A Low-complexity Sub-Nyquist Sampling System for Wideband Radar ESM Receivers Mehrdad Yaghoobi * , Michael Lexa † , Fabien Millioz ‡ and Mike E. Davies * * Institute for Digital Communications (IDCom), the University of Edinburgh, EH9 3JL, UK † Sensor and Signal Analytics Lab, GE Global Research, 1 Research Circle Niskayuna, NY 12309, USA ‡ CRNL, Lyon Neuroscience Research Center, INSERM, CNRS, University Lyon 1, Dycog Team, 95 Bd Pinel, 69500 Bron, France [email protected] Abstract — Wideband radio frequency sampling generally needs a sampling rate at least twice the maximum frequency of the signals, i.e. Nyquist rate, which is generally very high. However, when the signals are highly structured, like wideband Radar signals, we can use the fact that signals do not occupy the whole spectrum and instead, there exists a parsimonious structure in the time-frequency domain. Here, we use this fact and introduce a novel low complexity sampling system, which has a recovery guarantee, assuming that received RF signals follow a particular structure called the Approximate Disjoint Aliased Support (ADAS). The proposed technique is inspired by the compressive sampling of sparse signals and it uses a multi-coset sampling setting, however it does not involve a computationally expensive reconstruction step, and do not use the standard dictionary based sparsity. We call this here Low-Complexity Multi-Coset (LoCoMC) sampling technique. Simulation results, show that the proposed sub-Nyquist sampling technique works well with the simulated electronic surveillance scenarios. . Compressive Sampling Frameworks Random Demodulator (Tropp et. al. 2007) Multi-coset Sampling (Feng&Bresler 1996) Modulated Wideband Convertor (Mishali&Eldar 2010) Why sub-Nyquist sampling? 1. Sampling at Nyquist rate: difficult and costly in some applications. 2. Sampling at a rate higher than information rate: a waste of resources. 3. An application specific sampling strategy, i.e. exploring signal structures. How? 1. Using underlying signal structures, e.g. sparsity. 2. Non-uniform sampling or random sam- pling. 3. Non-linear reconstruction of signals. Challenges? 1. Analog Hardware: complexity of design. 2. Computational Complexity: complexity of re- covery algorithm. 3. Noise Sensitivity: noise folding effect. 4. Robustness: signal model mismatch and circuit design tolerance. LoCoMC Sampling Technique The aim here is to use a simple analog hardware and present a low complexity recovery algorithm for the digital reconstruction part. ⇒ a Multi-coset sam- pling analog hardware with a novel thresholding based technique for signal recovery. • A bank of multi-coset channels: it has distinguished delays. • Delay selection: using parameters of a Harmonic Equiangular Tight Frame (HETF). • Analog Delays: implementing by delaying the clocks of ADC’s. • Fractional Delays : efficient implementation by combining with the TF transforms [1]. • Time-Frequency transform: STFT has currently been used. • Subband Classifier: Composed of a linear operator, i.e. HETF, followed by a simple maximum-absolute value operator. LoCoMC for Wideband Radar ESM Receivers Electronic Support Measures (ESM) • Detecting all RF emitters to identify pres- ence of threats. • Instantaneous Frequency Measurements: limited spectral sensitivity. • Rapid Frequency Sweeping ADC’s: lim- ited temporal sensitivity. Wideband Directional Finding Receiver High-Sensitivity Receiver Processor Display and Control Panel Omnidirectional Antenna Directional Finding Antenna Array • Wideband Analog to Digital Converters: multi GHz ADC’s, e.g. 20 GHz! LoCoMC Reconstruction Algorithm Simulations and Summary Radar ESM with LoCoMC Spectrogram of Clean Signal. time frequency 0.5 1 1.5 2 2.5 3 3.5 x 10 −4 0 2 4 6 8 10 x 10 8 Spectrogram of aliased signal, with 13−times undersampling. time frequency 0.5 1 1.5 2 2.5 3 3.5 x 10 −4 0 1 2 3 4 5 6 7 8 9 x 10 7 Spectrogram of noisy signal, SNR = 29.9889 time frequency 0.5 1 1.5 2 2.5 3 3.5 x 10 −4 0 2 4 6 8 10 x 10 8 Spectrogram of reconstructed signal by LoCoMC using 4 channels. SNR = 34.0946 time frequency 0.5 1 1.5 2 2.5 3 3.5 x 10 −4 0 2 4 6 8 10 x 10 8 Spectrogram of reconstructed signal by MUSIC, using 4 channels. SNR = 22.9263 time frequency 0.5 1 1.5 2 2.5 3 3.5 x 10 −4 0 2 4 6 8 10 x 10 8 Spectrogram of reconstructed signal by windowed MUSIC, using 4 channels. SNR = 25.2133 time frequency 0.5 1 1.5 2 2.5 3 3.5 x 10 −4 0 2 4 6 8 10 x 10 8 LoCoMC at a Glance • Pros: – Non-iterative: it may be pipelined. – Can use only a few multi-coset channels, e.g. as few as q =2. – Uses a different signal model, which matches well to some classes of signals, e.g. ESM. – Simple analog hardware (digitiser): periodic non-uniform sampling pattern, which is generally easier to implement than a random sampling pattern. – Large Dynamic Range, e.g. 70 dB, which makes it suitable for the low probability of intercept signals. – Continuously monitoring wideband RF signals, in a con- trast with the rapid frequency sweeping technique. • Cons: – Noise folding: 3 dB processing gain loose per octave. A characteristic of sub-Nyquist sampling techniques. – Fast “sampler”. The “holder/tracker” can be slow. Future Work • An optimal TF transform to maximise coherent processing gain. • Sensitivity and robustness analysis. • Comparison with canonical ESM methods, i.e. Rapid Frequency Sweeping. • Fully integrating DFD’s with TF transform. • Pulse descriptor word extraction. • Designing Hardware Demonstrator Acknowledgement This work was supported by EPSRC grants EP/K014277/1, EP/H012397/1 and the MOD University Defence Research Col- laboration in Signal Processing. The authors acknowledge Andy Stove of Thales UK, for the provision of the stream of ESM pulses and useful discussion. [1] M. Yaghoobi, B. Mulgrew and M. E. Davies, “An Efficient Implementation of the Low-Complexity Multi-Coset Sub-Nyquist Wideband Radar Electronic Surveillance” submitted to SSPD conference, Edinburgh, UK, September8-9, 2014.