iq_imbalance: dc offset is not calculated properly

[nalexandros]

Describe the bug IQ Imbalance considers that the hardware has non-idealities and that the in-phase and quadrature are not perfectly aligned. As a result, the IQ data will have slightly different amplitude, phase and dc-offset.

Problem description: By setting to zero the amplitude_imbalance_db and the phase_imbalance we can isolate the effect of the dc_offset_db. The expectation is that the constellation diagram will be moved to a different location, while keeping the scaling, rotation and shape. However, this is not the case as is shown in iq_imbalance.png. Instead the data are scaled in a similar manner as with amplitude imbalance.

Solution: The function iq_imbalance_fixed modifies a couple of lines. The resulting plot (iq_imbalance.png) shows that the IQ data have been shifted as expected.

To Reproduce to_torchsig_debug_iq_imbalance.zip

Use the Python code and the *.npy file to reproduce the bug and get the bugfix.

Expected behavior The IQ data must be shifted, not scaled, as seen in the picture.

def iq_imbalance_fixed(
    iq: np.ndarray,
    amplitude_imbalance_db: float,
    phase_imbalance: float,
    dc_offset_db: float,
) -> np.ndarray:
    amplitude_imbalance_linear = 10 ** (amplitude_imbalance_db / 10.0)
    iq_transformed = (amplitude_imbalance_linear * iq.real + 1j * amplitude_imbalance_linear * iq.imag)

    iq_transformed = (np.exp(-1j * phase_imbalance / 2.0) * iq_transformed.real +
                      np.exp(1j * (np.pi / 2.0 + phase_imbalance / 2.0)) * iq_transformed.imag)

    dc_offset_linear = 10 ** (dc_offset_db / 10.0)
    dc_offset_linear_complex = dc_offset_linear + 1j * dc_offset_linear
    iq_transformed += dc_offset_linear_complex
    return iq_transformed