Blind Matched Filter Design for Communication Chains Involving Frequency Multipliers: LSTM-based Approach

Frequency multipliers are increasingly utilized for signal up-conversion in modern wireless communication systems, particularly in millimeter-wave (mmWave) and sub-terahertz (sub-THz) bands, owning to their simplicity and ease of integration. However, their inherent nonlinearity causes distortions, fundamentally altering the temporal and spectral characteristics of transmitted signals. This distortion transforms well-defined baseband pulses (e.g., sinc, raised cosine) into complex, hardware-dependent waveforms, where the matched-filter depends both on the multiplication order and the specific hardware implementation. Notably, the spectral occupancy of the transmitted signal expands after frequency multiplication. Without accurate knowledge of the multiplier-induced distortions at the receiver, applying a mismatched filter can cause severe inter-symbol interference and loss of critical frequency components, signal-to-noise ratio degradation thereby degrading detection performance. In this paper, we propose a blind, adaptive matched-filter estimation approach leveraging a Long Short-Term Memory (LSTM) neural network. Our method directly estimates the matched filter from sampled segments of the noisy modulated received signal without requiring pilot symbols. The proposed model adapts to dynamic pulse shapes and amplitudes by implicitly learning the spectral transformations introduced by hardware-induced nonlinearities. Simulation results demonstrate high accuracy of the matched filter estimation, with a mean-square error precision of four decimal places.