Design and Properties of a Family of Reduced Interference Distributions

Abstract

A family of Doppler-lag kernels is introduced to design the reduced interference distributions. The proposed kernel functions with two parameters \({{\varvec{n}}}\) and \({\varvec{\alpha }}\) are of the product \({\varvec{\nu }} {\varvec{\tau }} \) and satisfy all the nine desirable kernel constraints. The family of Cohen time–frequency distributions with these kernels includes some existing reduced interference distributions such as Margenau–Hill, Born–Jordan and Bessel distributions. Also the signal-to-interference ratio (SIR) in time–frequency plane is defined, and reduced interference capabilities with \({{\varvec{n}}}\) and \({\varvec{\alpha }}\) are discussed. Simulations show that the greater the \({{\varvec{n}}}\) and \({\varvec{\alpha }}\) are, the greater the SIR.