A Combinatorial Approach to One-Bit Compressive Radar Sensing

We propose a new sensing method for one-bit compressive pulsed radar. The method involves a sparse algorithm based on the concept of union-free family of sets, which is a combinatorial structure. The proposed algorithm is supported by a theorem which guarantees the accuracy of the method under certain conditions. Unlike some well-known sparse support recovery methods, the proposed method here is needless of knowing how sparse the signal vector is. Simulation results confirm the reliability of the proposed sensing algorithm. Specifically the method is shown to detect target indices accurately with a probability above 0.9, even at a signal-to-noise ratio of 0 dB.

[1]  Onkar Dabeer,et al.  Signal Parameter Estimation Using 1-Bit Dithered Quantization , 2006, IEEE Transactions on Information Theory.

[2]  Jian Li,et al.  One-bit compressive sampling with time-varying thresholds: Maximum likelihood and the Cramér-Rao bound , 2016, 2016 50th Asilomar Conference on Signals, Systems and Computers.

[3]  Prateek Jain,et al.  One-Bit Compressed Sensing: Provable Support and Vector Recovery , 2013, ICML.

[4]  Ming Yan,et al.  Robust 1-bit Compressive Sensing Using Adaptive Outlier Pursuit , 2012, IEEE Transactions on Signal Processing.

[5]  Stephen P. Boyd,et al.  Compressed Sensing With Quantized Measurements , 2010, IEEE Signal Processing Letters.

[6]  Ingrid Daubechies,et al.  Single-Bit Oversampled A/D Conversion With Exponential Accuracy in the Bit Rate , 2007, IEEE Transactions on Information Theory.

[7]  Wotao Yin,et al.  Trust, But Verify: Fast and Accurate Signal Recovery From 1-Bit Compressive Measurements , 2011, IEEE Transactions on Signal Processing.

[8]  Georg Zeitler,et al.  Bayesian Parameter Estimation Using Single-Bit Dithered Quantization , 2012, IEEE Transactions on Signal Processing.

[9]  Michael Unser,et al.  One-Bit Measurements With Adaptive Thresholds , 2012, IEEE Signal Processing Letters.

[10]  Jian Li,et al.  Compressive pulse-Doppler radar sensing via 1-bit sampling with time-varying threshold , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[11]  Jian Li,et al.  Compressive radar sensing via one-bit sampling with time-varying thresholds , 2016, 2016 50th Asilomar Conference on Signals, Systems and Computers.

[12]  Zoltán Füredi,et al.  Families of Finite Sets in Which No Set Is Covered by the Union of Two Others , 1982, J. Comb. Theory, Ser. A.

[13]  Yaniv Plan,et al.  Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach , 2012, IEEE Transactions on Information Theory.

[14]  Yaniv Plan,et al.  One‐Bit Compressed Sensing by Linear Programming , 2011, ArXiv.

[15]  Richard G. Baraniuk,et al.  Robust support recovery using sparse compressive sensing matrices , 2011, 2011 45th Annual Conference on Information Sciences and Systems.

[16]  Elias Masry,et al.  The reconstruction of analog signals from the sign of their noisy samples , 1980, IEEE Trans. Inf. Theory.

[17]  Rayan Saab,et al.  One-Bit Compressive Sensing With Norm Estimation , 2014, IEEE Transactions on Information Theory.

[18]  Anders Høst-Madsen,et al.  Effects of sampling and quantization on single-tone frequency estimation , 2000, IEEE Trans. Signal Process..

[19]  Onkar Dabeer,et al.  Multivariate Signal Parameter Estimation Under Dependent Noise From 1-Bit Dithered Quantized Data , 2008, IEEE Transactions on Information Theory.

[20]  Jian Li,et al.  One-bit compressive sampling with time-varying thresholds for sparse parameter estimation , 2016, 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM).

[21]  Laurent Jacques,et al.  Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors , 2011, IEEE Transactions on Information Theory.

[22]  Alejandro Ribeiro,et al.  Bandwidth-constrained distributed estimation for wireless sensor networks-part II: unknown probability density function , 2006, IEEE Transactions on Signal Processing.