AN EXACT VARIANCE EXPRESSION OF THE k-PHD SINGLE-TONE FREQUENCY ESTIMATOR: RANDOM PHASE CASE

Year 2019, , 419 - 428, 30.08.2019

Betofe Mboyo Keyta Sevim Hazal Uz Erdoğan Dilaveroğlu

https://doi.org/10.17482/uumfd.559986

Abstract

The
k-PHD method, a generalization of the well-known Pisarenko harmonic
decomposition (PHD) method, is considered for frequency estimation of a single
real random-phased sinusoid in noise. With the use of a simple variance
analysis technique, an exact expression of the k-PHD frequency variance is
derived. An approximate k-PHD variance formula for sufficiently large data
lengths and signal-to-noise ratios is also given. Computer simulations are
included to validate the theoretical development.

Keywords

Frequency estimation, Real sinusoid, PHD method, k-PHD method, Variance analysis

k-PHD Tek-Ton Frekans Kestiricisinin Bir Kesin Değişinti İfadesi: Rasgele Faz Durumu

Abstract

İyi
bilinen Pisarenko harmonik ayrışım (PHD) metodunun bir genelleştirilmesi olan
k-PHD metodu gürültü içindeki bir reel rasgele fazlı sinüsün frekans kestirimi
için ele alınmıştır. Basit bir değişinti analiz tekniği kullanılarak, k-PHD
frekans değişintisinin bir kesin ifadesi çıkarılmıştır. Yeteri kadar geniş veri
uzunlukları ve yüksek işaret gürültü oranları için bir yaklaşık k-PHD değişinti
formülü de verilmektedir. Kuramsal sonuçları teyit eden bilgisayar benzetimleri
dâhil edilmiştir.

Keywords

Frekans kestirimi, Reel sinus, PHD metodu, k-PHD metodu, Değişinti analizi

References

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