Blind Signal Estimation in Widely-Linear Signal Models With Fourth-Order Circularity: Algorithms and Application to Receiver I/Q Calibration

In-phase/quadrature (I/Q) imbalance degrades heavily the image rejection performance of direct-conversion radios. I/Q imbalance also changes the statistics of the received signal, and in particular makes a circular signal non-circular. This fact has been utilized in compensating receiver I/Q imbalances, utilizing second-order statistics. In this article, we investigate whether moment circularity of order higher than two can be exploited in receiver I/Q imbalance compensation. It is established that the fourth-order moment E[x(3)x*] is a suitable statistic for measuring the circularity of common communications signals based on complex-valued alphabets such as M-QAM and M-PSK with M > 2. Two blind algorithms, based on Newton's method, are then proposed for receiver I/Q imbalance compensation. They are shown by simulations to converge faster or, alternatively, to give lower steady-state variance, than the reference methods that are based on second-order statistics.