MsPF-Trans: A Generative Transformer for Multi-step Probabilistic Forecasting of Radar Pulse Repetition Interval Sequences

One central purpose of modern electronic receivers is to perform automatic analysis of non-cooperative radar signals. There is an urgent need to develop intelligent forecasting algorithms for these devices due to emerging complexity and agility of radar pulse sequences. The increased flexibility and agility of modern radars especially multi-function radars in transmitted pulse sequences with complex inter and inner-pulse modulations and dynamically varying scheduled waveforms pose great challenges for modern electronic receivers or radar warning receivers for conducting rapid and effective countermeasures. This paper considers the pulse level Multi-step Probabilistic Forecasting (MsPF) of non-cooperative radar Pulse Repetition Interval (PRI) sequences. At first, the complex intercepted PRI sequences are modeled through State Space Models (SSM) with non-Markovian and nonlinear dynamics. Then, a generative Transformer called MsPF-Trans is proposed with consideration of both deterministic and stochastic factors in the received PRI sequences. The MsPF-Trans parameterize the PRI sequences with non-Markovian and nonlinear temporal structures. A sparse attention module is designed to further facilitate model training and to reduce computational complexity in full attention. Variational inference is utilized in model training. The timestep-wise variational lower bound is maximized with minibatch stochastic optimization to obtain estimates of model parameters. Finally, the multi-step probabilistic forecasting is achieved through estimating the parameters of the conditional observation Probability Density Function (PDF) of each individual pulse in future time steps non-auto-regressively. Comprehensive simulation experiments validate the effectiveness, superiority and robustness of the proposed method against state-of-the-art methods in terms of forecasting accuracy and adaptation ability to non-ideal conditions.