arXiv subjects

Lu Wei

Publications and source records attributed to Lu Wei.

65 records · Page 4Linked to original sources

arXiv2015

Volume of Metric Balls in High-Dimensional Complex Grassmann Manifolds

Volume of metric balls relates to rate-distortion theory and packing bounds on codes. In this paper, the volume of balls in complex Grassmann manifolds is evaluated for an arbitrary radius. The ball is defined as a set of hyperplanes of a fixed dimension with reference to a center of possibly different dimension, and a generalized chordal distance for unequal dimensional subspaces is used. First, the volume is reduced to one-dimensional integral representation. The overall problem boils down to evaluating a determinant of a matrix of the same size as the subspace dimensionality. Interpreting this determinant as a characteristic function of the Jacobi ensemble, an asymptotic analysis is carried out. The obtained asymptotic volume is moreover refined using moment-matching techniques to provide a tighter approximation in finite-size regimes. Lastly, the pertinence of the derived results is shown by rate-distortion analysis of source coding on Grassmann manifolds.

cs.IT↗

arXiv2015

From Random Matrix Theory to Coding Theory: Volume of a Metric Ball in Unitary Group

Volume estimates of metric balls in manifolds find diverse applications in information and coding theory. In this paper, some new results for the volume of a metric ball in unitary group are derived via various tools from random matrix theory. The first result is an integral representation of the exact volume, which involves a Toeplitz determinant of Bessel functions. The connection to matrix-variate hypergeometric functions and Szegő's strong limit theorem lead independently from the finite size formula to an asymptotic one. The convergence of the limiting formula is exceptionally fast due to an underlying mock-Gaussian behavior. The proposed volume estimate enables simple but accurate analytical evaluation of coding-theoretic bounds of unitary codes. In particular, the Gilbert-Varshamov lower bound and the Hamming upper bound on cardinality as well as the resulting bounds on code rate and minimum distance are derived. Moreover, bounds on the scaling law of code rate are found. Lastly, a closed-form bound on diversity sum relevant to unitary space-time codes is obtained, which was only computed numerically in literature.

cs.IT↗

arXiv2015

Outage Capacity of Rayleigh Product Channels: a Free Probability Approach

The Rayleigh product channel model is useful in capturing the performance degradation due to rank deficiency of MIMO channels. In this paper, such a performance degradation is investigated via the channel outage probability assuming slowly varying channel with delay-constrained decoding. Using techniques of free probability theory, the asymptotic variance of channel capacity is derived when the dimensions of the channel matrices approach infinity. In this asymptotic regime, the channel capacity is rigorously proven to be Gaussian distributed. Using the obtained results, a fundamental tradeoff between multiplexing gain and diversity gain of Rayleigh product channels can be characterized by closed-form expression at any finite signal-to-noise ratio. Numerical results are provided to compare the relative outage performance between Rayleigh product channels and conventional Rayleigh MIMO channels.

cs.IT↗

arXiv2014

On the Outage Capacity of Orthogonal Space-time Block Codes Over Multi-cluster Scattering MIMO Channels

Multiple cluster scattering MIMO channel is a useful model for pico-cellular MIMO networks. In this paper, orthogonal space-time block coded transmission over such a channel is considered, where the effective channel equals the product of n complex Gaussian matrices. A simple and accurate closed-form approximation to the channel outage capacity has been derived in this setting. The result is valid for an arbitrary number of clusters n-1 of scatterers and an arbitrary antenna configuration. Numerical results are provided to study the relative outage performance between the multi-cluster and the Rayleigh-fading MIMO channels for which n=1.

cs.IT↗

arXiv2013

Singular value correlation functions for products of Wishart random matrices

Consider the product of $M$ quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalises the classical Wishart-Laguerre Gaussian Unitary Ensemble with M=1. In this paper we first compute the joint probability distribution for the singular values of the product matrix when the matrix size $N$ and the number $M$ are fixed but arbitrary. This leads to a determinantal point process which can be realised in two different ways. First, it can be written as a one-matrix singular value model with a non-standard Jacobian, or second, for $M\geq2$, as a two-matrix singular value model with a set of auxiliary singular values and a weight proportional to the Meijer $G$-function. For both formulations we determine all singular value correlation functions in terms of the kernels of biorthogonal polynomials which we explicitly construct. They are given in terms of hypergeometric and Meijer $G$-functions, generalising the Laguerre polynomials. Our investigation was motivated from applications in telecommunication of multi-layered scattering MIMO channels. We present the ergodic mutual information for finite-$N$ for such a channel model with $M-1$ layers of scatterers as an example.

math-ph↗

arXiv2013

Network Coding for Energy-Efficient Distributed Storage System in Wireless Sensor Networks

A network coding-based scheme is proposed to improve the energy efficiency of distributed storage systems in WSNs (wireless sensor networks), which mainly focuses on two problems: firstly, consideration is given to effective distributed storage technology in WSNs; secondly, we address how to repair the data in failed storage nodes with less resource. For the first problem, we propose a method to obtain a sparse generator matrix to construct network codes, and this sparse generator matrix is proven to be the sparsest. Benefiting from the sparse generator matrix, the energy consumption required to implement distributed storage is reduced. For the second problem, we designed a network coding-based iterative repair method, which adequately utilizes the idea of re-encoding at intermediate nodes from network coding theory. Benefiting from the re-encoding, the energy consumption required by data repair is significantly reduced. Moreover, we provide an explicit lower bound of field size required by this scheme, which implies that this scheme can work over a very small field and the required computation overhead of coding is very low. The simulation result verifies that by using our scheme, the total energy consumption required to implement distributed storage system in WSNs can be reduced on the one hand, and on the other hand, this method can also balance energy consumption of the networks.

cs.NI↗

arXiv2012

A Blind Time-Reversal Detector in the Presence of Channel Correlation

A blind target detector using the time reversal transmission is proposed in the presence of channel correlation. We calculate the exact moments of the test statistics involved. The derived moments are used to construct an accurate approximative Likelihood Ratio Test (LRT) based on multivariate Edgeworth expansion. Performance gain over an existing detector is observed in scenarios with channel correlation and relatively strong target signal.

cs.IT↗

arXiv2012

Approximation to Distribution of Product of Random Variables Using Orthogonal Polynomials for Lognormal Density

We derive a closed-form expression for the orthogonal polynomials associated with the general lognormal density. The result can be utilized to construct easily computable approximations for probability density function of a product of random variables, when the considered variates are either independent or correlated. As an example, we have calculated the approximative distribution for the product of Nakagami-m variables. Simulations indicate that accuracy of the proposed approximation is good with small cross-correlations under light fading condition.

cs.IT↗

arXiv2012

Locally Best Invariant Test for Multiple Primary User Spectrum Sensing

We consider multi-antenna cooperative spectrum sensing in cognitive radio networks, when there may be multiple primary users. A noise-uncertainty-free detector that is optimal in the low signal to noise ratio regime is analyzed in such a scenario. Specifically, we derive the exact moments of the test statistics involved, which lead to simple and accurate analytical formulae for the false alarm probability and the decision threshold. Simulations are provided to examine the accuracy of the derived results, and to compare with other detectors in realistic sensing scenarios.

cs.IT↗

arXiv2012

On the Exact Distribution of the Scaled Largest Eigenvalue

In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have been derived for the probability density function and the cumulative distribution function. The derived results involve only finite sums of polynomials. These results are obtained by taking advantage of properties of the Mellin transform for products of independent random variables.

cs.IT↗

arXiv2012

Spectrum Sensing in the Presence of Multiple Primary Users

We consider multi-antenna cooperative spectrum sensing in cognitive radio networks, when there may be multiple primary users. A detector based on the spherical test is analyzed in such a scenario. Based on the moments of the distributions involved, simple and accurate analytical formulae for the key performance metrics of the detector are derived. The false alarm and the detection probabilities, as well as the detection threshold and Receiver Operation Characteristics are available in closed form. Simulations are provided to verify the accuracy of the derived results, and to compare with other detectors in realistic sensing scenarios.

cs.IT↗