Estimasi Rapat Spektral Daya Berbasiskan Compressive Sampling
Abstract
This paper focus on spectrum sensing based on power spectral density (PSD) reconstruction from sub-Nyquist-rate samples. In the existing works on PSD reconstruction from sub-Nyquist-rate samples, the resulting system of linear equations (SLE) is generally overdetermined, which allows the PSD reconstruction using least-squares (LS). Note that there is a lower bound for the achievable sampling rate ensuring that the resulting SLE is overdetermined. This paper aims for a further sampling rate reduction, which results in an underdetermined SLE. However, when the resulting SLE is underdetermined, the LS method cannot be used to reconstruct PSD and additional constraints are required. Under this circumstance, a sparsity assumption (which is applicable for some applications) can be applied on the PSD. The use of the orthogonal matching pursuit (OMP) and the least absolute shrinkage and selection operator (LASSO) algorithms to reconstruct the PSD for the case of underdetermined SLE is examined. The simulation study shows that if an appropriate regularization parameter is used, the quality of the PSD reconstructed using LASSO is only slightly below the one produced using Nyquist-rate sampling. From the detection point of view, the PSD reconstructed using LASSO can accurately locate the occupied frequency band when the user signal power is sufficiently high compared to the noise power. Meanwhile, OMP can be used only in the noiseless scenario. These results indicate that the sampling rate alleviation up to a very low rate is possible while maintaining the quality of the spectrum sensing results at the acceptable level.
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