Optimal Singular Value Decomposition Based Pre-coding for Secret Key Extraction from Correlated Orthogonal Frequency Division Multiplexing Sub-channels

Secret key extraction is a crucial issue in physical layer security and a less complex and, at the same time, a more robust scheme for the next generation of 5G and beyond. Unlike previous works on this topic, in which Orthogonal Frequency Division Multiplexing (OFDM) sub-channels were considered to be independent, the effect of correlation between sub-channels on the secret key rate is addressed in this paper. As an assumption, a realistic model for dependency among sub-channels is considered. Benchmarked by simulation, the result shows that the key exchange rate may decline by up to 72% due to the correlation of sub-channels. A new approach for efficient key extraction is used in this study. To do this, a Singular Value Decomposition based (SVD-based) pre-coding is utilized to alleviate the sub-channels correlation and the channel noise. The low computational complexity of our proposed approach makes it a promising candidate for developing secure and high-speed networks. Results obtained through simulation indicate that applying pre-coding on the measured correlated data resulted in a minimum gain of 9 dB. In addition, the result also depicts the advantage of SVD versus other pre-coding techniques, namely PCA, DCT, and WT.