Testing Uncorrelation of Multi-Antenna Signals Using Linear Spectral Statistics of the Spatio-Temporal Sample Autocorrelation Matrix

We consider the use of the spatio-temporal sample autocorrelation matrix in order to determine whether the signals received by a distributed antenna system are spatially correlated. The asymptotic behavior of linear spectral statistics built from this matrix is studied, assuming that (i) the number of antennas, (ii) the sample size and (iii) the number of tested time lags all converge to infinity. In this asymptotic regime, linear spectral statistics of the spatiotemporal sample correlation matrix are shown to be asymptotically equivalent to the corresponding functional average with respect to a Marchenko-Pastur distribution. This means that the eigenvalue distribution of the original sample autocorrelation matrix essentially behaves as a sample covariance matrix of spatio-temporal white noise with equivalent dimensions. This result turns out to be useful in order to address the problem of detecting the presence of wideband directional signals with a number of uncalibrated receivers distributed over a large area.