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

Area of Science:

• Electrical Engineering
• Signal Processing
• Nonlinear System Modeling

Background:

• Nonlinear signal models are crucial for power amplifier predistortion and self-interference cancellation.
• The parallel Hammerstein (PH) model, while effective, presents challenges in performance analysis and coefficient estimation due to its hybrid architecture.
• Understanding and optimizing PH model performance is vital for advanced wireless communication systems.

Purpose of the Study:

• To analyze the performance of the parallel Hammerstein (PH) model in nonlinear systems with memory effects.
• To develop an efficient coefficient estimation method for the PH model.
• To compare the PH model's performance with the memory polynomial (MP) model.

Main Methods:

• Comparative analysis of PH and memory polynomial (MP) models using identical basis functions.
• Performance evaluation across varying parallel branches, nonlinear orders, and memory depths.
• Derivation of a closed-form performance expression for the PH model under underdetermined conditions using singular value decomposition (SVD).
• Development of a coefficient generation method combining SVD and least squares (LS).

Main Results:

• A closed-form expression for PH model performance was derived, linking it to the singular values of the MP model's coefficient matrix.
• The proposed SVD-LS method enables direct coefficient computation and real-time performance assessment.
• Simulations demonstrated that selecting parallel branches corresponding to larger singular values yields near-optimal performance with reduced complexity.

Conclusions:

• The SVD-LS method effectively addresses PH model coefficient estimation and performance analysis challenges.
• Optimizing parallel branch selection based on singular values is key to achieving high performance and efficiency in PH models.
• This research provides a valuable framework for designing and implementing advanced nonlinear signal processing techniques.