (11) 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. V. R ECENT N ONLINEAR R ADAR A DVANCEMENTS 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 This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. MAZZARO et al.: NONLINEAR RADAR FOR FINDING RF ELECTRONICS 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. VI. C ONCLUSION 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 targets-of-interest. 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. ACKNOWLEDGMENT 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. R EFERENCES [1] R. O. Harger, “Harmonic radar systems for near-ground in-foliage nonlinear scatterers,” IEEE Trans. Aerosp. Electron. Syst., vol. 12, no. 2, pp. 230–245, Mar. 1976. [2] H. M. Aumann and N. W. Emanetoglu, “A wideband harmonic radar for tracking small wood frogs,” in Proc. IEEE Radar Conf., May 2014, pp. 108–111. [3] P.-H. Jau et al., “Signal processing for harmonic pulse radar based on spread spectrum technology,” IET Radar, Sonar Navigat., vol. 8, no. 3, pp. 242–250, Mar. 2014. [4] D. Milanesio, M. Saccani, R. Maggiora, D. Laurino, and M. Porporato, “Design of an harmonic radar for the tracking of the Asian yellow-legged hornet,” Ecol. Evol., vol. 6, no. 7, pp. 1–9, Mar. 2016. [5] Z. M. Tsai et al., “A high-range-accuracy and high-sensitivity harmonic radar using pulse pseudorandom code for bee searching,” IEEE Trans. Microw. Theory Techn., vol. 61, no. 1, pp. 666–675, Jan. 2013. 9 [6] H. Aniktar, D. Baran, E. Karav, E. Akkaya, Y. S. Birecik, and M. Sezgin, “Getting the bugs out: A portable harmonic radar system for electronic countersurveillance applications,” IEEE Microw. Mag., vol. 16, no. 10, pp. 40–52, Nov. 2015. [7] K.-S. Min and J.-W. Kim, “Circularly polarized triple band patch antenna for non-linear junction detector,” in Proc. IEEE Int. Symp. Antennas Propag., Jul. 2012, pp. 1–2. [8] T. Aballo, L. Cabria, J. A. Garcia, T. Fernaindez, and F. Marante, “Taking advantage of a Schottky junction nonlinear characteristic for radiofrequency temperature sensing,” in Proc. Eur. Microw. Conf., Sep. 2006, pp. 318–321. [9] B. Kubina, J. Romeu, C. Mandel, M. Schüßler, and R. Jakoby, “Design of a quasi-chipless harmonic radar sensor for ambient temperature sensing,” in Proc. IEEE SENSORS, Nov. 2014, pp. 1567–1570. [10] V. Viikari et al., “Technical solutions for automotive intermodulation radar for detecting vulnerable road users,” in Proc. IEEE Veh. Technol. Conf., Apr. 2009, pp. 1–5. [11] M. Hirsch, B. Crowgey, G. Charvat, E. Rothwell, and L. Kempel, “Recent developments in miniaturized planar harmonic radar antennas,” in Proc. Antennas Meas. Techn. Assoc. Conf., Nov. 2008, pp. 1–6. [12] A. Singh and V. Lubecke, “Respiratory monitoring and clutter rejection using a CW Doppler radar with passive RF tags,” IEEE Sensors, vol. 12, no. 3, pp. 558–565, Mar. 2012. [13] L. Chioukh, H. Boutayeb, D. Deslandes, and K. Wu, “Noise and sensitivity of harmonic radar architecture for remote sensing and detection of vital signs,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 9, pp. 1847–1855, Sep. 2014. [14] G. J. Mazzaro, A. F. Martone, and D. M. McNamara, “Detection of RF electronics by multitone harmonic radar,” IEEE Trans. Aerosp. Electron. Syst., vol. 50, no. 1, pp. 477–490, Jan. 2014. [15] D. Dardari, “Detection and accurate localization of harmonic chipless tags,” EURASIP J. Adv. Signal Process., vol. 77, pp. 1–13, Aug. 2015. [16] C. Fazi, F. Crowne, and M. Ressler, “Link budget calculations for nonlinear scattering,” in Proc. 6th Eur. Conf. Antennas Propag. (EUCAP), Mar. 2012, pp. 1146–1150. [17] M. Ivanou and V. Chertkov, “Nonlinear junction locator with the possibility of identifying nonlinear objects,” in Proc. 6th Mater. Junior Res. Conf., Apr. 2014, pp. 134–137. [18] V. Polacek and R. Pavlik, “The use of digital modulation signals in radar system for detection of nonlinear scatterers,” in Proc. Int. Radar Symp., Sep. 2011, pp. 743–747. [19] P. V. Nikitin and K. V. S. Rao, “Harmonic scattering from passive UHF RFID tags,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., Jun. 2009, pp. 1–4, [20] L. Rong and W. Hai-Yong, “The re-radiation characteristics of nonlinear target in harmonic radar detection,” in Proc. China–Jpn. Joint Microw. Conf., Sep. 2008, pp. 661–664. [21] J. C. Pedro and N. B. Carvalho, Intermodulation Distortion in Microwave and Wireless Circuits. Norwood, MA, USA: Artech House, 2003. [22] F. Meloche and P. M. Albert, “A lighter transponder for harmonic radar,” in Proc. Eur. Radar Conf., Sep. 2006, pp. 233–236. [23] J. Kiriazi, J. Nakakura, K. Hall, N. Hafner, and V. Lubecke, “Low profile harmonic radar transponder for tracking small endangered species,” in Proc. Int. Conf. IEEE Eng. Med. Biol. Soc., Aug. 2007, pp. 2338–2341. [24] N. Tahir and G. Brooker, “Recent developments and recommendations for improving harmonic radar tracking systems,” in Proc. 5th Eur. Conf. Antennas Propag. (EUCAP), Apr. 2011, pp. 1531–1535. [25] G. L. Charvat, E. J. Rothwell, and L. C. Kempel, “Harmonic radar tag measurement and characterization,” in Proc. Antennas Propag. Soc. Int. Symp., vol. 2. Jun. 2003, pp. 696–699. [26] B. G. Colpitts and G. Boiteau, “Harmonic radar transceiver design: Miniature tags for insect tracking,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 2825–2832, Nov. 2004. [27] K. Rasilainen, J. Ilvonen, A. Lehtovuori, J.-M. Hannula, and V. Viikari, “Harmonic transponders: Performance and challenges,” Prog. Electromagn. Res. M, vol. 41, pp. 139–147, Mar. 2015. [28] H. Aumann, E. Kus, B. Cline, and N. W. Emanetoglu, “A lowcost harmonic radar for tracking very small tagged amphibians,” in Proc. IEEE Int. Instrum. Meas. Technol. Conf. (I2MTC), May 2013, pp. 234–237. [29] R. D. Brazee, E. S. Miller, M. E. Reding, M. G. Klein, B. Nudd, and H. Zhu, “A transponder for harmonic radar tracking of the black vine weevil in behavioral research,” Trans. Amer. Soc. Agricult. Eng., vol. 48, no. 2, pp. 831–838, 2005. [30] M. A. Flemming, F. H. Mullins, and A. Watson, “Harmonic radar detection systems,” in Proc. Int. IEE Radar Conf., Oct. 1977, pp. 552–555. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 10 [31] S. Gruszczynski and K. Wincza, “Analog coherent detection in application to high-sensitivity nonlinear junction detectors,” in Proc. AFRICON, Sep. 2011, pp. 1–5. [32] K. Wincza, S. Gruszczynski, and J. Borgosz, “Dual-band capacitive feed antenna for nonlinear junction detection device,” in Proc. Conf. Microw. Techn., Apr. 2008, pp. 1–4. [33] J. R. Riley and A. D. Smith, “Design considerations for an harmonic radar to investigate the flight of insects at low altitude,” Comput. Electron. Agricult., vol. 35, nos. 2–3, pp. 151–169, Aug. 2002. [34] O. M. Bucci, A. De Bonitatibus, and I. Pinto, “Harmonic radar crosssection of bistatic nonlinear responder,” Alta Freq., vol. 53, no. 3, pp. 172–176, 1984. [35] J. A. Kosinski, W. D. Palmer, and M. B. Steer, “Unified understanding of RF remote probing,” IEEE Sensors, vol. 11, no. 12, pp. 3055–3063, Dec. 2011. [36] E. J. Powers, J. Y. Hong, and Y. C. Kim, “Cross sections and radar equation for nonlinear scatterers,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-17, no. 4, pp. 602–605, Jul. 1981. [37] F. Alimenti and L. Roselli, “Theory of zero-power RFID sensors based on harmonic generation and orthogonally polarized antennas,” Prog. Electromagn. Res., vol. 134, pp. 337–357, Jan. 2013. [38] B. G. Colpitts, D. M. Luke, and G. Boiteau, “Harmonic radar for insect flight pattern tracking,” in Proc. Can. Conf. Elect. Comput. Eng., May 2000, pp. 302–306. [39] H.-Y. Hsu et al., “Harmonic radar using multiple receivers and angle of arrival positioning technique for environment with obstacles,” in Proc. Eur. Microw. Conf., Sep. 2015, pp. 975–978. [40] D. Psychoudakis, W. Moulder, C.-C. Chen, H. Zhu, and J. L. Volakis, “A portable low-power harmonic radar system and conformal tag for insect tracking,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 444–447, 2008. [41] J.-W. Kim, K.-S. Min, I.-H. Kim, and C.-J. Park, “Triple band spiral antenna for non-linear junction detector,” in Proc. Int. Symp. Antennas Propag., 2012, pp. 802–805. [42] S. A. Novikov and D. V. Zelentsov, “Radar study of nonlinear scattering in L-band microwave range by semiconductor objects,” in Proc. Int. Symp. Appl. Convers. Res. Results Int. Cooper., May 1999, pp. 403–405. [43] U. Olgun, D. Psychoudakis, C.-C. Chen, and J. L. Volakis, “High gain lightweight array for harmonic portable RFID radar,” in Proc. IEEE Antennas Propag. Soc. Int. Symp., Jun. 2009, pp. 1–4. [44] G. J. Mazzaro, S. F. McGowan, K. A. Gallagher, K. D. Sherbondy, A. F. Martone, and R. M. Narayanan, “Phase responses of harmonics reflected from radio-frequency electronics,” Proc. SPIE, vol. 9829, Apr. 2016, Art. no. 98290O. [45] D. Mascanzoni and H. Wallin, “The harmonic radar: A new method of tracing insects in the field,” Ecol. Entomol., vol. 11, no. 4, pp. 387–390, 1986. [46] I. Hertl, M. Strycek, V. Polacek, and V. Brno, “Monopulse direction finder for harmonic radar system,” in Proc. Int. Conf. Microw. Radar Wireless Commun., Jun. 2010, pp. 1–3. [47] G. J. Mazzaro, A. F. Martone, K. A. Gallagher, R. M. Narayayan, and K. D. Sherbondy, “Maximizing harmonic-radar target response: Duty cycle vs. peak power,” in Proc. IEEE SoutheastCon, Apr. 2016, pp. 1–4. [48] G. J. Mazzaro, K. A. Gallagher, A. F. Martone, and R. M. Rarayanan, “Stepped-frequency nonlinear radar simulation,” Proc. SPIE, vol. 9077, May 2014, Art.no. 90770U. [49] D. Liao, “Generalized wideband harmonic imaging of nonlinearly loaded scatterers,” IEEE Trans. Antennas Propag., vol. 63, no. 5, pp. 2079–2087, May 2015. [50] T. Berger and S. E. Hamran, “Harmonic synthetic aperture radar processing,” IEEE Geosci. Remote Sens. Lett., vol. 12, no. 10, pp. 2066–2069, Jul. 2015. [51] V. V. Belyaev, A. T. Mayunov, and S. N. Razin’kov, “Object detection range enhancement by means of nonlinear radar employing two signals with linear frequency modulation,” Meas. Techn., vol. 46, no. 8, pp. 802–805, Aug. 2003. [52] V. B. Avdeev, E. V. Kravtsov, and S. N. Panychev, “Characteristic features of schemes for optimal processing of LFM signals in nonlinear radiolocation,” Telecomm. Radio Eng., vol. 72, no. 1, pp. 81–89, 2013. [53] G. J. Mazzaro, K. A. Gallagher, A. F. Martone, K. D. Sherbondy, and R. M. Narayanan, “Short-range harmonic radar: Chirp waveform, electronic targets,” Proc. SPIE, vol. 9461, Apr. 2015, Art. no. 946108. [54] M. L. Hsu et al., “Bee searching radar with high transmit–receive isolation using pulse pseudorandom code,” IEEE Trans. Microw. Theory Techn., vol. 64, no. 12, pp. 4324–4335, Dec. 2016. IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES [55] X. Gao, A. Singh, O. Boric-Lubecke, and V. M. Lubecke, “Small-scale displacement measurement with passive harmonic RF tag using Doppler radar,” in Proc. IEEE Int. Wireless Symp., Apr. 2013, pp. 1–4. [56] K. A. Gallagher, G. J. Mazzaro, A. F. Martone, K. D. Sherbondy, and R. M. Narayanan, “Filter selection for a harmonic radar,” Proc. SPIE, vol. 9461, Apr. 2015, Art. no. 94610A. [57] V. V. Belyaev, A. T. Mayunov, and S. N. Razin’kov, “Improving the accuracy of experimental prediciton of the detectability of nonlinear objects by radar,” Meas. Techn., vol. 42, no. 11, pp. 1068–1074, Nov. 1999. [58] D. Liao, “Scattering and imaging of nonlinearly loaded antenna structures in half-space environments,” IEEE Trans. Antennas Propag., vol. 62, no. 8, pp. 4230–4240, Aug. 2014. [59] K. Hong, S. Braidwood, A. Halappa, T. Kilpatrick, B. Keane, and D. Longstaff, “Influence of field polarity on harmonic radar detection of concealed electronics,” in Proc. Int. Conf. Electromag. Adv. Appl., Sep. 2016, pp. 560–563. [60] J. R. Wilkerson, K. G. Gard, A. G. Schuchinsky, and M. B. Steer, “Electro-thermal theory of intermodulation distortion in lossy microwave components,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 12, pp. 2717–2725, Dec. 2008. [61] K. I. Ranney, K. A. Gallagher, K. D. Sherbondy, A. F. Martone, G. J. Mazzaro, and R. M. Narayanan, “Instantaneous, stepped-frequency, nonlinear radar,” Proc. SPIE, vol. 9461, p. 946109, Apr. 2015. [62] K. A. Gallagher, G. J. Mazzaro, A. F. Martone, K. D. Sherbondy, and R. M. Narayanan, “Derivation and validation of the nonlinear radar range equation,” Proc. SPIE, vol. 9829, Apr. 2016, Art. no. 98290P. [63] K. A. Gallagher, R. M. Narayanan, G. J. Mazzaro, and K. D. Sherbondy, “Linearization of a harmonic radar transmitter by feed-forward filter reflection,” in Proc. IEEE Radar Conf., May 2014, pp. 1363–1368. [64] K. A. Gallagher, G. J. Mazzaro, K. I. Ranney, L. H. Nguyen, K. D. Sherbondy, and R. M. Narayanan, “Nonlinear synthetic aperture radar imaging using a harmonic radar,” Proc. SPIE, vol. 9461, Apr. 2015, Art. no. 946109. [65] K. A. Gallagher, R. M. Narayanan, G. J. Mazzaro, K. I. Ranney, A. Martone, and K. D. Sherbondy, “Moving target indication with nonlinear radar,” in Proc. IEEE Radar Conf., May 2015, pp. 1428–1433. [66] K. I. Ranney, G. J. Mazzaro, K. A. Gallagher, A. F. Martone, K. D. Sherbondy, and R. M. Narayanan, “Instantaneous, steppedfrequency, non-linear radar part 2: Experimental confirmation,” Proc. SPIE, vol. 9829, Apr. 2016, Art. no. 98291P. [67] G. J. Mazzaro, K. G. Gard, and M. B. Steer, “Linear amplification by time-multiplexed spectrum,” IET Circuits Devices Syst., vol. 4, no. 5, pp. 392–402, Sep. 2010. 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. MAZZARO et al.: NONLINEAR RADAR FOR FINDING RF ELECTRONICS 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. 11 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 Radar and the IEEE T RANSACTIONS ON A EROSPACE AND E LECTRONIC S YSTEMS .