Perturbation Analysis of Root-MUSIC-Type Methods for Blind Network-Assisted Diversity Multiple Access

We perform a first-order perturbation analysis of a root-MUSIC-type method for resolving collisions in the context of blind network-assisted diversity multiple access (BNDMA). Polynomial roots are computed as an intermediate step of the root-MUSIC algorithm for the purpose of blindly identifying the set of transmitters involved in a collision. We derive expressions for the individual and joint distributions of the noise-induced angular shifts of the computed roots. The expressions are analyzed in relation to the signal-to-noise ratio and the number of packet retransmissions made to resolve a collision. Results are verified numerically.