scholarly journals Fisher-Information-Matrix Based Analysis of Semiblind MIMO Frequency Selective Channel Estimation

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Aditya K. Jagannatham ◽  
Bhaskar D. Rao
Keyword(s):  
Fisher Information ◽  
Fisher Information Matrix ◽  
Finite Impulse Response ◽  
Mimo System ◽  
Multiple Input Multiple Output ◽  
Information Matrix ◽  
Wireless Channel ◽  
Mimo Channel ◽  
Minimum Number ◽  
Frequency Selective

We present a study of semiblind (SB) estimation for a frequency-selective (FS) multiple-input multiple-output (MIMO) wireless channel using a novel Fisher-information matrix (FIM) based approach. The frequency selective MIMO system is modeled as a matrix finite impulse response (FIR) channel, and the transmitted data symbols comprise of a sequence of pilot symbols followed by the unknown blind symbols. It is demonstrated that the FIM for this system can be expressed as the sum of the blind FIM Jb and pilot FIM Jp. We present a key result relating the rank of the FIM to the number of blindly identifiable parameters. We then present a novel maximum-likelihood (ML) scheme for the semiblind estimation of the MIMO FIR channel. We derive the Cramer-Rao Bound (CRB) for the semiblind scheme. It is observed that the semi-blind MSE of estimation of the MIMO FIR channel is potentially much lower compared to an exclusively pilot-based scheme. Finally, we derive a lower bound for the minimum number of pilot symbols necessary for the estimation of an FIR MIMO channel for any general semi-blind scheme. Simulation results are presented to augment the above analysis.

scholarly journals Implementation of Sparse Techniques for MIMO Channel Estimation

2021 ◽  
Vol 9 (VI) ◽  
pp. 1450-1456
Author(s):  
S. Ramith
Keyword(s):  
Channel Estimation ◽  
Compressed Sensing ◽  
Mimo System ◽  
Multiple Input Multiple Output ◽  
Adaptive Methods ◽  
Wireless Channel ◽  
Mimo Channel ◽  
Computational Time ◽  
Pilot Symbols ◽  
Sparsity Level

Channel estimation plays a very important role on the performance of wireless communication systems.Channel estimation can be carried out in different ways: with or without the help of a parametric model, using frequency and/or time correlation properties in the wireless channel, blind methods or those based on training pilots, adaptive or non-adaptive methods. As more antennas are added to Multiple Input Multiple Output (MIMO) system more computational resources and power are required. There is a need to address this problem of the overhead in training symbol based models for channel estimation. Compressed Sensing (CS) algorithms are beneficial in addressing these limitations in the system to increase the spectral efficiency can help free up resources and prevent additional taxing on the hardware. Compressed sensing the pilot symbols by using CS algorithms like OMP, SP, and CoSaMP algorithms. The channel coefficients are obtained through LS, MMSE and LMS techniques. Then, a very small amount of frequency-domain orthogonal pilots are used for the accurate channel estimation.The traditional algorithms like LS , MMSE and LMS combined with CS algorithms have better performance at low SNRs compared to conventional techniques alone in terms of computational time complexity and Normalised Mean Square Error(NMSE) performance. There is a halving of pilot symbols used for training by using the CS algorithm. MSE performance is increased with increase in sparsity level. CoSaMP performs better than SP and OMP at low SNRs. With increase in sparsity level after 50K, the performance of SP is comparable to that of CoSaMP. OMP is simple to implement but MSE performance is less and computational time is more compared to SP and CoSaMP.

scholarly journals Optimal design for population pk/pd models

2012 ◽  
Vol 51 (1) ◽  
pp. 115-130
Author(s):  
Sergei Leonov ◽  
Alexander Aliev
Keyword(s):  
Optimal Design ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Optimal Sampling ◽  
Design Algorithm ◽  
Sampling Schemes ◽  
Population Pk ◽  
Different Types

ABSTRACT We provide some details of the implementation of optimal design algorithm in the PkStaMp library which is intended for constructing optimal sampling schemes for pharmacokinetic (PK) and pharmacodynamic (PD) studies. We discuss different types of approximation of individual Fisher information matrix and describe a user-defined option of the library.

Singularities Affect Dynamics of Learning in Neuromanifolds

2006 ◽  
Vol 18 (5) ◽  
pp. 1007-1065 ◽  
Author(s):  
Shun-ichi Amari ◽  
Hyeyoung Park ◽  
Tomoko Ozeki
Keyword(s):  
Model Selection ◽  
Parameter Space ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Gaussian Mixture ◽  
Multilayer Perceptrons ◽  
Hierarchical Systems ◽  
Space Forms ◽  
Training Error

The parameter spaces of hierarchical systems such as multilayer perceptrons include singularities due to the symmetry and degeneration of hidden units. A parameter space forms a geometrical manifold, called the neuromanifold in the case of neural networks. Such a model is identified with a statistical model, and a Riemannian metric is given by the Fisher information matrix. However, the matrix degenerates at singularities. Such a singular structure is ubiquitous not only in multilayer perceptrons but also in the gaussian mixture probability densities, ARMA time-series model, and many other cases. The standard statistical paradigm of the Cramér-Rao theorem does not hold, and the singularity gives rise to strange behaviors in parameter estimation, hypothesis testing, Bayesian inference, model selection, and in particular, the dynamics of learning from examples. Prevailing theories so far have not paid much attention to the problem caused by singularity, relying only on ordinary statistical theories developed for regular (nonsingular) models. Only recently have researchers remarked on the effects of singularity, and theories are now being developed. This article gives an overview of the phenomena caused by the singularities of statistical manifolds related to multilayer perceptrons and gaussian mixtures. We demonstrate our recent results on these problems. Simple toy models are also used to show explicit solutions. We explain that the maximum likelihood estimator is no longer subject to the gaussian distribution even asymptotically, because the Fisher information matrix degenerates, that the model selection criteria such as AIC, BIC, and MDL fail to hold in these models, that a smooth Bayesian prior becomes singular in such models, and that the trajectories of dynamics of learning are strongly affected by the singularity, causing plateaus or slow manifolds in the parameter space. The natural gradient method is shown to perform well because it takes the singular geometrical structure into account. The generalization error and the training error are studied in some examples.

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