What are the mathematical equations that represent the imbalances in the "I/Q Imbalance" block found in Communication Blockset 4.0 (R2008a)?

I would like to know the mathematical equation/method being used to calculate phase imbalance in the "I/Q Imbalance" block found in the Communications Blockset under RF Impairments library. Also, I would like to know if there are imbalance equations for I/Q gain and DC offset.

Answer 1

[MathWorks Support Team]

Additional information has been incorporated into the documentation in Release 2009a (R2009a). For previous releases, read below for more information:

The equations for the imbalances are provided below:

Let Ia = I/Q amplitude imbalance (dB)

Let Ip = I/Q phase imbalance (deg)

Let Idc = in-phase DC offset

Let Qdc = quadrature DC offset

Let x = xr + xi be the complex input to the block, with xr and xi being the real and imaginary parts, respectively, of x

Let y = complex output of the block

Thus, for an I/Q amplitude imbalance(Ia),

y = [10^(0.5*Ia/20) * xr] + j[10^(-0.5*Ia/20) * xi]

For an I/Q phase imbalance Ip,

y = [exp(-0.5*j*pi*Ip/180) * xr] + {exp[j(pi/2 + 0.5*pi*Ip/180)] * xi}

For DC offsets Idc and Qdc,

y = (xr + Idc) + j(xi + Qdc)