The passive intermodulation (PIM) interference in simultaneous transmit-receive system is difficult to deal with because the process of generating PIM signal is both nonlinear and with memory. To cancel such PIM interference digitally, this paper proposes the symmetrized basis function approximation network. Firstly, we recognize and justify one methodology underlying the current cascaded model, by which the two physically coupled causes, nonlinearity and memory, are mathematically decoupled. After decoupling, the nonlinear block in the system model only needs to be a static nonlinear mapping without memory. This recognition to the role of nonlinear block, along with the concept of basis transformation in linear space, leads to the idea of basis function approximation network (BFAN). Secondly, we point out that the PIM generating process is an odd mapping. Building this prior information into system modelling, we propose further the symmetrized BFAN, which greatly improves cancellation performance and reduces computational complexity. Lastly, we believe that the number of the nonlinear functions used in the system model should correspond to the number of the PIM sources. Building this belief into system modeling, we let different nonlinear units share the same weights so that they represent the same nonlinear function corresponding to the same one PIM source. This turns out to be tremendously effective in PIM interference cancellation for the experiment data. Additionally, the critical point phenomenon is explained with experiment and data analysis by virtue of our simple but rational way to deal with nonlinearity in PIM.

A new one‐step particle smoother is explicitly given in the form of proper weighted samples. It is employed iteratively to improve the importance sampling in particle filtering through incorporating the current measurement information into the a priori distribution. An adaptive iteration strategy is proposed to accelerate the running, which introduces a parameter into the weight increment to adjust the iteration process. Then, new particle filtering method can be constructed through combining the one‐step smoothing and the adaptive iteration strategy.