Lightweight Machine Learning for Efficient Frequency-Offset-Aware Demodulation

Carrier frequency offset (CFO) arises from the intrinsic mismatch between the oscillators of a wireless transmitter and the corresponding receiver, as well as their relative motion (i.e., Doppler effect). Despite advances in CFO estimation and tracking techniques, estimation errors are still present. Residual CFO creates a time-varying phase error, which degrades the decoder's performance by increasing the symbol error rate. The impact is particularly visible in dense constellation maps (e.g., high-order QAM modulation), often used in modern wireless systems such as 5G NR, 802.11ax, and mmWave, as well as in physical security techniques, such as modulation obfuscation (MO). In this paper, we first derive the probability distribution function for the residual CFO under Gaussian noise. Using this distribution, we compute the maximum-likelihood demodulation boundaries for OFDM signals in a non-closed form. For modulation schemes with unequal-amplitude reference constellation points (e.g., 16-QAM and higher, APSK, etc.), the 'optimal' boundaries have irregular shapes, and more importantly, they depend on the time since the last CFO correction instance, e.g., reception of frame preamble. To approximate the optimal boundaries and provide a practical (real-time) demodulation scheme, we explore machine learning techniques, specifically, support vector machine (SVM). Our SVM approach exhibits better accuracy and lower complexity in the test phase than other state-of-the-art machine-learning approaches. As a case study, we apply our CFO-aware demodulation to enhance the performance of a MO technique. Our analytical results show a gain of up to 3dB over conventional demodulation schemes, which exceeds 3dB in complete system simulations. Finally, we implement our scheme on USRPs and experimentally corroborate our analytic and simulation-based findings.