State space method for modeling and identifying infinite memory of passive inter-modulation

It is difficult yet necessary to simultaneously address both the nonlinearity and the infinite-memory effects in the passive intermodulation (PIM) interference problem. To this purpose, the paper justifies a cascaded model for canceling PIM distortion in the simultaneous transmit–receive system. The model consists of a memory linear block, a memoryless nonlinear block, and another memory linear block. A key aspect of the system modeling is that the first memory linear block is a linear recursive filter with finite parameters, which effectively models infinite memory. Since a nonlinear block is cascaded after the first, at the output port of the first there are no actually measured data to use for directly estimating its parameters by normal identification method. This is the main issue in system identifying aspect in order to deal with both nonlinearity and infinity of memory. To solve this issue on identifying the recursive filter, the paper introduces the concept of state space to reformulate the model, which leads to the method of simultaneously estimating states and parameters. The second block is a linear combination of nonlinear basis functions, and the third is a normal FIR filter. In test experiments, the PIM distortion data are picked from the simultaneous transmit–receive systems in wireless communication, and are used to test the cancellation performance. The proposed method suppresses PIM distortion over 24 dB in the receive channel, and surpasses the current technical level in wireless communication practice.