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An Efficient Implementation of the Low-Complexity Multi-Coset Sub-Nyquist Wideband Radar Electronic Surveillance Mehrdad Yaghoobi, Bernard Mulgrew and Mike E. Davies Edinburgh Research Partnership in Signal and Image Processing Institute for Digital Communications, The University of Edinburgh SSPD, Edinburgh, 9 September, 2014

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Electronic Surveillance (ES) ��������������������������������� ������������ ������������� �������������������� ��������������������� ��������� ����������������� �������������� ����������������������� Task: detecting all RF emitters to identify the presence of threats. It has a passive monitoring system. While Radar ES signals are very dense , e.g. can be hundreds of thousands of pulses per second, they have very sparse TF representations. ES systems can be noise limited, rather than sparsity limited. 2

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Conventional Radar ES Receivers Instantaneous Frequency Measurements: limited spectral sensitivity. Rapid Frequency Sweeping ADC’s: limited temporal sensitivity. Wideband Analog to Digital Converters : need multi GHz ADC’s. Proposal: Sub-Nyquist Analog to Information Converter . 3

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Sub-Nyquist Sampling Why? Sampling at the rate of Nyquist is difficult or costly in some 1 applications, e.g. Wideband ADC’s and Wideband Digital Receivers. It is a waste of resources , if we sample at a rate, much higher 2 than the information rate. An application specific sampling strategy, i.e. exploring signal 3 structures. How? Using underlying signal structures, e.g. sparsity. 1 Incorporating non-uniform sampling (random?) in the sensing 2 framework. Non-linear reconstruction of signals. 3 4

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Sub-Nyquist Sampling, cont Challenges? Analog Hardware : How efficiently can we design the analog 1 part? Computational Complexity : How efficient can we implement the 2 non-linear recovery algorithm? Noise Sensitivity : Sensitivity to the input noise? 3 Robustness : How much the sub-Nyquist algorithm is sensitive to 4 the signal model mismatch and circuit design tolerances . 5

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Sub-Nyquist Sampling Techniques �������������������������������������������������� ��������������������� ������������������ ���������������������������� ������������������� �������������������� 6 ������������������������

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Multi-coset Sampling Framework Non-uniform sampling technique [Feng and Bresler, 1996]. Sparse multiband signal model. A subspace method for reconstruction by Feng et al. A convex optimisation problem for reconstruction by [Mishali and Eldar 2009]. � � � � � � � �� � � � 7

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Proposed Sub-Nyquist Sampling Framework A Multi-coset sampling strategy. Avoiding any complicated operations e.g. SVD, ℓ 1 minimisation. The signal model has to fit into the Radar ES. 8

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Components of Proposed Framework A bank of multi-coset channels: it has distinguished delays. Digital Fractional Delay (DFD) filters . Time-Frequency transform: STFT has currently been used. Subband Classifier: Composed of a linear operator (Harmonic Frame), followed by a simple maximum-absolute value operator. 9

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Digital Fractional Delay Implementation � � � � ��������������������� � � ������������ 10

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Discretisation of Time-Frequency Kernel 1 0.5 0 − 0.5 0 100 200 300 400 500 600 700 800 900 1 0.5 0 − 0.5 0 10 20 30 40 50 60 70 80 1 0.5 0 − 0.5 10 20 30 40 50 60 70 80 11

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Assumptions and Properties Approximate Disjoint Aliased Support: different to sparsity. Spectrogram of aliased signal, 8 Spectrogram of Fully Sampled Signal 7 with 13−times undersampling. x 10 x 10 9 8 10 7 8 6 frequency frequency 5 6 4 4 3 2 2 1 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0.5 1 1.5 2 2.5 3 3.5 4 4.5 time time −4 −4 x 10 x 10 No random sampling: optimal delay parameters from a Harmonic Equiangular Tight Frame (HETF). No DFD filter: absorption into TF transform. 12

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Evaluation with Radar ES signals LoCoMC, using Spectrogram of Clean Signal. Spectrogram of Noisy Signal, 4 of possible 13 channels. 8 8 8 SNR = 29.991dB SNR = 33.9789dB x 10 x 10 x 10 10 10 10 8 8 8 frequency frequency frequency 6 6 6 4 4 4 2 2 2 0 0 0 1 2 3 1 2 3 1 2 3 time time time −4 −4 −4 x 10 x 10 x 10 13

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Comparison with Other Methods LoCoMC, 4 Channels. Spectrogram of reconstructed signal by windowed MUSIC, Rapid Frequency Sweeping, 2 Channel(s), Undersampling Factor of 13. SNR = 34.1052 using 4 channels. SNR = 26.8553 Undersampling Factor of 6. SNR = 3.2083 8 8 8 x 10 x 10 x 10 10 10 10 8 8 8 frequency frequency frequency 6 6 6 4 4 4 2 2 2 0 0 0 0.5 1 1.5 2 2.5 3 3.5 0.5 1 1.5 2 2.5 3 3.5 0.5 1 1.5 2 2.5 3 3.5 −4 −4 −4 time x 10 time x 10 x 10 time Two overlapping ADC’s with 1/6 of Nyquist sampling rate for RFS method. 14

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Comparison with Rapid Frequency Sweeping 9 LoCoMC 9 Windowed MUSIC 9 Rapid Frequency Sweeped x 10 x 10 x 10 1.12 1.12 1.12 1.115 1.115 1.115 1.11 1.11 1.11 1.105 1.105 1.105 frequency frequency frequency 1.1 1.1 1.1 1.095 1.095 1.095 1.09 1.09 1.09 1.085 1.085 1.085 1.08 1.08 1.08 1 1.2 1.4 1.6 1.8 1 1.2 1.4 1.6 1.8 1 1.2 1.4 1.6 1.8 time time time −4 −4 −4 x 10 x 10 x 10 8 LoCoMC 8 Windowed MUSIC 8 Rapid Frequency Sweeping x 10 x 10 x 10 1.4 1.4 1.4 1.3 1.3 1.3 1.2 1.2 1.2 frequency frequency frequency 1.1 1.1 1.1 1 1 1 0.9 0.9 0.9 0.8 0.8 0.8 3 3.5 4 4.5 3 3.5 4 4.5 3 3.5 4 4.5 time time time −5 −5 −5 x 10 x 10 x 10 15

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace 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, i.e. ADAS , which matches well to some classes of signals, e.g. Radar ES. 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 contrast with the rapid frequency sweeping technique. Cons: Needs a Fast “sampler” . The“holder/tracker”can be slow. Noise folding: 3 dB processing gain loose per octave. A characteristic of sub-Nyquist sampling techniques. 16

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Noise Folding in Sub-Nyquist Sampling ��������� �������������� ����������� ���������� �� ��������������� �� �� ��������������� �� ��������������� �� �������������� �� �� � � ��� ��� ��� ��� ��� ��� ��� ��� ��� ������������������������ 17

University Defence Research Collaboration (UDRC) Signal Processing in a Networked Battlespace Conclusion and Future Work Conclusion: A low SWAP algorithm for Radar ES receiver. Exploring parsimonious structure of ES signals. When ES signals are ADAS, the signal recovery is guaranteed. Outperforms the MUSIC recovery algorithm in the given ES signals. Future work: CFAR analysis for parameter selection. Pulse descriptor word extraction. Sensitivity and robustness analysis. 18