Modeling error sensitivity of the MUSIC algorithm conditioned on resolved sources

When the correlation matrix is known, the resolution power of subspace algorithms is infinite. In the presence of modelling errors, even if the correlation matrix is known, sources can no longer be resolved with certainty. Focusing on the MUSIC algorithm, the purpose of this work is to provide closed form expression of bias and variance versus the model mismatch (these errors can be different for each source). Unlike previous work, these performance measures are derived conditioned on the success of a certain source resolution test. Among the resolution definitions proposed, we investigate which one is more suitable for our purposes. Numerical results support the theoretical investigations. Our findings are of a great interest for the determination of the necessary antenna calibration accuracy to achieve specifications on the estimator performance.