### Table of Contents

# Nikolaus_Hammler

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**Research interests**: Low-rate sampling, low-rate system identification, digital predistortion**<br> **

**Email**: nhammler AT stanford DOT edu<br>

# Sub-Nyquist Observation Path for Digital Predistortion of RF Power Amplifiers in Future Wireless Technologies

## Problem Statement<br>

Advanced wireless communication requires the use of digital predistortion (DPD) techniques to compensate for nonlinear effects in the transmit Power Amplifier (PA). This extends the linear range and hence power efficiency. Applying DPD requires knowledge of the frequency dependent, nonlinear behavior of the PA. In conventional approaches, this information is acquired using an analog-to-digital converter (ADC) operating at the Nyquist rate of the PA output containing wideband spectral regrowth. This figure shows the conventional DPD setup for LTE Advanced:<br>

Since the nonlinear behavior expands the bandwidth at the ADC input in this example to 500 MHz, the ADC needs to sample at least at 2×500 MHz. This performance is realizable today, however, as bandwidths increase, the observation ADC becomes a bottleneck. Current ADC products already cost on the order of $100 and dissipate more than 1W, which makes implementation in small base stations economically unreasonable even today. Thinking ahead, scaling the ADC bandwidth with the signal bandwidth does not appear to be sustainable for future wireless systems where ADC bandwidths of several GHz with a resolution of 14 bits will be required. Similarly, current DPD training approaches are not sustainable for massive MIMO systems (as proposed for 5G) because an expensive high-rate feedback receiver would be required for each channel.<br>

## Proposed Solution<br>

Recent advances in signal processing have shown that the minimum required sampling rate generally does not depend on the Nyquist rate but on the information content of a signal (the relevant frameworks are known as Compressed Sensing and Finite Rate of Innovation). A typical PA can be described with less than 100 coefficients (degrees of freedom), and hence, it is reasonable to assume that this information can be recovered using much lower rates than the Nyquist rate of the PA output with appropriate preprocessing. Previous work has mainly focused on sampling rate reduction and is based on aliasing. However, aliasing still requires an analog front end with a wide acquisition bandwidth for the ADC. To address this problem, we have proposed to take the measurements in the frequency domain, rather than the time domain, and extract the behavior of the PA from a set of Fourier coefficients of the output signal. The frequency domain measurements are obtained by mixing the output signal with a random frequency offset from the carrier and integrating the down-converted signal:

After down conversion, the signal is integrated for T0 seconds after which the integrator is reset. Since one sample is taken in every T0 interval, the sample rate is given by 1/T0. Due to the integration, the identification time is increased. However, the proposed method reduces the number of required measurements. For example, in a conducted experiment, the conventional architecture requires about 4000 measurements for Adjacent Channel Power Ratio (ACPR) below -50dBc while the proposed architecture requires only about 200 measurements. The sampling rate is reduced by a factor of 120 (from 491.52 MHz to 4 MHz) while the identification time is only increased by a factor of 6.<br>

The goal of this research is to implement a proof-of-concept in silicon with the basic feedback receiver implemented in ST 28FDSOI along with a test PCB board. For the purpose of the proof-of-concept, the LO clocks are generated externally and stepped sequentially from MATLAB via SCPI. A cheap external low-rate ADC (LTC2323) is used to convert the result to a digital output. The die photo and block diagram of the receiver IC are shown below:

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## References<br>

N. Hammler, B. Murmann and Y. C. Eldar, “Low-Rate Identification of Memory Polynomials”, IEEE International Symposium on Circuits and Systems, 2014.<br>

N. Hammler, “System Characteristic Identification Systems and Methods”, US patent US9362942B1, 2016.<br>

N. Hammler, C. Dick, “Model and Apparatus for Model Identification and Predistortion”, US patent US9935810B1, 2018.<br>

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