The Distributed and Centralized Fusion Filtering Problems of Tessarine Signals from Multi-Sensor Randomly Delayed and Missing Observations under Tk-Properness Conditions

This paper addresses the fusion estimation problem in tessarine systems with multi-sensor observations affected by mixed uncertainties when under Tk-properness conditions. Observations from each sensor can be updated, delayed, or contain only noise, and a correlation is assumed between the state and the observation noises. Recursive algorithms for the optimal local linear filter at each sensor as well as both centralized and distributed linear fusion estimators are derived using an innovation approach. The Tk-properness assumption implies a reduction in the dimension of the augmented system, which yields computational savings in the previously mentioned algorithms compared to their counterparts, which are derived from real or widely linear processing. A numerical simulation example illustrates the obtained theoretical results and allows us to visualize, among other aspects, the insignificant difference in the accuracy of both fusion filters, which means that the distributed filter, although suboptimal, is preferable in practice as it implies a lower computational cost.

\({\mathbb{T}}\)-Proper Hypercomplex Centralized Fusion Estimation for Randomly Multiple Sensor Delays Systems with Correlated Noises

The centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises is analyzed under different T-properness conditions. Based on Tk, k=1,2, linear processing, new centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised. These algorithms have the advantage of providing optimal estimators with a significant reduction in computational cost compared to that obtained through a real or a widely linear processing approach. Simulation examples illustrate the effectiveness and applicability of the algorithms proposed, in which the superiority of the Tk linear estimators over their counterparts in the quaternion domain is apparent.

T-proper Hypercomplex Centralized Fusion Estimation for Randomly Multiple Sensor Delays Systems with Correlated Noises

The centralized fusion estimation problem for discrete-time vectorial tessarine signals in multiple sensor stochastic systems with random one-step delays and correlated noises is analyzed under different T-properness conditions. Based on Tk, k=1,2, linear processing, new centralized fusion filtering, prediction, and fixed-point smoothing algorithms are devised. These algorithms have the advantage of providing optimal estimators with a significant reduction in computational cost compared to that obtained through a real or widely linear processing approach. Simulation examples illustrate the effectiveness and applicability of the algorithms proposed, in which the superiority of the Tk linear estimators over their counterparts in the quaternion domain is apparent.

Widely Linear Filtering for Multi-Impairment Compensation in Coherent Optical Systems

We propose a blind joint equalization algorithm for M-QAM signals based on a widely linear filtering approach. The proposed scheme jointly compensates receiver IQ imbalance and polarization mixing, along with carrier recovery, followed by transmitter IQ imbalance compensation. We first investigate the proposed scheme's tolerance to transceiver IQ Imbalance, polarization mixing, phase noise and frequency offset through numerical simulations for 32 GBd PM-16QAM and PM-64QAM signals and compare its performance with the conventional digital processing algorithms. Further, with the proposed algorithm, we experimentally demonstrate the improvement in Q² value to up to ~ 1.22 dB for a 32 GBd PM-16QAM and ~ 3.72 dB for a 16 GBd PM-64QAM signal with a phase imbalance of 9^o. We show that the MSE convergence of the proposed joint equalizer is much faster than conventional DSP algorithms. Deployment of such an equalizer in optical communication systems is beneficial due to its improved tolerance to multiple impairments, albeit with increased complexity.

Widely Linear Filtering for Multi-Impairment Compensation in Coherent Optical Systems

We propose a blind joint equalization algorithm for M-QAM signals based on a widely linear filtering approach. The proposed scheme jointly compensates receiver IQ imbalance and polarization mixing, along with carrier recovery, followed by transmitter IQ imbalance compensation. We first investigate the proposed scheme's tolerance to transceiver IQ Imbalance, polarization mixing, phase noise and frequency offset through numerical simulations for 32 GBd PM-16QAM and PM-64QAM signals and compare its performance with the conventional digital processing algorithms. Further, with the proposed algorithm, we experimentally demonstrate the improvement in Q² value to up to ~ 1.22 dB for a 32 GBd PM-16QAM and ~ 3.72 dB for a 16 GBd PM-64QAM signal with a phase imbalance of 9^o. We show that the MSE convergence of the proposed joint equalizer is much faster than conventional DSP algorithms. Deployment of such an equalizer in optical communication systems is beneficial due to its improved tolerance to multiple impairments, albeit with increased complexity.