The BID for blind equalization of FIR MIMO channels

Blind identification and/or equalization of FIR MIMO channels driven by unknown colored signals is useful in many applications including in particular "smart" microphones. A technique called blind identification via decorrelation (BID) can identify an FIR MIMO channel using the second-order statistics of the channel output if the channel transfer function is of full rank and column-wise coprime and the channel input signals are mutually uncorrelated and of sufficiently diverse power spectra. This identifiability condition is much weaker than those required by other related techniques (which are hence outperformed significantly by the BID). The BID first forms a bank of MIMO subchannels and then constructs a decorrelator for each subchannel. The decorrelators can then be used to form a bank of SIMO channels, and each of the input signals is then estimated before the channel transfer function is estimated (named BID-1). Alternatively, the decorrelators can be used to estimate the channel transfer function before the input signals are estimated (named BID-2), BID-2 is shown to be more robust than BID-1.