Study on the Method of Extracting Plasma Lines Based on Sanya Incoherent Scatter Radar

Abstract

The plasma lines observed by Sanya incoherent scatter radar (SYISR) are dependent on the enhancement of Langmuir waves due to superthermal photoelectrons generated by solar EUV radiation. The plasma line power spectrum can be obtained using long-pulse and alternating-code transmission signals during the period from sunrise to noon almost every day. For the power spectrum of the long pulse, the CLEAN algorithm that has been applied in this field is used to verify the feasibility of this method for SYISR in only a few cases. However, it is difficult to deal with alternating code with such a low SNR using the general deconvolution method. The irreversible-migration filtering (IMF) method has been developed to separate signal noise from the measurements of the alternating code. Some experimental results from the SYISR measurements validate the excellent performance of the IMF method for alternating code. Additionally, an example observation of the electron density with a high time and range resolution is derived. The results show that plasma line detection can be a powerful new observational capability for SYISR as an ionospheric experimental mode for ionospheric calibration, when possible, which can be simultaneously measured with the ion line for constant radar calibration in the standard fitting of the ion line.

1. Introduction

Incoherent scatter radar is used for measuring the properties of ionospheric plasma by receiving the radar backscatter echo signal modulated by the thermal fluctuation of electrons and ions in the ionosphere. Following the contribution of electrons and ions to the fluctuation of electron density, the incoherent scatter spectrum can be divided into the ion line near the zero frequency and the plasma line near the plasma frequency. Its spectral peak is related to the solution of the dispersion relationship in cold, magnetized plasma, namely, the ion acoustic wave and the Langmuir wave.

Because of strong echo power, the ion lines with a classical double-humped spectra shape are relatively easy to routinely detect, so they provide a wealth of information for obtaining the ionospheric parameter estimates of electron density, electron temperature, ion temperature and plasma drift velocity. Compared with ion lines, the echo signal amplitude of plasma lines is very weak, lower than the measured power spectrum noise level, which makes it difficult for most ISRs to detect the echo signal of plasma lines.

In the presence of suprathermal photoelectrons, the velocity of the superthermal charged particles matches the phase velocity of the Langmuir wave, the amplitude of the Langmuir wave can be enhanced, and the plasma lines near the plasma frequency can also be correspondingly enhanced and detected by ISR [1]. The first observation of plasma lines enhanced by the photoelectrons produced by solar UV radiation in the daytime was successfully performed with the Arecibo Observatory radar [2]. In the absence of direct solar EUV during the night, plasma lines enhanced by the injection of energetic particles into the ionosphere, such as auroral electron precipitation, can also be detected by EISCAT UHF and Sondrestrom ISR [3,4]. In addition, the technology of the artificially enhanced plasma line has also been developed by injecting high-power, high-frequency electromagnetic waves into the ionosphere through ground heating facilities. The Arecibo ISR [5,6,7] and Tromsø ISR [8,9] radar observed the enhanced plasma line after the artificial heating of the ionosphere.

The ionospheric electron density with a high time and range resolution can be determined based on the offset frequency of the plasma line from the transmitter frequency, which so far is the most accurate ground measurement method to obtain the absolute electron density [4,10,11]. In addition, plasma lines appear in pairs on both sides of the ion lines, which are regarded as up- and down-shifted plasma lines, respectively. If the plasma line with a high spectral resolution can be measured, then the high-precision electron temperature can be obtained by determining the asymmetrical frequency difference between the up- and down-shifted plasma lines [12,13,14]. In the study of Bjørnå and Kirkwood [15], the electron density and electron temperature measured by the plasma line were used as the prior knowledge of the ion line fitting to reduce the number of fitting parameters and eliminate the ambiguity of temperature–ion composition. Moreover, the offset frequency of the plasma lines was added into the ion line least-square fitting, and the ionospheric ion composition was successfully extracted from the measured data obtained by the EISCAT UHF and VHF radars [16]. Similarly, if the measurement of the plasma line is combined in the ion line fitting, then the ion neutral collision frequency in the lower height E region can also be obtained [17].

Although plasma lines have been studied by many scholars for a long time, the work on plasma lines in the low latitudes of East Asia has not yet been carried out. Sanya incoherent scattering radar (SYISR) is China’s first phased-array incoherent scatter radar located in Sanya (18.34°N, 109.62°E). Preliminary ion line results and evaluations are presented in Hao et al. [18]. A prominent capability of SYISR is the ability to detect weak plasma line spectra, except for ion lines, in the regular mode. In this paper, we focus on the natural enhanced plasma line power spectrum during the daytime measured by a long pulse and alternating code from SYISR. The signal-to-noise ratio of the echo from the long pulse is much stronger than that from the alternating code. So, we use the CLEAN method with iterative automatic extraction to process long-pulse data and also use a novel method, irreversible-migration filtering (IMF) for alternating-code data by mainly taking advantage of migration and de-migration. In Section 2, we describe the experimental details for obtaining the measured plasma power spectrum. We apply the CLEAN and IMF algorithms to extract the plasma frequency in Section 3. Further, the electron density estimation from the plasma lines is presented. The applicable requirements for the two different methods are summarized in Section 4.

2. Experimental Setup

The plasma line echo signal is the backscattered signal from the high-frequency Langmuir wave in the scatterer volume, whose Doppler shifts from transmitter frequency are approximately equal to the plasma frequency. In most cases, the plasma frequency near Sanya is in the range of several MHz to twenty MHz. Therefore, in order to detect the complete plasma line, SYISR adopts three channels for simultaneous digital down-conversion and filtering. Different digital oscillators for the three channels are presented according to the plasma frequency requirements. The local oscillation frequency of one channel is used for both transmission and reception in ion line measurement, and the other two only for different receiver channels in plasma line measurement. Each channel obtains the power spectrum at a different frequency band, and the spectra at these three frequency bands are further synthesized into the full incoherent scatter spectrum, including the ion line and plasma lines. The digital filter bandwidth and output data rate for each channel are 4 MHz, so the maximum coverage of the spectrum that can be detected at once during the plasma line experiments is 12 MHz. If the plasma line is to be continuously observed for a long time, then the digital local oscillator frequency of the plasma line channel needs to be flexibly adjusted, so that the receiver frequency covered by the filter window exactly matches the plasma frequency.

Currently, coded and uncoded long-pulse transmission schemes have been developed for incoherent scatter radar to obtain the measurements of plasma lines [10,19]. Over SYISR, the 430~450 MHz radar frequency is operated at a peak power near 2 MW, and plasma lines enhanced by the natural superthermal electrons can be routinely detected during the daytime with an uncoded long pulse and alternating code. In order to ensure the maximum antenna gain and a better signal-to-noise ratio (SNR) of the plasma line echo, the radar beams in the following experimental results are all pointed vertically. The processing of the observations is offline. For the same code type, the solution of the plasma line power spectrum is the same as that of the ion line spectrum, except that more data samples need to be calculated on a range gate and it is more time-consuming. The examples of the full incoherent scattering spectrum of the ion line and up- and downshifted plasma lines detected at noon are shown in Figure 1. The left panel shows the spectrum measured by 32-bit alternating code with a 20 μs baud length. The right panel represents the spectrum measured by a long pulse with a 100 μs pulse length.

The results spectra displayed in Figure 1 are the spliced power spectra of the three respective channels after removing the background. Due to a different channel background noise for each channel, the intensity shown in the combined power spectrum is not the real relative intensity of the ion line and plasma lines. Here, it is mainly demonstrated that the ion line and plasma lines can be simultaneously obtained by a long pulse or alternating code. The range resolution of the 100 μs long pulse is theoretically 15 km so that the plasma lines can be visibly detected. Then, the corresponding frequency resolution is 5 kHz. The alternating code has a higher range resolution of 3 km and a frequency resolution of 0.781 kHz. Note that we use a 3 km range step for two radar transmit codes in Figure 1, but this measurement of the long pulse is in fact clearly smeared in this range. Based on the characteristic that the plasma line has a strong frequency dependence, alternating code is used to determine the plasma frequency with good accuracy.

3. Method

The obtained echo power spectrum can be regarded as the two-dimensional convolution of the spectral ambiguity function and the incoherent scatter power spectrum in terms of frequency and range. Due to its detectability depending on the intensity of the SNR, the intensity of the decoded plasma line power spectrum is very noisy under the lower SNR condition. In addition, it may also be affected by the response of the radar receiver, which may cause the calculated plasma line power spectrum to contain some unwanted signal contributions, referred to as background noise signal. As shown in Figure 1, there exists obvious convolutional distortion in the range of the long-pulse power spectrum. In comparison, the range resolution of the alternating code is much better, but the SNR is much worse. Therefore, the following different methods are used to extract plasma line profiles as a function of altitude and frequency for the long pulse and alternating code, respectively.

3.1. Deconvolution for Long-Pulse Spectrogram

In order to recover the true spectrogram from the convolutional distortion, the well-known CLEAN algorithm [20] is utilized, which is widely used to reconstruct images in radio astronomy. The algorithm is effective against point sources, that is, based on the fact that the map to be deconvolved is itself a convolution of multiple point sources and the point spread function (PSF) that describes the features of the radar receiver. Then, the measured plasma line spectrogram can be regarded as a dirty map to be deconvoluted, the ambiguity function generated from the radar transmit waveform and the receiver impulse response as the PSF, and the plasma frequency at each range gate as a point source. Therefore, the CLEAN algorithm can be used to deconvolve the plasma line spectrogram. It has been proven that this method can remove range-Doppler smearing for the long-pulse measurement with a sufficient SNR, and thus extract the plasma line profiles [4,21].

The CLEAN algorithm is implemented by repeatedly subtracting the dirty beam from the dirty map until the maximum intensity of the residual map is less than the specified noise level or reaches a preset number of iterations, thus removing the smearing in the range. The PSF required is the receiver response to a point source in plasma, and its accurate formation is very important. To obtain complete information, the PSF should be constructed by the real transmitted radar sampling. This allows a more realistic model of the ambiguity of the plasma echo at each height in the range direction. However, the receiver of SYISR does not support the sampling of transmitted signals. Here, we instead use an idealized rectangular pulse as the transmission waveform and receiver pulse response, respectively, to create a matrix of the PSF where the transmitted pulse sampling is at the center. It is achieved by multiplying the transmitted pulse sampling by the shifted version of its complex conjugate signal, where the shifted operation is performed at one sampling interval each time. Then, the non-overlapping part of each row of the matrix undergoes zero-padding, so that the total length of the product is consistent with the transmitted pulse. In this study, we performed the deconvolution procedures as described above for the long-pulse plasma line spectrogram.

Figure 2(left) shows the distorted upshifted plasma line spectrum measured by a long pulse at noon. At this time, the electron density is very high, and the plasma line spectrum with a sufficiently strong SNR can be obtained as a detectable and recognizable feature. The power spectrum of the echo signal with a 100 μs transmitting pulse width are obtained by averaging 36,037 pulses with an integration time of 2 min, so that a thin plasma line can be indistinctly seen, even though it is smeared by about 15 km in the altitude direction. In this case, we can use the CLEAN algorithm to remove range smearing; otherwise, this method is invalid for recovering the true plasma line profiles from the convolutional distortion under a very low SNR. To better estimate the plasma line frequency, it is necessary to remove the background noise from the deconvolved spectrum. We select the median of the spectrum at the last few heights as the background noise, and then subtract it from the spectrum after deconvolution. The result of the deconvolved plasma line spectrum with the background noise removed after 300,000 iterations is shown in Figure 2 (right). It can be seen that the plasma line is extracted below 200 km, but not above 200 km because of contamination from the strong background noise level. The parts that can be recognized by the human eye are actually discrete plasma frequency points.

This method has also been used to handle plasma line observations with lower SNRs at other local times. Figure 3 shows an example of the detectable plasma line profile. Although the signal intensity near the maximum electron density is strong enough to clearly exhibit a distorted plasma line profile, it also includes strong background noise, causing the true plasma line to be completely submerged in noise. That is to say, the point source strength is very weak compared to the extended structures in the range. Under such circumstances, convergence instability in the CLEAN process may occur when the PSF is inaccurately generated with limited information. With more iterations or a smaller loop gain, it is also impossible to find the location of the true plasma line. Therefore, larger error bars are produced after deconvolution, and we do not show the deconvolved result here.

3.2. Separating Signal–Noise for Alternating-Code Spectrogram

When transmitting pulses with a longer pulse width for sufficient radar efficiency, alternating code can be used to achieve a higher range resolution of plasma line measurements, up to one baud width. However, there have been difficulties with using general deconvolution methods to extract the plasma line profiles of alternating code. We use an irreversible-migration filtering (IMF) method [22] to perform signal–noise separation, which can achieve the purpose of background noise removal and SNR improvement. Then, some maximum-intensity points on some range gates are found, which are the plasma frequency values at the corresponding heights.

To illustrate the effectiveness of this method of plasma line extraction, we take the plasma line echo data of 64-bit alternating code with a 10 μs code width as an example. The sampling interval is 0.25 μs. For the alternating code with a 640 μs pulse width, the maximum lag number of the decoded autocorrelation function (ACF) is 2560. In order to improve the SNR of the plasma line power spectrum, we utilize the first 256 complex-valued lags of the ACF with a Hamming window. The resulting frequency resolution is 7.8125 kHz. Figure 4 shows the raw upshifted plasma line power spectrum contaminated by background noise on 8 March 2021. The range step is 10 μs, which results in a 1.5 km altitude resolution, and the integration time is 2 min. Note that there exist some obvious vertical stripe background signals, but a strong intensity of the plasma line at the peak of the F layer is obtained in Figure 4. Thus, under such strong background noise, it is very difficult to obtain the plasma frequency at other range gates, except the peak of the F layer.

The IMF method is predominantly employed for wavefield separation in seismic data processing and has demonstrated its efficacy in various applications, including diffraction separation, structural noise elimination, and surface wave separation. The underlying principle of this technique involves partitioning the migration domain into evanescent and propagating regions; wavefield components residing within the evanescent region undergo automatic attenuation, whereas those within the propagating region are inherently preserved. Consequently, adjusting the migration velocities enables the separation of wavefield components with distinct slopes throughout the migration and de-migration procedures. Given the dissimilar slopes of the background noise and signals, this approach can also be extended to signal–noise separation within radar signal processing. Hence, we can convert the signal in f–k space into the migrated domain as [22,23]:

$$A\left(k,\omega ,z\right)=e^{jz\sqrt{\frac{4{\omega }^2}{v^2}-k^2}}A\left(k,\omega ,0\right)$$

(1)

where $A\left(k,\omega ,0\right)$ is the signal power spectrum, $z$ is the transformed travel time, $v$ is the migration velocity, $k$ is the wavenumber, and $\omega =2\pi f$ is the circular frequency of the echo signal. The exponential term in Equation (1) contributes to the phase change when $4{\omega }^2/v^2-k^2>0$; on the contrary, it is an attenuation term and the signals are migrated to the evanescent region during de-migration, when $4{\omega }^2/v^2-k^2<0$. To do this, we tune the migration velocity, although it might not have any obvious physical meaning, so that the background noise with large absolute slope values is irreversible after de-migration, as far as possible. However, the other signals are returned to the original region. Thus, the background signal can be separated from the raw plasma line power spectrum.

To eliminate the background noise more effectively with the IMF method, we need to distinguish the data near the peak of the F layer from the data at the other heights. As can be seen from Figure 4, compared with other range gates, the slope value at the peak of the F layer is relatively large, close to vertical. For example, if we choose a larger migration velocity, then the raw effective plasma line will fall in the irreversible region in the migrated domain, and vice versa. In other words, this method may mistakenly remove the signal at the peak of the F layer as the background if an inappropriate migration velocity is used. Hence, the crucial feature of the IMF method is to choose an optimal velocity. Figure 5 shows an example of signal–noise separation from the raw power spectrum in Figure 4 using the IMF method. The power spectrum results after background removal are shown in Figure 5a,c,e. Figure 5b,d,f shows the separated background noise power spectrum. For range gates less than 200 km and more than 250 km, we use the same relatively large migration velocity (e.g., v = 8.5 m/s), while the smaller migration velocity (e.g., v = 0.8 m/s) is used between 200 and 250 km. It can be seen that the vertical stripe background has been removed so well that we can find the plasma frequency more accurately at each altitude in the subsequent processing.

The white circles in Figure 5a,c,e indicate the plasma frequency extracted at some heights where the plasma line is enhanced. The plasma frequency estimation mainly includes three steps. First, the frequency value corresponding to the maximum intensity at each height is obtained. Second, the second-order difference values of the plasma frequency between different heights are calculated. Finally, these difference values are combined with the threshold value to eliminate the falsely selected points greater than the threshold value. An appropriate threshold value should be selected against the background signal. A constant threshold value is usually enough, even for complex data. For the data of the example discussed here, we set the threshold value as 0.03.

Figure 6 shows sections of the power spectrum before and after using the IMF method at various altitudes. The data in Figure 6a,c,e are all from the raw power spectrum in Figure 4. The data in Figure 6b,d,f are selected from the results after using the IMF method in Figure 5a,c,e respectively. The red circles indicate the true plasma frequency position at the corresponding height. The green circles represent obvious strong background signals, some of which are even greater than the intensity of the true plasma line, as shown in Figure 6a,e. Note that the desired plasma frequency values are well-retained without damaging the valid information, and the unwanted strong signals are clearly removed. Consequently, the signal after background removal by this method is also the result of filtering and smoothing the input signal.

3.3. Plasma Line Profile Fitting

In most cases, only a limited number of plasma frequency values can be obtained from the observed plasma line power spectra. This is not good for reproducing a plasma line profile containing the complete altitude information. Based on the finite number of effective plasma frequency values extracted in the previous process, the α-Chapman function is used to fit the change of the enhanced plasma line to the height. Here, we use the varied scale height to fit the profile of the plasma line that is similar to the fitted form of the electron density profiles used in [24]

$$\{\begin{array}{l}{f}_p\left(h\right)=f_o{F}_{2}exp(0.5\left(1-z-e^{-z}\right))\\ z=\frac{h-h_m{F}_2}{H_m+\alpha \left(h-h_m{F}_2\right)}\end{array}$$

(2)

where $h_m{F}_2$ and $f_o{F}_2$ are the F2 layer peak height and critical frequency, respectively. $H_m$ is the scale height at the F2 layer peak, $\alpha$ is the ratio of altitude variations of the scale height. In those four parameters, the peak height and density are known. Thus, $f_o{F}_2$, $h_m{F}_2$, $H_m$ and $\alpha$ can be determined by using the least-squares fitting approach.

The comparison of the fitted results with the raw enhanced plasma lines from Figure 4 is shown in Figure 7 (left). It can be seen that the white dotted line basically coincides with the enhanced plasma spectral line above 220 km, and the fitting result is the best between 220 km and 250 km. The deviation below 220 km may be caused by the lack of effective plasma frequency points for the fitting between 180–220 km due to a poor SNR.

The power spectrum containing the background signal as white noise is shown in Figure 7 (right). Compared with the results in Figure 6 (left), there is no obvious large slope for the background signal. The IMF method can also deal with this situation. If a migration velocity is selected, then the smoothing effect of the noisy power spectrum can be achieved, which also improves the SNR of the plasma line power spectrum. Further, the plasma frequency extraction method described above is used to accurately extract the plasma line profile.

3.4. Computation of Plasma Electronic Density

Based on the incoherent scatter theory of magnetized plasma, the linear dispersion relationship of the Langmuir wave with a magnetic field is expressed as [25]

$$f_{r\pm }^2=f_{pe}^2+\frac{3k_{\pm }^2}{4{\pi }^2}\frac{k_b{T}_e}{m_e}+f_{ce}^2{sin}^2\alpha$$

(3)

where $f_{r\pm }$ is the plasma frequency, $f_{pe}=\sqrt{n_e{e}^2/4{\pi }^2{\epsilon }_0{m}_e}$ is the electron plasma frequency, which is also called Langmuir frequency, $f_{ce}=\sqrt{eB/4{\pi }^2{m}_e}$ is the electron cyclotron frequency, $k_b$ is the Boltzmann constant, $T_e$ is the electron temperature, $m_e$ is electron mass, $k_{\pm }$ is the scatter wave number, and $\alpha$ is the angle between the backscattered wave vector and the magnetic field. For SYISR, the angle between the zenith direction and the magnetic field is about 65° in the F region over Sanya. Due to the main dependence of the plasma frequency on the Langmuir frequency, which is only related to the electron density and some fundamental constants, the inaccuracies associated with using the simplified Langmuir dispersion relation are usually negligible when determining the electron density from plasma line measurements [26]. Simplistically, the derived electron density can be approximately expressed as $n_e=e^{-2}4{\pi }^2{\epsilon }_0{m}_e{f}_r^2$. Therefore, if the plasma frequency can be accurately recovered, then the absolute electron density profile can be calculated.

4. Discussion and Conclusions

In this paper, the methods of extracting the plasma frequency with a long pulse and alternating code on the basis of SYISR plasma line experiment data are introduced. Each method has its own advantages and limitations. The CLEAN algorithm does not have the ability to deal with weaker signals under the condition of a lower SNR, since the algorithm is largely dependent on the intensity of the true signal. In other words, the feature of the true signal to be deconvoluted must be clearly identified by human experts and is merely smeared through the convolution process, but without losing its inherent characteristics. For SYISR, this method is used for the plasma line spectrum, which is greatly enhanced by photoelectrons produced by solar UV irradiation over a very short period at noon, when the electron density is at its highest. In addition, it is a time-consuming calculation task to use the highly iterative algorithm to remove the smearing and background noise and obtain the true plasma line profiles. Consequently, the CLEAN algorithm is only suitable for long-pulse deconvolution with a sufficiently strong SNR, not for alternating code with a high range resolution but weak intensity.

The proposed IMF method describes a non-iterative algorithm for separating the signal–noise of the alternating-code spectrogram, and we have conducted a large amount of statistical analyses using this method and presented some examples on SYISR data in this paper to verify its capability. Although the SNR of the alternating-code echo is worse than that of the long pulse, the obtained power spectrum has the great advantage that the features of the plasma line profile are prominent due to the small ambiguity in the range direction. As long as the appropriate migration velocity is selected for the plasma line spectrogram with obvious characteristics, the background noise can be removed well and the plasma line profiles can be obtained after fitting. Further, the electron density profiles can be obtained by the detailed method outlined above for processing such alternating-code data.

A comparison of the electron density derived from the ion line, plasma line and ionosonde analyses is shown in Figure 8. Figure 8a,b uses the same alternating-code echo data and the integration time of 2 min. The electron density in Figure 8a is derived from the standard ion line analysis and is the result of further calibration with Figure 8c after fitting. The result of Figure 8b is derived from the plasma line analysis with the IMF method. We can see that the magnitude of the electron density measured by the ion line is not very smooth in terms of time and height compared with that by the plasma line. This is because there is parameter ambiguity in the multiparameter fitting of the ion line, where the incoherent scatter model is a highly nonlinear function of its plasma parameters. The high-time and range resolution of the electron density obtained by the plasma line measurement can also be used as a calibration method for the electron density of the ion line. For the plasma line measurement, the SNR only needs to be sufficient to obtain the corresponding plasma frequency, and then the electron density with a high range resolution from the alternating-code data can be directly obtained.

The plasma line technique is the most accurate approach to obtain the absolute electron density with a high time and range resolution, but it also has some drawbacks. For the present SYISR method, only enhanced plasma line profiles above and below the peak height can be detected, such as from sunrise to noon, and then the complete electron density profile can be derived through the IMF method. Hence, its detectability largely depends on the radar power and receiver sensitivity, as well as the local time. Especially, the developing SYISR Tristatic System will double the transmitter power of the current SYISR method. It is expected that the simultaneous measurement of the ion line and plasma line can be routinely carried out when the radar energy is strong enough. In this case, the electron density measured by the plasma line can be used for the real-time calibration of a constant radar system instead of ionosonde. Considering that a large number of effective plasma line spectra will be obtained in the future, we will also develop a deep-learning approach to achieve the automatic recognition and extraction of plasma lines. Then, the IMF algorithm will be used as a potential method to extract plasma lines with different scales of the ionosphere structure as its training dataset, which also solves the manual scaling problem in the processing of deep learning. This is beneficial for the real-time efficiency of obtaining calibration factors that vary with local time and altitude [27]. In addition, due to the superiority of SYISR’s geographical location, the radar scanning detection angle can almost meet the requirements of any angle of the magnetic field. Therefore, while conducting plasma line detection, plasma line splitting may be found from a lower-SNR echo when possible, which will greatly improve the global contribution of SYISR to space plasma experiments and basic plasma scatter theory.