DOA - 1D Music Algorithm
If you have three or more antennas, simply don't put them in a linear array. Any other array setup doesn't suffer from the ambiguity. Linear array is the worst choice here.

Of course, that breaks the periodicity constraint on the linear array that makes the autocorrelation space method MUSIC So, you'd need to change that algorithm. 

Luckily, you can simply put them in a circular array and change from cartesian to polar coordinates, and keep a very similar structure for your MUSIC implementation. Just remember that the resulting estimate you get might not be in angles, but in trigonometric function of angles, and needs to be converted back.

Another option is to use two different linear arrays and to combine the observation.

As long as you stick to the linear array, you simply never get any information that can tell one side from the other, and that's the end of the story :(