Question about the MUSIC algorithm

Hi,
I am curious if anyone knows a way around a problem I've encountered with the MUSIC algorithm (Multiple Signal Classification method people
use to determine a signal's angle of arrival). I've just started working with MUSIC, and since I know there are many different variations on this method, I am thinking that perhaps someone has addressed this problem.
Suppose you have a uniform linear array of antennas with some spacing L0/2, where L0 is some effective wavelength for which this array is a "resolving array" (as defined by Cantoni and Godara).
Now suppose you have 2 signals where for the sake of specificity has wavelengths L1 =0.9*L0 and and L2 =1.1*L0 and AOAs, alpha1 = pi/6 and alpha2 = pi/3
You do a FFT and find that there are two freqs present in the signal, f1 = c/L1 and f2 = c/L2.
If you run MUSIC by doing a simple search over the AOA values at freq f1, you should get two peaks: one at the true AOA (alpha1), but a second false peak since we can find some angle alpha' such that at f1 it produces a phase that is identical to that for the second source, i.e.: f1 *Cos(alpha') = f2*Cos(Alpha2), or if we work it out, we'd find 52 degrees. In other words, when we run MUSIC at this frequency, the freq mismatch between f1 and f2 results in a misestimation in the second AOA.
How does MUSIC handle this problem? Is there some variation of MUSIC (ESPIRT, etc) that deals with this type of case?
MTIA,
Matt B
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