Estimation of Covariance Matrix in Signal Processing When the Noise Covariance Matrix is Arbitrary

Estimation of Covariance Matrix in Signal Processing When the Noise Covariance Matrix is Arbitrary

Estimation of Covariance Matrix

Estimation of population covariance matrices from samples of multivariate data is important. (1) Estimation of principle components and eigenvalues. (2) Construction of linear discriminant functions. (3) Establishing independence and conditional independence. (4) Setting confidence intervals on linear functions. Suppose we observed p dimensional multivariate samples X1, X2, · · · , Xn i.i.d. wi...

Effects of estimated noise covariance matrix in optimal signal detection

There is loss of efficiency when an estimated noise covariance matrix is used in the place of the unknown true noise covariance matrix in the construction of the optimum filter for signal detection. In the case of detecting a single signal specified by a real or a complex vector, we investigate the extent of this loss by obtaining an exact confidence bound for the realized signal to noise ratio...

Covariance Matrix Estimation in Time Series

Covariances play a fundamental role in the theory of time series and they are critical quantities that are needed in both spectral and time domain analysis. Estimation of covariance matrices is needed in the construction of confidence regions for unknown parameters, hypothesis testing, principal component analysis, prediction, discriminant analysis among others. In this paper we consider both l...

Covariance Matrix Estimation in Massive MIMO

Interference during the uplink training phase significantly deteriorates the performance of a massive MIMO system. The impact of the interference can be reduced by exploiting second order statistics of the channel vectors, e.g., to obtain minimum mean squared error estimates of the channel. In practice, the channel covariance matrices have to be estimated. The estimation of the covariance matri...