Capacity Scaling Limits and New Advancements in Optical Transmission Systems

Optical transmission technologies have gone through several generations of development.Spectral efficiency has significant ly improved,and industry has begun to search for an answer to a basic question：What are the fundamental linear and nonlin ear signal channel limitations of the Shannon theory when there is no compensation in an optical fiber transmission system？Next-generation technologies should exceed the 100G transmis sion capability of coherent systems in order to approach the Shannon limit.Spectral efficiency first needs to be improved be fore overall transmission capability can be improved.The means to improve spectral efficiency include more complex modulation formats and channel encoding/decoding algorithms,prefiltering with multisymbol detection,optical OFDM and Ny quist WDM multicarrier technologies,and nonlinearity compen sation.With further optimization,these technologies will most likely be incorporated into beyond-100G optical transport sys tems to meet bandwidth demand.

The convergence on spectrum of sample covariance matrices for information-plus-noise type data

In this paper,we consider the limiting spectral distribution of the information-plus-noise type sample covariance matrices Cn=1/N（Rn＋σXn）（Rn＋σXn）,under the assumption that the entries of Xn are independent but non-identically distributed random variables.It is proved that,almost surely,the empirical spectral distribution of Cn converges weakly to a non-random distribution whose Stieltjes transform satisfies a certain equation.Our result extends the previous one with the entries of Xn are i.i.d.random varibles to a more general case.The proof of the result mainly employs the Stein equation and the cumulant expansion formula of independent random variables.

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.

On eigenvalues of a high-dimensional Kendall's rank correlation matrix with dependence

In this paper,we investigate the limiting spectral distribution of a high-dimensional Kendall’s rank correlation matrix.The underlying population is allowed to have a general dependence structure.The result no longer follows the generalized Marcenko-Pastur law,which is brand new.It is the first result on rank correlation matrices with dependence.As applications,we study Kendall’s rank correlation matrix for multivariate normal distributions with a general covariance matrix.From these results,we further gain insights into Kendall’s rank correlation matrix and its connections with the sample covariance/correlation matrix.