Skip to main content

Table 1 Summary of the proposed algorithm

From: An RMT-based generalized Bayesian information criterion for signal enumeration

Step 1:

Perform eigenvalue decomposition on \({\hat{R}}\) given in (4), and descending order the sample eigenvalues \({\hat{\lambda }}_1>\ldots >{\hat{\lambda }}_m\). The corresponding sample eigenvectors are denoted as \({\hat{\varvec{u}}}_1, \ldots , {\hat{\varvec{u}}}_m\)

Step 2:

For \(k = 0, 1, \ldots , \min (m,n)-1\), execute the following step 3 and step 4

Step 3:

Calculate \({\hat{\varvec{S}}}_w^{(k)}, {\hat{\beta }}_i^{(k)} (i = 1, 2, 3, 4), {\hat{\alpha }}_1^{(k)}, {\hat{\alpha }}_2^{(k)}, {\hat{\alpha }}_4^{(k)}, {\hat{\gamma }}^{(k)}\), and \({\hat{T}}^{(k)}\) with (20)–(24)

Step 4:

Compute the function of the proposed GBIC-based method with (27)

Step 5:

The signal number is estimated by minimizing the proposed criterion of (28)