IQ Imbalance Impairment Simulation in MATLAB

This document details a MATLAB implementation demonstrating the impact of IQ imbalance impairment, specifically IQ amplitude and phase imbalance, on a constellation diagram. The code snippet below, referred to as PART B, introduces the IQ imbalance. Parts A and C of the MATLAB code, which are not shown here, are assumed to be identical to those described in the AWGN (Additive White Gaussian Noise) page.

MATLAB Source Code (PART B)

IQ_amp_imb = input('Enter IQ amplitude imbalance(default:0.03):'); % amplitude imbalance
IQ_phase_imb = input('Enter IQ phase imbalance(default:0.03):'); % phase imbalance

N = size(mapper_out_ori);

IQ_amp_imb = IQ_amp_imb.*randn(1,N); % linear value (not in %)
IQ_phase_imb = IQ_phase_imb*2.*(rand(1,N)-0.5); % in radians

mapper_out=mapper_out';

for i=1:N
    alph = cos(IQ_phase_imb(i))-j*sin(IQ_phase_imb(i))*IQ_amp_imb(i);
    beta = IQ_amp_imb(i)*cos(IQ_phase_imb(i))+j*sin(IQ_phase_imb(i));
    out(:,i) = alph*mapper_out(:,i)+beta*conj(mapper_out(:,i));
end

figure;
plot(real(out),imag(out),'b+');
title('constellation with IQ imbalance');

Code Explanation

1. Input: The code prompts the user to enter the IQ amplitude imbalance and IQ phase imbalance. Default values of 0.03 are suggested. These values represent the amount of imbalance to be introduced.

2. Imbalance Generation: Random variations are introduced to both the amplitude and phase imbalances.

   • IQ_amp_imb = IQ_amp_imb.*randn(1,N); generates a random amplitude imbalance with a normal (Gaussian) distribution, scaled by the user-provided input. This results in a linear amplitude imbalance (not a percentage).
   • IQ_phase_imb = IQ_phase_imb*2.*(rand(1,N)-0.5); generates a random phase imbalance with a uniform distribution between -IQ_phase_imb and +IQ_phase_imb radians.

3. Imbalance Application: The core of the IQ imbalance implementation lies within the for loop. For each symbol:

   • The complex coefficients $\alpha$ and $\beta$ are calculated based on the phase and amplitude imbalances.

   • $\alpha = \cos(\theta_i) - j\sin(\theta_i) \cdot A_i$

   • $\beta = A_i \cos(\theta_i) + j\sin(\theta_i)$ Where $A_i$ is the amplitude imbalance for the $i$-th symbol, and $\theta_i$ is the phase imbalance for the $i$-th symbol.

   • The output signal out(:,i) is generated by applying these coefficients to the original signal mapper_out(:,i) and its complex conjugate conj(mapper_out(:,i)). The equation that represents the IQ imbalance effect is:

   • $out_i = \alpha \cdot mapper_out_i + \beta \cdot conj(mapper_out_i)$

4. Constellation Plot: Finally, the code generates a constellation diagram of the distorted signal out using the plot function, with the real part on the x-axis and the imaginary part on the y-axis. The title of the plot is set to ‘constellation with IQ imbalance’.

Input and Output Constellation Diagrams

The following images illustrate the effect of IQ imbalance on a constellation diagram.

Input Constellation Diagram

Constellation Diagram with IQ Imbalance