High-Order Derivative Detection for FSK Ambient Backscatter Communications in Edge-Intelligent Sensing Systems

Edge-intelligent sensing systems demand ultra-low-power wireless connectivity to sustainably support massive sensor deployments. Ambient backscatter communication (AmBC) meets this demand by harvesting and modulating existing radio-frequency (RF) signals, eliminating dedicated carriers. However, conventional on-off keying (OOK) demodulation in AmBC is highly susceptible to noise, while existing frequency-shift keying (FSK) alternatives relying on first-order derivatives perform poorly at low signal-to-noise ratios (SNRs), compromising the reliability of edge sensing data. In this paper, we propose a signal detection method that exploits high-order derivatives to enhance the demodulation of FSK-modulated ambient backscatter signals. By analytically evaluating the power of interference and noise after high-order differentiation, we reveal that the interference power is minimized at the second order while the noise power increases monotonically with the derivative order, leading to a favorable trade-off in typical AmBC regimes where the modulation frequency is much smaller than the sampling rate and comparable to the ambient signal bandwidth. We then design a phase-preserving frequency amplitude comparison detection (FACD) rule to recover the embedded information. Simulation results show that the proposed second-order derivative-based FACD achieves the lowest bit error rate among all compared schemes, particularly at low SNR.