Pamukkale Univ Muh Bilim Derg. Baskýdaki Makaleler: PAJES-62293 | DOI: 10.5505/pajes.2024.62293

FMSDR’nin AKFD tabanlý seyrek formda algýlanmasý ve az sayýda örnekle geri çatýmý

Pýnar Özkan
Marmara Üniversitesi, Teknoloji Fakültesi, Elektrik Elektronik Mühendisliði, Ýstanbul

2000’li yýllarda ortaya çýkan Sýkýþtýrmalý Algýlama (SA) kavramý, sinyallerin zaman ekseni ya da var olduklarý eksenden baþka bir transformasyon alanýnda seyrek hallerinin var olmasý üzerinedir. Amaca uygun düzenlenen birincil veri ya da amaca uygun toplanan ikincil veri, veri yapýsýna uygun bir boyutta seyrek olarak ifade edilebilir. Transformasyon neticesinde oluþturulan seyrek formdan rasgele toplanan verilere uygulanan SA yöntemi, sinyalden örnek toplamanýn zor, eksik ve maliyetli olduðu durumlarda avantaj saðlar. Toplamda alýnabilecek miktar %100 olarak tanýmlandýðýnda bu miktarýn daha altýnda alýnan ve ölçüm olarak isimlendirilen miktara geri çatým algoritmasý uygulanýr ve sinyalin aslýna yakýn bir sinyal elde edilir. Bu çalýþma, Frekans Modülasyonlu Sürekli Dalga Radarlarýna (FMSDR), Ayrýk Kesirli Fourier Dönüþüm (AKFD) Tabanlý SA yöntemi uygulanmasý üzerinedir. FMSDR’ nin ilk birkaç taramasýnda KFD derece kestirimi yapýlarak, sonraki taramalarda sinyal rasgele olarak %25 miktarýnda alýnmaktadýr. Geri çatým aþamasýnda konveks optimizasyonun l1 normu uygulanmýþ ve baþarýsý test edilmiþtir. Derece kestirimi neticesinde en uygun derece tespit edilip %25 miktarýndaki rasgele toplanan sinyale yöntem uygulandýðýnda; sinyalin %75’i alýnmadýðýnda bile sinyalin geri çatýmýnda oldukça yüksek baþarým elde edildiði görülmektedir. Bu baþarýmýn sonuçlarý diðer kesir dereceleri ile karþýlaþtýrma yapýlarak tablo halinde ifade edilmiþtir.

Anahtar Kelimeler: Kesirli Fourier Dönüþümü (KFD), Ayrýk Kesirli Fourier Dönüþümü (AKFD), Frekans Modüleli Sürekli Dalga Radar(lar) (FMSDR), Sýkýþtýrmalý Algýlama (SA)

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Sparse sensing of FMCWR with DFrFT basis and reconstruction with fewer samples

Pýnar Özkan
Marmara University, Faculty of Technology, Department of Electrical- Electronics Engineering, Istanbul

The concept of Compressive Sensing (CS), which emerged in the 2000s, is about the existence of sparse states of signals in a transformation area other than the time axis or the axis they exist. Primary data organized in accordance with the purpose or secondary data collected in accordance with the purpose can be expressed sparsely in a size appropriate to the data structure. The CS method, which is applied to randomly collected data from the sparse form created as a result of the transformation, provides an advantage in cases where sample collection from the signal is difficult, incomplete and costly. When the total amount that can be taken is defined as 100%, the reconstruction algorithm is applied to the amount taken below this amount and called the measurement, and a signal close to the original of the signal is obtained. This study is about CS method to Frequency Modulated Continuous Wave Radars (FMCWR) based on Discrete Fractional Fourier Transform (DFrFT). The degree of FrFT is estimated with the first few scans of the FMCWR and the signal is randomly received in the amount of 25% in the next scans. In the reconstruction phase, the l1 norm of convex optimization is applied and its success is tested. When the most appropriate degree is determined as a result of degree estimation and the method is applied to 25% of the randomly collected signal; It can be seen that even when 75% of the signal is not received, very high performance is achieved in reconstructing the signal. This performance was compared with other fraction degrees and the results were expressed in a table.

Keywords: Fractional Fourier Transform (FrFT), Discrete Fractional Fourier Transform (DFrFT), Frequency Modulated Continuous Wave Radars (FMCWR), Compressive Sensing (CS)

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