This paper investigates the consistency of the LASSO-based DOA estimation of the narrow-band signals in infinitely high SNR. Such a method provides a robust and accurate approximation of the Maximum Likelihood estimation. However, as we show, unlike the standard techniques such as subspace methods the LASSO-based estimation is generally not consistent in high SNRs. In return, considering the true DOA's, we show that the method is consistent for certain configuration of the sources. This approach leads us to relate such a conditional consistency to the resolution concept. We next give a condition to verify the consistency of a given set of directions and simplify it to a computationally fast equivalent algorithm. The results show that the resolution in infinitely high SNR case for m sensors decreases by speed 1 over m
