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

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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