Polynomial ambiguity resistant precoders (PARP) for MIMO channels: Necessity and sufficiency for the blind identifiability and PARP characterization and construction

In this paper, we consider the following precoded MIMO system blind identifiability problems: Let Y(z) = H(z)G(z)X(z); what is the condition on a precoder G(z) such that the input signal X(z) and/or the MIMO channel inverse H^-1(z) can be recovered from the received signal Y(z) and the precoder G(z)? How to construct such precoders? In the above MIMO system, signals are deterministic. We propose (strong) polynomial ambiguity resistant precoders (PARP). For an almost surely given MIMO channel H(z), an input signal X(z) can be blindly identified from Y(z) and G(z) if and only if G(z) is PARP; an input signal X(z) and the MIMO channel inverse H^-1(z) can be blindly identified from Y(z) and G(z) if and only if G(z) is strong PARP. We also provide some properties and constructions on (strong) PARP precoders.