Abstract Spin-torque diodes (STDs) with interfacial perpendicular magnetic anisotropy (IPMA) in the free layer (FL) demonstrate outstanding microwave signal rectification performances. Large sensitivity values in such systems are usually associated with an easy-cone (EC) magnetic state, when the magnetization in the FL is tilted from the normal to the plane of the film. Here, we theoretically investigate the phase diagram for the EC state in an infinite FL of the magnetic tunnel junction (MTJ) considering both IPMA (of the first and of the second order) and magnetostatic interaction. We show that the increase of the magnetostatic field leads to the EC state phase expansion. For elliptical MTJ nanopillars we investigate the influence of the orientation of the nanopillar ellipticity on the obtained phase diagrams. And finally, we consider the dynamic properties and rectification efficiency of the STD under microwave current injection. Our results clarify the role of magnetostatic interaction for microwave rectification with the IPMA-based STDs and suggest approaches to the EC state effective rectification phase extension through the parameters optimization.