Method for Estimating and Compensating the Phase Imbalance of Quadrature Signal Components

Currently, methods of direct modulation using complex signals are widely used. A complex signal consists of in-phase I (In-phase) and quadrature Q (Quadrature) components. When a signal passes through a communication channel and a receiving path, mismatches of the signal components occur as a result of interference. The mismatch, in turn, leads to increase in bit error rate (BER) during signal demodulation. The quality of the received signal is expressed in terms of bit error rate. The article considers phase imbalance of the quadrature components of a complex signal. Phase imbalance occurs in the receive path and depends on the quality of the receiver's local oscillators, on the operating temperature and the difference in propagation time of the I and Q components. The article shows an algorithm for estimating the phase imbalance of the quadrature signal components for digital modulation methods. Examples of signal constellation distortions in case of phase imbalance of quadrature signal components are considered. The phase imbalance estimation is based on the modulation constellation method for measuring signal parameters. Formulas for calculating the angle of phase error and the magnitude of quadrature error are given. Formulas for compensating the phase imbalance are also given, taking into account the calculated quadrature error. A mathematical model of the transmitter, communication channel and receiver has been developed to study the method for estimating and compensating for phase imbalance. The mathematical model is built in the Matlab software environment and is an m-script software model. With the help of the mathematical model, method for estimating and compensating for phase imbalance has been studied. In the course of the study, relationships of error probability due to the mismatch of the quadrature components of the signal were obtained. The noise immunity of the receiver paths with and without compensation for the phase mismatch of the quadrature signal components is compared. Based on the results of the study, diagrams of the error probability and the phase mismatch of the receiver's local oscillators were obtained. The study shows that phase mismatch of the receiver local oscillators at a fixed signal-to-noise ratio leads to an increase in the probability of received bit errors. But when applying the phase imbalance compensation method, the error probability remains fixed as the phase mismatch of receiver local oscillators increases at a fixed signal-to-noise ratio.