A Spaceborne Demonstration of P-Band Signals-of-Opportunity (SoOp) Reflectometry

Land-reflected signals from a geosynchronous communication satellite broadcasting in P-band (367.5 MHz) were captured in low Earth orbit (LEO) using a simple dipole antenna. A delay-Doppler map (DDM) was generated through autocorrelation. Estimates of the specular point delay were obtained from the lag of the second peak in the DDM with a bias of 239.4 m and a standard deviation of 44 m (12 m over a frozen lake) with respect to a predicted orbit model. Relative magnitudes of the first and second DDM peaks fell within the range of values predicted using dielectric models for the frozen ground and lake. Finally, retrievals of surface reflection coefficient were generated using a range of realistic values for the transmitter link budget $G/T$ , and these also fell within the range of possible values for the antenna gain pattern. Given the lack of calibration and the large uncertainties in the receiver orbit and attitude, this agreement is sufficient to conclude a successful demonstration of the fundamental principle of single-antenna reflectometry in P-band. P-band reflectometry may offer a new approach to remote sensing of sub-canopy and root-zone soil moisture.

Signals-of-opportunity reflectometry (SoOp-R), the use of signals transmitted by noncooperative sources, offers an alternative to active radar or passive radiometry for P-band remote sensing, allowing observations to be made in bands allocated to communications. SoOp signals can typically be captured by small, low-gain antennas, a consequence of both the forward scatter geometry and link budgets defined by communication requirements. Resolution is approximated by the first Fresnel zone, assuming specular reflection. Circular polarization, used by some sources, will be resistant to the Faraday rotation effect of the ionosphere. P-band SoOp was first demonstrated using an airborne instrument prototype [9], followed by the selection of "signals of opportunity P-band investigation" (SNOOPI), satellite mission to evaluate P-band SoOp remote sensing from orbit [10]. SNOOPI will utilize a single antenna, making use of the interference between the direct and reflected signals "in space," rather than capturing the two signals independently. Sensitivity of P-band SoOp to soil moisture has been studied in a number of tower-based experiments [11], [12].
An opportunity became available to test this concept by capturing a short (30 s) time series of the P-band signal environment in low Earth orbit (LEO) through reprogramming a software-defined radio (SDR) on the Djara satellite (Satellite Catalog Number (SATCAT) 46926) operated by Spire Global Inc. This satellite had reached the end of its operational life, allowing this experiment to be conducted at little cost and no risk to the principal operation of the satellite. Djara was equipped with a single-dipole (wide beam, linearly polarized) antenna. A model for the gain pattern is shown in Fig. 1.
Prior studies of interferometric GNSS reflectometry (iGNSS-R) showed that very high antenna gains (∼23 dB) are required to obtain a useable signal-to-noise ratio (SNR) from cross correlating the direct and reflected signals without knowledge of the signal model [13]. P-band land reflection, however, is predicted to be coherent for surface roughness up to 15-30 cm [14], resulting in a free-space path loss in the reflected signal ∝ r −2 ts r −2 sr versus ∝ (r ts + r sr ) −2 for incoherent scatter (r ts and r sr are the ranges from the specular point to transmitter and the receiver, respectively). For the specific geometry in this experiment, the direct and reflected SNRs at the receiver input are SNR D = −8.7 dB and SNR R = −22.7 dB, assuming 1-dB antenna gain and 490.5-K noise temperature. In contrast, the iGNSS-R example in [13] requires 23-dB antennas to produce SNR D = 2.2 dB and SNR R = −28.5 dB. The post-correlation SNR loss is only 7.1 dB larger for the Djara experiment versus the iGNSS-R study, despite a 21-dB difference in antenna gain. Finally, the objective of this experiment is only to demonstrate detection of a reflected signal and validate models for its properties and not to perform altimetric retrievals.

II. EXPERIMENT
Publicly available two-line elements (TLEs) [15] for both Djara and two multiuser objective system (MUOS) communication satellites [16] (SATCAT 38093, 41622) visible in the continental United States were used to predict specular point tracks on the WGS-84 ellipsoid (using the unit-difference method [17]). The following criteria were used to search for favorable data collection times: 1) inland areas of high reflectivity, such as lakes or rivers; 2) angle of incidence ≤60 • ; 3) direct signal antenna gain greater than −3 dB; 4) direct-reflected antenna gain difference <3 dB; 5) direct and reflected ray path within the same MUOS spot beam, estimated from public information [16], [18], [19]. A 30-s batch of data was collected starting at 13:12Z 23 December, 2021; 9.175 s was ultimately recovered before Djara deorbited. Complex data were captured with a sample rate of 5 MHz using 12-bit quantization in both in-phase (I ) and quadrature (Q). The RF receiver's filter was centered at 367.5 MHz with a passband of 5 MHz corresponding to one wideband code division multiple access (WDCMA) channel transmitted from MUOS.

III. DATA PROCESSING
A delay-Doppler map (DDM) was generated from autocorrelation of the total received signal, x(t), consisting of the sum of the direct signal, reflected signal, and noise. If a reflected signal was present in the data, the DDM is expected to have two peaks, one at the origin and one at lag equal to the additional path delay through the specular point. The ratio of the magnitude of these two peaks can be shown to be a function of the surface reflection coefficient (see Section IV).

A. DDM Generation
A sequence of 1834 DDMs was generated (using the fast Fourier transform (FFT) for numerical efficiency) with a coherent integration time of T I = 5 ms over a delay range of ±5 ms and a Doppler frequency range of ±2 kHz. No incoherent averaging was performed. Fig. 2 presents two example DDMs. On the left-hand side of each subplot, the delay window is centered at τ = 0 and covers the range |τ | <∼ 190 m. In each of these examples, a definite peak is present at the origin, representing the sum of direct, reflected, and noise power. On the middle subplot, the delay window is centered at the second peak. The right plot shows a slice in delay through the peak for both the origin and reflected peak. Peak value is normalized to unity and aligned with the origin. This clearly shows that the shape of the DDM at the origin (solid) is the same as the shape at the specular delay, supporting the hypothesis of a specular reflection.
The third-order polynomial interpolation was applied to each DDM and was used to estimate the lag of the second peak,τ RD , with higher precision than that defined by the sample rate (59.96 m). The magnitude of this peak was used to estimate the effective reflection coefficient at the receiver as described in Section IV. The peak in the lower plot (3175 ms) is clearly larger than that in the top plot (530 ms), relative to the noise, indicating a higher reflected power at that time. In Section IV, the specular point ground track is matched to a surface map to propose an explanation for this increase.

B. Signal Model and Retrieval Method
The transmitted signal is modeled as follows: Baseband signal modulation, a(t), is approximated as a zero-mean wide sense stationary process with autocorrelation R a (τ ). C is the carrier power, and f C is the carrier frequency. This signal reaches the antenna along two paths: 1) direct line of sight with delay τ d , Doppler frequency f Dd , and 2) reflected path, with τ r and f Dr . A coherent reflection at the surface is assumed. From orbit, the reflected path delay is much longer than the correlation time of the signal, R a (τ r ) = 0. For simplicity, the effect of the attenuation and the antenna gain pattern in the direct (G d ) and reflected (G r ) direction are grouped together with the surface reflectivity, |R| 2 , into a single variable, defined as the "effective reflection coefficient" The combined signal captured by the receiver is, therefore, G is the receiver gain, L d is the total direct-path loss, and n(t) is zero-mean thermal noise with bandwidth B n .
]. The DDM is generated using autocorrelation over Use of the direct signal in lieu of a model signal (which is unknown) is based upon the iGNSS-R approach [13], [20]. Autocorrelation of a signal consisting of the in-space interference between the direct and reflected signal also shares some features with GNSS multipath reflectometry [21]. Substituting (4) into (5) and evaluating the expected value at the origin and specular point delay, τ rd , give Assuming that the contribution from the noise n(t) to Y (τ, f ) is small, the first term can be linearized. The simple observable formed by the ratio of the two peaks in the autocorrelation is, thus, approximated as follows: is an SNR and ν d is a zero-mean random variable. (G d /T n ) is the only variable needed to calibrate the measurement, incorporating both the system gain and the noise floor. Assuming observations of d are unbiased, (8) is a quadratic, which can be solved for an estimate of |R e | |R e | = |d| − |d| 2 − 1 + S −1 .

IV. RESULTS
A histogram of the difference between peak delay estimated from the data and the predicted delay is shown in Fig. 3. Predicted path delay was computed using the TLEs and the WGS-84 ellipsoidal Earth model as described in Section II. The NeQuick-2 model [22], incorporating the observed F10.7-cm solar flux from the date of the experiment, was used to remove an ionospheric delay of 24.9 m (18.4 times larger than for GNSS).
Scintillation [23] was not considered due to the short period of data analyzed. The ensemble of these differences has a bias of −252 m (<0.1% of total path delay) and a standard deviation of of 44 m. Outliers with any of the following were removed: 1) reflected peak with an SNR lower than 4.3; 2) observed Doppler difference >100 Hz; and 3) reflected peak >3σ away from the mean value. Tests 1) and 2) removed approximately 50% of the DDMs exhibiting low or no reflection. Test 3) removed the few cases of RFI.
After identifying the time between 2800 and 3240 ms as likely corresponding to the specular point transversing the frozen lake, the delay estimate for this segment was analyzed separately and found to have a bias of −239 m and a significantly lower standard deviation of 12 m, confirming reflection from a smoother surface.
A model for the gain pattern was randomly sampled with 10 4 points uniformly distributed in solid angle; 90% of these samples had a gain between −8.4 and 2.7 dB, and 52% were above −2 dB. To account for uncertainty in the attitude, three different values of (G/T ), corresponding to G D = {−2, −1, 1} dB and T n = 490.5 K, were used to produce different retrievals, along with one assuming infinite signal to noise [(G/T ) → ∞]. A transmitted power of C = 34 dBW (including a 3-dB reduction to account for the linearly polarized antenna) was assumed. The resulting|R| time series, with a 25-point moving average applied, is shown in Fig. 4. Specular point locations using a color scale for reflection coefficient (G/T = −27.9 dB) are plotted on a Google Earth image in Fig. 5. Most of the terrain covered by the specular point track is uniform and believed to be frozen ground. There is a short period between 2.775 and 3.375 s, in which the reflection coefficient does increase (evident in Figs. 2 (bottom) and 4).
Given that Djara was near the end of its orbital life (deorbit 4 January, 2022), the position of the satellite is not expected  to be known to better than a few km. We adjusted the satellite position by shifting it 2540-m cross track in the direction of the orbit normal (approximately NNE in Fig. 5) and 1.8-s along track to place this peak reflection coefficient over Mud Lake South of Quamba, MN. The positions of the transmitter satellites were not adjusted.
A dielectric mixing model [24], [25] was used to compute representative values for the reflection coefficient over frozen ground. Fraction of unfrozen water is expressed as a function of soil temperature T ( • C) by the empirical relationship, A|T | −B , in this model. Fresnel coefficients of the air-soil interface, R a−s , were computed from this dielectric constant and then adjusted to account for roughness and vegetation effects where W v is the vegetation water content (VWC) and h = 4σ 2 (2π/λ) 2 cos 2 θ is the roughness coefficient. W v and h, along with sand and clay fraction, were obtained from SMAP auxiliary data with h scaled by wavelength, λ, and incidence angle, θ (60 • ). Soil moisture (m v ) and soil temperature were obtained from the nearest U.S. Climate Reference Network (USCRN) site (Sandstone, MN, 6 W, 177 km away).
The lake was assumed to be covered in a smooth ice layer. The Rouard method [26] was used to compute the surface reflection coefficient, R lake , from the Fresnel coefficients of the air-ice (R a−i ) and ice-water (R i−w ) interfaces as a function of the unknown path-delay phase, φ Numerical values for these models are in Table I. Two values for the phase, φ, which produced the maximum and minimum |R lake |, were used to set a range of possible values.
A right-hand circularly polarized (RHCP) electromagnetic wave is assumed to be transmitted. The dipole antenna is linearly polarized. The receiver attitude (and, thus, antenna gain in the direction of direct and reflected signals) was also assumed to be unknown. Both horizontal (H) and vertical (V) polarizations were computed, with V producing much lower values than what were observed, so comparison was made only to the HH reflection coefficients.
We first compute the ratio |R| lake /|R| soil and compare it with that retrieved from the data. During the short duration of the experiment, the observation geometry is not expected to vary significantly enough to change the relationship in (3), so |R| lake /|R| soil ≈ |R e | lake /|R e | soil . Fig. 4 shows that this ratio does not depend strongly on G/T and |R e,lake |/|R e,land | ≈ 3.9. This falls within the range of feasible values from Table I (considering both polarization and the full range of φ for the lake reflection) of 2.2-6.8.
Next, we compared the frozen ground reflection coefficient retrieval for each assumed value of (G/T ) to that predicted in Table I. For each of these three cases, we computed the gain ratio (G R /G D ) required to satisfy (3). Finally, we look at the range of possible gain ratios (G R /G D ) from the random sampling of the gain pattern described earlier. For each sample of G D , the gain G R was found for 73 points (evenly spaced in 5 • increments about the direct line of sight) meeting the geometric constraint between the two lines of sight. Table II summarizes these numerical values, in which we can see that the required (G R /G D ) falls within the range of possible values from the gain pattern associated with each of assumed G/T . Details of these calculations are provided in the Supplemental Material.
Finally, we present an example of possible RFI observed during this experiment. Fig. 6 shows the DDM generated at 5820 ms in which there is significant power distributed around the reflected signal delay. This potentially indicates a saturation of the front-end amplifier. We have not attempted to determine any specific source for this RFI, given the limited knowledge of the experiment configuration, but this presents evidence that RFI could be an important consideration in a future P-band SoOp mission.

V. CONCLUSION
We present evidence for detecting a coherently reflected P-band signal from a GEO transmitter by a receiver in LEO (≈280 km) using the autocorrelation of the signal captured by a dipole antenna. This was verified by agreement between the lag and amplitude of the second autocorrelation peak with the predicted specular point delay. Shape of the autocorrelation also supports the hypothesis of a specular reflection. The estimated reflection coefficient and its change from frozen land to frozen lake all fell within the range of possible values. Evidence of potential RFI was found.