In this paper, we present a simple method for determining the number o
f signals impinging on a uniform linear array that is applicable even
in the extreme case of fully correlated signals. This technique uses w
hat we term modified rank sequences, which is a modification of the co
nstruction implicit in the matrix decomposition method of Di. We prove
that if a particular rank sequence stabilizes (the last two terms of
the sequence are equal) to a value strictly less then the common row s
ize of the defining block matrices, then this value equals the number
of signals, provided that the number of signals has not exceeded a Bre
sler-Macovski-type bound. Using the above characterization of stabilit
y, we formulate an algorithm that either determines the number of sign
als or indicates that the resolution capability of the algorithm has b
een exceeded. We also provide theorems that show that under certain co
nditions, a rank sequence can stabilize to a value strictly less than
the number of signals. This result allows us to find simple counterexa
mples to all of the existing rank sequence methods.