autocorrelation of multiple signals Problem: I am looking at an adaptive filtering application where the eigenvaluespread of the autocorrelation matrix $R$ is important for the convergence of the algorithm. For a single channel system the autocorrelation matrix $R$ for iterationstep $n$ can be calculated by $R=E\{ x(n)  x^H(n)\}$ where $x(n)$ is the input signal of the adaptive filter at iterationstep $n$ consisting of a number of samples $N$ recorded over a timespan. The calculation of the eigenvalues is straight forward.
Question: What is the &quot;multichannel equivalent&quot; for $R$ in the case of e.g. an adaptive filtering multichannel application? Do I need to calculate some sort of autocorrelation tensor?
You apply the same formula, but instead of using a scalar $x(n)$, you will have $x(n) \in \mathbb{C}^{M \times 1}$, where $M$ is the number of channels, and $x^{H}(n)$ is the $1 \times M$ matrix whose entries are the complex conjugate of the entries in $x(n)$. As a result $R \in \mathbb{C}^{M \times M}$ is an Hermitian matrix, and its eigenvalues are all real.