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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

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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

• f thousands of pulses per second, they have very sparse TF

representations. ES systems can be noise limited, rather than sparsity limited. 2

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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

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Sub-Nyquist Sampling

Why?

1

Sampling at the rate of Nyquist is difficult or costly in some applications, e.g. Wideband ADC’s and Wideband Digital Receivers.

2

It is a waste of resources, if we sample at a rate, much higher than the information rate.

3

An application specific sampling strategy, i.e. exploring signal structures.

How?

1

Using underlying signal structures, e.g. sparsity.

2

Incorporating non-uniform sampling (random?) in the sensing framework.

3

Non-linear reconstruction of signals.

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Sub-Nyquist Sampling, cont

Challenges?

1

Analog Hardware: How efficiently can we design the analog part?

2

Computational Complexity: How efficient can we implement the non-linear recovery algorithm?

3

Noise Sensitivity: Sensitivity to the input noise?

4

Robustness: How much the sub-Nyquist algorithm is sensitive to the signal model mismatch and circuit design tolerances.

5

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Sub-Nyquist Sampling Techniques

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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].

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Proposed Sub-Nyquist Sampling Framework

A Multi-coset sampling strategy. Avoiding any complicated operations e.g. SVD, ℓ1 minimisation. The signal model has to fit into the Radar ES.

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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.

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Digital Fractional Delay Implementation

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Discretisation of Time-Frequency Kernel

100 200 300 400 500 600 700 800 900 −0.5 0.5 1 10 20 30 40 50 60 70 80 −0.5 0.5 1 10 20 30 40 50 60 70 80 −0.5 0.5 1

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Assumptions and Properties

Approximate Disjoint Aliased Support: different to sparsity.

Spectrogram of Fully Sampled Signal time frequency 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10

−4

2 4 6 8 10 x 10

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Spectrogram of aliased signal, with 13−times undersampling. time frequency 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10

−4

1 2 3 4 5 6 7 8 9 x 10

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No random sampling: optimal delay parameters from a Harmonic Equiangular Tight Frame (HETF). No DFD filter: absorption into TF transform.

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Evaluation with Radar ES signals

Spectrogram of Clean Signal. time frequency 1 2 3 x 10

−4

2 4 6 8 10 x 10

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Spectrogram of Noisy Signal, SNR = 29.991dB time frequency 1 2 3 x 10

−4

2 4 6 8 10 x 10

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LoCoMC, using 4 of possible 13 channels. SNR = 33.9789dB time frequency 1 2 3 x 10

−4

2 4 6 8 10 x 10

8

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Comparison with Other Methods

LoCoMC, 4 Channels. Undersampling Factor of 13. SNR = 34.1052 frequency

time time time

0.5 1 1.5 2 2.5 3 3.5 x 10

−4

2 4 6 8 10 x 10

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Spectrogram of reconstructed signal by windowed MUSIC, using 4 channels. SNR = 26.8553 frequency 0.5 1 1.5 2 2.5 3 3.5 x 10

−4

2 4 6 8 10 x 10

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Rapid Frequency Sweeping, 2 Channel(s), Undersampling Factor of 6. SNR = 3.2083 frequency 0.5 1 1.5 2 2.5 3 3.5 x 10

−4

2 4 6 8 10 x 10

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Two overlapping ADC’s with 1/6 of Nyquist sampling rate for RFS method. 14

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Comparison with Rapid Frequency Sweeping

LoCoMC time frequency 1 1.2 1.4 1.6 1.8 x 10

−4

1.08 1.085 1.09 1.095 1.1 1.105 1.11 1.115 1.12 x 10

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Windowed MUSIC time frequency 1 1.2 1.4 1.6 1.8 x 10

−4

1.08 1.085 1.09 1.095 1.1 1.105 1.11 1.115 1.12 x 10

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Rapid Frequency Sweeped time frequency 1 1.2 1.4 1.6 1.8 x 10

−4

1.08 1.085 1.09 1.095 1.1 1.105 1.11 1.115 1.12 x 10

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LoCoMC time frequency 3 3.5 4 4.5 x 10

−5

0.8 0.9 1 1.1 1.2 1.3 1.4 x 10

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Windowed MUSIC time frequency 3 3.5 4 4.5 x 10

−5

0.8 0.9 1 1.1 1.2 1.3 1.4 x 10

8

Rapid Frequency Sweeping time frequency 3 3.5 4 4.5 x 10

−5

0.8 0.9 1 1.1 1.2 1.3 1.4 x 10

8

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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.

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Noise Folding in Sub-Nyquist Sampling

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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.

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We gratefully acknowledge the support from:

Thanks for your attention.