Nikolaus Hammler

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Research interests: Low-rate sampling, low-rate system identification, digital predistortion

Email: nhammler AT stanford DOT edu

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Nearly 60% of a cellular network is used by the base stations and from them, the major part by the Power Amplifier (

PA power.png

Nearly 60% of a cellular networks total energy consumption is used in wireless base stations and within a base station, the major part is used by a fundamentally inefficient device: Up to 80% power can be dissipated as heat by the Power Amplifier (PA). It is possible to increase the efficiency by operating the device in a non-ideal region but this results in non-acceptable distortion. One way to decrease the distortion problem is to modify the transmitted data with the inverse distortion (digital predistortion, DPD). However, this technique requires to "measure" the transmitted signal and demands for another potentially expensive and power-hungry component: An Analog-to-Digital Converter (ADC). Today already, the ADC can make up a big portion of a base stations cost.

This problem becomes even more pronounced in future: As bandwidths increase such as in LTE (4G) or even LTE Advanced and beyond, more base stations are required and the requirements on the PA and the ADC become more stringent.

Motivated by this "ADC bottleneck" my approach is to solve the problem at the algorithmic level and to decouple the requirements of the ADC from the signal bandwidth. Potentially, this would not only make today's base stations cheaper and more energy efficient but also enable future wireless technologies in a sustainable manner.

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

Advanced wireless communication requires the use of digital predistortion (DPD) techniques to compensate for nonlinear effects in the power amplifier (PA) of the transmitter which extends the linear range and hence power efficiency.
DPD requires knowledge of the frequency dependent, nonlinear behavior of the PA and hence, conventional approaches use an analog-to-digital converter (ADC) operating at the Nyquist rate to obtain the PA model. A generic DPD architecture looks as follows:


Prevalent approaches sample the output signal y(t) at the Nyquist rate. However, advanced technologies such as LTE Advanced require bandwidths of 100 MHz and more. Together with the spectral regrowth, this results in sampling rates in the Gigahertz range at resolutions of 14 bits, placing a high burden on the ADC. Scaling the ADC bandwidth with the signal bandwidth is not sustainable for future wireless systems. Similarly, prevalent DPD solutions are not sustainable for massive MIMO systems as proposed for 5G because an expensive high rate feedback receiver is required for each channel.

On the other hand, PAs are usually modeled with only few degrees of freedom. For example, a typical class AB or Doherthy amplifier can be modelled with a Memory Polynomial (MP, a truncated Volterra series) having as few as 20 coefficients. The motivating question "Do we really need to sample at this high rate just to obtain a few coefficients?" is similar as in Compressive Sampling or Finite Rate of Innovation (FRI). Based on the ideas from FRI, we propose to acquire a set of measurements which is related to the degrees of freedom in the model, rather than the Nyquist rate. We obtain the measurements in a domain similar to the Fourier domain, by splitting the signal into blocks and obtaining one measurement per block. This process can be interpreted as demodulating one (or possibly multiple) Fourier-like coefficients per block. By choosing the coefficients randomly, we obtain the flexibility to set the bandwidth requirement and the sampling rate arbitrarily while offering a rich space of tradeoffs between bandwidth requirement, model fidelity, identification time or hardware cost.

The goal of this research is to implement a proof-of-concept system with the basic feedback receiver implemented in ST28FDSOI. The receiver performs frequency conversion and integration while a cheap external low-rate ADC is used to convert the result to digital domain. For the prototype, the random frequencies will be generated off-chip.


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

N. Hammler, "System Characteristic Identification Systems and Methods", US patent US9362942B1, 2016.

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