Deriving Effects of IQ-Imbalance on Phase-and Amplitude Noise in Radars

The combined effects of local oscillator (LO) phase noise (PN), in-phase / quadrature imbalance (IQI), and range correlation are studied in this paper. We show how PN from an LO appears as PN and amplitude noise (AN) in the received signal of a coherent radar. We derive expressions for the relations between the transmitted signal’s and the received signal’s autocorrelation function (ACF) and power spectral density (PSD) respectively using a first-order Taylor series. The results demonstrate that the PSDs of the PN and AN in the received signal are proportional to the PN-PSD of the transmitted signal. Two coefficients quantifying the PN -scaling and the $\mathbf{P N}$-to-AN conversion are derived as a function of the parameters describing the receiver’s IQI. The derived analytical expressions are compared to the results from MATLAB simulations using a PN PSD typical for a state-of-the-art transceiver. The results demonstrate excellent alignment between theoretical expressions and simulation results.