Numerical Solution to MUSIC and MVDR DOA estimator?

As we know, ESPRIT is a Direction-of-Arrival finding method which can
provide us a close-form solution, i.e. the source bearing is
calculated directly by this method.

However, for MUSIC and MVDR methods, they have no close-form solution.
The source bearing is determined by searching for the peaks in the
spatial spectrum plot. It is difficult especially when two or more
sources are present. We need to find the bearings corresponding to
local maximum peaks. My question is how to get a numerical solution to
these two DOA methods. It should be a peak detection problem. Is there
any other easier approach?

Thanks!

waters@starhub.net.sg (Yan.L) wrote in message news:<df850db4.0407080834.6d570aa3@posting.google.com>...
> As we know, ESPRIT is a Direction-of-Arrival finding method which can
> provide us a close-form solution, i.e. the source bearing is
> calculated directly by this method.
> 
> However, for MUSIC and MVDR methods, they have no close-form solution.
> The source bearing is determined by searching for the peaks in the
> spatial spectrum plot. It is difficult especially when two or more
> sources are present. We need to find the bearings corresponding to
> local maximum peaks. My question is how to get a numerical solution to
> these two DOA methods. It should be a peak detection problem. Is there
> any other easier approach?
> 
> Thanks!

I don't remember off the top of my head what MVDR is, but what MUSIC is 
concerned, the answer is no, there is no easy way of finding the DoAs.

As you know, the reason why ESPRIT provides a closed-form solution is 
that it exploits a spatial translation invariance between two spatial 
sub-arrays, and estimate the rotation matrix that that transforms the 
spatial covariance of one sub-array into the covariance of the other. 
Since the temporal frequency and array geometries are known, the 
translation matrix can be solved for DoAs. This means that ESPRIT only 
works with arrays that can be separated into spatially translation 
invariant subarrays. Not all arrays can be separated like this, so 
it follows that ESPRIT does not work with all arrays.

Now, MUSIC is a generic DoA estimator where no restrictions are imposed 
with respect to array geometry. This means, in turn, that there are no 
"extra" properties to exploit when solving for DoAs. Granted, there are 
versions of MUSIC that provide closed-form solutions, e.g. Root MUSIC, 
but these versions impose additional restrictions on the array (line 
array with uniform element spacing, in the case of Root MUSIC) that 
Classical MUSIC does not assume. 

In the general case, you are basically left with the search over frequency, 
as you suggest. If you implement MUSIC, just remember that the peaks of 
the pseudo spectrum have nothing whatsoever to do with the power of 
the sines. 

Rune