This paper proposes a new technique to identify the parameters of a digital predistorter based on iterative learning control (ILC). ILC is a well-established control theory technique that can obtain the inverse of a system. Instead of focusing on identifying the predistorter parameters, the technique proposed here first uses an iterative learning algorithm to identify the optimal power amplifier (PA) input signal that drives the PA to the desired linear output response. Once the optimal PA input signal is identified, the parameters of the predistorter are estimated using standard modeling approaches, e.g., least squares. To this end, in this paper, we present a complete derivation of an ILC scheme suitable for the linearization of PAs, which includes convergence conditions and the derivation of two learning algorithms. The proposed ILC scheme and parameter identification technique were demonstrated experimentally and compared with the indirect learning architecture (ILA) and direct learning architecture (DLA). The experimental results show that, even for the most difficult cases, the proposed ILC scheme can successfully linearize the PA. The experimental results also indicate that the proposed parameter identification technique is more robust to measurement noise than ILA and can provide better linearity performance when the PA nonlinearities are strong. In addition, the proposed parameter identification technique can achieve similar or better linearity performance than DLA but with a simpler identification process.

Iterative Learning Control for RF Power Amplifier Linearization

Pre-distortion in digital baseband is a cost-effective method to linearise the transmit power amplifiers of spectrally efficient communication systems From a signal processing point of view, the functional structure of the pre-distorter is primarily determined by the decision which model to choose, as well as by the selected adaptive algorithm During the last two decades, in literature, a multitude of pre-distorter structures has been proposed and analysed In this work, we focus on simple and commonly employed models (the Wiener model and the Hammerstein model) consisting of a linear filter and a static nonlinearity The latter is represented using a basis of orthogonal polynomials First, applying practical transmission signals, different orthogonal polynomial bases are compared with respect to the numerical condition of least squares estimation, and with respect to the convergence behaviour of gradient methods In a second step, pre-distorters which employ orthogonal polynomials are adapted by the indirect learning structure, respectively, the nonlinear filtered-x least mean squares algorithm Based on simulations and burst measurements with a commercial power amplifier, the real-world performance of such pre-distortion systems is investigated

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Adaptive pre-distortion techniques based on orthogonal polynomials

Distributed base station architectures represent the new trend that operators follow in order to resolve cost, performance and efficiency challenges when deploying 4G networks. Main components of such architectures are multimode radios capable of operating according to GSM, HSPA, WiMAX and LTE standards, known as remote radio heads (RRH). The key feature of remote radio heads is the extended software configurability which enables the deployment of more flexible and energy-efficient radio solutions. This paper describes a modern multi-mode radio system reference architecture and the major digital building blocks that when combined together enable multi-mode and more power efficient operation. It concentrates on blocks which can efficiently run multi-rate digital signal processing and blocks that increase radio power efficiency by linearizing the power amplifier output stage. The importance of a digital predistortion (DPD) block is emphasized and an adaptive polynomial approach based on cartesian to polar conversion is then proposed. Such radio architecture has successfully been implemented on a low-cost FPGA family meeting the WiMAX/LTE spectrum and Error Vector Magnitude (EVM) requirements.

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Advanced multimode radio for wireless & mobile broadband communication

The linearization of nonlinear systems is an important digital enhancement technique. In this paper, a real-time capable post- and pre-linearization method for the widely applicable time-varying discrete-time Volterra series is presented. To this end, an alternative view on the Volterra series is established, which enables the utilization of certain modified linear iterative methods for linearization. For one particular linear iterative method, the Richardson iteration, the corresponding post- and pre-linearizers are discussed in detail. It is motivated that the resulting algorithm can be regarded as a generalization of some existing methods. Furthermore, a simply verifiable condition for convergence is presented, which allows the straightforward evaluation of applicability. The proposed method is demonstrated by means of the linearization of a time-varying nonlinear amplifier, which highlights its capability of linearizing significantly distorted signals, illustrates the advantageous convergence behavior, and depicts its robustness against modeling errors.

Linearization of Time-Varying Nonlinear Systems Using A Modified Linear Iterative Method

An approach to linearization relaxes the requirements on the digitization of the analog output signal while maintaining the benefits of a high sampling rate of the output signal. The digitization approach extracts sufficient information to characterize the output signal over a wide bandwidth without necessarily determining sufficient information to fully represent the output signal, for example, without sampling the output signal at the Nyquist sampling rate with a sufficient precision to accurately represent the signal.

Relaxed digitization system linearization

This paper deals with iterative linearization of a nonlinear dynamical system. The methods proposed are suited for digital pre-distortion of power amplifiers working close to saturation, as it is common for efficiency reasons. Two methods (a well known successive approximation method based on a fixed-point formulation and a Newton method) are compared with respect to convergence speed, robustness against model uncertainties, and complexity. The presented methods are used to linearize a Volterra model of a measured power amplifier.

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M. Steinmair

Papers

Iterative linearization methods suited for digital pre-distortion of power amplifiers