The Theory Of Spectrum Sensing Based On Polyphase Filter Bank

Frequency estimation algorithms based on frequency domain have attracted a lot of attention by researchers due to their great advantages in estimation performance. These frequency estimation algorithms are mostly based on discrete Fourier transform (DFT), realized in digital systems by fast Fourier transform whose performance is much poorer than a special polyphase bank called fast filter bank (FFB) in terms of frequency response. Frequency estimation algorithms based on DFT and FFB is studied in this paper, and the main contents related to this study are organized as follows:Firstly, the mathematical model is established for frequency estimation, consists of real sinusoid and complex sinusoid signal, and the difference in spectrum analysis between them is studied. The Cramer-Rao bound is derived in detail on the basis of the two models of signal which is an important reference in frequency estimation.Secondly, the fundamental theory of fast filter bank is studied, and the better characteristics of frequency response and low complexity of the fast filter bank compared to fast Fourier transform is analyzed from the algorithm level. Two methods utilized to optimize the design of prototype filter of the fast filter bank are respectively studied after discussing the relationship between the fast filter bank and its sub filter and the method to design a fast filter bank.Thirdly, Several frequency estimation algorithms proposed in recent years based on the time domain and frequency domain are studied, consists of adaptive algorithm for direct frequency (DFE), modified covariance method (MC), Pisarenko harmonic decomposition (PHD), reformed Pisarenko harmonic decomposition (RPHD) and single sinusoidal frequency estimation using second and fourth order linear prediction errors, which are based on time domain, ODD-DFT frequency estimation algorithm, which is based on frequency domain. And the performance of part of them is compared.Last but not least, frequency estimation algorithm based on DFT which is enhanced by complex-valued least squares (CLS) is studied. The performance of CLS-DFT frequency estimation algorithm is greatly improved by observing results of computer simulations. The algorithm for widely linear signal is proposed by CLS-DFT by formula deriving. Moreover, frequency estimation algorithm for both of the real sinusoid signal and widely linear based on fast filter bank is respectively derived. Complex-valued least squares framework is also utilized to enhance its accuracy. And its formulas for real sinusoid signal and widely linear signal are respectively derived. Results through computer simulations show that FFB/CLS-FFB frequency estimation algorithms have better performance compared to DFT/CLS-DFT algorithms.