## 1 Introduction

[2] The Super Dual Auroral Radar Network (SuperDARN) is a global network of over 26 coherent scatter HF radars designed to detect backscatter from plasma density irregularities in the high latitude and midlatitude ionosphere [*Greenwald et al.*, 1983, 1995; *Chisham et al.*, 2007] and backscatter from the ground propagating via specular reflection from the ionosphere [*Andre et al.*, 1998]. The SuperDARN radars detect scatter from periodic electron density fluctuations in the ionosphere with wavelength equal to half the radar wavelength. Backscatter from the land surface is also observed due to natural surface roughness and suitably oriented mountain slopes [*Ponomarenko et al.*, 2010], and from the sea surface due to surface roughness and coherently from successive ocean wave fronts of half the radar wavelength [*Greenwood et al.*, 2011; *Wyatt et al.*, 2011].

[3] At middle to high latitudes, ionospheric irregularities are most commonly observed in regions of high-velocity plasma convection such as the auroral electrojet at *E* region altitudes [*Greenwald et al.*, 1975] and plasma flows in the *F* region driven by electric fields generated at the magnetospheric boundary mapping to the ionosphere along geomagnetic field lines [*Ruohoniemi and Baker*, 1998]. The irregularities tend to drift with the electron flow in the background plasma, providing an image of plasma convection in the ionosphere [*Greenwald et al.*, 1978; *Kelley et al.*, 1982]. The formation of ionospheric irregularities is thought to be associated with plasma instabilities, in particular the gradient drift instability in the ionospheric *F* region [*Simon*, 1963], and the cross-field two-stream Farely-Buneman instability [*Buneman*, 1963; *Farley*, 1963] and gradient drift instability [*Reid*, 1968] in the ionospheric *E*region.

[4] The SuperDARN HF radars operate in the frequency range 8–20 MHz, employing a linear phased array of 16 antennas to create a narrow, azimuthal, steerable beam [*Greenwald et al.*, 1995]. The radar measures the average backscatter power from each range cell for a number of discrete azimuthal beam directions. A multipulse scheme, such as the seven-pulse scheme [see, for example, *Farley*, 1972], is adopted to determine range information unambiguously and provide sufficient frequency resolution for the determination of line-of-sight Doppler velocities of the order of 1000 m/s without aliasing [*Greenwald et al.*, 1983, 1985]. The single-pulse width determines the range resolution; typically 300 μs for a resolution of 45 km. A longer pulse width would improve SNR at the expense of range resolution. The interpulse lag unit of around 2400 μs determines the frequency resolution. Quadrature samples are processed using autocorrelation techniques developed for use with incoherent scatter and VHF auroral radars [*Farley*, 1972; *Greenwald et al.*, 1978] in order to rapidly calculate Doppler velocities. Simultaneous measurement of the autocorrelation function (ACF) at multiple ranges is performed with up to 21 lagged products formed. The longest time lag is assumed to be comparable to the correlation time of the ionospheric scattering medium. Thus, there is an implicit assumption of spatial and temporal uniformity of backscatter targets within a given range/azimuth cell over the time taken to complete the multipulse sequence, of the order of 100 ms. Clutter from uncorrelated scatter from differing ranges, and noise, can be averaged out with integration over a sufficient time, typically 3 s [*Farley*, 1972]. The Fourier transform of the autocorrelation function gives the Doppler power spectrum. In practice, however, for statistical reasons, rather than perform a Fourier transform, the power and spectral characteristics are obtained from a functional fit to the decorrelation envelope of the ACF based on collective wave-scattering theory [*Villain et al.*, 1987; *Hanuise et al.*, 1993]. The basic unit of lag, typically around 3 ms, is a compromise between accurate determination of the decorrelation time and frequency resolution. The line-of-sight Doppler velocity is calculated from the rate-of-change of the phase of the complex ACF with lag.

[5] A second receive-only phased linear array with fewer antennas (typically four), displaced from the main array, acts as an interferometer for the calculation of elevation angle of arrival. The phase difference between the signals arriving at the main and interferometer arrays can be determined from the cross-correlation function of the combined signals from the main and interferometer arrays [*Farley et al.*, 1981; *Baker and Greenwald*, 1988]. The phase difference between the two planar arrays is then used to obtain the vertical (elevation) angle of arrival. The number of antennas in the auxiliary interferometer array can be considerably less than in the main array since only the correlated portion of the signals incident on the main and auxiliary arrays are used for the determination of the main-auxiliary phase lag.

[6] There is considerable variation in the displacement between the main and auxiliary (interferometer) arrays within the SuperDARN network, which is typically around 100 m. The main-auxiliary array spacing needs to be of the order of 100 m for accuracy of elevation angle measurements and to reduce shadowing effects between the two planar arrays [see, for example, *Custovic et al.*, 2013]. The interferometer spacing is, in all cases, larger than the wavelength of the HF signals, which is a maximum of 37 m at 8 MHz. This results in a 2*π* ambiguity or vertical angle-of-arrival *aliasing* effect where the *measured* phase difference in the range −*π* to *π*, between signals arriving at the main and auxiliary arrays, differs from the *total* phase difference by an unknown multiple of 2*π*[*Milan et al.*, 1997; *Ponomarenko et al.*, 2011]. The total phase difference or total *phase lag*between the main and auxiliary arrays is required for the unambiguous estimation of the angle of arrival.

[7] Elevation angle of arrival is critical for determining the propagation modes of received backscatter, the type of scatter observed (ionospheric scatter or ground scatter) and the altitude in the ionosphere from which scatter or ionospheric propagation originates [*Milan et al.*, 1997; *Uspensky et al.*, 2001]. However, only a small number of studies have utilized elevation angle-of-arrival information from SuperDARN radars. *Andre et al.* [1998] used ground scatter analysis of elevation angles versus group range to determine ionospheric parameters, *Milan and Lester* [2001] used elevation angles to determine the altitudes of particular classes of backscatter in the auroral electrojet *E* region, *Chisham et al.* [2008] explored the statistical relationship between elevation angle and group range for ionospheric scatter, *Gillies et al.* [2009] used elevation data to approximate the index of refraction in the ionospheric scattering region to refine Doppler velocity measurements, while *Ponomarenko et al.* [2011] used elevation to estimate the *F* region peak electron density directly. The determination of ground surface parameters such as sea state conditions [*Greenwood et al.*, 2011] using HF SuperDARN radars is also greatly enhanced by having accurate elevation angle-of-arrival data. Elevation data from many of the SuperDARN radars, however, is either unavailable or considered to be unreliable, despite nearly all the SuperDARN radars being equipped with interferometer arrays. It is likely that many more studies requiring information on scattering altitude, ionospheric propagation, and angle of incidence at the ionosphere and the ground surface would be possible with improvements to the performance of SuperDARN elevation interferometry.

[8] This paper aims to give a detailed description of the extent of the interferometer 2*π* phase ambiguity problem for HF radars in the SuperDARN network and investigate the application of a second interferometer array to a SuperDARN radar as a solution to this problem.