Performance Analysis and Coefficient Generation Method of Parallel Hammerstein Model Under Underdetermined Condition

Nonlinear signal models are widely used in power amplifier predistortion, full-duplex self-interference cancellation, and other scenarios. The parallel Hammerstein (PH) model is a typical nonlinear signal model, but its serial and parallel hybrid architecture brings difficulties in performance analysis and coefficient estimation. This paper focuses on the performance analysis and coefficient estimation of the PH model for nonlinear systems with memory effects, such as power amplifiers. By comparing the PH model with the memory polynomial (MP) model under identical basis functions, we analyze its performance across varying numbers of parallel branches, nonlinear orders, and memory depths. Using singular value decomposition (SVD), we derive a closed-form expression for the PH model's performance under underdetermined conditions, establishing its relationship to the non-zero singular values of the MP model's coefficient matrix. Based on this, we propose a coefficient generation method combining SVD and least squares (LS), which directly computes coefficients and assesses performance during execution. Simulations confirm the method's effectiveness, showing that selecting branches associated with larger singular values achieves near-optimal performance with reduced complexity.