GRADIENT-BASED BLIND ITERATIVE TECHNIQUES FOR I/Q IMBALANCE COMPENSATION IN DIGITAL RADIO RECEIVERS Lauri Anttila, Mikko Valkama, and Markku Renfors Tampere University of Technology Institute of Communications Engineering P.O. Box 553, FIN-33101 Tampere, FINLAND lauri.anttila@tut.fi ABSTRACT This paper considers the radio implementation related I/Q imbalance problem and its digital compensation in direct- conversion and low-IF type radio receivers. In general, I/Q imbalances result in mirror-frequency interference and can severely limit the receiver dynamic range and sensitivity, if not taken properly into account. Here the compensation algorithm developments build on the so-called circular na- ture of complex-valued communications waveforms which is known to hold only under perfect I/Q balance. A well- behaving non-circularity measure is first formed which is then minimized iteratively using gradient-descent type ap- proach. The derived compensator is computationally simple and operates blindly on the received signal, meaning that no known training or pilot data is needed. The compensation performance of the proposed method is analyzed using ex- tensive computer simulations and is shown to outperform the state-of-the-art adaptive reference techniques by several dB’s, when measured in terms of the obtained overall mir- ror-frequency attenuation. Index Terms — Adaptive filtering, circular random sig- nals, complex (I/Q) signals, digital radios, direct-conversion transceivers, I/Q imbalance, mirror-frequency interference. 1. INTRODUCTION In order to access the services of various currently existing and also emerging wireless systems and networks, the re- configurability and flexibility of the used terminal equip- ment are in key position [1], [2]. This together with keeping the implementation cost and size reasonable have steered the attention in radio transceiver design and implementation towards direct-conversion and low-IF type architectures [1], [2]. These radio architectures are based on the I/Q down- conversion principle and have rather simple analog front- ends in terms of the needed RF filtering. These kind of re- ceivers are, however, sensitive to the amplitude and phase matching of the I and Q signal branches, known as the I/Q imbalance problem [1]-[12]. This I/Q imbalance limits the receivers ability to suppress the mirror frequencies in the This work was supported by Nokia, the Academy of Finland, and the Technology Industries of Finland Centennial Foundation. front-end signal processing stages, and depending on the more detailed structure of the received waveforms can easily limit the receiver sensitivity and performance. With careful analog front-end design, mirror-frequency attenuations in the order of 25-40 dB are commonly stated feasible [1], [2]. This paper focuses on the above I/Q imbalance problem and especially its compensation using digital signal process- ing (DSP). In general, this has been a rather active area of research during the recent years, see, e.g., [4]-[12] and the references therein. Typically many compensation techniques rely on known pilot data or otherwise known signal structure such as known data modulation or constellation. This type of methods have been proposed recently, e.g., in [6] and [8] in which OFDM modulation is assumed together with some known pilot data. The work in [4], [10], [11], in turn, focus specifically on the low-IF architecture, while the work in [7] and [9] are assuming the direct-conversion case. In this paper, we make no assumptions as such on the used signaling or modulation scheme, but simply rely on the so-called circular nature of complex random signals [13]. The circularity of the received signal is generally lost due to I/Q imbalances, and thus the compensation can be based on projecting the received signal back to the “circular domain”. Notice that just recently [12], the circular nature of perfectly balanced I/Q signals has been shown to hold for arbitrary number of received carriers. Thus the approach here is gen- eral covering both single-carrier direct-conversion or low-IF as well as wideband multi-carrier direct-conversion receiver cases. Notice also that the compensation algorithm derived here resembles the algorithm derived in [12] to some extent, but has a solid analytical basis explicitly minimizing a well- behaving non-circularity measure by using gradient-descent. Furthermore, better steady-state performance is also ob- tained, compared to [12], with slightly higher yet more than reasonable computational complexity. The organization of the paper is as follows: The essential I/Q signal and system models used in the compensator de- velopments are first described in Section 2. Then in Section 3, a feasible non-circularity measure is established for im- balance compensation, together with an efficient and practi- cal iterative algorithm for its minimization. Performance simulations are then carried out in Section 4, and conclu- sions are drawn in Section 5. 1-4244-0955-1/07/$25.00 ©2007 IEEE.