We have recently extended the passive radar technique to permit interferometric observation of ionospheric irregularities. We discuss the implementation of a passive radar interferometer at VHF frequencies and show observations of field-aligned irregularities in the high-latitude E region ionosphere. The interferometer achieves very fine azimuthal resolution (as fine as 0.1°, or 2 km at a range of 1000 km); thus we can form two-dimensional spatial images of the target volume. Many E region scatterers are compact, with transverse extent no greater than 10 km; this is significantly smaller than the beam width of most coherent radars. By tracking interferometric position, we can estimate the transverse drift of the scattering region. By coupling this information with the line of sight Doppler shift and using the dispersion relation for meter scale irregularities, we estimate electric fields and velocity shears within the scattering volume.
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 In coherent scatter studies of the ionosphere, interferometric techniques have frequently been used to estimate the transverse structure and position of scattering regions within the field of view [Farley et al., 1981; Providakes et al., 1983]. Recently, passive coherent radar techniques have been applied in studies of the ionosphere; Sahr and Lind  describe a VHF passive radar for observation of the high-latitude E region which provides Doppler power spectrum as a function of range, with high range, time, and Doppler resolution. Howland  has implemented an interferometer using the passive radar technique with television broadcasts and successfully used it to track compact aerospace targets. We describe here an interferometric extension of range-Doppler estimation using commercial FM broadcasts near 100 MHz. We present the first observations of ionospheric targets with such an instrument, and offer initial analysis of these data.
 The Manastash Ridge Radar (MRR) is a passive, bistatic system which detects the scatter of commercial FM radio broadcasts in order to observe ionospheric field-aligned irregularities [Sahr and Lind, 1997; Lind et al., 1999]. Its field of view covers a region over southwestern Canada in the sub-auroral zone, looking northward from central Washington State. The MRR provides range and Doppler information at VHF frequencies (near 100 MHz; most frequently at 96.5 MHz) with superb sensitivity and resolution that is comparable or superior to that of conventional coherent radars. The addition of interferometry permits the estimation of transverse structure as well, extending the data sets it provides into ones which are functionally equivalent to those of conventional active radar interferometers (e.g., CUPRI [Providakes et al., 1985]), and allowing direct comparison between these data sets. The simplicity, safety, and low cost of passive radar permits continuous and unattended operation; a separate report in preparation will summarize several thousand irregularity events observed during the nearly continuous operation of the MRR since January 2002.
 Commercial FM radio broadcasts provide convenient and surprisingly useful illumination for radio scattering studies of the ionosphere. FM transmitters are CW, broadcast antennas are usually omnidirectional, and the effective radiated power is high (on the order of 100 kW). The 100 MHz carrier frequency is nearly immune to ionospheric refraction and atmospheric absorption effects, yet scatters readily from meter-scale plasma turbulence. Most importantly, the typical FM waveform has an excellent ambiguity function in the average sense, often completely free of range and Doppler aliasing [Sahr and Lind, 1997]. In essence, the FM transmission acts like a stochastically coded long pulse [Harmon, 2002], which is very useful for overspread targets such as Bragg scattering ion-acoustic turbulence in the ionosphere. Furthermore, the bandwidth of the FM transmission is large compared to that of fluctuations in the ionospheric plasma, and this permits overspread target pulse compression.
 To recover the time series of the scatterer, we must correlate the scattered signal with the original illuminating signal. Rather than attempt to distinguish the direct-path and scattered signals in a single receiver, we use separate receivers: one near the transmitter to provide a reference, and another located approximately 150 km away, behind the Cascade mountain range, so that it is primarily exposed only to the scattered signal. This drastically reduces the dynamic range required of the receivers.
 We have implemented the interferometer with multiple antennas collecting the scattered signal, arranged in such a way as to emphasize azimuthal structure; each antenna's signal is correlated with the same reference signal. A sketch of the interferometer geometry is shown in Figure 1. Currently there are three antennas in the system which collect scatter, providing possible baselines of 3.5λ, 12.5λ, and 16λ (≈47 m). We will discuss only a two-antenna case here, however. The observations we report have been performed with the 16λ separation; thus 32 separate interferometer lobes are contained in the full 180° field of view. The shorter baselines were recently constructed to address this azimuthal aliasing.
 Some of the azimuthal ambiguity may be removed by considering the gain patterns of the receiving antennas, but we do not address this here. The strongly field-aligned nature of E region irregularities further constrains possible target location, however, and in many cases we are able to resolve even the potentially wide auroral targets coherently.
 To extract the interferometric information, we pursue the suggestion for interferometry made by Sahr and Lind . We denote the signal arising from the transmitter by x(t) (the reference), and the scattered signals collected by the remote receivers by yp(t), where p indicates a particular antenna in the interferometric array. Our signal processing algorithm first performs a partial correlation (essentially a matched filter operation with a coherent integration, usually of 50 samples or greater). When implemented on a computer, this operation reduces the raw data rate (from 100 kHz, typically) and has a smoothing lowpass effect, as follows:
where t advances in multiples of the coherent integration factor D. The resulting signal zp(r0, t) is a time series of the scatterer at a particular bistatic range r ≈ r0 × c/2 which evolves at the low bandwidth rate of the scatterer (about 2 kHz). Because of the matched filter, the clutter from signals arriving from other ranges is greatly reduced and spectrally whitened; thus zp(r0, t) is an unbiased estimate of the scattering voltage. Next, we assemble sequences of zp(r0, t), of length M, into sub-time series for conventional FFT-based spectrum estimation. If the original length of zp(r0, t) is N, we are able to use ⌊N/M⌋ incoherent averages to arrive at our power spectrum estimate, as follows:
 The frequency series Ppp(r0, f) is the self-power spectrum received on antenna p. The number of incoherent averages depends on the duration of the observation (total integration time) and the number of points M used in each FFT. In Figure 2 we provide an example of Doppler power spectra (with M = 256) as a function of range, estimated from 10 s of raw data (with data rate 100 kHz and initial coherent integration factor 50), thus using an incoherent average of 78 spectra.
 The unbiased time series zp(r0, t) is also available for conventional cross spectral analysis [Farley et al., 1981]. We correlate voltage spectra from different antennas in the frequency domain as follows:
Here the sum over l represents point-by-point incoherent averaging of L cross-power spectra. Usually L = ⌊N/M⌋, but this is not necessary. Normalizing the cross spectrum by the self power on each antenna, we have
The normalized cross spectrum Cpq(r0, f) is a complex-valued function which represents the coherence and phase shift between the signals arriving at antennas p and q for each range delay r0 and for each Doppler shift f.
 The phase of the cross spectrum ϕ is directly related to the angle of arrival of the signal incident on the antennas, denoted θ; however, the potential to uniquely determine θ depends on the spacing between the antennas with respect to the wavelength of the incoming signal. An antenna spacing of allows a full 180° of azimuth to be mapped uniquely onto the available 2π radians in ϕ.
 Where the coherence is high, we expect the interferometer phase ϕ to be compact and organized, since the majority of the power is coming from a single direction. Also, because the noise processes polluting the two antennas are uncorrelated, the expected noise floor of Ppq(r0, f) is zero for ranges and Dopplers in which no echo is present. It will be necessary, however, to compensate for self-clutter and other interfering signals which are correlated on the interferometer antennas, as we show below.
 To illustrate the properties of our interferometer, we describe an estimator for cross correlation (the inverse Fourier transform of the cross spectrum) for passive radar. Our goal is to compute
which is the complex cross correlation of a target signal of interest s as it arrives on antennas p and q. With a conventional (pulsed) radar, the natural estimator takes the form
where vp and vq are voltages on the scatter-receiving antennas. However, in the passive radar case, we first need to deconvolve the reference signal from the received scatter, as shown above (equation (1)). The additional z = yx* correlation step results in a much larger number of terms to consider when evaluating the statistics of our interferometer cross-correlation estimator:
For simplicity, we have not considered a coherent integration here (i.e., D = 1). Using D > 1 will help reduce the variance of the estimate, and also somewhat alleviate the computational load. Thus the estimate (r0, τ) represents a single sample of the cross correlation between antennas p and q of the scatterer described by the time series zp or q(r0, t). Hereafter we will drop the r0 and τ arguments of , as they will remain the same. We wish to find the expected value of this estimator. However, the scattered signal is itself formed from the interaction of the transmitter signal x and any target signals it encounters. We therefore introduce a model for the received scatter on antenna p:
 Here ℛ is the number of contributing range gates, and depends on the receiver sampling rate (usually 100 kHz) and the farthest distance from which we expect significant backscatter to arise. At distances greater than 1200 km from the Manastash Ridge Radar receivers, E region targets are below the horizon, and we do not expect other coherent backscatter from beyond this distance, as perpendicular magnetic aspect angle cannot be achieved. (The signals scattered from spacecraft are not significant sources of clutter; furthermore, their high Doppler content is eliminated in the coherent integration.) Therefore ℛ ≈ 800; we must include all ℛ ranges, because the transmitter operates continuously.
 For simplicity in this model, we assume that only one target is present at each range. (In practice, multiple targets at the same range may often be distinguished in the frequency domain by their Doppler shifts.) The complex signal sa(t) contains amplitude and Doppler information about the target at range a; a is a unit vector in the direction of this target with respect to the origin (defined as the midpoint between the two antennas); and p represents the location of antenna p (and therefore carries information about the distance between that antenna and the origin). Thus the phase term due to the angle of arrival is kp · a (where k is the transmitter wavenumber). These vectors can be seen in the interferometry illustration of Figure 1. The signal x, as above, is the appropriately time-shifted illuminating waveform.
 Also present are a sum over all (an unknown total of Γ) interference sources, denoted γg, and a receiver noise term, np, which is specific to antenna p. By specific, we mean that the receiver noise associated with the signal from one antenna is uncorrelated with that associated with other antennas.
 Substituting this model into the estimator above yields second- and fourth-order correlations in the transmitted signal, target signals and interfering signals, as follows:
 We have assumed that the transmitter signal, target signals, interference sources, and receiver noise are all zero mean and independent of each other. We note that under these assumptions, the receiver noise terms np(t) disappear completely from the cross-correlation expected value. We likewise assume that target signals at different ranges are uncorrelated (thus the Kronecker δab), and that different sources of interference are uncorrelated (δgh). These assumptions will select b = a and h = g, and free us of two summations.
 Finally, we use the approximation Rxx(τ) = Rxx(0)δ(τ); i.e., the transmitter autocorrelation function is sharply peaked, and we model it as white noise. This is justified when the sampling period for x(t) is greater than its correlation time such that the sampled x(t) is a white process, a reasonable claim in this case (a typical correlation time for FM waveforms carrying rock music is 10 μs, matching our current receiver sampling period). We arrive at
which is the expected value of the interferometer cross correlation estimator for a target at range r0. This expression contains the interferometer phase term that we seek, k(p − q) · r0, which is related to the angle of arrival of the target signal (as well as the coherence, if we model with a random distribution, as in Farley et al. ). The autocorrelation of the target, (τ), is also present, since we have not normalized the magnitude of , and each term is scaled by the transmitter power Rxx(0). However, the estimate is biased by “self-clutter” and all sources of interference arriving on the scatter receiving antennas. The self-clutter bias is similar to the excess power in the zero lag of all autocorrelation function estimates of overspread targets [Farley, 1969]. As indicated by the δ(τ) term discussed earlier, the self-clutter and the bias due to interference are present only at lags shorter than the correlation time of the transmitter signal. Therefore this “white bias” will translate into a flat noise floor in the frequency domain, degrading signal detectability, and also affecting the phase spectrum. At present we estimate and remove the interferometer bias by computing the cross spectrum at a distant range which is presumed to be free of any detectable scatter. We then subtract this bias estimate from the cross spectrum at the range of interest. Point-by-point subtraction allows us to distinguish between the bias that may be present in different Doppler bins, which will be useful in a frequency-selective fading environment, or in the presence of narrowband interference sources.
 Finally, we note that the cross correlation estimator discussed above has the desirable second-moment property of consistency (i.e., its variance decreases as it is supplied with more data), by extension of the single-antenna case worked out by Sahr and Lind . This reduction of uncertainty in the estimate is due to the coherent and incoherent averaging processes described above in equations (1) and (3) or (4).
 In Figure 3 we show interferometer data versus frequency for one range (989 km) of the irregularity echo of Figure 2. This, and all other interferometer data we show, has been done with a two-antenna combination with the 16λ baseline. The two antennas are a Yagi and a log periodic dipole array; their individual power spectra for this particular event can be seen in the bottom panel of Figure 3. The top panel shows the phase difference between the two antennas; the middle panel shows the coherence. We have also plotted the level of a 95% significance test for coherence; i.e., the likelihood is 95% or greater that any signal exceeding this line is due to scattering as opposed to noise.
 It is apparent that the power spectra on both antennas are consistent; a spectral peak is present on both antennas with the same Doppler characteristics we see in the range-Doppler plot of Figure 2 (a bright, fast moving, narrow Doppler component alongside a slower moving Type II body). As with conventional interferometry, the cross spectrum phase and coherence are also consistent with backscatter from a sufficiently localized volume in that the coherence becomes large in the same area that the phase becomes organized. We therefore conclude that this auroral echo is most likely contained within one interferometer lobe (approximately 100 km wide at this range).
 Following Farley et al. , we estimate the angular width of the target scattering volume from the coherence (middle panel of Figure 3). Over the Doppler bins in which the coherence exceeds the 95% significance line, we find several peak coherence values ranging from 0.30 to 0.91. The theoretical model for the coherence given by Farley et al.  assumes a Gaussian distribution for the angular position(s) of the scatterer(s) (θf), and depends on the transmitter wavenumber and interferometer baseline as well as the angular spread (σf). It also uses the approximation sin θ ≈ θ, valid for small θ, and will underestimate target angular widths more severely as the arriving signal deviates from perpendicular to the interferometer axis (see Figure 1). Using the coherence values stated above, we estimate transverse width by multiplying the angular width 2σf by the range. We find that the scattering volume at range 989 km for the 2 February 2002 echo shown in Figure 2 spans a transverse width of up to approximately 32 km, and is as narrow as 9 or 10 km for appropriate Doppler bins (i.e., the strong, narrowband spike at 650–690 m/s).
 We can also make interpretations based on the structure of the interferometer phase over the area of significant coherence. In the case of Figure 3, the phase estimates appear to remain roughly constant, but then “step” to a new level in faster Doppler bins, indicating the separation of the scattering volume in the transverse dimension. The entire echo spans a Doppler width of about 500 m/s; the change in phase over these increasing Doppler bins suggests a velocity shear across the scattering volume in the transverse direction. In general, we expect velocity shears to accompany large field-aligned currents.
3.1. Two-Dimensional Images
 The irregularity scattering volume from Figure 2 spans approximately 100 km in range; in the discussion above we have addressed only a single range (989 km). Therefore, in Figure 4 (leftmost panels), we show power spectra and interferometer phase spectra from several evenly spaced ranges in this scattering volume. Examining cross spectra at nearer ranges gradually reveals a smoother, more linear upward trend in phase across Doppler, but at more distant ranges, the discontinuity discussed above becomes more pronounced, indicating the complete separation of the slower- and faster-moving parts of the scatterer. Finally, at far ranges where the strong, narrow Doppler feature does not exist, and only the broader Type II echo remains, the interferometer phase stays roughly constant over the entire Doppler span of the echo, suggesting a single scattering volume. It is clear that much can be learned by examining interferometer data over the complete range span of an irregularity echo. Therefore we also use a phase distribution method to create two-dimensional “images” of range versus transverse dimension, such as the one in Figure 5. Here we show a grid of intensities - total power received at each range (frequency information is integrated out) - separated, via interferometer information, into 50 phase bins. Essentially, we create phase histograms at each range, and weight them by the appropriate cross spectrum magnitude; examples of these weighted phase distributions (with corresponding spectra at each range) can be seen in the rightmost panel of Figure 4. We then use a simple arc length method, combined with range information and interferometer lobe width, to map these phase values into approximate transverse positions. Our transverse resolution in Figure 5, selected by the number of bins used in the phase distribution analysis, is approximately 2 km, while the range resolution is 1.5 km. The larger-scale structure of the echo is now easily visible: the strong, shorter echo appears to split from the lower-intensity Type II echo (which we know from Doppler information to be moving more slowly than the strong echo). This observation is consistent with the speculations from the individual cross spectra above; also, the apparent transverse widths at 989 km for the slow- and fast-moving echoes match the approximations found using coherence in the previous section.
 Since our interferometer baseline is quite large, our data are strongly aliased in angle. Therefore it is unclear whether these two echoes are part of the same scattering volume, or whether they exist in different parts of the sky. Also, the absolute location (of either or both echoes) in the sky is unknown. However, recognizing the highly field-aligned nature of these phenomena, it is reasonable to speculate that the observed scatter exists in a single region of the sky. Coherent backscatter from field-aligned irregularities is strongly attenuated (by as much as 15 dB/deg [Foster and Erickson, 2000]) as the magnetic aspect angle deviates from perpendicular. In our bistatic case, the bisector of the incident and reflected wavevectors must be very close to perpendicular to the terrestrial magnetic field, , to achieve sufficient backscatter. At a range of 1000 km, our radar view geometry provides a 90° ± 1° magnetic aspect angle over a transverse span of about 200 km. At this same range, our interferometer beams are approximately 100 km wide, indicating that any irregularity scatter we see will most likely be contained within two lobes of the interferometer.
Figure 6 shows another example of a two-dimensional interferometer image (right panel) and its range-Doppler counterpart (left panel). This echo, observed on 24 March 2002, spans over 100 km in range and has similar interesting Doppler features to the example above. It appears to have a Type IV component (narrow spectral peak near 900 m/s), again accompanied by a weaker and slower-moving Type II feature. Doppler characteristics such as these are often seen together [Schlegel, 1996]. The interferometer image suggests three distinct components within a limited scattering volume; this is not an apparent structure when only range and Doppler information are considered.
 Near the 1100 km mark, in ranges which contain both the Type II and Type IV echoes, the image does not show a clear delineation between separate scattering volumes. To investigate this area, we again examine interferometer phase spectra at individual ranges; several of these (1088–1104 km) are shown in Figure 7 along with corresponding single-antenna power spectra. We note that the interferometer phase remains approximately constant over both the Type II and Type IV Doppler features. Although this evidence does not necessarily indicate that the different Doppler features exist in the same location (due to aliasing), it is nevertheless strongly suggestive, especially in light of the aspect angle dependency discussed above.
3.2. Velocity and Electric Field Measurements
 It is also possible to estimate the transverse drift velocity of a scatterer by observing the temporal progression of interferometer phase information. This apparent motion can arise in two ways. First, a stable large-scale electric field structure can convect across the field of view in an orderly fashion. Second, a time-varying electric field can sporadically excite irregularities in adjacent regions, mimicking “true” motion. As the radar observes scatter from locally generated irregularities, apparent motion is equivalent to transverse motion only in the first case. The Doppler shift reveals the line of sight irregularity phase speed. Additional factors can confuse velocity measurements, such as the possibility of significant neutral winds (of the order 100 m/s).
 Nevertheless, it is tempting to assemble the apparent transverse motion and Doppler velocity information to estimate a vector velocity (perpendicular to ). Furthermore, at meter scales the predominant irregularity generation mechanism is through a streaming instability in which the velocity is approximately equal to the electron Hall drift [Schlegel, 1996], so we may also estimate a vector electric field. Data from the SuperDARN HF radar are used in a similar fashion to map F region convection at high latitude [Hanuise et al., 1993]. Acknowledging the several uncertainties associated with measuring the drifts, we can at least roughly characterize the vector velocity and electric field from Doppler and interferometric drift measurements. Occasionally we can corroborate such estimates with other instruments.
 For example, on 24 March, 2002, MRR detected irregularities over a period of roughly 10 hours. This extensive amount of data allowed us to make many successive interferometer measurements, each continuous over 10 s, spaced at intervals of 4 min. We measured the total velocity at several ranges in one scattering volume as it evolved over a 12-min period (three 10-s data sets). In this particular example, the Doppler shifts were large (on the order of 800 m/s) and toward the radar; the apparent transverse drifts were relatively small (15–60 m/s). Therefore the total irregularity drift speeds were between 700 and 900 m/s, corresponding roughly to electric field strengths of 50–60 mV/m, which are relatively large values and indicate the disturbed ionospheric conditions under which they were measured (the Kp index during these observations was 6.0; GPS total electron content data showed depletions in the MRR field of view, indicating low conductivity and a region able to support large electric fields (A. Coster, private communication, 2003)). We can also estimate the direction of by reasoning that the radar field of view is northward, so predominantly blueshifted echoes would be moving southward. With directed “down” (into the Earth), this would mean a westward directed electric field.
4. Analysis of Data Products
 Occasionally imperfections appear in the interferometer data products, such as phase estimates which appear organized where no target is present and coherences which exceed unity. These imperfections can be caused by ambiguities in the FM waveform and by the bias removal process (discussed in section 2.1).
 In creating the two-dimensional interferometer images, such as the one in Figure 5, we have made some simplifying assumptions. First, the azimuthal beam width of the interferometer is taken to be 5.6°; this value assumes 32 equally spaced lobes in a 180° field of view. Second, we have taken contours of constant range to be circles, which is accurate for a monostatic radar, but in our bistatic case this is an approximation. For ranges at which we routinely observe field-aligned irregularities (>750 km), however, the monostatic approximation is reasonable; the baseline between transmitter and receiver is less than 20% of the range calculated from 1/2 the time of flight. While transverse position may be inferred using range information together with the 5.6° beam width approximation above, the transverse dimension plotted in Figures 5 and 6 remains, at best, phase information rather than a true physical dimension. Other issues concerning this azimuth aliasing were discussed earlier.
 Due to the very finely spaced interferometer lobes and the 4-min wait between successive data recordings that is currently in use at MRR, it is possible that the transverse drift measurements reported in section 3.2 could be aliased by multiples of roughly 400 m/s. This is a rather large error to incur; unfortunately, experimentation with splitting the 10-s data sets into multiple parts to get finer time resolution was unsuccessful, as the variance of the phase estimates grew too large (from the necessary decrease in the number of incoherent averages) to distinguish small changes in the interferometer phase. One simple way to alleviate this problem is to take bursts of data much more often (once every minute should be frequent enough for our purposes, as we do not often observe irregularities with drift speeds greater than 1600 m/s); however, this technique was not in use during the March 24 event (or for any event thus far). We do have 2-min-long data bursts from recent irregularity events, which would also serve to eliminate transverse drift aliasing, but these are plagued by as-yet-unsolved interference problems.
 We have described the first implementation of a passive radar interferometer for volumetric targets. This new technique enables us to produce results that are functionally equivalent and comparable to those of conventional radar interferometers. We are able to form two-dimensional images of scattering volumes with very fine resolution, as well as extract geophysical properties of scatterers, such as velocity and electric field. Furthermore, with our passive system we have the advantage of reprocessing the raw data as many times as is desired, with as many different settings and parameters as we wish. It is therefore possible to perform many different experiments on the same observation, allowing thorough analysis of the events we record and the possibility of making our data available in a format useful to other scientists.
 With the recent addition of a third antenna for collecting scattered signals, we will soon begin making interferometric observations with two additional baselines, as well as with all three antennas at once, using an imaging method such as the maximum entropy method, as Hysell  has done, and as the radio astronomy community has demonstrated [Thompson et al., 1986]. Here we have presented the first passive VHF radar interferometry observations of ionospheric targets. The data are of high quality, and adds to the power of passive radar as a potent tool for ionospheric radar remote sensing.
 The authors are grateful for support from the National Science Foundation Graduate Research Fellowship Program and NSF Division of Atmospheric Sciences (award ATM-0310233).