Identification and analysis of source emissions through harmonic phase comparison

Abstract

The present invention is a signal processing method to significantly improve the detection and identification of source emissions. More particularly, the present invention offers a processing method to reduce the false alarm rate of systems which remotely detect and identify the presence of electronic devices through an analysis of a received spectrum the devices' unintended emissions. The invention identifies candidate emission elements and determines their validity based on a frequency and phase association with other emissions present in the received spectrum. The invention compares the measured phase and frequency data of the emissions with a software solution of the theoretically or empirically derived closed-form expression which governs the phase and frequency distribution of the emissions within the source. Verification of this relationship serves to dramatically increase the confidence of the detection.

Claims

1. A method of determining a targeted electronic or electrical device as a source or a non-source of emission of electromagnetic energy, said method comprising the steps of: receiving, with a receiver, coupled to an antenna, emissions of electromagnetic energy; digitizing, with an analog-to-digital converter, an output signal from said receiver into a digitized signal; selecting, with a processor, a spectral region of said received electromagnetic energy that spans an expected emission variation of a harmonic of said targeted electronic or electrical device, said harmonic being associated with a frequency location and a harmonic index; selecting, with a processor, a candidate emission from said emissions of electromagnetic energy for said harmonic; determining, with said processor, based on said frequency location, an existence of one or more additional harmonics; identifying, with said processor, a phase and a frequency relationship between said harmonic and said one or more additional harmonics; generating, with said processor, a time vector for each of said harmonic and said one or more additional harmonics based on phase values for said one or more additional harmonics; identifying an existence or an absence of at least a single value in an intersection vector of all time vectors; and determining, with said processor based on said existence or said absence of said single value, said targeted electronic or electrical device as said source or said non-source of said emission of electromagnetic energy.

2. The method of claim 1, wherein the step of identifying said phase and frequency relationship includes a step of comparing harmonic spacing in frequency of said electromagnetic energy emission.

3. The method of claim 1, wherein the step of identifying said phase and frequency relationship includes a step of one of measuring, comparing and a combination thereof, one of amplitude, phase, and a combination thereof between said at least two harmonics of said electromagnetic energy emission.

4. The method of claim 1, wherein the step of identifying said phase and frequency relationship between said harmonic and said one or more additional harmonics of said electromagnetic energy emission comprises a step of revealing a phase and magnitude of said electromagnetic energy emission.

5. The method of claim 1, wherein the step of identifying said phase and frequency relationship between said harmonic and said one or more additional harmonics of said electromagnetic energy emission comprises a step of using Fourier series of a time-domain waveform.

6. The method of claim 1, wherein the step of identifying said phase and frequency relationship between said harmonic and said one or more additional harmonics of said electromagnetic energy emission comprises a step of generating a range of phase values.

7. The method of claim 6, further including a step of identifying, with a time vector, a condition wherein a harmonic has an instantaneous phase within said range of phase values.

8. The method of claim 1, wherein the step of identifying said phase and frequency relationship between said harmonic and said one or more additional harmonics of said electromagnetic energy emission includes a step of predicting a location of additional harmonics.

9. The method of claim 1, further including a step of identifying interference unrelated to said source of said electromagnetic energy emission.

10. The method of claim 1, wherein the step of receiving said emission of electromagnetic energy includes a step of receiving at least two emissions of electromagnetic energy, a step of using a multi-channel receiver and a step of collecting said at least two electromagnetic energy emissions simultaneously at all applicable channels.

11. The method of claim 10, further including a step of identifying phase and frequency values of components of said at least two electromagnetic energy emissions prior to the step of identifying said at least one phase and frequency relationship between said harmonic and said one or more additional harmonics of said electromagnetic energy emissions.

12. The method of claim 1, further comprising locating or geolocating said electronic or electrical device.

13. The method of claim 1, further comprising determining an instantaneous phase of an underlying source signal to identify at least one short term event.

14. The method of claim 1, further comprising differentiating harmonic content of said source from electro-magnetic background noise.

15. The method of claim 1, further comprising detecting at least one electronically triggered event.

16. The method of claim 1, further comprising monitoring, verifying or predicting a health of one of said electronic device, an electrical component, and a combination thereof.

17. The method of claim 1, further comprising identifying that a set of harmonics is being related to a specific class of said electronic or electrical device.

18. The method of claim 1, further comprising identifying that a set of harmonics is being related to a specific electronic or electrical device.

19. The method of claim 1, wherein said emission of electromagnetic energy is an unintended emission.

20. The method of claim 1, wherein said target electronic or electrical device comprises a pre-characterized emission pattern and pre-characterized variation.

21. The method of claim 1, comprising amplifying, using a low noise amplifier, said emission of electromagnetic energy received with said receiver.

22. A method of determining a targeted device with a pre-characterized emission pattern and pre-characterized variation as a source or a non-source of emissions of electromagnetic energy, said method comprising: receiving, with a sensor, emissions of electromagnetic energy in an electromagnetically noisy environment; digitizing, with an analog-to digital converter (ADC), an output signal from said receiver into a digitized signal; and processing said digitized signal with a processor to: reveal a phase and a magnitude information; identify a spectral region of said received electromagnetic energy that spans an expected emission of a harmonic h.sub.a of said targeted device, said harmonic h.sub.a being associated with a harmonic index k.sub.a; select a candidate emission in said spectral region for said harmonic h.sub.a; measure a frequency location of said candidate emission; record, in a memory, said frequency location of said candidate emission as f.sub.a; determine, based on said frequency location f.sub.a, an existence of a harmonic h.sub.b, being associated with a harmonic index k.sub.b, at a frequency location f.sub.b=f.sub.a*k.sub.b/k.sub.a; determine, based on said frequency location f.sub.a and said existence of said harmonic h.sub.b, an existence of a harmonic h.sub.c, being associated with a harmonic index k.sub.c, at a frequency location f.sub.c=f.sub.a*k.sub.c/k.sub.a; measure phase values of each of said harmonic h.sub.b and said harmonic h.sub.c; convert, by adding an error term, each phase value into a phase range; generate, using a Fourier series, a time vector for each harmonic h.sub.a, h.sub.b, and h.sub.c as t.sub.a, t.sub.b, and t.sub.c respectively; determine an existence or an absence of at least a single value in an intersection vector t.sub.int of times t.sub.a, t.sub.b, and t.sub.c at which phase ranges of harmonics h.sub.a, h.sub.b, and h.sub.c occur simultaneously; and identify said targeted device as said source of said emissions of electromagnetic energy upon existence of said at least single value in said intersection vector t.sub.int or as said non-source of said of said emissions of electromagnetic energy upon absence of said at least single value in said intersection vector t.sub.int.

23. The method of claim 22, comprising repeating steps of selecting said candidate emission in said spectral region for said harmonic h.sub.a; measuring said frequency location of said candidate emission; and recording, in said memory, said frequency location of said candidate emission as f.sub.a; if said existence of said harmonic h.sub.b is not determined.

24. The method of claim 22, comprising repeating steps of selecting said candidate emission in said spectral region for said harmonic h.sub.a; measuring said frequency location of said candidate emission; recording, in said memory, said frequency location of said candidate emission as f.sub.a; and determining, based on said frequency location f.sub.a, said existence of said harmonic h.sub.b at said frequency location f.sub.b=f.sub.a*k.sub.b/k.sub.a; if said existence of said harmonic h.sub.c is not determined.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

(1) FIG. 1 depicts one embodiment of an unintended emission sensor;

(2) FIG. 2 depicts a received unintended emission pattern.

(3) FIG. 3 depicts a square wave and its associated Fourier series components;

(4) FIG. 4 depicts a flow-chart of the preferred embodiment of the present invention for verifying electronic device presence; and

(5) FIG. 5 depicts the results of an analysis with the preferred embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

(6) Referring now to the drawings, in FIG. 1 there is shown a specific embodiment of a system 102 for the detection of source emissions, specifically the detection of unintentional emission from electronic devices. The system 102 is used to capture electromagnetic emissions with the intention of identifying the existence of an electronic device 114. The system detects electromagnetic radiation 116 which radiates unintentionally from a device 114. The radiation 116 is detected through use of an antenna 118. The detected radiation is amplified above the background noise through use of a low noise amplifier 112 to generate a received signal. The received signal is then filtered 110 to prevent signal aliasing and reduce the noise bandwidth of the signal. The signal is then received 108 to reveal the in-phase (I) and quadrature (Q) components and digitized through the use of an analog-to-digital converter 106. The digitized output is analyzed with a processor 104 to reveal the phase and magnitude information of the received signal.

(7) Referring now to FIG. 2, a typical device emission spectrum 202 is depicted as measured through use of a receiving system 102. The individual device emissions 204 radiate from wires and traces inside of the device. The emissions are typically the distinct components of a complex underlying time-domain signal within the device. The underlying time-domain signal is composed of multiple single-frequency signals. These single-frequency signals are referred to as the Fourier series of the time-domain waveforms and are well known in the art. The system 102 detects a subset of these individual emissions 204 to identify the device.

(8) Referring now to FIG. 3, a square-wave, which is an example of a common complex time-domain waveform found in electronic devices, is depicted 302 with a periodicity of 1/f.sub.f. The emission components may be represented mathematically by a Fourier series of the time-domain waveform. The Fourier series of a square wave 302 is composed of sine waves 304 at odd harmonic indices. Each sine wave has an argument which is a function of the harmonic, h, being associated with a harmonic index, k, the fundamental frequency, f.sub.f, and the evaluated function time, t., as shown in Equation 1:

(9) $\begin{array}{cc}\underset{k=1,3,5\mathrm{.Math.}}{\overset{}{.Math.}}\sin \left(\mathrm{��}\left(k,f_f,t\right)\right)=\underset{k=1,3,5\mathrm{.Math.}}{\overset{}{.Math.}}\sin \left(k.Math.2.Math.f_f.Math.t\right)& \left(1\right)\end{array}$

(10) The Fourier series components have phase values which are periodic with the period of the time-domain signal. In Equation 1, the time t=0 is equivalent to the rising edge 308 of the square-wave 302; t=*f.sub.f is equivalent to the falling edge 310 of the square-wave 302; and t=1/f.sub.f is the time of a next rising edge of the square-wave 302. For a square-wave, the Fourier series components each begin with a phase of 0 radians at t=0 306. As t is increased, each Fourier series component cycles through phase values 0 to 2 for a number of times dependent on the harmonic index, k, until each reaches a phase value of 0 radians at t=1/f.sub.f.

(11) An additional example of a device time-domain waveform is the waveform generated in the time-domain by the summation of inter-modulation components within a device. For example, a push-pull LC oscillator is known to produce both a desired frequency, f.sub.o, and a series of undesired frequencies at integer multiples. These signals may be viewed as an aggregated complex periodic time-domain waveform and represented by a Fourier series of single-frequency waves. The Fourier series may be constructed through measurement and analysis of the time-domain waveform or through multiple measurements of the single-frequency components. Further, it is clear to anyone skilled in the art that any complex periodic time-domain signal may be represented as a series of sine terms wherein the constituent cosine terms may be expressed as sine terms with a /2 phase shift and combined with sine terms of the same frequency.

(12) The relationship of the instantaneous phase and the frequency of each of the waveforms in the series persist as the signals are radiated from the device 114 and propagate through the air 116. The path length from the device to the receiving element is identical for all emissions, even in the cases where the device 114 or the receiving instrument 102 or both are in motion; therefore, if the device emissions are collected simultaneously or at precisely known times relative to one another, the phase and frequency relationship of the emissions is preserved. When collected under these circumstances, all emission components collected will have phase and frequency values related to one another as defined by the Fourier series of the complex time-domain signal within the device.

(13) If a particular component at harmonic h=h.sub.x of the Fourier series of any particular source waveform is detected by a system 102 and the phase is measured as =.sub.x, there exist a finite number of time values in a single period of the time-domain waveform at which the particular emission component may take on this measured phase. That is, harmonic h.sub.x will cycle one or more times through phase values of 0 to 2n within a single period of the time-domain waveform and, further, harmonic h.sub.x will have an instantaneous phase of precisely .sub.x once during each cycle of the harmonic and therefore one or more times during the source period. However, practical considerations in system resolution and the received signal strength require the addition of an error term, =.sub.x, to this phase measurement, effectively creating a range of phase values, .sub.x.sub.x, rather than a precise value, .sub.x. The error term is derived empirically such that the defined phase range, .sub.x.sub.x, contains the true phase value. The times within a single source waveform period at which the harmonic h.sub.x has an instantaneous phase within the phase range .sub.x.sub.x is denoted with vector t=t.sub.x. This time vector, t, may be identified through a solution to the following equation:
Find t such that: |(k,f.sub.f,t)modulus 2)|<(2)
where (k.sub.1, f.sub.f, t) is the argument of the sine terms of the Fourier series expression for the complex time-domain waveform and t is a series of time values, uniformly separated, within the boundaries of t=0 and t=1/f.sub.f. If a second component at harmonic h=h.sub.y of the Fourier series of this same complex time-domain waveform is detected simultaneously by the system 102 and the phase is measured as =.sub.x, with an error of .sub.y, the solution of Equation 2 will again yield a finite number of time values, denoted with vector t.sub.y, at which this phase may occur in a single period of the time-domain source waveform. The intersection of the values in t.sub.y and t.sub.x yields a reduced vector of time values, t.sub.int. The time values within the vector t.sub.int are the times within a single period of the source time-domain waveform at which harmonics h.sub.x and h.sub.y have an instantaneous phase within the measured phase ranges, .sub.x.sub.x and .sub.x.sub.x respectively. Any additional harmonic, h.sub.x, may be further included through measurement and the use of Equation 2 to obtain an additional time vector, t.sub.z. This vector, t.sub.z, may be intersected with the vector t.sub.int to form a new reduced intersection vector of time values, t.sub.int.

(14) Interfering emissions which are included in this analysis will often yield an empty set, { }, in the intersection solution, t.sub.int. An empty set in the intersection implies with high certainty that the received emissions are not all emitted from a source with the modeled Fourier series.

(15) The Fourier series model of a time-domain waveform of a targeted device is further useful to overcome device variations issues. Electronic emissions are known to vary in the fundamental frequencies of their internal time-domain waveforms due to both thermal and manufacturing variations. Any variation in the fundamental frequency of the time-domain signal causes even larger variations in the frequency of the higher-order Fourier series terms. These variations complicate the reception of any given harmonic emission when a system 102 attempts to identify received emissions. The harmonics themselves, however, are related in frequency to one another based on the Fourier series of the time-domain waveform. That is, the frequency values of the harmonics are modified through a change in the fundamental frequency, f.sub.f, but the relationship between harmonic frequencies is undisturbed. Therefore, the frequency of any emission element may be identified given the frequency of any other harmonic through:

(16) $\begin{array}{cc}{f}_b=f_a.Math.\frac{k_b}{k_a}& \left(3\right)\end{array}$

(17) Equation 3 may be applied to any received harmonic to predict the location of additional harmonic emissions. The preferred embodiment of the present invention searches a spectral region to identify a candidate emission element which is preliminarily assigned to be part of a Fourier series emitted from a source. Additional emissions are predicted according to Equation 3 and, if present, the received emissions are verified for association with the source through use of the phase relationships detailed in Equation 2. If the additional harmonics are not present, or the measured phases of the harmonics are not verified with the Fourier series model, the candidate is classified as interference unrelated to the source.

(18) Referring now to the drawing of FIG. 4, a flow-chart of the preferred embodiment of the present invention is given. A particular device with a pre-characterized emission pattern and pre-characterized variation is selected for detection. Emissions are received with a sensor system 102 in an electromagnetically noisy environment 402 and electromagnetic energy is detected, digitized and processed for phase and frequency information 404. A particular spectral region of the received energy which spans the expected emission variation of harmonic h.sub.a of the device is identified 406. A candidate emission, if present, is selected from this region for analysis 406. The frequency of the candidate emission is then taken and recorded to memory as f.sub.a within the system 408.

(19) The frequency location of the candidate emission at f.sub.a is used to determine the precise location of additional harmonic emission elements. Harmonic h.sub.b, being associated with a harmonic index k.sub.b is predicted to at frequency f.sub.b=f.sub.a*k.sub.b/k.sub.a 410, while harmonic h.sub.c, being associated with a harmonic index k.sub.c is predicted to be at frequency f.sub.c=f.sub.a*k.sub.c/k.sub.a 412. If an emission element is not present within the received spectrum at either frequency f.sub.b or f.sub.c, the candidate emission is classified as interference and a different initial candidate emission within the region of interest is chosen 406. The process is repeated until either: all candidate emissions within the region of interest are exhausted, in which case the targeted electronics was not identified; or the two additional harmonics h.sub.b and h.sub.c are identified.

(20) If both of the additional harmonics h.sub.b and h.sub.c do exist in the predicted frequency range centered about frequencies f.sub.b and f.sub.c, a measurement of each emission's phase is taken 414. Each phase value is ascribed an error boundary, , which effectively changes the phase value to a phase range centered about the measured phase value 414. The error term is defined for the system based on the measurement sensitivity such that the defined phase range will contain the true phase of a measured signal.

(21) A comparison of the phases of the emissions is then made through the following process to significantly reduce the false alarm rate of the system, effectively allowing detection and identification of signals within considerably noisy backgrounds. Each of the phase ranges for harmonics h.sub.a, h.sub.b, and h.sub.c, and their associated measured frequencies, f.sub.a, f.sub.b, and f.sub.c, are applied to the known model of a Fourier series of emissions of the targeted device. The model assumes a single period of the fundamental tone, 1/f.sub.f in duration, where f.sub.f=f.sub.a/k.sub.a, which begins at t=0. A series of time vectors is generated for each emission, {t.sub.a, t.sub.b, t.sub.c}, as follows:
Find t.sub.a such that: |((k.sub.a,f.sub.f,t.sub.a)modulus 2).sub.a|<.sub.a
Find t.sub.b such that: |((k.sub.b,f.sub.f,t.sub.b)modulus 2).sub.b|<.sub.b
Find t.sub.c such that: |((k.sub.c,f.sub.f,t.sub.c)modulus 2).sub.c|<.sub.c

(22) The vectors t.sub.a, t.sub.b and t.sub.c define the times within the source time-domain waveform period, from t=0 to t=1/f.sub.f, at which the measured emissions at frequencies f.sub.a, f.sub.b, and f.sub.c may have measured instantaneous phases within the phase ranges of e.sub.a6.sub.a, .sub.b.sub.b, and .sub.c.sub.c 416. The intersection of the time vectors t.sub.a, t.sub.b and t.sub.c yields a vector t.sub.int of times at which the phase ranges of the harmonic emissions may occur simultaneously. If a single time solution, or more than one time solution, exists within t.sub.int 418, the measured emissions are consistent with the time-domain waveform of the device and the target is considered identified 420. Positive association of the phases of any harmonic signal with two other harmonic signals implies with high certainty that the analyzed signals are harmonics which originated from a single source, rather than independent signals or noise sources. The decision process 418 is stated as:

(23) If intersection of {t.sub.a, t.sub.b, t.sub.c}empty set, the measured harmonics are predicted to have originated from the targeted source device 420.

(24) If intersection of {t.sub.a, t.sub.b, t.sub.c}=empty set, the measured harmonics are predicted not to have originated from the targeted source device and a new candidate emission is chosen for analysis from the spectral region of harmonic h.sub.a 406.

(25) Referring now to FIG. 5, depicted is the results of an analysis of a phase comparison on a 20 MHz square-wave. The 39.sup.th harmonic is identified at a frequency of 780 MHz and found to have a phase of 3.0 radians with a measurement uncertainty of 0.05 radians. The 49.sup.th harmonic is simultaneously received with the 39.sup.th harmonic and found to have a phase of 1.0 radian with a phase uncertainty of 0.05 radians. The intersection of the time solutions to the Fourier series, as described above, is evaluated. All harmonics from the 50.sup.th to the 99.sup.th are then examined to determine the required phase values at the intersection times for these harmonics to be part of the harmonic series. As shown in FIG. 5, the phase of any third chosen harmonic between k=50 and k=99 will be defined to reside within a narrow phase region. FIG. 5 depicts possible phase values of a third harmonic in white and not-possible phase values in black. Therefore, a third emission measurement at any of these harmonics is required to have a measured phase range within the region defined in FIG. 5 for a positive prediction of association with the targeted source to be made.

(26) The specific embodiment expressed through reference to the flow chart of FIG. 4 is not intended to limit the application of this technique. It is clear to anyone skilled in the art that variations on the above specific embodiment may be applied. For example, although the preferred embodiment for the present invention makes use of three harmonics, the present invention may be applied to only two signals within the spectrum to provide a meaningful verification of the emission relationship or to reject interfering signals. Similarly, the present invention may be applied to more than three harmonics to yield increased confidence and increased precision in the instantaneous phase of the device's time-domain signal. Irrespective of the number of harmonic emissions analyzed in the present invention, the precision of the results of the present invention are dependent on the selection of the harmonic indices for reception. That is, certain choices of received harmonic emissions result in an intersection vector, t.sub.int, with fewer values than other choices of received harmonic emissions.

(27) A benefit of this processing technique is that with repeated observations of the emissions there is a continued increase in the confidence of the prediction of target presence and identity. Phase relationships are expected to change if the emissions are not in fact related through an underlying time-domain waveform. Therefore, repeated observations and verifications of the phase relationship between received emissions serves to reduce the likelihood that the measured emissions are coincidentally present at the expected frequencies and coincidentally have the appropriate phases needed for association with a targeted device.

(28) Further, it is considered that if the phases of the source emissions are verified through the present invention with three or more harmonics, the instantaneous position within a single period of the target's time-domain signal is determined. For example, the use of three harmonics in the present invention defines a short, contiguous vector of time values, t.sub.int, which resides within the period of the time-domain waveform from t=0 to t=1/f.sub.f. If the analyzed source were the unintended emissions of an electronic clock, the transition edges of this clock source may be easily determined, with an error based on the largest and smallest values within t.sub.int. Tracking the location within the fundamental period of a remote source allows precise remote synchronization between devices allowing, for example, phase timing in widely separated array receivers, or timed analysis of short duration events for which knowledge of the source phase is relevant. This information is further useful in directed energy applications which would benefit from synchronizing the pulses of a directed energy weapon with the target's internal functionality.

(29) An additional benefit of the present invention is that it may be used to mitigate interfering signals while on a moving platform or when receiving from a moving source. The aforementioned phase and frequency relationships between received harmonics will be maintained independent of any motion induced Doppler shifting. In addition, interfering signals will vary in phase differently when they are not geometrically co-located with the source of interest. Therefore, relative Doppler shifting of the harmonics and interferers, which is apparent in a frequency and phase analysis of the receive emissions, allows for the discrimination between sources with higher accuracy than available from a static separation. When the interfering signals are from a similar device, the Doppler effect from the relative motion serves to improve differentiation between the two devices.

(30) Moreover, the present invention may be used to improve the geolocation of detected electronics by providing a improved resolution of the received phase of the source emissions through the analysis of their mutual relation.

(31) An additional benefit of the present invention is that the received emission elements may be considerably higher frequency (harmonic index>>1) than the fundamental harmonic of the source for operation. Any harmonic signals of the emission pattern which may be received by the sensing system may be used by the present invention. A benefit of this ability of the invention is that it allows for the verification of the device presence through only the narrowband reception of a few emissions in any particular frequency range, often desirable due to limitations in antenna size and performance in a sensing system.

(32) In a broad embodiment, the present invention is a method to identify an emission source through an analysis of the relation of the phase and frequency of a subset of the received emissions with a model of the Fourier series of the emission waveform. The invention may be applied to any emission content which is composed of a pattern of frequencies with related phases, including without limitation the emissions of x-rays, terahertz waves, millimeter waves, radio waves, microwaves, optical waves, infrared waves, low frequency waves, and sonic waves.

(33) While the foregoing written description of the invention enables one of ordinary skill to make and use what is considered presently to be the best mode thereof, those of ordinary skill will understand and appreciate the existence of variations, combinations, and equivalents of the specific embodiment, method, and examples herein. The invention should therefore not be limited by the above described embodiment, method, and examples, but by all embodiments and methods within the scope and spirit of the invention as claimed.