Doppler Spectrum Estimation by Ramanujan Fourier Transforms

The Doppler spectrum estimation of a weather radar signal in a classic way can be made by two methods, temporal one based in the autocorrelation of the successful signals, whereas the other one uses the estimation of the power spectral density PSD by using Fourier transforms. We introduces a new tool of signal processing based on Ramanujan sums cq(n), adapted to the analysis of arithmetical sequences with several resonances p/q. These sums are almost periodic according to time n of resonances and aperiodic according to the order q of resonances. New results will be supplied by the use of Ramanujan Fourier Transform (RFT) for the estimation of the Doppler spectrum for the weather radar signal

Analysis and improved design considerations for airborne pulse Doppler radar signal processing in the detection of hazardous windshear

High resolution windspeed profile measurements are needed to provide reliable detection of hazardous low altitude windshear with an airborne pulse Doppler radar. The system phase noise in a Doppler weather radar may degrade the spectrum moment estimation quality and the clutter cancellation capability which are important in windshear detection. Also the bias due to weather return Doppler spectrum skewness may cause large errors in pulse pair spectral parameter estimates. These effects are analyzed for the improvement of an airborne Doppler weather radar signal processing design. A method is presented for the direct measurement of windspeed gradient using low pulse repetition frequency (PRF) radar. This spatial gradient is essential in obtaining the windshear hazard index. As an alternative, the modified Prony method is suggested as a spectrum mode estimator for both the clutter and weather signal. Estimation of Doppler spectrum modes may provide the desired windshear hazard information without the need of any preliminary processing requirement such as clutter filtering. The results obtained by processing a NASA simulation model output support consideration of mode identification as one component of a windshear detection algorithm

An Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance

Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system

The feasibility of data whitening to improve performance of weather radar

The problem of efficient processing of correlated weather radar echoes off precipitation is considered. An approach based on signal whitening was recently proposed that has the potential to significantly improve power estimation at a fixed pulse repetition rate/scan rate, or to allow higher scan rates at a given level of accuracy. However, the previous work has been mostly theoretical and subject to the following restrictions: 1) the autocorrelation function (ACF) of the process must be known precisely and 2) infinite signal-to-noise ratio is assumed. Here a computational feasibility study of the whitening algorithm when the ACF is estimated and in the presence of noise is discussed. In the course of this investigation numerical instability to the ACF behavior at large lags (tails) was encountered. In particular, the commonly made assumption of the Gaussian power spectrum and, therefore, Gaussian ACF yields numerically ill-conditioned covariance matrices. The origin of this difficulty, rooted in the violation of the requirement of positive Fourier transform of the ACF, is discussed. It is found that small departures from the Gaussian form of the covariance matrix result in greatly reduced ill conditioning of the matrices and robustness with respect to noise. The performance of the whitening technique for various meteorologically reasonable scenarios is then examined. The effects of additive noise are also investigated. The approach, which uses time series to estimate the ACF from which the whitener is constructed, shows up to an order of magnitude improvement in the mean-squared error of the estimated power for a range of parameter values corresponding to typical meteorological situations

Spectrum Modal Analysis for the Detection of Low-Altitude Windshear with Airborne Doppler Radar

A major obstacle in the estimation of windspeed patterns associated with low-altitude windshear with an airborne pulsed Doppler radar system is the presence of strong levels of ground clutter which can strongly bias a windspeed estimate. Typical solutions attempt to remove the clutter energy from the return through clutter rejection filtering. Proposed is a method whereby both the weather and clutter modes present in a return spectrum can be identified to yield an unbiased estimate of the weather mode without the need for clutter rejection filtering. An attempt will be made to show that modeling through a second order extended Prony approach is sufficient for the identification of the weather mode. A pattern recognition approach to windspeed estimation from the identified modes is derived and applied to both simulated and actual flight data. Comparisons between windspeed estimates derived from modal analysis and the pulse-pair estimator are included as well as associated hazard factors. Also included is a computationally attractive method for estimating windspeeds directly from the coefficients of a second-order autoregressive model. Extensions and recommendations for further study are included

Ocean waves and turbulence as observed with an adaptive coherent multifrequency radar

An adaptive coherent multifrequency radar system is developed for several applications. The velocity distribution (Doppler spectrum) and spectral intensity of 15 different irregularity scales (waves and turbulence) can be measured simultaneously. Changing the azimuth angle of the antennas at regular intervals, the directivity of the wave/turbulence pattern on the sea surface can also be studied. A series of measurements for different air/sea conditions are carried out from a coast based platform. Experiments in the Atlantic are also performed with the same equipment making use of the NASA Electra aircraft. The multifrequency radar allows the measurement of the velocity distribution (""coherent and incoherent component'') associated with 15 different ocean irregularity scales simultaneously in a directional manner. It is possible to study the different air/sea mechanisms in some degree of detail

A satellite-based radar wind sensor

The objective is to investigate the application of Doppler radar systems for global wind measurement. A model of the satellite-based radar wind sounder (RAWS) is discussed, and many critical problems in the designing process, such as the antenna scan pattern, tracking the Doppler shift caused by satellite motion, and backscattering of radar signals from different types of clouds, are discussed along with their computer simulations. In addition, algorithms for measuring mean frequency of radar echoes, such as the Fast Fourier Transform (FFT) estimator, the covariance estimator, and the estimators based on autoregressive models, are discussed. Monte Carlo computer simulations were used to compare the performance of these algorithms. Anti-alias methods are discussed for the FFT and the autoregressive methods. Several algorithms for reducing radar ambiguity were studied, such as random phase coding methods and staggered pulse repitition frequncy (PRF) methods. Computer simulations showed that these methods are not applicable to the RAWS because of the broad spectral widths of the radar echoes from clouds. A waveform modulation method using the concept of spread spectrum and correlation detection was developed to solve the radar ambiguity. Radar ambiguity functions were used to analyze the effective signal-to-noise ratios for the waveform modulation method. The results showed that, with suitable bandwidth product and modulation of the waveform, this method can achieve the desired maximum range and maximum frequency of the radar system

Noise radar technology as an interference prevention method

In some applications, such as automotive and marine/navigation, hundreds of radars may operate in a small environment (e.g., a road complex or a strait) and in an allocated frequency band with limited width. Therefore, a compatibility problem between different radars arises that is not easily solved by time, frequency, space, or polarization diversity. The advent of fast digital signal processing and signal generation techniques makes it possible to use waveform diversity to solve this problem that will be exacerbated in the next future. Ideal waveforms for the diversity are supplied by Noise Radar Technology (NRT), whose application is promising in some military applications as well as in the civilian applications considered in this paper. In addition to being orthogonal as much as possible, the random signals to be transmitted have to satisfy requirements concerning side lobe level and crest factor, calling for novel, original design and generation processes