# Nikolaus Hammler

### From Murmann Mixed-Signal Group

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

**Email**: nhammler AT stanford DOT edu

## 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 power amplifier in the linear region results in poor efficiency. For this reason, PAs are often operated in their **non-linear region**, near the saturation. The price paid for the better efficiency is distortion and spectral regrowth of the signal due to the non-linear 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 non-linear way, such that the overall transfer function is **linear again**. However, since the behavior of the PA changes during operation (due to self-heating, biasing networks etc.) 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 to the Nyquist rate - Invert the estimated system to obtain the PD,
*H*^{-1}

The block diagram of this scheme is shown below: