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In this paper, we present a theoretical convergence analysis of the affine projection algorithm (APA) based on the arguments of energy conservation. Although the APA and its convergence analysis have been widely studied, the dependency of weight-error vector on past noise is usually neglected for simplicity. To obtain accurate theoretical results for the APA, we here consider the dependency between the weight-error vector and past noise in the mean-square analysis presented by Shin and Sayed in [“Mean-square performance of a family of affine projection algorithms,” IEEE Transactions on Signal Processing, vol. 52, no. 1, pp. 90–102, January 2004]. Through this work, we can also theoretically analyze the behavior of the periodic APA, which updates its weights periodically. Simulation results show that our theoretical results coincide closely with simulations. [ABSTRACT FROM AUTHOR]

Multibaseline phase unwrapping is a critical processing procedure of multibaseline synthetic aperture radar interferometry (InSAR). It has an advantage over single-baseline phase unwrapping in discontinuous-terrain-height estimation. In this paper, the pixels' combination information of multiple InSAR interferograms with different baseline lengths is deeply investigated, and the term ambiguity vector is proposed to represent a pixel's ambiguity number of multiple interferograms. It is also revealed that pixels with the same ambiguity vector have an exclusive pattern among them. A fast cluster-analysis (CA)-based method is proposed for multibaseline phase unwrapping. In this method, all pixels are first clustered into different groups according to their patterns, and then, information of the cluster center is used to unwrap the phases of pixels group by group. Simulation results are shown to verify the effectiveness, efficiency, and noise robustness of CA multibaseline phase-unwrapping method. [ABSTRACT FROM AUTHOR]

A novel number theoretic transform called Inverse Gray Robust Symmetrical Number System (IGRSNS) is proposed for error control coding in this paper. IGRSNS is obtained by modifying Robust Symmetrical Number System (RSNS) that was proposed earlier, using Inverse Gray code property. Due to ambiguities present in each residue, RSNS has a short dynamic range (DR) compared to that in other number systems. The short DR of RSNS enables it to be effectively used for error detection without the addition of any redundant modulus as in Redundant Residue Number System. Although RSNS has a large redundant range, its detection ability is not optimal due to the Gray code property associated with it. In an attempt to overcome this limitation, we have proposed Inverse Gray coding to be combined with RSNS in increasing its effectiveness in error detection. The resulting IGRSNS thus inherits properties of both RSNS and Gray code. Analysis and simulations show that IGRSNS has a near-optimal error detection ability. The potential of IGRSNS for error correction is also investigated. Further, a novel error correction algorithm using one redundant modulus is proposed. Simulations show that the proposed algorithm performs well under all cases of single bit errors. [ABSTRACT FROM PUBLISHER]