Signal Amplitude Estimation and Detection From Unlabeled Binary Quantized Samples

Signal amplitude estimation and detection from unlabeled quantized binary samples are studied, assuming that the order of the time indexes is completely unknown. First, maximum likelihood (ML) estimators are utilized to estimate both the permutation matrix and unknown signal amplitude under arbitrary but known signal shape and quantizer thresholds. Sufficient conditions are provided, under which an ML estimator can be found in polynomial time, and an alternating maximization algorithm is proposed to solve the general problem via good initialization. In addition, the statistical identifiability of the model is studied. Furthermore, an approximation of the generalized likelihood ratio test detector is adopted to detect the presence of the signal. In addition, an accurate approximation of the probability of successful permutation matrix recovery is derived, and explicit expressions are provided to reveal the relationship between the signal length and the number of quantizers. Finally, numerical simulations are performed to verify the theoretical results.

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

[2]  Giuseppe Caire,et al.  Signal Recovery From Unlabeled Samples , 2017, IEEE Transactions on Signal Processing.

[3]  Steven Kay,et al.  Fundamentals Of Statistical Signal Processing , 2001 .

[4]  Robin J. Evans,et al.  A Bayesian solution and its approximations to out-of-sequence measurement problems , 2003, Inf. Fusion.

[5]  Husheng Li,et al.  Time Synchronization Attack in Smart Grid: Impact and Analysis , 2013, IEEE Transactions on Smart Grid.

[6]  Martin J. Wainwright,et al.  Linear regression with an unknown permutation: Statistical and computational limits , 2016, 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

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

[8]  P.K. Varshney,et al.  Target Location Estimation in Sensor Networks With Quantized Data , 2006, IEEE Transactions on Signal Processing.

[9]  Martin J. Wainwright,et al.  Denoising linear models with permuted data , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).

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

[11]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[12]  Luca Schenato,et al.  Optimal Estimation in Networked Control Systems Subject to Random Delay and Packet Drop , 2008, IEEE Transactions on Automatic Control.

[13]  Paolo Braca,et al.  Asymptotic Efficiency of the PHD in Multitarget/Multisensor Estimation , 2013, IEEE Journal of Selected Topics in Signal Processing.

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

[15]  Dimitri P. Bertsekas,et al.  Nonlinear Programming , 1997 .

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

[17]  Sean P. Meyn,et al.  Universal and Composite Hypothesis Testing via Mismatched Divergence , 2009, IEEE Transactions on Information Theory.

[18]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[19]  Pramod K. Varshney,et al.  Channel Aware Target Localization With Quantized Data in Wireless Sensor Networks , 2009, IEEE Transactions on Signal Processing.

[20]  Stefan Aachen,et al.  Signal Detection In Non Gaussian Noise , 2016 .

[21]  James Y. Zou,et al.  Linear Regression with Shuffled Labels , 2017, 1705.01342.

[22]  T. Humphreys,et al.  Assessing the Spoofing Threat: Development of a Portable GPS Civilian Spoofer , 2008 .

[23]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[24]  Paolo Braca,et al.  Adaptive filtering of imprecisely time-stamped measurements with application to AIS networks , 2015, 2015 18th International Conference on Information Fusion (Fusion).

[25]  E. Lehmann.  Elements of large-sample theory , 1998 .

[26]  Alejandro Ribeiro,et al.  Bandwidth-constrained distributed estimation for wireless sensor Networks-part I: Gaussian case , 2006, IEEE Transactions on Signal Processing.

[27]  Suhas N. Diggavi,et al.  Identity Aware Sensor Networks , 2009, IEEE INFOCOM 2009.

[28]  Martin Vetterli,et al.  Unlabeled sensing: Solving a linear system with unordered measurements , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[29]  Haralabos C. Papadopoulos,et al.  Sequential signal encoding from noisy measurements using quantizers with dynamic bias control , 2001, IEEE Trans. Inf. Theory.

[30]  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).

[31]  Lijun Qian,et al.  GPS spoofing attack on time synchronization in wireless networks and detection scheme design , 2012, MILCOM 2012 - 2012 IEEE Military Communications Conference.

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