Bayesian filters can be made robust to outliers if the solutions are developed under the assumption of heavy-tailed distributed noise. However, in the absence of outliers, these robust solutions perform worse than the standard Gaussian assumption based filters. In this work, we develop a novel robust filter that adopts both Gaussian and multivariate t-distributions to model the outliers contaminated measurement noise. The effects of these distributions are combined within a Bayesian Model Averaging (BMA) framework. Moreover, to reduce the computational complexity of the proposed algorithm, a restricted variational Bayes (RVB) approach handles the multivariate t-distribution instead of its standard iterative VB (IVB) counterpart. The performance of the proposed filter is compared against a standard cubature Kalman filter (CKF) and a robust CKF (employing IVB method) in a representative simulation example concerning target tracking using range and bearing measurements. In the presence of outliers, the proposed algorithm shows a 38 % improvement over CKF in terms of root-mean-square-error (RMSE) and is computationally 2.5 times more efficient than the robust CKF.

In this work, a variable step-size (VSS) blind equalization algorithm is presented for a multimodulus blind equalization scheme. The parameters of the proposed algorithm are selected using a particle swarm optimization strategy. Eventually, the best parameters for the proposed VSS blind equalization algorithm are obtained and better performance is obtained when compared to the trial-and-error method for choosing these parameters. Ultimately, a considerable reduction in computational complexity when compared to the fixed-step algorithm with extra constraints. Simulation results support this new proposed technique.

Multimodulus algorithms (MMA) based adaptive blind equalizers mitigate inter-symbol interference in a digital communication system by minimizing dispersion in the quadrature components of the equalized sequence in a decoupled manner, i.e., the in-phase and quadrature components of the equalized sequence are used to minimize dispersion in the respective components of the received signal. These unsupervised equalizers are mostly incorporated in bandwidth-efficient digital receivers (wired, wireless or optical) which rely on quadrature amplitude modulation based signaling. These equalizers are equipped with nonlinear error-functions in their update expressions which makes it a challenging task to evaluate analytically their steady-state performance. However, exploiting variance relation theorem, researchers have recently been able to report approximate expressions for steady-state excess mean square error (EMSE) of such equalizers for noiseless but interfering environment. In this work, in contrast to existing results, we present exact steady-state tracking analysis of two multimodulus equalizers in a non-stationary environment. Specifically, we evaluate expressions for steady-state EMSE of two equalizers, namely the MMA2-2 and the βMMA. The accuracy of the derived analytical results is validated using different set experiments and found in close agreement.

In this paper, we design and analyze a Newton-like blind equalization algorithm for the APSK system. Specifically, we exploit the principle of minimum entropy deconvolution and derive a blind equalization cost function for APSK signals and optimize it using Newton׳s method. We study and evaluate the steady-state excess mean square error performance of the proposed algorithm using the concept of energy conservation. Numerical results depict a significant performance enhancement for the proposed scheme over well established blind equalization algorithms. Further, the analytical excess mean square error of the proposed algorithm is verified with computer simulations and is found to be in good conformation.

A constant modulus algorithm is presented for blind equalization of complex-valued communication channels. The proposed algorithm is obtained by solving a novel deterministic optimization criterion which comprises the minimization of a priori as well as a posteriori dispersion error, leading to an update equation having a particular zero-memory continuous Bussgang-type nonlinearity. We also derive a stochastic bound for the range of step-sizes for a generic Bussgang-type constant modulus algorithm. The theoretical result is validated through computer simulations.

In this letter, we adaptively optimize the equalizer output energy to obtain a joint blind equalization and carrier-phase recovery solution. The resulting (multimodulus) update algorithm possesses a particular zero-memory Bussgang-type nonlinearity. We provide evidence of good performance, in comparison to existing adaptive methods, like RCA, MMA and CMA, through computer simulations for higher-order quadrature amplitude modulation signalling on symbol- and fractionally-spaced channels.

By generalizing and modifying some existing cost-functions, we present two new, generic and efficient multimodulus families of blind equalization algorithms for use in higher-order quadrature amplitude modulation based digital communication systems. Proposed algorithms are shown to be capable of blindly equalizing and recovering carrier-phase at convergence speed much faster than existing counterparts on certain QAM sizes. We show that particular examples of the proposed cost-functions include a number of existing algorithms. We also provide detailed dynamic convergence analysis which is found in good conformation with those obtained from Monte-Carlo experiments.

This letter presents two new blind equalization algorithms that are specifically designed for cross-QAM signals. Proposed algorithms minimize the dispersion of the equalizer output with respect to single or multiple cross-shaped zero error contour(s). Simulations and analysis demonstrate the good performance of the proposed algorithms

A new multimodulus algorithm is presented for blind equalization of complex-valued communication channels. The proposed algorithm is obtained by solving a novel deterministic optimization criterion that constituted the dispersion minimization of a priori as well as a posteriori quantities, leading to an update equation having a particular zero-memory continuous nonlinearity. Analyses of automatic phase-recovery and interference cancellation capabilities of the proposed algorithm are provided

In this letter, a new multimodulus algorithm for blind equalization of complex communication channels is derived by solving a constrained optimization problem with relaxation. The intersymbol interference (ISI) optimization and phase-recovery capabilities of the proposed algorithm are analyzed. It is shown from computer simulations that superior performance for the derived algorithm over Lin's algorithm is obtained.

In this work, a new algorithm, based on the minimum-disturbance principle with relaxation, is presented for the blind equalization of complex signals. This algorithm combines the benefits of the well-known reduced constellation algorithm (RCA) and constant modulus algorithm (CMA). The convergence characteristics of the proposed algorithm are demonstrated by way of simulations. In addition, closed form expressions are obtained for the statistical (dispersion) constants used in these algorithms.

Stop-and-go decision-directed (S-and-G-DD) equalization is the most primitive blind equalization (BE) method for the cancelling of intersymbol-interference in data communication systems. Recently, this scheme has been applied to complex-valued multilayer feedforward neural network, giving robust results with a lower mean-square error at the expense of slow convergence. To overcome this problem, in this work, a fast converging recursive least squares (RLS)-based complex-valued backpropagation learning algorithm is derived for S-and-G-DD blind equalization. Simulation results show the effectiveness of the proposed algorithm in terms of initial convergence.