Low-Complexity Autocorrelation-Based OFDM Detection under Sub-Nyquist Sampling

Sub-Nyquist sampling has emerged as an attractive approach for reducing the hardware complexity and computational burden associated with orthogonal frequency division multiplexing (OFDM) spectrum sensing. However, sampling below the Nyquist rate modifies the statistical behavior of autocorrelation-based detection metrics, which can adversely affect detection performance. In this work, we investigate the effect of uniform undersampling on the distribution of OFDM autocorrelation detection statistics. It develops two low-complexity compensation methods that operate directly on undersampled data without signal reconstruction or iterative processing. The first employs statistical restoration to recover the distribution of the detection statistic relative to its Nyquist-rate equivalent, whereas the second employs a constant false-Alarm rate (CFAR) threshold calibrated to the undersampling factor. Analytical expressions for the detector statistics and threshold are derived and validated through simulations. The results show that reducing the sampling rates by factors of two and four leads to a modest performance loss, requiring approximately 1-3 dB additional signal-To-noise ratio (SNR) to achieve a detection probability (Pd ) of 0.9. The proposed methods maintain reliable detection performance across a wide SNR range while significantly reducing sampling requirements, offering a low-complexity solution for resource-constrained cognitive radio networks (CRNs) and Internet of Things (IoT) spectrum sensing.