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, yPA(n), of the PA for a given input, xin(n), can be given by:
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 . Mathematically, the output of an I/Q modulator is given by :
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 . 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 .
Figure 6.11 Parallel Hammerstein based model for the alleviation of PA nonlinearity and I/Q imbalance