Beam resolution improvement of linear array using MVDR beamformer
The MVDR beamformer is an adaptive technique - the response is dependent on the the interfering signals i.e. their locations, their SNRs and their correlations. This makes it difficult to say what the resolution is in traditional 3dB width type of terms. Essentially the MVDR will try to place nulls in the beampattern where the interferers are - so a 3dB width doesn't really tell you anything about the resolution.

You can also get strange effects, e.g. you'll get 0 dB gain in the desired look direction, and you'll have a sidelobe level of +10 dB somewhere, because it's trying to place a null in the beampattern in a particular location.

As a purely hypothetical example - consider you're forming a beam at 90$^\circ$ look direction and you have an interferer at 135$^\circ$. You apply the MVDR and you'll see your beampattern has a null at 135$^\circ$ and the mainlobe around 90$^\circ$ will have a certain width. Now if you add another interferer  at 45$^\circ$ and apply the MVDR - you'll have nulls in both the interfering bearing locations, but your mainlobe width around 90$^\circ$ has now increased. So that mainlobe width in the single interferer case doesn't really tell you much about what's going to happen when you add another interferer. Essentially you are using up another degree of freedom to null out the additional interferer.

What is probably more interesting to look at is - how close can I place an interferer before the MVDR can no longer null it out.

A good discussion on MVDR is in "Array Signal Processing" by Johnson and Dudgeon, Prentice Hall.

You can also look at "Optimum Array Processing" by Van Trees, Wiley Interscience - this may be overkill for what you want. You also have to be careful - he a uses slightly different definition of MVDR.