Source enumeration using the bootstrap for very few samples

We consider the problem of source enumeration in array processing when only few samples are available. In this case, the noise eigenvalues spread, so that most existing methods, which assume equality of the noise eigenvalues implicitly, suffer large performance loss or even break down. We present a method based on hypothesis testing with the bootstrap. The test statistic is derived by using the exponential profile property of the noise eigenvalues. Simulations show the significant performance gain offered by the proposed method in terms of correctly detecting the number of sources for a very small sample size.