Frequency-domain adaptive sparse signal reconstruction at sub-Nyquist rate

Sub-Nyquist sparse signal reconstruction technique can significantly reduce the cost of hardware design. Many sub-Nyquist reconstruction algorithms (e.g., greedy relax and convex optimization) have been developed to reconstruct the real frequency-sparse signal by utilizing its sparsity. However, greedy algorithms require a large memory size and convex optimization algorithms exhaust a long calculation time. Unlike previous schemes, in this paper, we propose a frequency-domain adaptive sparse signal reconstruction scheme under sub-Nyquist to achieve better performance and lower computational time. Specifically, discrete Hartley transform (DHT) is adopt to find a sparse representation in frequency domain accompanying with sub-Nyquist random demodulation sampling rate and £ 0 -NLMS algorithm is utilized to reconstruct sparse signal. Experiment results are conducted to confirm the advantages of the proposed method in terms of computational time and mean square error.