IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1 Sparse signal recovery in MIMO specular meteor radars with waveform diversity Juan M. Urco, Jorge L. Chau, Tobias Weber, Senior Member, IEEE Juha Vierinen, and Ryan Volz Abstract—Since the 1950s, specular meteor radars (SMRs) have been used to study the mesosphere and lower thermosphere (MLT) dynamic. Atmospheric parameters derived from SMRs are highly dependent on the number of detected meteors and the accuracy of the meteor’s location. Recently, incoherent and coherent multiple-input-multiple-output (MIMO) radar ap- proaches combined with waveform diversity have been proposed to increase the number of detected meteors and to improve time, altitude, and horizontal resolution. The incoherent MIMO approach refers to the addition of new transmit sites (widely separated), whereas the coherent MIMO refers to the addition of new transmit antennas in the same site (closely separated), in both cases, transmitting a different pseudorandom sequence from each antenna element. Unfortunately, the addition of new transmit antennas with different code sequences degrades the performance of conventional signal recovery algorithms. This is a consequence of the cross-interference between the transmitted signals, making it worse as the number of transmitters increase. In this work, we propose a signal recovery approach based on Compressed Sensing, taking advantage of the sparse nature of specular meteor echoes. The approach allows exact recovery of weak echoes even in interference environments. Besides the advantage of the proposed approach to recover the meteor signal, we discuss the optimal selection of the transmitted waveforms and the minimum code length required for exact recovery. Additionally, we propose a modification of the Orthogonal Matching Pursuit algorithm used in sparse problems to make it applicable in real-time analysis of large data. The success of the proposed approach is corroborated using Montecarlo simulations and real data from a multi-static spread spectrum meteor radar network installed in northern Germany. Index Terms—Specular meteor radar, MIMO radar, spread- spectrum, waveform diversity, sparse recovery, compressed sens- ing, orthogonal matching pursuit, mesosphere and lower ther- mosphere. I. I NTRODUCTION M ETEOROIDS entering the Earth’s atmosphere heat up and ablate forming an ionized plasma trail. The plasma trails drift with the neutral wind. By the aid of radars, one can measure the trail velocity projected on the radar line-of- sight. Later, by combining several measurements, these are used to estimate the background wind. When the radar line-of- sight is approximately perpendicular to the trail, the scattered signal is strong and low-power radars can be used. This J. M. Urco and J. L. Chau are with Leibniz-Institute of Atmospheric Physics at the Rostock University, K¨ uhlungsborn, Germany (e-mail: urco@iap- kborn.de, chau@iap-kborn.de) T. Weber is with EE, University of Rostock, Germany (e- mail:tobias.weber@uni-rostock.de) J. P. Vierinen is with UiT, The Arctic University of Norway, Tromso, Norway (e-mail:juha-pekka.vierinen@uit.no) R. Volz is with MIT Haystack Observatory, Massachusetts, USA (e- mail:rvolz@mit.edu) perpendicular point is also known as the specular point. Since the 1950s, specular meteor radars (SMRs) have been used to characterize the atmospheric dynamic in the mesospheric and lower thermospheric (MLT) region [1]–[3]. Typically, mean wind estimations are done using several meteor detections within a certain volume and time, assuming horizontal homogeneity [4], [5]. The fidelity of the estimation is highly dependent on the number of meteor detections and the meteor location accuracy. Indeed, there are many thousands of meteors per minute entering to the Earth’s atmosphere. However, only a few of them accomplish the specular con- dition and can be detected by a given SMR. Recently, multi- static meteor radar networks have been proposed to increase the number of meteor detections and to improve the time, altitude, and horizontal resolution of estimated wind fields [6]–[8]. A multi-static radar network consists of multiple transmitters (Txs) and multiple receivers (Rxs) placed in the same or at different locations. As described in [9], these radars can be classified as coherent and incoherent MIMO radars, respectively. Figure 1 shows a sketch of a coherent and an incoherent MIMO radar both with two transmitting and two receiving antennas. In case of a coherent MIMO, the Tx antennas are collocated or closely separated. Whereas in an incoherent MIMO the Tx antennas are widely separated. In order to separate the contribution of each transmitter some kind of diversity is required; either time, polarization, frequency or waveform diversity [9]. Recently, Stober and Chau [6] proposed a meteor radar network employing two transmit and multiple receive stations widely separated. The Tx stations work at two different frequencies and the Rx stations listen both frequencies with interferometry capability. This radar network can be classified as an incoherent MIMO radar using frequency diversity. Its main advantage is that this network can be implemented with commercial radars working at different frequencies, keeping the data analysis the same. Nevertheless, the complexity comes by using a broad spectrum bandwidth as the number of transmitters increases, complicating also the receiving side. Similarly, Vierinen et al. [7] proposed a multi-static radar network using Tx stations transmitting different pseudorandom code sequences at the same frequency, i.e. spread-spectrum, leaving the receive side unchanged. This network can also be classified as an incoherent MIMO radar but using waveform diversity. In the same way, Chau et al. [8] proposed the use of a combination of coherent and incoherent MIMO radars to simplify the deployment of these networks. Among other advantages, MIMO with waveform diversity allows reusing the spectrum bandwidth. However, it makes the decoupling