# Modeling and Linearization of Nonlinear MIMO Systems

## Impairments in MIMO Systems

Crosstalk is the coupling effect between two or more signals sources. Such coupling results in interference between the different signals. In the case of MIMO

Figure 10.6 Detailed block diagram of the dual-conjugate-input memory polynomial structure

transmitters, crosstalk is the result of coupling between signals in separate paths. In MIMO configurations where the various paths use the same operating carrier frequency, crosstalk results in problematic interference between the paths. This crosstalk would be more significant in integrated circuit (IC) designs, where the physical distance between the signal paths is small and their perfect isolation is not possible.

One can categorize crosstalk in MIMO transmitters in two different categories: linear or antenna crosstalk and nonlinear crosstalk. The crosstalk is said to be linear if it can be modeled using linear functions of the interfering signals and the desired signal. In fact, if the signal affected by cross-coupling from other signal paths does not pass through a nonlinear system, the crosstalk can be modeled by a linear function and is considered as linear crosstalk. However, if the cross-coupled signal passes through a nonlinear system, the crosstalk includes nonlinear terms of the cross-coupling and can only be modeled using nonlinear equations. In this case, it is said nonlinear crosstalk. Since the PA is the main source of nonlinearity in wireless transmitters, crosstalk that occurs in the transmitter circuit before the PA is the main source of nonlinear crosstalk, while any crosstalk taking place after the PA is considered as linear crosstalk [20,21]. Figure 10.7 shows a block diagram of a typical MIMO transmitter and illustrates the previously mentioned two types of crosstalk.