Performance Limits of Alphabet Diversities for FIR SISO Channel Identification

Finite impulse responses (FIR) of single-input single-output (SISO) channels can be blindly identified from second-order statistics of transformed data, for instance when the channel is excited by binary phase shift keying (BPSK), minimum shift keying (MSK), or quadrature phase shift keying (QPSK) inputs. Identifiability conditions are derived by considering that noncircularity induces diversity. Theoretical performance issues are addressed to evaluate the robustness of standard subspace-based estimators with respect to these identifiability conditions. Then benchmarks such as asymptotically minimum variance (AMV) bounds based on various statistics are presented. Some illustrative examples are eventually given where Monte Carlo experiments are compared to theoretical performances. These comparisons allow to quantify limits to the use of the alphabet diversities for the identification of FIR SISO channels, and to demonstrate the robustness of algorithms based on high-order statistics.