MUSIC and ESPRIT are methods that use subspace decomposition to identify signal Parameters. Subspace decomposition is achieved either by SVD or Eigen Value Decomposition. Subspace decomposition separates signal and noise singular/ eigen vectors which are then used to determine system parameters.
They both work on the principle that under high SNR, the noisy vector X can best approximated by its signal subspace. However, if SNR falls below a certain threshold, the vector X would find its better approximation in noise subspace. There is a lot of literature that can be found on this topic. Performance breakdown in MUSIC
Threshold Analysis of SVD based Algorithms
I am looking for a mathematical expression that would define bounds (if any) on the amplitudes of the signals impinging on the antenna array. For example, take 3 signals A, B and C. Also suppose that noise is fairly low. I want to know if there is a bound for subspace methods to work: $$ \|{amplitude(A) - amplitude(B)} \| >= \epsilon \\ \|{amplitude(B) - amplitude(C)} \| >= \epsilon \\ \|{amplitude(A) - amplitude(C)} \| >= \epsilon $$
In Matlab, I set amplitude of A as small as 1/10000 of B. C was same as B. MUSIC still worked. I need to present the results in a report and I would like to have proper analytical or numerical proofs.