Efficient Estimation and Pilot-Free Online Re-Calibration of $I/Q$ Imbalance in Broadband Direct-Conversion Transmitters

This paper proposes an efficient estimation and pilot-free online re-calibration scheme for frequency-selective I/Q imbalance in broadband direct-conversion transmitters (Txs) with multi-band multi-standard capability. For such Txs, the main challenge lies in the online re-calibration during normal operation, where an ordinary Tx signal, instead of dedicated pilot signals, is used for estimation. In particular, it can happen that the Tx signal consists of noncontiguous subbands and has large spectral gaps, which will cause a severe ill-conditioned matrix problem in existing state-of-the-art (SoA) schemes deploying least squares (LS) estimation. In the proposed scheme, this problem is avoided by exploiting the fact that the frequency-selective part of I/Q imbalance is approximately time invariant. Therefore, before normal operation, pilot-based initial estimation is carried out to achieve high-precision estimation of the frequency-selective part. Afterward, pilot-free online re-calibration is applied to cope with the time-varying frequency-independent part. Both theoretical analysis and numerical simulations show that the proposed re-calibration scheme is well conditioned and clearly outperforms the existing SoA schemes deploying LSE. To emphasize practical deployments, we also conduct performance analysis considering time synchronization error (TSE) and provide a Toeplitz-extension-based solution to make the scheme robust against TSE. We further provide complexity analysis and show that the proposed scheme has much lower complexity than the SoA schemes. Finally, the performance of the proposed scheme and the fundamental working assumptions are verified by both numerical simulations and hardware-in-the-loop (HIL) experiments with real radio-frequency signal measurements, including real-time field-programmable gate-array (FPGA) implementation of the developed digital calibration circuits.