Statistical study of incoherent integration applied to simulated power spectra of radar signals backscattered from equatorial electrojet irregularities

Abstract

ABSTRACT. Spectral analysis of radar echoes through spectral moment estimation allows to identify the characteristics of plasma irregularities from equatorial electrojet. The curve fitting using the maximum likelihood estimator (MLE) was chosen as the technique to obtain the plasma irregularity information. The implication of applying distinct number of incoherent integration to simulated Type 1 plasma irregularity radar spectra is investigated. The response of the fitting is evaluated using the covariance matrix of the MLE. A statistical study of incoherent integration applied to equatorial electrojet plasma irregularity spectra is presented in order to determine its effects over the estimation of Doppler velocities. The optimal values of incoherent integrations in relation to the goodness of the fitting are obtained in order to better determine the Type 1 plasma irregularity characteristics.Keywords: ionosphere, aeronomy, radar, digital signal processing, curve fitting. RESUMO.A análise espectral de ecos de radar através da estimação dos momentos espectrais permite a identificação das características das irregularidades de plasma das irregularidades do eletrojato equatorial. Dentre as técnicas usadas para obtenção das informações de irregularidades de plasma,é utilizado o ajuste de curvas pela estimação de máxima verossimilhança. Este trabalho analisa a aplicação de valores distintos de integração incoerente a espectros simulados de radar de irregularidades de plasma do Tipo 1. A resposta do ajusteé avaliada utilizando a matriz de covariâncias do estimador de máxima verossimilhança. Um estudo estatístico da integração incoerente aplicado a espectros de irregularidades do EEJé apresentado de modo a determinar seus efeitos sobre a estimação das velocidades Doppler. Os valoreś otimos de integrações incoerentes em relaçãoà qualidade do ajuste são obtidos de forma a melhor determinar as características de irregularidades de plasma do Tipo 1 do EEJ.Palavras-chave: ionosfera, aeronomia, radar, processamento de sinais digitais, ajuste de curvas.

Variance Analysis of Incoherent Integration Applied to Simulated Equatorial Electrojet Irregularities Radar Power Spectra

“…Other point we would like to address in this paper is the dependence of the average variance of f d (VAR fd ) from the number of integrated spectra (NICH). Our results (not presented in graphical format) shows a linear dependence between the natural logarithmic of variance of f d and the natural logarithmic of the incoherent integrations as described by Aveiro et al (2007). In order to quantify the dependences for the different SNR's, we have performed a linear fitting to these data in ln-ln domain, fiitting the following equation to the data:…”

“…It also presents that the higher the SNR the lower the variances. Those indicates that the curve fitting hardly ever have good estimates for this parameter (Aveiro et al, 2007).…”

“…An example of a spectrum simulated is presented in Figure 1 where the quantities mentioned above are indicated in different colors. The green dashed line represents the noise power density (P N ), the vertical red line shows the center of frequency distribution (f d ), the difference between the vertical orange and red lines determines the standard deviation of the curve fitted to the power spectrum and the area between the blue dashed line and the green dashed line defines the power of the signal (P) (Aveiro et al, 2007).…”

“…Since the white noise is a random component, the resulting spectrum will have lower variance. Figure 2 presents an illustration of the resulting spectrum (on the right side) from incoherent integration of hundred consecutive spectra (on the left side), where a noisy bunch of spectra (represented by the first one) became a smoothed one (Aveiro et al, 2007). The incoherent integration reduces the variance of the noise (σ N 2 ) and better defines the power spectra, but it does not change the mean values of signal (P) and noise spectral (P N ) densities (Fukao, 1989).…”

“…Figure1-Power spectrum resulting from the incoherent integration of one hundred simulated power spectra (black line) superimposed by a Gaussian curve (red line) fitted to the spectrum using Least Square Error Method. The green line represents the noise power density (P N ), the vertical blue line shows the center of frequency distribution (f d ), the difference between the vertical brown and blue lines determines the standard deviation of the Gaussian curve fitted to the spectrum (σ) and the area between the red and the green line defines the power of the signal (P) (AfterAveiro et al, 2007).…”