Misspecified Cramer–Rao Bounds for Blind Channel Estimation Under Channel Order Misspecification

IEEE Transactions on Signal Processing - Tập 69 - Trang 5372-5385 - 2021
Le Trung Thanh1,2, Karim Abed-Meraim3, Nguyen Linh Trung2
1PRISME Laboratory, University of Orléans, Orleans, France
2Advanced Institute of Engineering and Technology, University of Engineering and Technology, Vietnam National University, Hanoi, Vietnam
3PRISME Laboratory, University of Orléans, Orléans, France

Tóm tắt

In estimation, the misspecified Cramer–Rao bound (MCRB), which is an extension of the well-known Cramer–Rao bound (CRB) when the underlying system model is misspecified, has recently attracted much attention. In this paper, we introduce a new interpretation of the MCRB, called the generalized MCRB (GMCRB), via the Moore–Penrose inverse operator. This bound is useful for singular problems and particularly blind channel estimation problems in which the Hessian matrix is noninvertible. Two closed-form expressions of the GMCRB are derived for unbiased blind estimators when the channel order is misspecified. The first bound deals with deterministic models where both the channel and unknown symbols are deterministic. The second one is devoted to stochastic models where we assume that transmitted symbols are unknown random variables i.i.d. drawn from a Gaussian distribution. Two case studies of channel order misspecification are investigated to demonstrate the effectiveness of the proposed GMCRBs over the classical CRBs. When the channel order is known or accurately estimated, both generalized bounds reduce to the classical bounds. Besides, the stochastic GMCRB is lower than the deterministic one, especially at high SNR.

Từ khóa

#Peformance lower bounds #constrained Cramer-Rao bound #misspecification #MIMO #channel order

Tài liệu tham khảo

rencher, 2008, Linear Models in Statistics

10.1016/j.sigpro.2017.07.029

10.1109/TSP.2016.2546222

benjamin, 1995, Direction finding using noise covariance modeling, IEEE Trans Signal Process, 43, 1557, 10.1109/78.398717

davidson, 2004, Econometric Theory and Methods

10.1109/TCYB.2018.2838680

10.1016/j.neunet.2008.06.017

fortunati, 2017, Misspecified Cramér–Rao bounds for complex unconstrained and constrained parameters, Proc Eur Signal Process Conf, 1644

10.1109/LSP.2016.2546383

10.1109/TSP.2016.2526961

10.2307/1912526

10.1371/journal.pone.0008915

10.1109/ICASSP40776.2020.9054139

10.1109/ICASSP40776.2020.9054370

pajovic, 2018, Misspecified Bayesian Cramér–Rao bound for sparse Bayesian, Proc IEEE Statist Signal Process Workshop, 263

10.1109/TSP.2003.811227

magnus, 2019, Matrix Differential Calculus with Applications in Statistics and Econometrics, 10.1002/9781119541219

10.1109/TIT.2012.2193116

10.1137/130912839

10.1109/TSP.2015.2411222

stykel, 2002, Analysis and numerical solution of generalized lyapunov equations

vuong, 1986, Cramer-Rao bounds for misspecified models, Social Science Working Paper, 652, 1

10.1017/CBO9781139020411

farah, 2012, Generalized and quadratic eigenvalue problems with Hermitian matrices

10.1109/MSP.2017.2738017

10.1109/5.622507

10.1109/TSP.2004.823504

10.1109/78.489039

10.1016/j.sigpro.2005.04.014

10.1109/COMST.2007.382406

10.1109/SPAWC.1997.630172

10.1109/ICASSP.2004.1326847

10.1109/GLOCOM.2000.891295

10.1109/ACSSC.2014.7094597

10.1109/TVT.2007.895562

10.1109/ACCESS.2020.3022710

10.1109/TWC.2017.2717406

10.1561/2000000008

10.1109/78.890346

10.1137/151005099

thanh, 0, Performance lower bounds of blind system identification techniques in the presence of channel order estimation error, Proc Eur Signal Process Conf, 1646

10.1109/LSP.2004.836948

10.1109/97.700921

10.1109/TSP.2012.2208105

10.1109/78.533723

10.1109/TSP.2018.2883915

10.1109/TIT.2017.2731845

10.1016/0005-1098(78)90005-5

10.1109/TAC.1974.1100705

sedghi, 2019, The singular values of convolutional layers, Proc Int Conf Learn Representations, 1

10.1109/78.806077

10.1109/78.942620

10.1109/TSP.2006.879271

10.1109/TBC.2009.2023201

10.1109/TSP.2010.2100384

10.1109/VTCSpring.2015.7145718

10.1109/ACCESS.2017.2788020

kay, 1993, Fundamentals of Statistical Signal Processing

10.1186/s13638-015-0318-1

10.1109/TWC.2013.022713.120961

10.1109/78.650264

10.1109/78.558487

10.1109/18.556108

10.1109/TSP.2002.1003068

10.1109/MSP.2008.918027

10.1109/78.476442

10.1109/TCOMM.2017.2761384

10.1109/TWC.2010.112310.091576

10.1109/10.650350

10.1111/rssb.12187

10.1016/j.cmpb.2007.07.002

10.1109/10.900248

10.1109/TVT.2007.891429

10.1371/journal.pone.0008520

Thông tin
Thông tin xuất bản

IEEE Transactions on Signal Processing

Tập 69

5372-5385

Thông tin tác giả