# Polynomial Based Model with I/Q and DC Impairments

The previous sections focus mainly on the issue of PA nonlinearity. However, there are other imperfections related to various components of a transmitter. As mentioned earlier, the output, *y _{PA}(n),* of the PA for a given input,

*x*can be given by:

_{in}(n),

Here, *M* represents the memory depth and *k* is the nonlinearity index.

In actual transmitters, in addition to the nonlinearity caused by the PA, there are other problems that affect its performance. One such issue is the in-phase (I) and quadrature phase (Q) imbalance caused during the up-conversion of the input signal, giving rise to mirror frequency imaging and DC offset mainly due to carrier leakage [15]. Mathematically, the output of an I/Q modulator is given by [15]:

where *M* is the memory present in the system and *dc* represents the dc offset. The second term in Equation 6.42 represents the image caused by the imbalance.

There are various methods that deal with imperfections in transmitters; two of which-the parallel Hammerstein based model and a generalized two-box model - are discussed in the following subsections.

There are other methods that mitigate various imperfections of transmitters. The Volterra series has been used to consider the effect of *I/Q* imbalance [16]. However, due to the large number of coefficients, the model bears very high complexity. A rational function based model for the joint alleviation of PA nonlinearity effects and I/Q imbalance has been proposed in [17].

**Figure 6.11 **Parallel Hammerstein based model for the alleviation of PA nonlinearity and I/Q imbalance