# Two-Box Polynomial Models

## Models’Descriptions

A two-block model for the modeling and digital predistortion (DPD) of PAs has been proposed [10], for the purpose of reducing the complexity of the system. One of the blocks is a MP based model, while the other is a LUT model. Different arrangements of the blocks lead to the following twin-nonlinear two-box (TNTB) models:

- •
*Forward-cascaded polynomial model:*In the forward twin-nonlinear two-box model (FTNTB), the LUT is placed before the MP function, as shown in Figure 6.8a. - •
*Backward-cascaded polynomial model:*In the backward twin-nonlinear two-box model (BTNTB), the LUT is placed after the MP function, as shown in Figure 6.8b. - •
*Parallel-cascaded polynomial model:*In the parallel twin-nonlinear two-box model (PTNTB), the LUT and MP functions are placed parallel to each other, as shown in Figure 6.8c.

The MP model is one type of polynomial that can be used to mimic the dynamic nonlinear behavior of a PA: other polynomial models, such as the Volterra series, can also be used instead of the MP block. Similarly, the LUT is used to model the memoryless nonlinear behavior of the PA; however, other memoryless polynomial functions can be used instead.

**Figure 6.8 **Twin nonlinear twin box models. (a) Forward TNTB model, (b) reverse TNTB model, and (c) parallel TNTB model

## Identification Procedure

As mentioned earlier, TNTB models have an advantage over conventional polynomial models, as they reduce the complexity of the system. The reason for this is that the highly nonlinear memoryless behavior and the mildly nonlinear memory effects are modeled separately, thereby decreasing the number of coefficients. The identification procedure for the coefficients is composed of two steps:

- 1. The coefficients for the nonlinear memoryless behavior (modeled by an LUT) of the device under test are obtained.
- 2. The coefficients for the dynamic nonlinear behavior (modeled by a MP) are then obtained.

The proposed model has been tested with a 300-watt Doherty PA and a four-carrier WCDMA (Wideband Code Division Multiple Access) 1001 test signal [10]. It was shown that the complexity of the system was reduced by 50%, while improving the normalized mean square error (NMSE) by 2 dB.