Markku S. Lehtinen

General incoherent scatter analysis and GUISDAP

Abstract In modern incoherent scatter measurements very complicated coding schemes are used to achieve the necessary statistical accuracy in the measurements. The ambiguity functions specify how the measurement weights the plasma autocorrelation function in the two-dimensional space of range and lag. Alternatively one can work in the space of range and frequency, and it is necessary to derive the ambiguity (instrument, weighting) functions also in terms of these variables. In this paper we summarize the theory of ambiguity functions and discuss the use of lag profiles as tools of describing arbitrary kinds of incoherent scatter measurements. We also develope a general way to calculate error estimates of estimated autocorrelation function values values. Finally, we shortly discuss how the formalism is used in the GUISDAP (Grand Unified Incoherent Scatter Design and Analysis Package) software.

Stochastic inversion in ionospheric radiotomography

The stochastic inversion method in ionospheric radiotomography is reviewed with a special emphasis on regularization used in the inversion process. Regularization is used both for preventing vigorous point-to-point oscillations and for controlling the peak altitude and thickness of the inversion result. The latter usually means importing a priori information on the layer height and thickness to the solver. In this paper it is pointed out that due to the curvature of the Earth and of the ionosphere, the measurements contain some information on the ionospheric altitude and the profile shape even in the case of a purely horizontally stratified layer. If this information could be used in choosing an appropriate regularization, no additional information would be needed. Simulation tests are presented which indicate that the altitude of a horizontally stratified layer can be determined with a reasonable accuracy without any a priori information. An attempt is also made to use the data for determining the shape of a proper regularization profile. Although some success is achieved in this effort, it is concluded that available a priori information, for example, ionosonde or incoherent scatter measurements, should be used in choosing the regularization profile. The ideas are tested with true data obtained from difference Doppler measurements carried out in Scandinavia, and the results are compared with simultaneous observations made by the European incoherent scatter radar. The comparison shows a reasonable agreement, although clear discrepancies also occur, for instance, in the shape of the bottomside profile.

Fractional lags in alternating codes: Improving incoherent scatter measurements by using lag estimates at noninteger multiples of baud length

Alternating codes are nowadays a standard measurement technique in the incoherent scatter observations. In most conditions they give the best accuracy for the plasma autocorrelation function estimates in the E and F region measurements. We explain here how oversampling can be used to further increase the speed of the experiments. In an oversampled alternating code the sampling interval and the length of the postdetection filter are a fraction of the baud length, and autocorrelation function estimates are calculated both for integer lag values, which are multiples of the baud length, and for the intermediate values, which are called fractional lags. We show that alternating codes with fractional lags give data for multiple range resolutions and that the experiments are always more efficient than the standard alternating code experiments. Finally, we study how the oversampling affects the signal processing.

Range ambiguity effects in Barker-coded multipulse experiments with incoherent scatter radars

Abstract A Barker-coded multipulse is the best of the classical modulations when high spatial resolution is needed in incoherent scatter measurements. Unfortunately, this type of modulation generates range ambiguities which reduce the quality of data. In this paper, range ambiguity functions for an EISCAT experiment, ESLA-T4, are displayed. A method of eliminating the ambiguities in data analysis is developed and its applicability is demonstrated. It is found that the method can remove the effects of the range ambiguities in the lower part of the E-region, but above 120 km altitude the correction is not sufficient. The residual of the fit is reduced by an order of magnitude. The changes in the temperatures are a few Kelvin at the lowest altitudes and a few tens of Kelvin between 110 and 120 km.

Randomization of alternating codes: Improving incoherent scatter measurements by reducing correlations of gated autocorrelation function estimates

Incoherent scatter radar autocorrelation function estimates produced by alternating codes are found to contain significant correlations between different lags and different heights. While no correlations are caused by the background thermal noise, the special structure of the alternating code sequences causes clutter or the self-noise contribution of the codes themselves to introduce maximal positive correlations between the different lag estimates. Because of this, postintegration of adjacent heights does not improve the results as much as could be expected. For a high signal-to-noise ratio, alternating code results are worse than estimates produced by similar random codes. In this paper we show that we can correct the situation by randomizing the alternating codes. This is accomplished by multiplying each alternating code sequence in the alternating code cycle by a fixed random-looking sequence. This multiplying sequence can be changed and randomly chosen at the end of each alternating code cycle. The multiplying sequence can also be kept constant with almost equally good results. If this is done, the special structure of the alternating code sequences actually causes the correlations to become less than the correlations produced by random codes. The improvement in accuracy is discussed in various situations. The reasons for the appearance of maximal positive correlations with alternating codes are explained in a mathematical appendix.

A Proposed Solution to the Range-Doppler Dilemma of Weather Radar Measurements by Using the SMPRF Codes, Practical Results, and a Comparison with Operational Measurements

Abstract Based on the measurement principles used on incoherent scatter radars, the authors have developed the Simultaneous Multiple Pulse Repetition Frequency (SMPRF) code that is intended to solve the range–Doppler dilemma and that can be used with modern magnetron radars. The working principle of the code is explained in mathematical terms and with the help of a simplified model. Results from the SMPRF and traditional fixed PRF weather radar measurements are compared, and the reasons for the differences are explained. The practical results show that the SMPRF code seems to work in the manner that is predicted by the theoretical and model calculations. The SMPRF code provides enough information to produce a high-resolution measured spectrum for each range gate. The shape of these measured spectra are seldom purely Gaussian. It is possible that more advanced raw products, other than just reflectivity, velocity, and width, can be produced with the help of these high-resolution spectra.

Mismatched Filtering of Aperiodic Quadriphase Codes

Matched filtering of quadriphase coded radar signals creates unwanted sidelobes, which may mask important information. This correspondence presents a method of eliminating these sidelobes in aperiodic quadriphase codes. This is done by using a mismatched filter. The signal-to-noise ratio (SNR) at the output of the mismatched filter is less than the SNR at the output of the corresponding matched filter. A thorough computer search has been carried out to find quadriphase code-mismatched filter pairs with minimum possible SNR losses by considering a point target in the presence of white Gaussian noise. The phase patterns of the optimal codes, which were chosen from a total number of 1.466 times 1012 investigated codes, are shown. It turned out that the mismatched filter of a quadriphase Barker code with 15 elements (1, 1, 1, j, j, 1, - j, - j, j, -1, - j, j, 1, -1, 1) has a loss in SNR of only 6.7% when compared with the corresponding matched filter. The mismatched filter of the well known 13-element Barker code, which has a loss in SNR of 4.8%, outperforms this filter. Finally, using numerical experiment it is shown that a randomly selected long code will most likely have very large SNR losses.

On optimization of incoherent scatter measurements

Abstract The design of incoherent scatter measurements, as well as other radar measurements is constrained by technical factors, the most important of which are radar power and duty cycle. If these are fixed, it is possible to improve detection accuracy by using different kinds of coding methods. We study a situation where radar backscatter autocorrelation functions (ACF) of a continuously distributed medium are to be measured with a specified radar range and autocorrelation lag resolution. As the measurement is disturbed by thermal noise, it is then shown that the accuracy of the resulting ACF estimates cannot be better than a certain limit, whatever kinds of coding schemes are used. The accuracies of alternating codes are compared to this limit for a range of pulse lengths used. We suppose that the noise power due to thermal fluctuations in the system and background noise is higher than the signal power itself. The proof of the limiting accuracy is based on linear statistical inversion theory.

Transmission code optimization method for incoherent scatter radar

When statistical inversion of a lag profile is used to determine an incoherent scatter target, the posterior variance of the estimated target can be used to determine how well a set of transmission codes perform. In this work we present an incoherent scatter radar transmission code optimization search method suitable for different modulation types, including binary phase, polyphase and amplitude modulation. We found that the combination of amplitude and phase modulation provides better performance than traditional binary phase coding, in some cases giving better accuracy than alternating codes.

Parameter mixing errors within a measuring volume with applications to incoherent scatter

Abstract The effect on parameter error estimates resulting from parameter variations within the measuring volume under consideration is studied in the framework of linear statistical inversion theory. It is shown that using estimates for the parameter averages is equivalent to having the theory corrected by the covariances of the variables coupled with the second derivatives of the theory function. If the parameter distributions were known exactly, this would only introduce a bias in the linear theory and hence a systematic error in the parameter centre point estimates. When the distributions are not known exactly, there is another source of error consisting of the uncertainties in the parameter variation estimates. This leads to new error bounds on the allowed parameter variability within the volume under consideration if some prescribed accuracy in the parameter average estimates is required. These considerations are applied to incoherent scatter (IS) radar measurements, where it is important to be able to estimate the effect of integrating both in space and time over a volume with varying parameters in order to obtain spectra or autocorrelation functions. Numerical examples are given in the case of the O + content estimates in measurements with the EISCAT UHF radar, when for example the ion temperature varies over the integration ranges. The results obtained may be used in the design of experiments when high resolution composition measurements are required.