CaSCADE: Compressed Carrier and DOA Estimation

Spectrum sensing and direction of arrival (DOA) estimation have both been thoroughly investigated. Estimating the support of a set of signals and their DOAs is crucial to many signal processing applications, such as cognitive radio (CR). A challenging scenario, faced by CRs, is that of multiband signals, composed of several narrowband transmissions spread over a wide spectrum each with unknown carrier frequency and DOA. The Nyquist rate of such signals is high and constitutes a bottleneck for both analog and digital processing. To alleviate the sampling rate issue, several sub-Nyquist sampling methods, such as multicoset or the modulated wideband converter (MWC), have been proposed in the context of spectrum sensing. In this paper, we first suggest an alternative sub-Nyquist sampling and signal reconstruction method to the MWC, based on a uniform linear array (ULA). We then extend our approach to joint spectrum sensing and DOA estimation and propose the CompreSsed CArrier and DOA Estimation (CaSCADE) system, composed of an L-shaped array with two ULAs. In both cases, we derive conditions for perfect recovery of the signal parameters and the signal itself and provide two reconstruction algorithms. The first is based on the ESPRIT method and the second on compressed sensing techniques. Both our joint carriers and DOA recovery algorithms overcome the well-known pairing issue between the two parameters. Simulations demonstrate joint carrier and DOA recovery from CaSCADE sub-Nyquist samples. In addition, we show that our alternative spectrum sensing system outperforms the MWC in terms of recovery error and design complexity.