250430_Asilomar_extended_abstract.pdf

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Passive Ambient Noise Radar via Cross-correlation Frank C. Robey

Strategic Technology Office & Defense Sciences Office

Defense Advanced Research Projects Agency Arlington, VA, 22203 frank.robey@darpa.mil, Samuel L. Earp S.L. Earp Inc

Arlington, VA, 22203

Abstract—This paper considers the use of ambient noise as the illumination for use in radar. We investigate whether the multitude of natural and man-made radio frequency (RF) sources can be put to use for radar illumination without the need to isolate and process individual emitters as discrete sources of radar waveforms. There is a continuing desire to repurpose the radio spectrum to commercial communications use. With thousands of emitters sharing the spectrum, we consider the question of whether the processing needs to isolate specific emitters, or whether we can process the spatial-temporal spectrum to convert what would otherwise just be noise to provide radar illumination.

The paper describes two representative scenarios and develops models for the observations that result. Two simplified models that are analyzed are where the noise sources are independent and distributed such as to create a noise field that is isotropic either spherically or hemispherically, or are isotropic in a plane.

This topic of passive noise radar is being investigated in the Defense Advanced Research Projects Agency (DARPA) Defense Applications of Innovative Remote Sensing (DAIRS) program.

Results of the DAIRS program, which includes an extensive data collection and analysis effort, are shown.

Keywords—passive radar, RF daylight, surface wave radar, noise, clutter, DARPA, disruption opportunity.

I. INTRODUCTION

Geophysicist, oceanographers and helio-physicists have developed techniques that utilize environmental noise sources to understand structure below the surface without providing active transmission in a process sometimes referred to as acoustic daylight [1,2]. In this paper we seek to apply similar techniques to radar for the purpose of detecting objects and understanding the environment without the need for high power transmission.

Natural sources are hypothesized as illuminators that will create radio frequency (RF) daylight enabling radar applications in more austere environments where high power transmitters are unrealistic.

This topic of passive noise radar is being investigated in the Defense Advanced Research Projects Agency (DARPA) Defense Applications of Innovative Remote Sensing (DAIRS) program. The DAIRS program was released to potential performers as a DARPA Defense Sciences Office (DSO) Disruption Opportunity (DO), which is intended to be a rapid contracting and acquisition approach for innovative exploration and scientific investigations.

Current passive radar methods are primarily based on estimating or knowing waveform temporal properties and the transmission location for a small number of transmitters. Diffuse radio emissions such that occurring due to the aurora or galactic noise, or the radio noise from distant lightning are not used and can degrade radar performance. We explore a passive noise radar approach without the need to know or estimate the temporal properties of the received waveforms.

One concept for passive radar using indigenous ambient noise is shown in Fig. 1. One or more receive arrays collect and support the processing of the signals received from the environment, which includes those signals that propagate directly from the noise field to the receiver and those that are scattered from objects in the scene and then propagate to the receive array. This scenario forms the basis for the signal model and observation of the signals received by each of the apertures.

In the next section of the paper, we develop the model based on simplified physics associated with the scenario. This is followed by development of the cross-correlation of the signals received by the two apertures. The paper shows that scattering centers in the scene are represented in the data that would be collected. The development in the paper includes both theoretical and simulation results. The paper is then used to discuss key research needed to realize the promise of using ambient noise for radar illumination.

II. THEORETICAL ASPECTS

We illustrate the potential for remote sensing with a simple model that assumes we have two receiving apertures located

This research was developed with funding from the Defense Advanced Research Projects Agency (DARPA). The views, opinions and/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S. Government. Distribution Statement A: Approved for public release:

distribution is unlimited.

Figure 1. Passive illumination using ambient emitters for radar.

mailto:frank.robey@darpa.mil within a noise field that is uniform, isotropic and with sources located at such distance that they can be modeled as being from infinite range. In this simplified model, the two receivers, 𝑠𝑠1and 𝑠𝑠2 are located at 𝑠𝑠1 = {𝑥𝑥, 𝑦𝑦, 𝑧𝑧} = �0,0, 𝑑𝑑

� and, 𝑠𝑠2 = �0,0,−𝑑𝑑 with a scattering cell or object, 𝑣𝑣, and a single noise source, 𝑛𝑛𝑖𝑖 as shown in Fig. 2. In this model, the signal received by each of the apertures are the sum of the direct path from the noise source to the receiver plus the path that is scattered to the receiver by way of the scattering center in the field. In the frequency domain, the received signals referenced to the origin at each of the apertures are 𝑠𝑠1(𝜔𝜔) = 𝑛𝑛𝑖𝑖(𝜔𝜔,𝜃𝜃,𝜙𝜙)𝑒𝑒 𝑗𝑗𝑗𝑗𝑗𝑗cos𝜃𝜃

2𝑐𝑐 + 𝑛𝑛𝑖𝑖(𝜔𝜔, 𝜃𝜃,𝜙𝜙)𝑒𝑒 𝑗𝑗𝑗𝑗(𝑛𝑛�𝑖𝑖⋅𝑣𝑣��⃗ ) 𝑐𝑐 𝑒𝑒− 𝑗𝑗𝑗𝑗𝑅𝑅1

𝑐𝑐 (1) 𝑠𝑠2(𝜔𝜔) = 𝑛𝑛𝑖𝑖(𝜔𝜔, 𝜃𝜃,𝜙𝜙)𝑒𝑒− 𝑗𝑗𝑗𝑗𝑗𝑗cos𝜃𝜃

2𝑐𝑐 + 𝑛𝑛𝑖𝑖(𝜔𝜔, 𝜃𝜃,𝜙𝜙)𝑒𝑒 𝑗𝑗𝑗𝑗�𝑛𝑛�𝑖𝑖⋅𝑣𝑣��⃗ � 𝑐𝑐 𝑒𝑒− 𝑗𝑗𝑗𝑗𝑅𝑅2

𝑐𝑐 (2)

Where 𝜔𝜔 is the center frequency, 𝑅𝑅1 and 𝑅𝑅2 are the distances from the object to the first and second receive aperture respectively, 𝑛𝑛�𝑖𝑖 is a unit vector in the direction of 𝑛𝑛𝑖𝑖, and 𝑣⃗𝑣 is a vector from the origin to the scattering object. The inner product, 𝑛𝑛�𝑖𝑖 ⋅ 𝑣⃗𝑣, indicates the projected distance in the direction of the noise source away from the origin. In this equation, the receive effective height, which converts from electric field strength to received signal is assumed to be unity.

A. The cross-correlation function Multiple authors have derived the narrow-band correlation between two omnidirectional receivers in an isotropic noise field [3-5] when integrated over the sphere without a scattering object in the field. By extension, we write the correlation of the signals received by the two apertures, 𝐶𝐶12(𝜔𝜔) as

𝐶𝐶12(𝜔𝜔) = 𝐼𝐼(𝜔𝜔) �sinc �𝜔𝜔𝜔𝜔 𝑐𝑐 � + 𝜎𝜎

𝑅𝑅1

𝑒𝑒 𝑗𝑗𝑗𝑗𝑅𝑅1

𝑐𝑐 sinc �𝜔𝜔𝑅𝑅2 𝑐𝑐 𝜎𝜎

𝑅𝑅2

𝑒𝑒− 𝑗𝑗𝑗𝑗𝑅𝑅2

𝑐𝑐 sinc �𝜔𝜔𝑅𝑅1 𝑐𝑐 � + 𝜎𝜎2𝑒𝑒− 𝑗𝑗𝑗𝑗 𝑐𝑐 (𝑅𝑅1−𝑅𝑅2)

𝑅𝑅1𝑅𝑅2

� (3)

A challenge that is exemplified by this cross correlation is how to perform the signal processing to detect and estimate the parameters of a scattering cell given the observables in received data. While this has similarity to previous work in generalized cross correlation for time delay estimation, there are enough differences that those techniques cannot be applied directly and new algorithms must be developed.

In this section we build on (3) to develop the wide-band correlation function. Here we use the true frequency 𝑓𝑓 as opposed to the angular frequency 𝜔𝜔. Denote the perfectly band-limited white spectrum as

𝐼𝐼(𝑓𝑓) = 𝑁𝑁0𝟏𝟏[𝑓𝑓0−(𝐵𝐵/2),𝑓𝑓0−(𝐵𝐵/2)](𝑓𝑓)

where 𝟏𝟏[𝒂𝒂,𝒃𝒃](𝑓𝑓) is the indicator function and 𝑁𝑁0 is the magnitude of the cross-power spectrum at the receivers.

The cross-correlation function of the receiver pair, function 𝑅𝑅12(𝜏𝜏), is the inverse Fourier transform of the cross-spectral density function 𝐶𝐶12(𝜔𝜔). Define the components of the cross-power spectral density as

𝐶𝐶12𝐷𝐷𝐷𝐷(𝑓𝑓) = 2𝜋𝜋𝑁𝑁0 sinc � 2𝜋𝜋𝜋𝜋𝜋𝜋 𝑐𝑐

𝐶𝐶12𝑆𝑆𝑆𝑆(𝑓𝑓) = 2𝜋𝜋𝜋𝜋𝑁𝑁0

𝑒𝑒 𝑗𝑗2𝜋𝜋𝜋𝜋𝑅𝑅1

𝑐𝑐

𝑅𝑅1

sinc �

2𝜋𝜋𝜋𝜋𝑅𝑅2

𝑐𝑐

𝐶𝐶12𝐷𝐷𝐷𝐷(𝑓𝑓) = 2𝜋𝜋𝜋𝜋𝑁𝑁0

𝑒𝑒− 𝑗𝑗2𝜋𝜋𝜋𝜋𝑅𝑅2

𝑐𝑐

𝑅𝑅2

sinc �

2𝜋𝜋𝜋𝜋𝑅𝑅1

𝑐𝑐

𝐶𝐶12𝑆𝑆𝑆𝑆(𝑓𝑓) = 2𝜋𝜋𝜎𝜎2𝑁𝑁0𝑒𝑒

−𝑗𝑗2𝜋𝜋𝜋𝜋𝑐𝑐 (𝑅𝑅1−𝑅𝑅2),

Then the cross-correlation function 𝑅𝑅12(𝜏𝜏), is the sum of four integrals:

𝑅𝑅12(𝜏𝜏) = � 𝑅𝑅𝑋𝑋𝑋𝑋(𝜏𝜏)

𝑋𝑋,𝑌𝑌𝑌𝑌[𝐷𝐷,𝑆𝑆]

= � � 𝑑𝑑𝑑𝑑 𝑒𝑒𝑗𝑗2𝜋𝜋𝜋𝜋𝜋𝜋𝐶𝐶12𝑋𝑋𝑋𝑋(𝑓𝑓)

𝑓𝑓0+(𝐵𝐵/2)

𝑓𝑓0−(𝐵𝐵/2)𝑋𝑋,𝑌𝑌𝑌𝑌[𝐷𝐷,𝑆𝑆]

We analyze each of these terms separately.

1) The 𝑅𝑅𝑆𝑆𝑆𝑆 term This integral is elementary, and results in:

𝑅𝑅𝑆𝑆𝑆𝑆(𝜏𝜏) = 2𝜋𝜋𝜎𝜎2𝑁𝑁0𝐵𝐵𝑒𝑒𝑗𝑗2𝜋𝜋𝜋𝜋(𝜏𝜏−[𝑅𝑅1−𝑅𝑅2]/𝑐𝑐)sinc(𝜋𝜋𝜋𝜋[𝜏𝜏 − [𝑅𝑅1 − 𝑅𝑅2]/𝑐𝑐])

The magnitude of this term peaks at 𝜏𝜏 ≈ −𝑑𝑑cos(𝜃𝜃𝑣𝑣)/𝑐𝑐.

2) The 𝑅𝑅𝑆𝑆𝑆𝑆 term The remaining terms in the cross-correlation function do not have tractable closed-form expressions and must be numerically integrated or approximated. We choose to use an approximation here, obtained by expanding the term of 1/𝑓𝑓 = exp(−ln(𝑓𝑓)) in the integrand using the Taylor series for ln(f) centered at 𝑓𝑓0 . The function 𝑅𝑅𝑆𝑆𝑆𝑆(𝜏𝜏) is given as

𝑅𝑅𝑆𝑆𝑆𝑆(𝜏𝜏) = 2𝜋𝜋𝜋𝜋𝑁𝑁0 � 𝑑𝑑𝑑𝑑

𝑒𝑒𝑗𝑗2𝜋𝜋𝜋𝜋(𝜏𝜏+𝑅𝑅1/𝑐𝑐)

𝑅𝑅1

sinc �

2𝜋𝜋fR2 𝑐𝑐 𝑓𝑓0−(𝐵𝐵/2)

Define the following quantities:

𝛼𝛼± = 𝜋𝜋𝜋𝜋(𝜏𝜏 + [𝑅𝑅1 ± 𝑅𝑅2]/𝑐𝑐)

𝛽𝛽± = 𝛼𝛼± + 𝑗𝑗 �

𝐵𝐵

2𝑓𝑓0 𝜏𝜏± =

𝑅𝑅1 ± 𝑅𝑅2

𝑐𝑐

𝐼𝐼0

𝐵𝐵𝐵𝐵𝑗𝑗2𝜋𝜋𝑓𝑓0�𝜏𝜏±𝜏𝜏±�

4𝜋𝜋𝑓𝑓0(𝑅𝑅2/𝑐𝑐)

Applying the approximation and simplifying, the 𝑅𝑅𝑆𝑆𝑆𝑆 term is

Figure 2. Coordinate system illustrating a single noise source.

𝑅𝑅𝑆𝑆𝑆𝑆(𝜏𝜏) ≈

𝜆𝜆0𝑁𝑁0𝐵𝐵𝐵𝐵

2𝑅𝑅1𝑅𝑅2

𝑒𝑒𝑗𝑗(2𝜋𝜋𝑓𝑓0[𝜏𝜏−𝜏𝜏1]−𝜋𝜋/2)�𝑒𝑒𝑗𝑗2𝜋𝜋𝑓𝑓0𝜏𝜏2sinc(𝛽𝛽+)

− 𝑒𝑒−𝑗𝑗2𝜋𝜋𝑓𝑓0𝜏𝜏2sinc(𝛽𝛽−)�

The maxima of the sinc functions occur at 𝜏𝜏 = −𝜏𝜏± = −

𝑅𝑅1 ± 𝑅𝑅2

𝑐𝑐

3) The 𝑅𝑅𝐷𝐷𝐷𝐷 term

There is considerable symmetry that can be used for this term. Note that when viewed as a function parameterized by 𝜏𝜏1,2 = 𝑅𝑅1,2/𝑐𝑐 then

𝑅𝑅𝐷𝐷𝐷𝐷(𝜏𝜏; 𝜏𝜏1, 𝜏𝜏2) = 𝑅𝑅𝑆𝑆𝑆𝑆(𝜏𝜏;−𝜏𝜏2, 𝜏𝜏1).

So, 𝑅𝑅𝐷𝐷𝐷𝐷(𝜏𝜏) ≈ 𝜆𝜆0𝑁𝑁0𝐵𝐵𝐵𝐵

2𝑅𝑅1𝑅𝑅2

𝑒𝑒𝑗𝑗(2𝜋𝜋𝑓𝑓0[𝜏𝜏+𝜏𝜏2]−𝜋𝜋/2)�𝑒𝑒𝑗𝑗2𝜋𝜋𝑓𝑓0𝜏𝜏1sinc�𝛽𝛽�+�

− 𝑒𝑒−𝑗𝑗2𝜋𝜋𝑓𝑓0𝜏𝜏1sinc�𝛽𝛽�−��

The changed parameters are defined as 𝛽𝛽�± = 𝛼𝛼�± + 𝑗𝑗 �

𝐵𝐵

𝛼𝛼�± = 𝜋𝜋𝜋𝜋(𝜏𝜏 − [𝑅𝑅2 ± 𝑅𝑅2]/𝑐𝑐)

4) The 𝑅𝑅𝐷𝐷𝐷𝐷 term

The integral defining this term is 𝑅𝑅𝐷𝐷𝐷𝐷(𝜏𝜏) = 2𝜋𝜋𝑁𝑁0 � 𝑑𝑑𝑑𝑑𝑒𝑒𝑗𝑗2𝜋𝜋𝜋𝜋𝜋𝜋sinc �

2𝜋𝜋fd 𝑐𝑐 𝑓𝑓0−(𝐵𝐵/2)

Applying the approximation, 𝑅𝑅𝐷𝐷𝐷𝐷(𝜏𝜏) ≈

2𝜋𝜋𝑁𝑁0𝐵𝐵

4𝜋𝜋𝑓𝑓0𝜏𝜏0 𝑒𝑒𝑗𝑗[2𝜋𝜋𝑓𝑓0𝜏𝜏−𝜋𝜋/2][𝑒𝑒𝑗𝑗2𝜋𝜋𝑓𝑓0𝜏𝜏0sinc(𝛽𝛽+) − 𝑒𝑒−𝑗𝑗2𝜋𝜋𝑓𝑓0𝜏𝜏0sinc(𝛽𝛽−)]

For this expression the parameters are 𝜏𝜏0 = 𝑑𝑑/𝑐𝑐 𝛼𝛼± = 𝜋𝜋𝜋𝜋[𝜏𝜏 ± 𝜏𝜏0] 𝛽𝛽± = 𝛼𝛼± + 𝑗𝑗

𝐵𝐵

The resonances occur at 𝜏𝜏 = ±𝜏𝜏0 = ±𝑑𝑑/𝑐𝑐

The total cross-correlation function is a sum of these four terms. Viewed as a function of the time lag, there are a total of six peaks. Four of these peaks are in the interval |𝜏𝜏| ≤ 𝑑𝑑/𝑐𝑐, and two carry information on the range, |𝜏𝜏| = ±𝑅𝑅/𝑐𝑐 to the modeled scattering center.

III. FULL PAPER SUMMARY

This paper develops the model and the observables possible for passive remote sensing of the environment via cross correlation of noise data received at two apertures. These observables potentially provide an alternative approach to passive radar. In the full paper, the details of this derivation will be moved to an appendix. Analytic plots and results from simulations will be used to illustrate the observables that result from the model. Experimental results will be presented. One of the arrays used in the experiments is shown in Fig. 3. Challenges inherent in the development of systems based on this concept will be presented.

IV. REFERENCES

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[2] J. Rickett and J. Claerbout, “Acoustic daylight imaging via spectral factorization: Helioseismology and reservoir monitoring,” The Leading Edge 1999 18:8, 957-960.

[3] H. Cox, “Spatial correlation in arbitrary noise fields with applications to ambient sea noise,” Journal of the Acoustical Society of America, vol. 54,

no. 5, pp. 1289–1301, May 1973.1892, pp.68–73.

[4] B. F. Cron and C. H. Sherman, “Spatial-correlation functions for various noise models,” Journal of the Acoustical Society of America, vol. 34,38,

no. 11, pp. 1732–1736,885, November 1962.

[5] F. C. Robey, “A covariance modeling approach to adaptive beamforming and detection,” Ph.D. dissertation, Washington University, St. Louis, MO, Dec. 1990, also published as MIT Lincoln Laboratory Technical Report 918, 30 July 1991. Available through DTIC. Accessed: 2025-03-

08. [Online]. Available: https://apps.dtic.mil/sti/tr/pdf/ADA241887.pdf

Figure 3. An array of 8 three-axis antennas that is being used to collect model validation data.