It has been widely shown in the literature that the transmitter exhibits memory effects caused by electrical and thermal dispersion effects, which cannot be ignored in real systems [3]. The various causes of the electrical memory effects have been discussed in [3]. A behavioral model should, therefore, include both linear and nonlinear memory effects for proper modeling and compensation of the dynamic PA nonlinearity.

Augmented Wiener Model

The augmented Wiener model is an extended version of the Wiener model (which uses linear filters) that aims to add a nonlinear memory effect component into the system. In this architecture, a parallel filter branch is added to the linear FIR filter, in which the input is multiplied by its magnitude to form a weak nonlinear filter. This model takes into account the memory effects more appropriately and results in better accuracy than the conventional Wiener model. The block diagram of this extended model is shown in Figure 6.3.

The new output, x_{AW}(n), of the parallel filters can be described by:

Figure 6.3 Augmented Wiener model

Figure 6.4 Augmented Hammerstein model

where M_{1} and M_{2} are the memory depth of the first and second filter, respectively; and, к_{щ} and к_{щ} are the filter responses.

When Equation 6.10 is compared to Equation 6.2, the effect of the additional FIR filter can be seen. As mentioned earlier, additional memory has been added to the system in order to capture the nonlinear dynamic behavior of the PA more accurately:

y_{AW} is the output of the model and G_{AW} is the gain of the static nonlinear function modeled by the LUT. The recursive least squares method can also be used in the augmented Wiener model to extract the model parameters. Experimental results for the augmented Wiener model have been presented in [3], where it was shown that the augmented model can predict the memory effects better than the conventional model.

Augmented Hammerstein Model

The augmented Hammerstein model [5] is similar to the augmented Wiener model, but with two parallel branches of the LUT and FIR filters, as shown in Figure 6.4. The output of the LUT box, x_{AH}(n), and the total model output, y_{AH}(n), is:

y_{AH} is the output of the model and G_{AH} is the gain of the static nonlinear function modeled by the LUT; and, where M_{1} and M_{2} are the memory depth of the first and second filters, respectively. Н_{щ} and k_{m2} are the filter responses.