Data-Driven Bandpass Filter Design for Estimating Symbol Rate of Sporadic Signal at Low SNR

Symbol rate is one of the most important parameters in signal demodulation process. In real-time signal processing, traditional symbol rate estimation algorithms for the Multiple Phase Shift Keying (M-PSK) and the Multiple Quadrature Amplitude Modulation (M-QAM) are based on the Fourier transform of signal’s complex envelope. At the low signal-to-noise ratio (SNR), the accuracy of symbol rate estimation can be improved by increasing the number of symbols as much as possible. However, this improvement is infeasible in many applications such as the energy-limited Internet of Things devices and sporadic noncooperative transmissions. In this paper, we propose a data-driven bandpass filter (BPF) design scheme for accurate estimation of symbol rate under low SNR with only a small number of symbols available. The proposed scheme considerably improves the estimation performance by optimizing the BPF design using the equivalent dynamic linearization model with time-varying pseudo-partial derivatives. Specifically, the proposed scheme iteratively optimizes the upper and lower cut-off frequencies of the BPF based on the measured complex envelope spectrum until achieving the optimal BPF. Therefore, the peaks of the complex envelope spectrum are extracted as the estimate of the symbol rate by applying the optimal BPF. Experimental results indicate the promise of the proposed scheme as an efficient symbol rate estimator for sporadic signal at low SNR and with a small number of symbols.