Bounds on MIMO channel estimation and equalization with side information

We present constrained Cramer-Rao bounds for multi-input multi-output (MIMO) channel and source estimation. We find the MIMO Fisher information matrix (FIM) and consider its properties, including the maximum rank of the unconstrained FIM, and develop necessary conditions for the FIM to achieve full rank. Equality constraints provide a means to study the potential value of side information, such as training (semi-blind case), constant modulus (CM) sources, or source non-Gaussianity. Non-redundant constraints may be combined in an arbitrary fashion, so that side information may be different for different sources. The bounds are useful for evaluating various MIMO source and channel estimation algorithms. We present an example using the constant modulus blind equalization algorithm.