Detects the phase error.

Parameters:¶

received: NDArray[complex128]¶

The received complex symbols \(\tilde{a}[k]\).

reference: NDArray[complex128]¶

The reference complex symbols, either the known transmitted complex symbols \(a[k]\) or the complex symbols decisions \(\hat{a}[k]\).

Returns:¶

The detected phase error \(\theta_e[k]\) in radians.