Estimasi Rapat Spektral Daya Berbasiskan Compressive Sampling

Dyonisius Dony Ariananda

Abstract


Makalah ini membahas proses penginderaan spektrum berbasiskan rekonstruksi rapat spektral daya (power spectral density, PSD) dari sampel-sampel digital yang diperoleh dari pencuplikan dengan pesat di bawah pesat Nyquist. Pada literatur mengenai rekonstruksi PSD berbasiskan pencuplikan sub-Nyquist, sistem persamaan yang dihasilkan umumnya bersifat overdetermined sehingga algoritme least-squares (LS) dapat dipakai. Namun, perlu diingat bahwa ada batas minimal pesat pencuplikan yang harus dipenuhi untuk menjamin diperolehnya sistem overdetermined ini. Pada makalah ini, batas minimal pesat pencuplikan di atas dicoba dilewati meskipun sistem persamaan yang diperoleh akan bersifat underdetermined yang tidak memungkinkan digunakannya algoritme LS. Agar rekonstruksi PSD tetap dapat dilakukan pada kondisi ini, asumsi sparsity (yang valid untuk beberapa aplikasi) dapat dikenakan pada PSD yang akan direkonstruksi. Makalah ini mengevaluasi penggunaan algoritme orthogonal matching pursuit (OMP) dan least absolute shrinkage and selection operator (LASSO) untuk rekonstruksi PSD pada kasus sistem underdetermined. Hasil studi menunjukkan bahwa bila parameter regularisasi yang tepat digunakan, hasil rekonstruksi PSD dengan metode LASSO masih mendekati hasil rekonstruksi PSD yang diperoleh pada pesat Nyquist. Hasil rekonstruksi PSD dengan metode LASSO juga dapat digunakan untuk mendeteksi lokasi pita frekuensi yang diduduki pengguna secara akurat saat daya isyarat pengguna relatif cukup tinggi terhadap daya derau. Sementara itu, OMP hanya dapat digunakan untuk kasus tanpa derau. Pada aplikasi yang membutuhkan proses rekonstruksi PSD, hasil ini mengindikasikan dimungkinkannya relaksasi pesat pencuplikan hingga pesat yang sangat rendah.

Keywords


Compressive Sampling; Penginderaan Spektrum; Pencuplikan Sub-Nyquist; Rapat Spektral Daya; Sistem Underdetermined; Least Absolute Shrinkage and Selection Operator

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DOI: http://dx.doi.org/10.22146/jnteti.v7i4.461

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