Cramer-Rao Bound for Sparse Signals Fitting the Low-Rank Model with Small Number of Parameters

In this paper, we consider signals with a low-rank covariance matrix which reside in a low-dimensional subspace and can be written in terms of a finite (small) number of parameters. Although such signals do not necessarily have a sparse representation in a finite basis, they possess a sparse structure which makes it possible to recover the signal from compressed measurements. We study the statistical performance bound for parameter estimation in the low-rank signal model from compressed measurements. Specifically, we derive the Cramer-Rao bound (CRB) for a generic low-rank model and we show that the number of compressed samples needs to be larger than the number of sources for the existence of an unbiased estimator with finite estimation variance. We further consider the applications to direction-of-arrival (DOA) and spectral estimation which fit into the low-rank signal model. We also investigate the effect of compression on the CRB by considering numerical examples of the DOA estimation scenario, and show how the CRB increases by increasing the compression or equivalently reducing the number of compressed samples.Comment: 14 pages, 1 figure, Submitted to IEEE Signal Processing Letters on December 201

Device-free Localization using Received Signal Strength Measurements in Radio Frequency Network

Device-free localization (DFL) based on the received signal strength (RSS) measurements of radio frequency (RF)links is the method using RSS variation due to the presence of the target to localize the target without attaching any device. The majority of DFL methods utilize the fact the link will experience great attenuation when obstructed. Thus that localization accuracy depends on the model which describes the relationship between RSS loss caused by obstruction and the position of the target. The existing models is too rough to explain some phenomenon observed in the experiment measurements. In this paper, we propose a new model based on diffraction theory in which the target is modeled as a cylinder instead of a point mass. The proposed model can will greatly fits the experiment measurements and well explain the cases like link crossing and walking along the link line. Because the measurement model is nonlinear, particle filtering tracing is used to recursively give the approximate Bayesian estimation of the position. The posterior Cramer-Rao lower bound (PCRLB) of proposed tracking method is also derived. The results of field experiments with 8 radio sensors and a monitored area of 3.5m 3.5m show that the tracking error of proposed model is improved by at least 36 percent in the single target case and 25 percent in the two targets case compared to other models.Comment: This paper has been withdrawn by the author due to some mistake

CRLBs for Pilot-Aided Channel Estimation in OFDM System under Gaussian and Non-Gaussian Mixed Noise

The determination of Cramer-Rao lower bound (CRLB) as an optimality criterion for the problem of channel estimation in wireless communication is a very important issue. Several CRLBs on channel estimation have been derived for Gaussian noise. However, a practical channel is affected by not only Gaussian background noise but also non-Gaussian noise such as impulsive interference. This paper derives the deterministic and stochastic CRLBs for Gaussian and non-Gaussian mixed noise. Due to the use of the non-parametric kernel method to build the PDF of non-Gaussian noise, the proposed CRLBs are suitable for practical channel environments with various noise distributions