Abstract:
A radar assembly for linear and nonlinear radar transmission and reception comprising a signal generator; at least one filter operatively connected to the signal generator; a transmitter operatively connected to the at least one filter for transmitting radar signals; a receiver operative to receiving received signals comprising linear and nonlinear responses from the reflected transmitted signals; the receiver comprising a first channel for processing the linear response of the received signal; a second channel for the processing the nonlinear response of the received signal; at least one switch operative to select one of the first or second channels; at least one high pass filter operatively connected to the second channel to attenuate the linear response; at least one amplifier to amplify the nonlinear response; and at least one display operatively connected to both the first and second channels for displaying both linear and nonlinear responses.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The invention described herein may be manufactured, used, and licensed by or for the United States Government without the payment of royalties. 
    
    
     REFERENCE TO COMPUTER PROGRAM LISTING APPENDIX 
     A computer program listing appendix has been submitted via EFS-Web labeled as “codeappendix” containing Appendices A through K. The material contained in the Appendices A through K is incorporated by reference herein as though rewritten fully herein. 
     BACKGROUND OF THE INVENTION 
     In the current state of operations, occasions arise such that threats (or targets) must be detected at a standoff distance. Some threats contain components whose permittivity contrasts substantially with that of the emplacement; such is the case with many threats that are buried. The reception of a subsurface linear radar response from an area whose surface is otherwise undisturbed indicates the presence of a threat. Others threats contain metal contacts and semiconductor junctions whose nonlinear electromagnetic response contrasts with that of the emplacement; such is the case with radio frequency (RF) electronics. The reception of a nonlinear radar response from an area that does not otherwise contain electronics indicates the presence of another class of threat. Often, threats contain dielectric, as well as electronic components, hence they will respond to both linear and nonlinear excitation and either linear or nonlinear radar with detect such as threat. Hence, there exists a need to detect both types of threats, whether or not they are collocated using a single assembly or unit. 
     SUMMARY OF THE INVENTION 
     A preferred embodiment comprises a combined radar assembly with linear and nonlinear modes. Either mode (linear/nonlinear) may detect a threat or target. By switching between two radar modes, additional information about the threat is received, and, thus, the probability that it is detected is improved. 
     A preferred embodiment radar assembly for linear and nonlinear radar transmission and reception comprises at least one signal generator; at least one filter operatively connected to the signal generator; a transmitter operatively connected to the at least one filter for transmitting radar signals, and a receiver operative to receive signals comprising the linear and nonlinear responses from the reflected transmitted signals. The receiver further comprises a first channel for processing the linear response from the received signal; a second channel for the processing the nonlinear response from the received signal; and at least one switch operative to select one of the first or second channels through at least one switch. At least one high pass filter is operatively connected to the second channel to attenuate the linear response and at least one first amplifier is operatively connected to the at least one high pass filter to amplify the nonlinear response. The receiver further comprises at least one analog-to-digital converter for converting the analog received signal to a digitized data stream, and at least one display operatively connected to both the first and second channels for displaying both the linear and nonlinear responses. 
     Optionally, the assembly may comprise two signal generators connected to a signal combiner. Optionally, the signal generated by the at least one signal generator is a single-tone pulse, a modulated chirp pulse having a carrier frequency that begins at a first frequency and increases linearly over a predetermined time interval, or a stepped-frequency chirp pulse. 
     An alternate preferred embodiment radar assembly for linear and nonlinear radar transmission and reception comprises a signal generator, at least one first filter operatively connected to the signal generator, at least one first amplifier operatively connected to the at least one filter, a transmitter operatively connected to the at least one filter for transmitting radar signals, and a receiver operative to receiving the received signals comprising the linear and nonlinear responses from the reflected transmitted signals. The receiver comprises a first channel for processing the linear response from the received signal, a second channel for the processing the nonlinear response from the received signal, at least one switch operative to select one of the first or second channels through at least one switch, at least one high pass filter operatively connected to the second channel to attenuate the linear response, at least one second amplifier to amplify the nonlinear response; and at least one display operatively connected to both the first and second channels for displaying both the linear and nonlinear responses. 
     Optionally, the at least one first filter, the at least one first amplifier and the at least one transmitter may operate to process both linear and nonlinear radar signals. The signal generator may generate both linear and nonlinear radar waveforms. The single generator may generate a single-tone pulse, a linear frequency-modulated chirp pulse, or a stepped-frequency chirp pulse. 
     An alternate preferred embodiment radar assembly for linear and nonlinear radar transmission and reception comprises a base; a transmitter for transmitting linear and nonlinear radar signals operatively associated with the base; a receiver operative to receive signals comprising linear and nonlinear responses from the reflected transmitted signals, the receiver being operatively associated with the base; the transmitter operating to transmit linear radar signals in a first mode and nonlinear radar signals in a second mode, and the receiver operating to receive linear responses from the reflected transmitted signals in the first mode and nonlinear responses from the from the reflected transmitted signals in the second mode; at least one antenna operatively associated with the receiver and the transmitter; and at least one switch operatively associated with the receiver for selecting between the first and second modes. 
     Optionally the receiver and transmitter may be mounted on the base. Optionally, the transmitter may comprise a linear radar transmitter portion and a nonlinear radar transmitter portion and the at least one antenna may be alternately connected to the linear and nonlinear radar transmitter portions by the at least one switch. Optionally, the receiver may comprise a linear radar receiver portion and a nonlinear radar receiver portion and the at least one antenna is alternately connected to the linear and nonlinear radar receiver portions by the at least one switch. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other objects, features, and advantages of the invention will be apparent from the following more detailed description of the preferred embodiments of the invention, as illustrated in the accompanying drawings, wherein: 
         FIG. 1  is a diagrammatic illustration of a target illuminated by a radar wave showing diagrammatically the incident and reflected radar waves for propagation normal to target. 
         FIG. 2A  is an illustration of a single-cycle impulse linear radar waveform and its spectrum. 
         FIG. 2B  is an illustration of a stepped-frequency waveform, which is an alternative linear waveform design that allows for more flexibility in the transmitted band. 
         FIG. 3A  is an illustration of an example of a single-tone nonlinear radar waveform showing the transmission of one tone and reception of harmonics of that tone. 
         FIG. 3B  is an illustration of an example of a two-tone nonlinear radar waveform showing the transmission of two-tones and reception of harmonics well as mixing products near those harmonics 
         FIG. 4  is a schematic illustration of a preferred embodiment combined linear and nonlinear radar architecture. 
         FIG. 5A  is a schematic illustration of a nonlinear buried target scene containing a target and two (linear) clutter objects. 
         FIG. 5B  is an illustration of an image of the target of  FIG. 5A  generated using harmonic multi-static received signal matrices at f 0 =840 MHz. 
         FIG. 5C  is an illustration of an image of the target of  FIG. 5A  generated using harmonic multi-static received signal matrices 2f 0 =1680 MHz. 
         FIG. 6  is a depiction of combined radar for the detection of threats containing both linear (depicted by a picture of the Synchronous Impulse Reconstruction (SIRE) radar) and also depicting nonlinear components. 
         FIGS. 7-10  illustrate four waveforms selected for the preferred embodiment linear/nonlinear transmitter: the single-tone pulse, the multi-tone pulse, the linear frequency-modulated (FM) chirp, and the stepped-frequency chirp. 
         FIG. 7  is an illustration of a Single-tone RF pulse output by an arbitrary waveform generator wherein f pulse =900 MHz, P env =0 dBm, T env =1 μs, Dc=10%. 
         FIG. 8  is an illustration of a Multitone RF pulse output by an arbitrary waveform generator wherein N=2 tones, fc=890 MHz, Ptone=−6 dBm per tone, Tenv=2 μs, Dc=20%. 
         FIG. 9  is an illustration of a Linear FM chirp pulse output by an arbitrary waveform generator wherein f start =860 MHz,f end =900 MHz, P env =−3 dBm, T env =4 μs, D c =50%. 
         FIG. 10  is an illustration of a Stepped-frequency pulse output by an arbitrary waveform generator wherein f start =870 MHz,f end =890 MHz, Δf=1 MHz, P env =0 dBm, T env =2.5 μs, D c =25%. 
         FIG. 11  is an illustration of an alternate preferred embodiment combined radar architecture where transmission from the radar and reception from the target is hardware simulated 
         FIG. 12  is an illustration showing electromagnetic properties of the transmitter amplifier and low-pass filters. 
         FIG. 13  is an illustration showing electromagnetic properties of the directional coupler and linear/nonlinear receiver chain. 
         FIG. 14  is an illustration of a graphical user interface to the alternate preferred embodiment radar system. 
         FIG. 15A  illustrates a plot of the raw Tx and Rx data from the preferred embodiment of  FIG. 11  showing the result of linear data capture and processing when reflecting a chirp from a simulated radar target, in this case an open circuit.  FIG. 15A  illustrates a plot of radar data, chirp Tx waveform, linear Rx mode, open-circuit target: fstart=880 MHz, fend=920 MHz, Penv=0 dBm, T env =1 μs (time interval during which the frequency steps from f start  to f end ), Dc=10% (the duty cycle of the waveform). 
         FIG. 15B  illustrates a plot of the correlation of Tx and Rx waveform data shown in  FIG. 15A . 
         FIG. 16A  illustrates the result of the cross-correlation when reflecting a chirp with a wider bandwidth than that of Linear Rx, Chirp Waveform from an open circuit (raw data, complete time scale).  FIG. 16A  illustrates a plot of radar data, RF pulse Tx waveform, linear Rx mode, FRS radio target: fpulse=900 MHz, Penv=0 dBm, Tenv=1 μs (time interval during which the frequency steps from f start  to f end ), Dc=10% (the duty cycle of the waveform). 
         FIG. 16B  illustrates the correlation when receiving the same waveform in the absence of a radar target; minimal reflection is hardware-simulated with a matched (50-Ω) load (raw data, zoomed-in time scale). 
         FIG. 17  illustrates the result of the nonlinear data capture (Radar data, RF pulse Tx waveform, linear Rx mode, FRS radio target: f pulse =900 MHz, P env =0 dBm, T env =1 μs, D c =10%) when reflecting an RF pulse from a hardware-simulated nonlinear target: a Motorola T4500 whose antenna has been replaced by an SMA end-launch connector. A 13-dB attenuator is placed between the end of the coaxial line and the FRS radio. The left side of  FIG. 17  plots the raw Tx and Rx data along a 5-μs time scale. The right side plots the same raw data along a 2-ns time scale between t=500 ns and t=502 ns. 
         FIG. 18  illustrates plots for a stepped-frequency waveform and the FRS radio target.  FIG. 18  illustrates a plot of Tx and Rx frequency content, stepped-frequency Tx waveform, nonlinear Rx mode, FRS radio target: fstart=890 MHz, fend=910 MHz, Δf=1 MHz, Penv=0 dBm, Tenv=2 μs, Dc=20%. 
         FIG. 19  illustrates a plot that shows the result of the nonlinear data capture and processing when reflecting a chirp from the FRS radio.  FIG. 19  (left) plots the raw Tx and Rx data.  FIG. 19  (right) plots the cross correlation of the Tx and Rx signal.  FIG. 19  illustrates a plot of radar data, linear chirp Tx waveform, nonlinear Rx mode, FRS radio target: fstart=880 MHz, fend=920 MHz, Penv=0 dBm, Tenv=1 μs, Dc=10%. 
         FIG. 20  illustrates results using a chirp Tx waveform using nonlinear Rx chain against a purely linear target in order to demonstrate that the transceiver does not indicate detection if the target is linear and the radar is listening for a nonlinear response.  FIG. 20  illustrates a plot of radar data, chirp Tx waveform, nonlinear Rx mode: fstart=890 MHz, fend=910 MHz, Penv=0 dBm, Tenv=1 is (time interval during which the frequency steps from f start  to f end ), Dc=10% (the duty cycle of the waveform). The left side of  FIG. 20  illustrates results from a FRS radio target and the right side is the result from an open circuit (a linear but highly reflective target). 
     
    
    
     A more complete appreciation of the invention will be readily obtained by reference to the following Description of the Preferred Embodiments and the accompanying drawings in which like numerals in different figures represent the same structures or elements. The representations in each of the figures are diagrammatic and no attempt is made to indicate actual scales or precise ratios. 
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The embodiments of the invention and the various features and advantageous details thereof are explained more fully with reference to the non-limiting embodiments that are illustrated in the accompanying drawings and detailed in the following description. It should be noted that the features illustrated in the drawings are not necessarily drawn to scale. Descriptions of well-known components and processing techniques are omitted so as to not unnecessarily obscure the embodiments of the invention. The examples used herein are intended merely to facilitate an understanding of ways in which the embodiments of the invention may be practiced and to further enable those of skill in the art to practice the embodiments of the invention. Accordingly, the examples should not be construed as limiting the scope of the embodiments of the invention. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, the dimensions of objects and regions may be exaggerated for clarity. Like numbers refer to like elements throughout. As used herein the term “and/or” includes any and all combinations of one or more of the associated listed items. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the full scope of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     It will be understood that when an element such as an object, layer, region or substrate is referred to as being “on” or extending “onto” another element, it can be directly on or extend directly onto the other element or intervening elements may also be present. In contrast, when an element is referred to as being “directly on” or extending “directly onto” another element, there are no intervening elements present. It will also be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present. 
     It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, channels and/or sections, these elements, channels and/or sections should not be limited by these terms. For example, when referring first and channels or sections, these terms are only used to distinguish one element, channel section from another region, layer or section. Thus, a first element, channel or section discussed below could be termed a second element, channel or section without departing from the teachings of the present invention. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     It will also be appreciated by those of skill in the art that references to a structure or feature that is disposed “adjacent” another feature may have portions that overlap or underlie the adjacent feature. 
     A preferred embodiment of the present invention comprises a combination of linear and nonlinear radar that detects a set of targets greater than either radar can detect alone. 
     Linear and Nonlinear Radar Comparision 
     Linear radar is well-suited to the detection of a target whose complex permittivity {circumflex over (∈)} contrasts greatly with that of its surroundings:
 
{circumflex over (∈)}=∈′− j·∈″   (1)
 
where ∈′ is the “real” part and ∈″ is the “imaginary” part of the permittivity. The permittivity of a material relative to that of free space is its dielectric constant {circumflex over (∈)} r :
 
     
       
         
           
             
               
                 
                   
                     
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       FIG. 1  is a diagrammatic illustration of a target illuminated by a radar wave showing diagrammatically the incident and reflected radar waves for propagation normal to target. The electric field of the incident wave E in  is represented by a single-tone sinusoid of frequency f 0  and amplitude E 0 :
 
 E   in ( t )= E   0  cos(2π· f   0   ·t ).  (4)
 
     Assuming normal incidence (i.e. the direction of propagation of the wave is normal to the boundary of the target), the reflected wave is: 
     
       
         
           
             
               
                 
                   
                     
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     The frequency of the reflected wave is the same as that of the incident wave, but its amplitude is scaled by the reflection coefficient Γ. For ∈ r =1, Γ=0; the target is transparent to the radar wave traveling in air and there is no reflection. 
     As the contrast in ∈ r  between a target and that of the medium through which the radar wave is propagating increases, the strength of the radar reflection from that target increases. The value of ∈″ r  for a typical conductor (e.g. aluminum) is greater than 10 7  S/m. Thus, conductive targets are very detectable, even if they are buried or obscured by insulators. For insulators, ∈″ r  is near zero but ∈′ r  can take on a wide range of values, from ∈′ r ≈1 for dry foam up to ∈′ r =80 for distilled water. Thus, insulating targets are not as detectable, as their radar reflections depend much more strongly on ∈ r ′. 
     Nonlinear radar exploits a completely different phenomenon: it relies on the nonlinear electromagnetic properties of a target to convert a portion of the incident radar wave into a reflected wave at a different frequency. Most materials found in nature are electromagnetically linear (with the exception of ferromagnetics), while many man-made materials are electromagnetically nonlinear. Semiconductor devices, such as radios and cell phones, are highly nonlinear. 
     A simple model for radio-frequency (RF) electromagnetic nonlinearity is the memoryless power series given by: 
                       E   refl     ⁡     (   t   )       =           a   1     ⁢       E   in     ⁡     (   t   )         +       a   2     ⁢       E   in   2     ⁡     (   t   )         +       a   3     ⁢       E   in   3     ⁡     (   t   )         +   …     =       ∑     n   =   1     N     ⁢           ⁢       a   n     ⁢       E   in   n     ⁡     (   t   )                     (   7   )               
where a n  are complex power-series coefficients, and E refl  is the electric field reflected by the target. The value of a 1  is the linear response of the target, Γ; the values {a 2 , a 3 , . . . } depend upon the nonlinear properties of the target. If a nonlinear target is illuminated by the radar wave given by equation (4), the reflected wave is
 
                       E   refl     ⁡     (   t   )       =       ∑     M   =   1     ∞     ⁢           ⁢            E   M          ⁢     cos   ⁡     (       2   ⁢           ⁢     π   ·   M   ·     f   0     ·   t       +     ϕ   ⁢     {     E   M     }         )                   (   8   )                 E   M     =       ∑     k   =   1     ∞     ⁢           ⁢       (             2   ⁢           ⁢   k     +   M   -   2               k   -   1           )     ⁢       a       2   ⁢           ⁢   k     +   M   -   2         2       2   ⁢           ⁢   k     +   M   -   3         ⁢     E   0       2   ⁢           ⁢   k     +   M   -   2                   (   9   )               
which is a sum of sinusoids at harmonics M of f 0 , each with amplitude |E M | and phase φ{E M }. If the radar measures E M =0 for all M&gt;1, then no nonlinear target is detected. If the radar measures E M  for some M&gt;1, however, a nonlinear target is detected.
 
     A preferred embodiment combined radar detects targets using linear as well as nonlinear reflective responses. The linear radar detects targets whose permittivity contrasts with that of the background, while the nonlinear radar detects targets whose electromagnetic properties produce a change in frequency between the incident and reflected waves. 
     Implementation 
     Linear radar can be implemented in different ways, commonly designated by the transmit waveform, such as continuous-wave (CW), pulsed single-tone, or chirp. To achieve an ultra-wide bandwidth for ground penetration as well as imaging resolution, the Army Research Laboratory (ARL) designed the Synchronous Impulse Reconstruction (SIRE) radar as described in F. Koenig, M. Ressler, G. Smith, L. Nguyen, and R. Harris, “Synchronous Impulse Reconstruction (SIRE) radar sensor,” U.S. Army Research Laboratory, Adelphi, Md., Technical Report ARL-TR-4661, November 2008, herein incorporated by reference. The SIRE radar uses a single-cycle impulse waveform, two transmit antennas, 16 receive antennas, and multiple data traces collected while the radar platform is in motion in order to form high-resolution images of surface and shallow-buried targets.  FIGS. 2A and 2B  are linear radar waveforms for impulse and stepped frequency, respectively. A single-cycle impulse and its spectrum are illustrated in  FIG. 2A . An alternative design that allows for more flexibility in the transmitted band is the stepped-frequency waveform illustrated in  FIG. 2B . Both impulse and stepped-frequency waveforms are broadband. For the impulse, the peak power is high but the average power is low. For the continuous stepped-frequency signal, the peak power and the average power are the same. Either waveform will provide linear detection and ranging. 
     One advantage of a stepped-frequency design, however, is that its underlying switched-frequency signal source is likely able to dwell on a single frequency for a long period of time. As dwell time increases while transmitting the same average power in a tone or a series of tones, the side lobes caused by interrupting the transmission (e.g. turning the source off or switching to another tone) diminish. This extended dwell time is necessary in order to minimize reflected linear side-lobes from nonlinear reflections, which are usually very weak. 
     Nonlinear radar can also be implemented in different ways. One popular technique is to transmit a single frequency f 0  and receive the target response at the second harmonic of the transmitted tone, 2f 0 , as described in U.S. patent application Ser. No. 13/870,519 to Dr. Gregory J. Mazzaro, et al. entitled “Multizone Harmonic Radar and Method of Use,” herein incorporated by reference. A slight variation of this technique tracks a Doppler shift at 2f 0  for moving targets. See for example, 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, March 2012, herein incorporated by reference. Other variations chirp (see for example, C. Stagner, A. Conrad, C. Osterwise, D. G. Beetner, and S. Grant, “A practical superheterodyne-receiver detector using stimulated emissions,”  IEEE Trans. Instrum. Meas ., vol. 60, no. 4, pp. 1461-1468, April 2011) or digitally-modulate (see for example, V. Polacek and R. Pavlik, “The use of digital modulation signals in radar system for detection of nonlinear scatterers,” in  Proc. Int. Radar Symp., IRS , pp. 743-747, September 2011) the transmit waveform for greater noise rejection. Another common technique is to transmit two tones f 1  and f 2  and receive the intermodulation tones 2f 1 −f 2  and 2f 2 −f 1  (see for example A. F. Martone and E. J. Delp, “Characterization of RF devices using two-tone probe signals,” in  Proc.  14 th Workshop on Stat. Sig. Process., IEEE/SP , pp. 161-165, August 2007). A technique recently developed at ARL transmits at least two tones and receives not only a harmonic of the transmitted tones (e.g. 2f 1  and 2f 2 ) but also the mixing products of those tones near that harmonic (e.g. 3f 1 −f 2 ,f 1 +f 2 , 3f 2 −f 1  as described in U.S. patent application Ser. No. 13/870,519 to Dr. Gregory J. Mazzaro, et al. entitled “Multitone Harmonic Radar and Method of Use,” herein incorporated by reference.  FIG. 3A  illustrates examples of transmit and receive spectra for a nonlinear radar that transmits one tone and receives harmonics of that tone.  FIG. 3B  shows examples of spectra for a radar that transmits two tones and receives harmonics as well as mixing products near those harmonics. 
     A common architecture for transmitting and receiving waveforms for both linear and nonlinear radar is necessary in order to minimize the size, weight, and power of the combined radar system. One preferred embodiment combines a wideband stepped-frequency approach with a narrowband two-tone nonlinear approach is given in  FIG. 4 . 
     The signal sources are two stepped-frequency waveform generators  11 A,  11 B. As an alternative, the generators  11 A,  11 B may be pulsed. For linear transmission, a single source  11 B is amplified by amplifier  12 , mixed by mixer  13 , amplified by amplifier  14 , and applied to the transmit antennas at terminal  15 . Mixer  13  is an upconverting mixer for the transmitter. Its function is to change the frequency of the original baseband (low frequency) signal to an appropriate radio-frequency (high frequency) signal for transmission and excitation of the nonlinear response from a target. 
     For nonlinear transmission, the outputs of the two sources  11 A,  11 B are combined), filtered by filters  17 ,  19  and amplified by amplifiers  16 ,  18 , and applied via terminal  21  and switch  22  to the transmit antennas  23 . Note that the switch  22  alternates between contact with terminal  21  (to transmit nonlinear radar) to terminal  15  (to transmit linear radar). 
     At the receiving end, for linear reception, the signal is received by receiver antennas  24  and switch  25  selects the output of one of the receiver antennas  24 , and passes the signal to the base of switch  26 . Switch  26  alternates between terminals  27  and  28 . For linear reception, the signal is amplified by amplifier  29  and lowpass filtered by low pass filter  30 , and downconverted by mixer  31 , filtered at filter  32  and inputted to an analog-to-digital converter  33 . Mixers  31  and  36  are downconverting mixer. Their function is to change the incoming radio-frequency signal to a baseband signal suitable for digitization (and ultimate decision as to the presence of a target). For nonlinear reception, the signal is highpass filtered by filter  34 , amplified by amplifier  35 , downconverted by mixer  36 , and filtered by bandpass filters  37 ,  39  (with an amplifier  38  therebetween). Separate analog-to-digital converter (ADC) units  33 ,  40  are used for linear and nonlinear signal capture. The ADC in the linear chain will likely be wideband at a lower bit-resolution in order to determine precise ranging for linear responses. The ADC  40  in the nonlinear chain will likely be narrowband at a higher bit-resolution in order to maintain a high dynamic range in the receiver to detect weak nonlinear responses. A pair of RF switches  22 ,  26 —switch  22  in the transmitter and switch  26  in the receiver, switched in tandem—adjust the mode-of-operation of the radar between linear and nonlinear. Transmitting from more than one antenna  23  (e.g. the two depicted in  FIG. 4 ) increases the overall aperture for illuminating targets-of-interest. Receiving from more than one antenna  24  (e.g. the four depicted in  FIG. 4 ) improves signal-to-noise ratio (SNR) and allows for the angle-of-arrival to the target to be determined. Stepping and/or pulsing the transmit waveform (from  11 A,  11 B) allows the range to the target to be determined. 
     The preferred embodiment comprises a transceiver comprising a transmit chain that generates waveforms that are appropriate for both linear and nonlinear modes of operation and a switchable receive chain, which captures either linear or nonlinear responses from a radar target. The response to be exploited by the nonlinear receiver may, for example, be the second harmonic of the transmitted waveform. 
     Target Localization 
     After the transmit waveform has reflected from the target and been received, an imaging algorithm can be used to process the reflections for localization. A time-reversal-based multiple-signal classification (TR-MUSIC) algorithm is proposed to generate the images using the steady-state harmonic response as described in D. Liao, “A hybrid approach for characterizing linear and nonlinear electromagnetic scattering: Theory and applications,” U.S. Army Research Laboratory, Adelphi, Md., Technical Report ARL-TR-6261, November 2012, herein incorporated by reference. For M nonlinear targets and N transmit/receive antennas, the received signal at frequency f s  received at the array due to excitation at frequency f i  by the n-th transmitter is
 
 s   r   sn ( f   s   ,f   i )=σ s1 ( f   s   ,f   i ) G ( r   F   s1   ,r   F   n   ,f   i ) G   r ( r   F   s1   ,f   s )+σ s2 ( f   s   ,f   i ) G ( r   F   s2   ,r   F   n   ,f   i ) G   r ( r   F   s2   ,f   s )+ . . . σ sM ( f   s   ,f   i ) G ( r   F   sM   ,r   F   n   ,f   i ) G   F ( r   F   sM   ,f   s )  (10)
 
where r F   n  (n=1, 2, . . . N) is the location of the n-th array element, r F   sm  (m=1, 2, . . . M) is the location of the m-th target, σ sm (f s ,f i ) is the scattering coefficient of the m-th target, and G(r F ,r F ,f) is the Green&#39;s function of the radar environment. From equation (10) the signal subspace is spanned by the Green&#39;s function vectors G r (r F   s1 ,f s ), r F   s2 ,f s ), . . . , G r (r F   sM ,f s ) i.e. the target locations are encoded within the subspace representation of the received signal. After invoking reciprocity, the frequency-domain N×N multi-static matrix for the antenna array can be written
 
                     K   ⁡     (       f   s     ,     f   i       )       =       ∑     m   =   1     M     ⁢           ⁢         σ   sm     ⁡     (       f   s     ,     f     i   ⁢                 )       ⁢       G   F     ⁡     (         r   F     sm     ,     f   s       )       ⁢         G   F     T     ⁡     (         r   F     sm     ,     f   i       )                   (   11   )               
in which  T  represents the transpose operation, and the matrix element K pq (f s ,f i ) is the response at the p-th array element due to excitation at the q-th array element. In practice, K(f s ,f i ) is simply the measurement matrix. For image generation, the signal subspace of K(f s ,f i ) is computed using singular value decomposition:
 
 K ( f   s   ,f   i )= U ( f   s   ,f   i )Λ( f   s   ,f   i ) V ( f   s   ,f   i ) H   (12)
 
where U(f s ,f i ) and V(f s ,f i ) are unitary matrices, Λ(f s ,f i ) contains the singular values of K(f s ,f i ), and  H  denotes the conjugate transpose operation. The column vectors of U(f s ,f i ) supply the singular vectors u p (f s ,f i ) (p=1, 2, . . . , N). Assuming that the received signal subspace is spanned by the singular vectors corresponding to the first L non-zero singular values and the null subspace is spanned by the remaining singular vectors corresponding to singular values equal to zero, an imaging functional can be constructed:
 
                     O   ⁡     (       r   F     ,     f   s     ,     f   i       )       =       (       ∑     p   =     L   +   1       N     ⁢           ⁢            〈         u   p     ⁡     (       f   s     ,     f     i   ⁢                 )       ,       G   F     ⁡     (       r   F     ,     f   s       )         〉          2       )       -   1               (   13   )               
where the Green&#39;s function vector G r (r F ,f s ) can be computed using numerical or analytical methods. The imaging functional in equation (13) peaks at the target locations. This functional is employed for imaging in the scenario displayed in  FIG. 5A . The scene consists of a nonlinear-circuit-loaded target  50  buried in the ground, along with two (linear) clutter objects  51 . The sensing array is composed of N=16 transceivers distributed over a 2-m-wide aperture with a standoff distance of 6.6 m. Here single-tone CW excitation is assumed (e.g., step-frequency excitation with a single frequency). The harmonic multi-static received signal matrices at f 0  (the excitation frequency) and 2f 0  (the second harmonic) are calculated using a hybrid solver as described within the aforementioned reference by D. Liao. The images at the two frequencies are displayed in  FIGS. 5B and 5C . The target  50  is accurately localized for both the f 0  and 2f 0  images. The clutter objects  51  do not appear in the image at 2f 0 .
 
       FIG. 6  is a depiction of combined radar for the detection of threats containing both linear (depicted by a picture of the Synchronous Impulse Reconstruction (SIRE) radar) and also depicting nonlinear components. Shown for example,  FIG. 6  shows a base  100 , a linear target  50 NL below ground and a nonlinear target  50  above ground. 
     Transmit Waveforms 
     The four waveforms selected for the linear/nonlinear transmitter are the single-tone pulse, the multitone pulse, the linear frequency-modulated (FM) chirp, and a stepped-frequency pulse. 
     A mathematical representation for a single-tone pulse produced by an arbitrary waveform generator (AWG) is
 
 V   AWG   =A   env  cos(2π· f   pulse   ·t ) s ( t )  (14)
 
with a carrier frequency f pulse . The amplitude A env  is computed from the power of the envelope of the pulse P env  (in decibels referenced to 1 mW) by:
 
 A   env =√{square root over (10 P     env       dbm     /10 ·2(50Ω)(10 −3  V/mV))}.  (15)
 
     The pulse modulation is given by the switching waveform s(t):
 
 s ( t )= u ( t )− u ( t−D   c   T )= s ( t+T ) D   c   T=T   env   (16)
 
which has a period T and a duty cycle D c . The pulse is active during the time interval T env . An example of an RF pulse generated by a Tektronix AWG7052 is given in  FIG. 7 . A Matlab function which generates a single-tone RF pulse is given in Appendix A.
 
     It should be noted that (a) signals presented in the following description were captured in time by a Lecroy Wavemaster 8300A oscilloscope and in frequency by an Agilent N9342C spectrum analyzer; (b) the sampling rate of the 8300A oscilloscope was 20 GS/s, and the resolution bandwidth of the N9342C analyzer was 1 kHz; and (c) the amplitude of each waveform is less than A env  computed by equation 15 due to the loss introduced by the 8-ft RG-58 Subminiature Version A (SMA) cable, which feeds each of the signal capture instruments. 
     Multitone Pulse 
     If, instead of a single RF carrier frequency, multiple frequencies are active during the pulse, a multitone pulse is generated:
 
 V   AWG   =A   tone {cos(2π· f   1   ·t )+cos(2π· f   2   ·t )+ . . . +cos(2π· f   N   ·t )} s ( t )  (17)
 
which contains N frequencies given by f 1 ,f 2 , . . . f N . In this representation, the amplitude of each tone is A tone  and each tone begins at a common initial phase (for maximum peak-to-average ratio, which generates a maximum nonlinear response). Also, the tones are centered at f c  and separated by f space :
 
     
       
         
           
             
               
                 
                   
                     
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     The active tones are again modulated by the on/off pulse waveform s(t). An example of a multitone pulse is shown in  FIG. 8 . A MATLAB function, which generates this waveform, is given in Appendix B. 
     Linear Frequency-Modulated Chirp Pulse 
     A pulse whose carrier frequency begins at f start  and increases linearly to f end  over the time interval T env  is given by
 
 V   AWG   =A   env  cos [2π·( f   start +( k/ 2) t )· t]s ( t ) k =( f   end   −f   start )/ T   env   (19)
 
where k is the linear chirp rate and A env  is the amplitude of the pulse envelope. An example of a linear FM chirp pulse is shown in  FIG. 9 . A Matlab function which generates this waveform is given in Appendix C.
 
Stepped-Frequency Pulse
 
     A chirp whose carrier frequency steps between discrete values can be represented by 
                     V   AWG     =       A   env     ⁢     cos   ⁡     [     2   ⁢           ⁢     π   ·     f   ⁡     (   t   )       ·   t       ]       ⁢     s   ⁡     (   t   )                 (   20   )                 f   ⁡     (   t   )       =     {               f   start           0   ≤   t   &lt;     Δ   ⁢           ⁢   t                   f   start     +     Δ   ⁢           ⁢   f               Δ   ⁢           ⁢   t     ≤   t   &lt;     2   ⁢   Δ   ⁢           ⁢   t                   f   start     +     2   ⁢   Δ   ⁢           ⁢   f               2   ⁢   Δ   ⁢           ⁢   t     ≤   t   &lt;     3   ⁢   Δ   ⁢           ⁢   t               …       …               f   start     -     Δ   ⁢           ⁢   f                 T   env     -     Δ   ⁢           ⁢   t       ≤   t   &lt;     T   env             ⁢   Δ   ⁢           ⁢   t     =       T   env       N   steps                   (   21   )               
where N steps  is the number of steps, T env  is the length of the stepped-frequency chirp, A env  is the amplitude of the chirp, Δf is the spacing in frequency between each step, and Δt is the spacing in time between each step. It should be noted that this representation for the chirp is not phase-continuous, i.e. the phase of the waveform changes abruptly across each frequency transition.
 
     An example of a stepped-frequency chirp pulse is shown in  FIG. 10 . A Matlab function which generates this waveform is given in Appendix D. 
     Linear and Nonlinear Transceiver 
     An architecture having components common to both linear and nonlinear modes for transmitting and receiving radar waveforms is necessary to minimize the size, weight, and power of the combined radar system. A bench-top architecture for an alternate preferred embodiment combined radar transceiver is given in  FIG. 11 . However, the invention is not limited to the specific components of the bench-top architecture. 
     In this alternate preferred embodiment (which includes a hardware simulation of the radar environment), the signal generator  61  is both linear and nonlinear radar waveforms, which may be for example a Tektronix AWG7052. The low pass filters  62  (which may for example be MiniCircuits NLP-1000+ low-pass filters) are highly linear with a passband below 1 GHz and remove much of the transmitter (Tx)-generated nonlinear (harmonic) distortion. The amplifier  63 , which may for example be a AR4W1000 amplifier, boosts the power of the AWG signal to a level sufficient to excite nonlinear responses from electronic targets. The dual-directional coupler  64 , which may for example be a HP 778D, provides one port for sampling the forward transmit, Tx waveform (which may be monitored for example by a digital oscilloscope  65 ) and another port for sampling the reverse (receive, Rx) signal. The “Simulated Radar Environment” consists of 100 ft of SMA cable  66  (four 25-ft cables in series), terminated by an SMA-connectorized target  50 A 
     Two receive chains are selected by a pair of switches  66 A,  66 B, which may for examples be Hittite HMC784MS8GE switches. Each switch  66 A,  66 B may be powered by 5 V from the 6-V/5-A port on an Agilent E3631A supply and controlled by 5 V/0 V from the ±25-V/1-A port. In  FIG. 11 , the “Linear Rx” chain is selected, and the signal is passed directly to the oscilloscope  65 A through an SMA cable  71 . Alternatively, the “Nonlinear Rx” chain may be selected. Along the nonlinear receiver path, the signal is filtered by four high-pass filters  68 A- 68 D (which may be for example MiniCircuits VHF-1320+ high-pass filters having passbands above 1.32 GHz), to remove the linear response from capture and processing) and amplified by amplifiers  69 A,  69 B (which may for example be two MiniCircuits PSA-5453+) and amplifier  70 , which may for example be a MiniCircuits PSA-545+. Each amplifier is mounted on an evaluation board and powered by 3 V from another E3631A supply. 
     RF Signal Generation and Capture 
     As measured by an Agilent N9923A network analyzer and observed in  FIG. 12 , the amplifier  63  (AR4W1000) provides more than a 40-dB gain to the transmit signal. For nonlinear (harmonic) responses, each NLP-1000+ filter ( 62 ) attenuates Tx-generated distortion at frequencies above 1500 MHz by more than 40 dB.  FIG. 12  is an illustration showing the signal at the transmitter amplifier  63  and low-pass filters  62   
     As seen in  FIG. 13 , illustrating signals relating to the directional coupler and linear/nonlinear receive chain, the Tx and Rx coupling from the 778D is approximately 20 dB. Also, the nonlinear Rx chain (measured from one HMC784 “RF common” port to the other) passes signals to the 8300A with a gain of approximately 40 dB, whereas the linear Rx chain passes signals through with a loss under 3 dB. 
     MATLAB Graphical User Interface 
     The AWG7052 generator  61 , 8300A oscilloscope  65 , and E3631A supplies are controlled via the General Purpose Interface Bus (GPIB). Communication is established using the Instrument Control Toolbox in MATLAB (v7.0.0.19920, R14). An example of a graphical user interface (GUI) for the combined-radar system is illustrated in  FIG. 14  and was created using MATLAB&#39;s “guide” function. The script and functions that govern the operation of the GUI are given in appendices E through K. 
     Using the upper panel as shown in  FIG. 14 , the four different waveforms presented in  FIGS. 7-10  may be uploaded to the arbitrary wave generator  61  for transmission to the target. Using the lower panel as shown in  FIG. 14 , the signal from the target may be captured using the linear or nonlinear receive chain and processed accordingly. For the single-tone pulse, the user may choose the power of the RF pulse while it is active (P env ), the RF frequency (f pulse ), the time interval during which the pulse is active (T env ), and the pulse duty cycle (D c ). The “waveform name” is the designation that appears on the AWG after the waveform is uploaded and is selected for waveform playback. 
     For the linear FM chirp pulse, the user may choose the power of the chirp envelope (P env ), the frequency at which the chirp starts (f start ), the frequency at which the chirp ends (f end ), the time interval during which the frequency linearly changes from f start  to f end  (T env ), and the duty cycle of the waveform (Dc). 
     For the multitone pulse, the user may choose the number of tones (N), power per tone (P tone ), the frequency at which the tones are centered (f c ), the time interval during which the pulse is active (T env ), and the pulse duty cycle (D c ). The frequency separation between the tones (f space ) is automatically set to 1/T env , so that the shortest waveform necessary to achieve N,f c , and T env  with negligible frequency aliasing is uploaded to the AWG. 
     For the stepped-frequency waveform, the user may choose the power of the pulse envelope (P env ), the frequency at which the stepping starts (f start ), the frequency at which the stepping ends (f end ), the time interval during which the frequency steps from f start  to f end  (T env ), the step size (Δf), and the duty cycle of the waveform (D c ). 
     As depicted in  FIG. 11 , the sampled Tx signal is fed to channel 2 of the 8300A oscilloscope  65 , and the sampled Rx signal is fed (through the linear/nonlinear receive chain) to channel 3. The user chooses the voltage scale per channel, the total data collection time per trace, and the number of integrations (i.e., the number of data traces averaged before capture). 
     The user chooses the trigger level and source for signal capture with a consistent time reference. In the experimental setup, Marker 1 from the arbitrary waveform generator  61  is fed to the External trigger port on the oscilloscope  65 . 
     The user chooses the receiver (Rx) mode and types a name for the native MATLAB (MAT) file that will store the time-sampled Tx and Rx voltage vectors. 
     Upon pressing the “Upload . . . ” button inside of one of the upper subpanels, the appropriate waveform is generated and sent to the arbitrary waveform generator  61 . A new figure panel (not shown) appears, which plots the software-generated waveform in frequency and time to confirm that the signal the user intended has been uploaded. 
     Upon pressing the “Capture . . . ” button inside the lower subpanel, the corresponding signal received from the target is recorded by the oscilloscope and processed in MATLAB. A second figure panel (shown in section  4 ) appears, which plots the raw Tx and Rx data in time. A third figure panel (also shown in the following Wireline Experiments section) appears, which plots the correlation of the Tx and Rx voltage samples. 
     Wireline Experiments 
     Several experiments were conducted in order to demonstrate the performance of the alternate preferred embodiment combined-radar transceiver  60  using three different waveforms (pulse, linear chirp, stepped-frequency), two Rx modes (linear and nonlinear), two hardware-simulated linear targets (open-circuit, matched load), and one hardware-simulated nonlinear target (Family Radio Service [FRS] radio). 
     Linear Rx, Chirp Waveform, Open-Circuit Target 
       FIG. 15A  illustrates a plot of the raw Tx and Rx data from the preferred embodiment of  FIG. 11  showing the result of linear data capture and processing when reflecting a chirp from a hardware-simulated highly-reflective linear target, in this case an open circuit. The specifications for  FIGS. 15A, 15B  are: Radar data, chirp Tx waveform, linear Rx mode, open-circuit target: fstart=880 MHz, fend=920 MHz, Penv=0 dBm, Tenv=1 Dc=10%.  FIG. 15B  plots the cross correlation of the Tx and Rx signals (of  FIG. 15A ):
 
[ V   trans   *V   rec ]( t )=∫ −∞   +∞   V   trans ( t )· V   rec ( t +τ) dτ   (22)
 
where time has been mapped to distance using the velocity of propagation of an RF signal in the MiniCircuits CBL-25FT coaxial lines (dielectric constant ∈ r ≈2.1):
 
     
       
         
           
             
               
                 
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     A factor of ½ is used in equation (23) because the distance plotted is half the round-trip distance from the transmitter (i.e. from the coupler output port) to the target (i.e. to the end of the 100-ft coaxial line) to the receiver (i.e. back to the coupler output port). 
     Cross-correlation is a basic form of target ranging. The peak of V trans *V rec  (as a function of distance) indicates the distance from the transmitter to the target. 
     In  FIG. 15A , a relatively constant-amplitude pulse is visible in the sampled Tx channel, and a distorted pulse is visible in the sampled Rx channel. These waveforms are expected, given the frequency-dependent characteristic of the coupler in  FIG. 13 . In  FIG. 15B , a sinc function is visible along with several sidelobes. This shape is expected from the cross correlation of two chirps. The peak of the sinc function is visible at a distance of d=101 ft. The calculated distance is very close to the length of the coaxial line (and slightly higher because the calculation does not account for the length of the Rx chain). 
     Linear Rx, Chirp Waveform, Open Circuit Versus Matched Load 
       FIG. 16A  shows the result of the cross-correlation when reflecting a chirp with a wider bandwidth than that of Linear Rx, Chirp Waveform from a hardware-simulated highly-reflective linear target, in this case an open circuit.  FIG. 16B  illustrates the correlation when receiving the same waveform from a hardware-simulated absent target, in this case a matched (50-Ω) load. Two results are notable: (1) the peak is sharper when the bandwidth of the Tx waveform is wider, and (2) very little signal reflects from the matched load. Both results are expected and indicate proper operation of the transmitter and the linear receive chain. For  FIGS. 16A .  16 B the specifications are Radar data, chirp Tx waveform, linear Rx mode: fstart=860 MHz, fend=940 MHz, Penv=0 dBm, Tenv=1 μs (time interval during which the frequency steps from f start  to f end ), Dc=10%, ( FIG. 15  A open-circuit target,  FIG. 15  B matched-load target). 
     Nonlinear Rx, Pulse Waveform, Nonlinear Target 
       FIG. 17  shows the result of the nonlinear data capture when reflecting an RF pulse from a hardware-simulated nonlinear target: a Motorola T4500 whose antenna has been replaced by an SMA end-launch connector. The specifications for  FIG. 17  are: Radar data, RF pulse Tx waveform, linear Rx mode, FRS radio target: f pulse =900 MHz, P env  0 dBm, T env =1 μs, D c =10%. A 13-dB attenuator is placed between the end of the coaxial line and the FRS radio. The left side of  FIG. 17  plots the raw Tx and Rx data along a 5-μs time scale. The right side plots the same raw data along a 2-ns time scale between t=500 ns and t=502 ns. 
     It is not apparent from  FIG. 17  (left side) that the transceiver is detecting the nonlinear response from the target. In the right side of  FIG. 17 , however, the observed response is clearly nonlinear, because the frequency of the received signal (1800 MHz) is twice that of the transmitted signal (900 MHz). 
     Nonlinear Rx Stepped-Frequency Waveform, Nonlinear Target 
     Nonlinearity is also visible in the frequency domain when the Tx and Rx signals are captured with a spectrum analyzer.  FIG. 18  provides such captures for a stepped-frequency waveform and the FRS radio. The signal output from the arbitrary waveform generator  61  and filtered by a NLP-1000+) is plotted above and the received spectrum is plotted below. For P AWG , all of the spectral content is centered at f=900 MHz and no spectral content exists near 2f=1800 MHz. For P rec , all of the spectral content is centered at 2f=1800 MHz and no spectral content exists near f=900 MHz. 
     Nonlinear Rx, Chirp Waveform, Nonlinear Target 
       FIG. 19  shows the result of the nonlinear data capture and processing when reflecting a chirp from the FRS radio.  FIG. 19  (left) plots the raw Tx and Rx data.  FIG. 19  (right) plots the cross correlation of the Tx and Rx signals:
 
[ V   trans   *V   rec ]( t )=∫ −∞   +∞   V′   trans ( t )· V   rec ( t +τ) dτ   (22)
 
where the Tx signal used for the correlation is a filtered 2 nd  harmonic of the captured V trans :
 
 V′   trans ( t )= h   BPF ( t )* V   trans   2 ( t )  (14)
 
and h BPF  is a bandpass filter with passband edges f L =3f c /2 and f U =5f c /2 with f c =(f start +f end )/ 2 .  FIG. 19  illustrates the radar data results for a linear chirp Tx waveform, nonlinear Rx mode, FRS radio target, starting frequency f start =880 MHz, ending frequency f end =920 MHz, P env 0 dBm, T env =1 μs, D c =10%.
 
     A sinc function is again visible, centered at d=103 ft. This distance is longer than d=101 ft measured previously because the nonlinear Rx chain contains slightly more propagation delay (through the filters and amplifiers) than the linear Rx chain (SMA cable, pass-through). 
     Nonlinear Rx Chirp Waveform, Nonlinear Vs. Open-Circuit Target 
     The nonlinear Rx chain was tested against a purely linear target in order to demonstrate that the transceiver does not indicate detection if the target is linear, and the radar is listening for a nonlinear response.  FIG. 20  gives the result of this test, which is performed with a chirp waveform. 
     From  FIG. 20  it is clear that the radar registers a detection (at d=103 ft) when the target is nonlinear and the Rx is expecting a nonlinear response. From  FIG. 20  (right side, open circuit target) it is clear that the nonlinear Rx chain does not register a detection when the target is linear.  FIG. 20  illustrates the radar data results for a chirp transmission waveform, nonlinear Rx mode, starting frequency f start =890 MHz, ending frequency f end =910 MHz, P env =0 dBm, T env =1 ms, D c =10%. 
     From the above it can be concluded that the alternate preferred embodiment combined-radar transceiver enables basic target ranging in both linear and nonlinear (harmonic) receive modes. The transceiver was constructed using an arbitrary waveform generator  61  as the signal source, a high-speed digitizing oscilloscope  65 A as the signal capture device, and commercial off-the-shelf (COTS) components for the radar front-end (amplification, filtering, and switching). A 100-ft length of SMA cable  66  terminated in an open circuit simulated a linear radar target; the same cable terminated in an SMA-connectorized FRS radio simulated a nonlinear radar target. A MATLAB GUI was developed in order to control the transceiver remotely. The associated script and helper functions are provided in the appendices. Ranging to the target was demonstrated experimentally using RF pulses, linear FM chirps, and stepped-frequency waveforms. 
     The preferred embodiment combines linear radar with nonlinear radar. Linear radar detects targets whose permittivity contrasts with that of the background media; detection is best when the physical dimensions of the target are near to or greater than the wavelength of the incident radiation. Nonlinear radar detects targets containing nonlinear junctions, regardless of physical size, whose RF properties convert incident radiation at a set of probe frequencies to reflected radiation at a set of completely different frequencies. The key advantage of the combined linear and nonlinear radar is that it detects both of these target sets. For a given transmitted wavelength λ trans , the combined radar detects linear targets whose physical size is near to or greater than λ trans  as well as nonlinear targets that can be much smaller than λ trans . 
     State-of-the-art linear radars are able to detect mines and bulk explosives, objects in the path of a vehicle, and personnel. The Synchronous Impulse Reconstruction (SIRE) radar constructed at ARL implements a wideband impulse transmit waveform, multiple transmit and receive antennas, and signal processing which creates synthetic aperture images. To date, the SIRE radar has demonstrated standoff detection of metallic and dielectric surface targets whose volume is at least 200 in 3  (see, for example M. Ressler, L. Nguyen, F. Koenig, D. Wong, and G. Smith, “The Army Research Laboratory (ARL) Synchronous Impulse Reconstruction (SIRE) forward-looking radar,” in  Proc. SPIE , pp. 656105(1-12), April 2007), buried dielectric targets whose volume is at least 1 ft 3 , and people walking inside buildings. 
     State-of-the-art nonlinear radars detect semiconductor junctions such as those found in RF electronics. The combination of linear wideband and nonlinear narrowband technology enables a single radar to detect a variety of threats: targets that produce a linear response, targets that produce a nonlinear response, and targets that produce both. Some threats contain components whose permittivity contrasts substantially with that of the emplacement; such is the case with many threats that are buried. Reception of a subsurface linear radar response from an area whose surface is otherwise undisturbed indicates the presence of a threat. Others threats contain metal contacts and semiconductor junctions whose nonlinear electromagnetic response contrasts with that of the emplacement; such is the case with RF electronics. Reception of a nonlinear radar response from an area that does not otherwise contain electronics indicates the presence of another class of threat. The combined radar is intended to detect both types of threats, collocated or not. 
     Often, threats contain dielectric as well as electronic components; hence, they will respond to both linear and nonlinear excitation, as depicted in  FIG. 5 . Either mode (linear/nonlinear) of the preferred embodiments shown in  FIGS. 4 and 11  will detect the threat. By switching between the two modes, additional information about the threat is received and thus the probability that it is detected is improved. By combining linear and nonlinear radar capabilities, several additional applications are evident including detection of landmines, weapons, and miscellaneous ordnance, subsurface mapping (of pipes, electrical wires, and other manmade structures), vehicle tracking and navigation (with or without nonlinear tags), through-the-wall personnel tracking (with nonlinear tags), and performing counter-surveillance. 
     The preferred embodiments of  FIGS. 4 and 11  enable detection of targets whose permittivity contrasts substantially with that of the emplacement; such is the case with many threats that are buried. Another class of threats contains metal contacts and semiconductor junctions whose nonlinear electromagnetic response contrasts with that of the emplacement; such is the case with RF electronics. Linear radar is a detection technique well-suited for targets whose permittivity contrasts with that of the background media, and whose physical dimensions are near to or greater than the wavelength of the incident radiation. Nonlinear radar is another technique, well-suited for detecting targets containing electronics, regardless of physical size, whose RF properties convert incident radiation at a set of probe frequencies to reflected radiation at a different set of frequencies. The preferred embodiments  FIGS. 4 and 11  combine linear and nonlinear radar so as to detect a set of targets greater than either radar can detect alone. The preferred embodiments  FIGS. 4 and 11  enable reception of a subsurface linear radar response or nonlinear from an area whose surface is otherwise undisturbed so as to indicate the presence of a threat. By switching between the linear and nonlinear radar modes, either type of threat is detected. For targets that contain both linear and nonlinear components, switching between the two radar modes provides additional information and the probability of detection is improved. 
     Obviously, many modifications and variations of the present invention are possible in light of the above teachings. It is therefore to be understood that, within the scope of the appended claims, the invention many be practiced otherwise than as specifically described.