SUB-NYQUIST DOPPLER RADAR WITH UNKNOWN NUMBER OF TARGETS A project by: Gil Ilan & Alex Dikopoltsev Guided by: Yonina Eldar & Omer Bar-Ilan Project #: 1489

Agenda Background 1 st goal – Low SNR Performance 2 nd goal – Model Order Estimation Artifacts Real Samples Problems Met Possible Solutions

Background – O 2 MP The bands chosen for sampling

Background – O 2 MP

Background – Doppler Focusing

Background – Past Performance So far all of the experiments were performed with high SNR, which is less applicative Algorithms handling of side lobes: Eli & Gal’s algorithm: OMP => O 2 MP Omer’s first algorithm: weren’t handled Amplitude recovery was inaccurate – biggest issue in separating targets from noise

Background – Sidelobes

Project Goals Extending the basic radar model to include Doppler shift detection Improving performance in different SNR scenarios Removing the model order constraint

Improving performance in different SNR scenarios 1 st Goal : Detection in Low SNR

Past Speed bin division and OMP for each once Pulse number as bin number Simple OMP speed detection Present Remove every target found and iterate Other bin number Off grid speed detection

Defining Speed Quant

1 st Goal : Detection in Low SNR Past Speed bin division and OMP for each Pulse number as bin number Simple OMP speed detection Present Remove every target found and iterate Other bin number Off grid speed detection

Results Comparison

2 nd Goal : Find Number of Targets Removing the model order constraint (4 targets)

The last implementation of O 2 MP, and most other CS algorithms required a priori knowledge of the model order. Remove this constraint by obtaining the information from the sampled signal 2 nd Goal : Find Number of Targets

Three conceptual ways: Pre processing determination of model order Determining model order as part of the processing Post processing determination of model order 2 nd Goal : Find Number of Targets

Three conceptual ways: Pre processing determination of model order Determining model order as part of the processing Post processing determination of model order 2 nd Goal : Find Number of Targets

Block Model Analog signal Analog processing Low rate ADC FFT for Fourier coeff. Subtract Target Focusing coeff. Using FFT Spectral analysis solver Stopping criteria

1 st Method : RMS calculating σ (RMS) and finding targets with amplitude larger then C * σ. By assuming Gaussian white noise we can calculate the probability of a Detection being false.

1 st Method : RMS

1 st Method : Model Assumptions

2 nd Method : Noise Floor

2 nd Method : Model Assumptions Again assuming FRI & Assumes there are a limited number of “similar” targets.

3 rd Method : Zero Target Noise Floor Calculating noise floor when the radar is aimed to a no target zone.

3 rd Method : Model Assumptions Again assuming FRI & Assumes we can calibrate the radar

Heuristic Parameters & Assumptions RMSNFZNF Parameter ratio of a false target and RMS Ratio between noise targets + Max Similar Amps Ratio between targets and noise floor Assumption Noise well defined by WGN approx. Artifacts smaller then threshold A known limit for target number Artifacts smaller then threshold

Compare Methods Results

Artifacts

There are always remnants when subtracting a target from the signal, resulting from estimation error

Artifact Estimation We simulated one target and forced the algorithm to find 2 We wanted to discover the amplitude of a first false target

We wanted to compare the 2 nd target found to the noise floor when there are no targets simulated Artifact Estimation

Fortunately we found that no false targets were added This proves that our subtraction is working well Artifact Estimation

Samples obtained from demo system Were analyzed by the algorithm Substantial artifacts remained Model order was properly estimated (after accounting for larger artifacts then simulation ) When sampling real (i.e. not complex) signals we cannot separate positive and negative velocities.

Problems encountered Targets that are sampled only in a real-valued channel with speed close to the edges (0 or maximal speed calculated) When simulating, the algorithms work well, however, while using real samples we have significant remnants Close targets (in time and speed space) cause a mismatch in model order

Speed Close to 0 and Remnants

Close Targets

Possible solutions Ignore targets found near previous hits (considering amplitude, distance and speed) For real signals - correlating the signal to an appropriate basis (DCT?)

What’s Next?

References J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit”, Information Theory, IEEE Trans. on, vol. 53, no. 12, pp. 4655–4666, E. Baransky, G. Itzhak, I. Shmuel, N. Wagner, E. Shoshan, and Y. C.Eldar, “A Sub- Nyquist Radar Prototype: Hardware and Algorithms”, submitted to IEEE Trans. on Aerospace and Electronic Systems, special issue on Compressed Sensing for Radar, Aug M. A. Herman and T. Strohmer, “High-resolution radar via compressed sensing,” IEEE Trans. Signal Processing, vol. 57,no. 6, pp. 2275–2284, Jun O. Bar-Ilan and Y. C. Eldar, “Sub-Nyquist Radar.” Munich, Germany: 9th International ITG Conference on Systems, Communications and Coding, Jan O. Bar-Ilan and Y. C. Eldar, “ Sub-Nyquist Radar via Doppler Focusing”, submitted to IEEE Trans. Sig. Proc., Nov

Questions ?

Appendixes The following slides are taken from our characterization presentation, they are here in case any background questions will be asked regarding those subject, for easier presentation.

Xampling via Doppler focusing Modulating with frequency

Xampling via Doppler focusing