Theoretical Analysis of Timing Error in a Direct Transmitter Self-Calibration System

This paper studies the performance of a least-square-based self-calibration technique for a direct frequency conversion quadrature modulator in the presence of timing error. The technique uses the in-phase (I) and quadrature (Q) signals and their corresponding instantaneous power measurement at the transmitter output to estimate the gain/phase/DC-offset coefficients. The time synchronization between the I/Q signals and the power measurement is important for accurate coefficient estimation. In this paper we theoretically analyze the effect of the time synchronization error on the coefficient estimation. It is shown by using Taylor series expansion that the estimation errors of the gain/phase/DC-offset coefficients will be proportional to tau ² , where tau is the timing error. Numerical simulations are used to validate the analysis