# Memory Polynomial Model

Kim and Konstantinou proposed the memory polynomial model [1]. It can be obtained by reducing the Volterra series model to its diagonal terms, that is, by removing all cross-terms. The baseband complex output signal (y_{MP}) of the memory polynomial model is expressed as a function of its baseband complex input signal (x) according to:

where *a _{mk}* represent the model’s coefficients; and

*K*and

*M*are the model’s nonlinearity order and memory depth, respectively.

Equation 5.2 can be rewritten in the generic formulation of Equation 5.1

where *q _{MP}(ri)* and A are defined by:

where [-]^{r} denotes the transpose operator. Based on Equation 5.2, the memory polynomial model has two degrees of freedom since its dimension is defined by both the nonlinearity order and the memory depth.

The block diagram of the memory polynomial model is shown in Figure 5.2. This figure shows that the model can be seen as the combination of *(M +* 1) polynomial functions, each of which is applied to a delayed version of the baseband complex input sample, *x(n).*