A Low-complexity Sub-Nyquist Sampling Systemfor 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, Francem.yaghoobi-vaighan@ed.ac.uk

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 lowcomplexity 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 thecompressive 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 thishere 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 andcostly in some applications.

2. Sampling at a rate higher than informationrate: 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 andcircuit design tolerance.

LoCoMC Sampling Technique

The aim here is to use a simple analog hardware and present a low complexityrecovery 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 LoCoMCSpectrogram of Clean Signal.

time

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Spectrogram of aliased signal,with 13−times undersampling.

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Spectrogram of noisy signal,SNR = 29.9889

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Spectrogram of reconstructed signal by LoCoMC using 4 channels. SNR = 34.0946

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Spectrogram of reconstructed signal by MUSIC,using 4 channels. SNR = 22.9263

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Spectrogram of reconstructed signal by windowed MUSIC,using 4 channels. SNR = 25.2133

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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, 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 implementthan a random sampling pattern.

– Large Dynamic Range, e.g. 70 dB, which makes it suitablefor 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. Acharacteristic 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 FrequencySweeping.

• Fully integrating DFD’s with TF transform.

• Pulse descriptor word extraction.

•Designing Hardware Demonstrator

AcknowledgementThis 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 AndyStove of Thales UK, for the provision of the stream of ESM pulsesand 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.