  An algorithm called MUSIC-like algorithm was originally proposed as an
alternative method to the MUltiple SIgnal Classification (MUSIC) algorithm for
direction-of-arrival (DOA) estimation. Without requiring explicit model order
estimation, it was shown to have robust performance particularly in low
signal-to-noise ratio (SNR) scenarios. In this letter, the working principle of
a relaxation parameter {\beta}, a parameter which was introduced into the
formulation of the MUSIC-like algorithm, is provided based on geometrical
interpretation. To illustrate its robustness, the algorithm will be examined
under symmetric {\alpha}-stable distributed noise environment. An adaptive
framework is then developed and proposed in this letter to further optimize the
algorithm. The proposed adaptive framework is compared with the original
MUSIC-like, MUSIC, FLOM-MUSIC, and SSCM-MUSIC algorithms. A notable improvement
in terms of targets resolvability of the proposed method is observed under
different impulse noise scenarios as well as different SNR levels.
