2506 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 63, NO. 6, JULY 2014 Efficient Estimation and Pilot-Free Online Re-Calibration of I/Q Imbalance in Broadband Direct-Conversion Transmitters Jian Luo, Andreas Kortke, Wilhelm Keusgen, and Mikko Valkama, Member, IEEE Abstract—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 ap- plied 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 empha- size practical deployments, we also conduct performance anal- ysis 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) experi- ments with real radio-frequency signal measurements, including real-time field-programmable gate-array (FPGA) implementation of the developed digital calibration circuits. Index Terms—Calibration, digital predistortion, direct- conversion architecture, dirty RF, frequency-selective I/Q imbalance, multi-band, multi-standard, online re-calibration, time-variant I/Q imbalance. Manuscript received June 15, 2013; revised October 17, 2013; accepted November 29, 2013. Date of publication December 23, 2013; date of current version July 10, 2014. The work of W. Keusgen was supported in part by the German Federal Ministry of Economics and Technology under BMWi Grant 01MT07007. The work of M. Valkama was supported in part by the Academy of Finland under Grant 251138 and in part by the Linz Center of Mechatronics under the framework of the Austrian COMET-K2 Programme. The review of this paper was coordinated by Dr. T. Taniguchi. J. Luo is with the European Research Center, Huawei Technologies Duesseldorf GmbH, 80992 Munich, Germany (e-mail: jianluo@huawei.com). A. Kortke is with Technische Universität Berlin, 10623 Berlin, Germany (e-mail: andreas.kortke@mk.tu-berlin.de). W. Keusgen is with the Fraunhofer Heinrich Hertz Institute, 10587 Berlin, Germany (e-mail: wilhelm.keusgen@hhi.fraunhofer.de). M. Valkama is with the Tampere University of Technology, 33720 Tampere, Finland (e-mail: mikko.e.valkama@tut.fi). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2013.2295940 I. I NTRODUCTION D IRECT (up/down) conversion architecture allows low- cost, low-power, and highly integrated implementation of wireless transceivers and enables flexible radio frequency (RF) signal generation and demodulation in different frequency bands [1]. Combined with broadband analog front ends, direct- conversion architecture even allows simultaneous multi-band (MB) transmission/reception [2]. Thus, direct-conversion archi- tecture has become a promising candidate for the implemen- tation of software-defined-type flexible radio with multi-band and multi-standard capability. This has obvious applications in cellular base-station devices and in mobile terminals through carrier aggregation, which is already specified, e.g., in Third- Generation Partnership Project Long-Term Evolution Ad- vanced (3GPP LTE-Advanced) [3]. However, the performance of direct-conversion architecture can be severely limited by the RF impairment called I/Q imbalance, which causes mirror- frequency interference (MFI) [2] and restricts the achievable spectral efficiency. Furthermore, I/Q imbalance degrades the baseband (BB) predistortion for the power amplifier (PA) [1]. Generally, I/Q imbalance consists of a frequency-independent part in the modulator (MOD)/demodulator (DMOD) and a frequency-selective part in the BB low-pass filters (LPFs) and data converters. For broadband systems, both parts have to be taken into account [1], [2], [4]. Here, we summarize the overall effect as “frequency-selective I/Q imbalance.” This paper investigates the estimation and calibration of frequency-selective I/Q imbalance in broadband direct- conversion transmitters (Txs) with multi-band multi-standard capability, where modulator dc offset is also considered. Gen- erally, such calibration consists of I/Q imbalance and dc offset parameter estimation and digital precompensation on the Tx signals [4]. Furthermore, for multi-band multi-standard Txs, such calibration should be standard independent. There are already a number of works on I/Q imbalance calibration in direct-conversion Tx, including [1], [2], [4]–[24], and the references therein. In [5]–[11], [14], and [18], only frequency- independent I/Q imbalance is considered; thus, these studies are not suitable for broadband applications. Frequency- selective I/Q imbalance has been taken into account in [1], [2], [4], [12], [15], [17], and [19]–[24]. Among these works, [15] only considers the LPF I/Q imbalance (assuming no modulator I/Q imbalance) and requires redundant hardware for calibration. Furthermore, the schemes in [17]–[19], [23], and [25] rely on dedicated pilot signals and are thus not 0018-9545 © 2013 IEEE. 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