Tighter Mean-Squared Error Bounds on Kurtosis-Based Fast-ICA

FastICA is a widely-used independent component analysis technique for blindly separating mixtures of instantaneouslymixed, independent sources recorded with multiple sensors. When using FastICA to estimate one source in interference, the unbiased mean-squared error can be bounded from above by the Schniter-Tong bounds on Shalvi-Weinstein estimators. We derive tighter upper bounds by extending both the Schniter-Tong proof and the Schniter-Johnson proof of upper bounds on constant-modulus estimators. These tighter bounds also exist over a wider range of sources and channels; existence gaps of over an order of magnitude of minimum-mean-squared error have been observed.