Nikolaus Hammler
From Murmann MixedSignal Group
Research interests: Lowrate sampling, lowrate system identification, digital predistortion
Email: nhammler AT stanford DOT edu
Elevator Pitch

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 part: Over 80% power is dissipated as heat by the Power Amplifier (PA). The reason for this poor efficiency lies in its inherent nonlinearity. One way to mitigate this issue is to linearize the PA with digital predistortion (DPD). However, this technique requires to "measure" the transmitted signal and demands for another potentially expensive and powerhungry component: An AnalogtoDigital 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 the PA itself. Motivated by this "ADC bottleneck" the approach in my research 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. 
LowRate 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 power amplifier 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 diminish this effect is to use a predistorter (PD). The PD distorts the original input signal in a nonlinear way, such that the overall transfer function is linear again. However, since the behavior of the PA changes during operation (due to selfheating or aging) it is necessary to continuously determine the appropriate PD. The general setup 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 modelled using a model with only few degrees of freedom. For example, a typical class AB 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 an inverse modeling approach:
 Identify the PA (system H) at a low rate using ideas from FRI. The sampling rate relates to the degrees of freedom in the PA model, rather than the Nyquist rate
 Invert the estimated system to obtain the PD, H^{1}
The block diagram of this scheme is shown below: