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 (

Nearly 60% of a cellular networks total energy consumption is used in wireless base stations. Within a base station, the major part is used by a fundamentally inefficient device: Over 80% power is 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 mitigate 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 total 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. For LTE Advanced, there would be hardly an ADC available using conventional technologies and even if, it could easily burn more power than saved by DPD.

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.

Low-Rate Linearization of Power Amplifiers

The last component of a wireless transmission system is usually the power amplifier (PA). Its task is to amplify the signal to be transmitted to drive the antenna. However, operating the PA in the linear region results in poor efficiency. For this reason, PAs are often operated in their nonlinear region, near the saturation. The price paid for the better efficiency is distortion and spectral regrowth of the signal due to the nonlinear behavior. This distortion is often not acceptable. A common approach to mitigate this effect is to use a digital predistorter (DPD). The DPD distorts the original input signal in a nonlinear way, such that the overall transfer function is as close to linear as possible. However, since the behavior of the PA changes during operation (due to self-heating or aging) it is necessary to continuously update the DPD coefficients. The general 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, placing a high burden on the ADC.

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, which we call Sequential Demodulation. 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. One possible DPD implementation is called pth-order pre-inverse and first estimates an MP model for the PA. This can be achieved with the method described above. Afterwards, this model is used in digital domain to invert it using indirect learning. The inverse model then corresponds to the digital predistorter (DPD) and can be used in an open-loop fashion.

The goal of this research is to implement a proof-of-concept on silicon, by implementing the feedback receiver containg mixers, driven by a frequency-hopping sequence and windowed integrators on a chip.


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

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