A Convex Relaxation Approach to Higher-Order Statistical Approaches to Signal Recovery

In this paper, we investigate an efficient numerical approach for solving higher order statistical methods for blind and semiblind signal recovery from nonideal channels. We develop numerical algorithms based on convex optimization relaxation for the minimization of higher order statistical cost functions. The new formulation through convex relaxation overcomes the local convergence problem of existing gradient-descent-based algorithms and applies to several well-known cost functions for effective blind signal recovery, including blind equalization and blind source separation in both single-input–single-output (SISO) and multiple-input–multiple-output (MIMO) systems. We also propose a fourth-order pilot-based cost function that benefits from this approach. The simulation results demonstrate that our approach is suitable for short-length packet data transmission using only a few pilot symbols.

[1]  C. Papadias,et al.  A constant modulus algorithm for multiuser signal separation in presence of delay spread using antenna arrays , 1997, IEEE Signal Processing Letters.

[2]  Pierre Comon,et al.  Optimal Step-Size Constant Modulus Algorithm , 2008, IEEE Transactions on Communications.

[3]  E. H. Satorius,et al.  An Alternative Methodology for Blind Equalization , 1993 .

[4]  Philip Schniter,et al.  Blind equalization using the constant modulus criterion: a review , 1998, Proc. IEEE.

[5]  Yong-Seok Choi,et al.  Joint blind equalization, carrier recovery, and timing recovery for HDTV modem , 1993, Other Conferences.

[6]  Rodney A. Kennedy,et al.  Least squares approach to blind channel equalization , 1999, IEEE Trans. Commun..

[7]  Ta‐Hsin Li.  Blind Deconvolution of Linear Systems with Multilevel Nonstationary Inputs , 1995 .

[8]  Zhi-Quan Luo,et al.  Blind constant modulus equalization via convex optimization , 2003, IEEE Trans. Signal Process..

[9]  N. Z. Shor,et al.  Modifiedr-algorithm to find the global minimum of polynomial functions , 1997 .

[10]  Jitendra K. Tugnait,et al.  Comments on 'New criteria for blind deconvolution of nonminimum phase systems (channels)' , 1992, IEEE Trans. Inf. Theory.

[11]  고봉환,et al.  Minimum Entropy Deconvolution을 이용한 회전체 시스템의 결함 모니터링 , 2013 .

[12]  Geoffrey Ye Li,et al.  Adaptive Blind Source Separation and Equalization for Multiple-Input/Multiple-Output Systems , 1998, IEEE Trans. Inf. Theory.

[13]  Walter Rudin,et al.  Sums of Squares of Polynomials , 2000, Am. Math. Mon..

[14]  R. Pickholtz,et al.  The recursive constant modulus algorithm; a new approach for real-time array processing , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[15]  Rodney A. Kennedy,et al.  Local stable minima of the Sato recursive identification scheme , 1990, 29th IEEE Conference on Decision and Control.

[16]  Zhi Ding,et al.  A fast linear programming algorithm for blind equalization , 2000, IEEE Trans. Commun..

[17]  Anton van den Hengel,et al.  Semidefinite Programming , 2014, Computer Vision, A Reference Guide.

[18]  J. Treichler,et al.  A new approach to multipath correction of constant modulus signals , 1983 .

[19]  P. Parrilo.  Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization , 2000 .

[20]  Zhi Ding,et al.  Stationary points of a kurtosis maximization algorithm for blind signal separation and antenna beamforming , 2000, IEEE Trans. Signal Process..

[21]  Pablo A. Parrilo,et al.  Minimizing Polynomial Functions , 2001, Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science.

[22]  B. P. Lathi,et al.  Modern Digital and Analog Communication Systems , 1983 .

[23]  Tho Le-Ngoc,et al.  Recursive least squares constant modulus algorithm for blind adaptive array , 2004, IEEE Transactions on Signal Processing.

[24]  Phillip A. Regalia.  A finite-interval constant modulus algorithm , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[25]  D. Godard,et al.  Self-Recovering Equalization and Carrier Tracking in Two-Dimensional Data Communication Systems , 1980, IEEE Trans. Commun..

[26]  Yurii Nesterov,et al.  Squared Functional Systems and Optimization Problems , 2000 .

[27]  Pierre Comon,et al.  Semi-blind constant modulus equalization with optimal step size , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[28]  Jian Yang,et al.  Blind equalization for broadband access , 1999, IEEE Commun. Mag..

[29]  Zhi Ding,et al.  On Steepest Descent Adaptation: A Novel Batch Implementation of Blind Equalization Algorithms , 2010, 2010 IEEE Global Telecommunications Conference GLOBECOM 2010.

[30]  C. L. Nikias,et al.  CRIMNO: criterion with memory nonlinearity for blind equalization , 1991, [1991] Conference Record of the Twenty-Fifth Asilomar Conference on Signals, Systems & Computers.

[31]  Zhi Ding,et al.  Blind Equalization and Identification , 2001 .

[32]  Kim-Chuan Toh,et al.  Solving semidefinite-quadratic-linear programs using SDPT3 , 2003, Math. Program..

[33]  B. G. Agee,et al.  The least-squares CMA: A new technique for rapid correction of constant modulus signals , 1986, ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[34]  Zhi Ding,et al.  A Linear Programming Receiver for Blind Detection of Full Rate Space-Time Block Codes , 2010, IEEE Transactions on Signal Processing.