Signal Detection From Unlabeled Ordered Samples

In this letter, a variant of the classical signal detection problem is studied, where the known signal is selected while preserving their relative order. A dynamic programming algorithm is utilized to recover the selection matrix, and a generalized likelihood ratio test detector is proposed to decide the null and the alternative hypothesis. Besides, a sufficient condition under which the selection matrix can be recovered with high probability is provided. Finally, the numerical simulations are conducted to verify the theoretical results.

[1]  Zhiwei Xu,et al.  Parameter Estimation via Unlabeled Sensing Using Distributed Sensors , 2017, IEEE Communications Letters.

[2]  Peter Willett,et al.  Sometimes They Come Back: Testing Two Simple Hypotheses (In The Realm Of Unlabeled Data) , 2018, 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[3]  Martin Vetterli,et al.  Unlabeled Sensing With Random Linear Measurements , 2015, IEEE Transactions on Information Theory.

[4]  Rick S. Blum,et al.  GPS spoofing attack characterization and detection in smart grids , 2016, 2016 IEEE Conference on Communications and Network Security (CNS).

[5]  Rick S. Blum,et al.  Signal Amplitude Estimation and Detection From Unlabeled Binary Quantized Samples , 2018, IEEE Transactions on Signal Processing.

[6]  Rémi Gribonval,et al.  Compressed sensing with unknown sensor permutation , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[7]  Giuseppe Caire,et al.  Signal recovery from unlabeled samples , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

[8]  Rick S. Blum,et al.  Hypothesis testing in the presence of maxwell's daemon: signal detection by unlabeled observations , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[9]  Martin J. Wainwright,et al.  Linear Regression With Shuffled Data: Statistical and Computational Limits of Permutation Recovery , 2018, IEEE Transactions on Information Theory.