# Three Layered Biased Memory Polynomial Model

The TLBMP model [12] is a cascade of two static polynomial models and a dynamic polynomial model, as illustrated in Figure 6.10.

For input signal *x _{in}*(n), the output of the first block is given by:

**Figure 6.10 **Three layered biased memory polynomial model

where *a _{k}* are the coefficients of the first block and

*K*

*is its nonlinearity order. Similarly, the output of the second block, which takes*

_{1}*x*

_{1}*(n)*as the input, is given by:

where are the coefficients of the second block and K_{2} is its nonlinearity order. The

final output of the model is given by:

)

where *c^ _{m}* are the coefficients of the third block and K

_{3}and

*M*are its nonlinearity order and memory depth, respectively.

In matrix notation, these equations (6.28-6.30) can be written in a similar way to Equation 5.1 as:

and

where

and

where A, B, and C are the vectors of the coefficients for each block. Further details on the definitions and formulations of the matrices and vectors in these equations are provided in [12]. These coefficients can be obtained using the linear least squares method, similar to the PLUME model.

Experimental validation has been conducted for a Doherty PA and a class AB PA; and, the TLBMP model exhibited a better performance than the conventional MP and orthogonal MP models (Section 5.4.1), while reducing the complexity significantly in terms of the number of coefficients and the number of operations to compute the models.