A simple formula for monitoring quadrature phase error with arbitrary signals

The authors consider the problem of monitoring quadrature receiver errors without using specifically designed test signals. A previously derived simple formula ρ=-sin φ where ρ is the cross-correlation coefficient at zero lag between the in-phase (i) and quadrature phase (q) components and φ is the receiver phase imbalance, is generalized in several ways. The generalized version, while still simple, is surprisingly robust because it applies to a wide variety of random and deterministic signals. However, it provides an estimate of φ in the case of known noise power or large SNR. The effects of the additive receiver noise are also included. The case of jointly Gaussian i and q distributions is examined further and the marginal pdf´s of the amplitude and phase of the random signal in the presence of quadrature errors are derived