Measurement and Analysis of Frequency-Domain Volterra Kernels of Nonlinear Dynamic $3 \times 3$ MIMO Systems

Multiple-input multiple-output (MIMO) frequency-domain Volterra kernels of nonlinear order 3 are experimentally determined in bandwidth-limited frequency regions. How the effect of higher nonlinear orders can be reduced and how this affects the estimated errors are discussed. The magnitude and the phase of the kernels are Kramers-Kronig consistent. The self-kernels and cross-kernels have different symmetries, and the kernels are therefore determined and analyzed in different regions in the 3-D frequency space. By analyzing the properties along certain paths in the 3-D frequency space, the block structures for the respective kernels are determined. These block structures contain the significant blocks of the general block structures for the third-order kernels. The device under test is an MIMO transmitter for radio frequency signals.