# Three-Box Polynomial Models

With increasing developments in technology, many models have been proposed to improve the performance of the DPD models. Two such techniques that also reduce the complexity of the system, which is also an important attribute of a behavioral modeling system, are presented in this section: the parallel LUT, MP, envelope memory polynomial (PLUME) method, and the three-layered biased memory polynomial (TLBMP) model for the compensation of PAsâ€™ nonlinear effects. The comparative results published in open literature has shown that these methods perform much better than conventional methods.

## Parallel Three-Blocks Model: PLUME Model

The PLUME model [11] is a three-block model composed of a LUT block, MP block, and an envelope memory polynomial (EMP) block. This architecture, as shown in Figure 6.9, provides better performance than the conventional MP model. It also provides more flexibility so that other polynomial models, such as variants of the MP model, can also be used instead of the blocks used in [11].

The method provided in the first block is a memoryless nonlinear function, that can be implemented using a LUT. The second block is a MP model given by Equation 5.2 as reiterated in Equation 6.24:

*M* and *K* indicate the memory depth and the nonlinearity order of the model respectively. The third block is an envelope MP block given by Equation 5.21, which is

**Figure 6.9 **PLUME model

restated as in Equation 6.25:

The modeling identification of *y _{MP}* and

*y*can be considered as a linear identification problem:

_{EMP}where A is the vector of coefficients, which can be obtained by using the linear least squares method and can be given by:

Experimental validation was provided in [11] for a Doherty PA with a peak power of 300 W operating in the frequency range of 2110-2170 MHz. The test signal was a 20 MHz WCDMA 1001 signal. It was shown that the PLUME model had a better performance than the conventional MP model (Section 5.3) and the PTNTB model discussed in Section 6.5 and a similar performance to that of the generalized MP model (Section 5.6). However, the major advantage of the PLUME model is the reduction in the complexity of the system in terms of number of coefficients, which makes it highly suitable for implementation in a field-programmable gate array (FPGA).