Asymptotic distribution of the MUSIC null spectrum

The asymptotic distribution of the MUSIC null spectrum at the source location is derived. It is shown that the asymptotic distribution of the MUSIC null spectrum has a x² distribution: the asymptotic mean and variance of the MUSIC null spectrum depend on the degree of freedom that is two times the difference between the number of sensors and that of signals. From this result, explicit expressions for the asymptotic variance of the MUSIC null spectrum are obtained. The result is a simpler alternative to and a special case of the result obtained independently by H. Lee and M. Wengrovitz (see ibid., vol.39, no.6, p.1333, 1991)