Induced ∞∞-norm FIR filter for recovering MPSK-type modulus signals

This paper proposes a method of perfectly recovering MPSK-type (multiple phase-shift keying) modulus input signals against component-wise norm-bounded disturbances via an induced ∞∞-norm finite impulse response (FIR) filter. The induced ∞∞-norm criterion maintains the distance between the input signals and the estimated signals within a given bound for perfectly recovering the input signals, and the FIR structure makes the system robust against temporary uncertainties or disturbances. The induced ∞∞-norm FIR filter is designed through solving linear matrix inequalities (LMIs) iteratively. Examples of the application to equalizers show that the induced ∞∞-norm FIR filter guarantees the perfect recovery of the MPSK-type modulus input signals.