Advances in Research on the Impacts of Tropospheric Over-the-Horizon Propagation on Radar Emitter Signatures

Abstract

Tropospheric over-the-horizon (OTH) propagation is an important research topic in radar countermeasures and reconnaissance. Clarifying how it affects radar emitter signatures provides an important basis for over-the-horizon radar emitter recognition (RER) in complex electromagnetic environments. In recent years, both the theoretical understanding and practical applications of tropospheric OTH propagation mechanisms and RER have continued to develop. However, the integration of these two areas remains limited, and a focused synthesis of the reported effects of OTH propagation on radar emitter signatures and their related mechanisms is still lacking. On this basis, this paper reviews the mechanisms and models of tropospheric OTH propagation, analyzes emitter signal characteristics from the perspective of propagation-channel characteristics, and summarizes the research progress in this field. Finally, this paper discusses the main challenges and possible improvement directions for RER in OTH scenarios, providing a reference for further research on the integration of OTH propagation and RER technologies.

1. Introduction

Modern warfare has undergone a broad transition from platform-centric operations to information-centric operations, in which electromagnetic spectrum dominance has become a critical factor affecting battlefield outcomes. Radar countermeasure reconnaissance, particularly passive radar emitter recognition (RER), is an important capability supporting Electronic Support Measures (ESM) and Electronic Intelligence (ELINT) systems. Unlike active detection systems, passive RER systems do not transmit electromagnetic waves and therefore offer advantages in concealment, anti-jamming capability, and survivability.

Over-the-horizon (OTH) propagation refers to the non-line-of-sight propagation of electromagnetic waves through mechanisms such as diffraction, refraction, scattering, and reflection by the Earth’s surface, the atmosphere, or other propagation media, when no direct line-of-sight path exists between the transmitter and the receiver. According to the dominant propagation mechanism and medium, OTH propagation is generally divided into ground-wave diffraction propagation, ionospheric propagation, tropospheric propagation, and relay propagation via space-based platforms. Among these mechanisms, tropospheric OTH propagation mainly relies on refraction, scattering, and anomalous atmospheric refractive structures in the troposphere, enabling electromagnetic waves to overcome the limitations imposed by the Earth’s curvature and the radar line of sight. It can support long-range signal transmission and target detection, and has potential advantages in low probability of interception (LPI), transmission capacity, confidentiality, and anti-jamming capability. Therefore, it has important application value in long-range radar detection, maritime target surveillance, passive detection, and electronic reconnaissance [1].

Radar signals are the physical carriers of radar emitter characteristics and contain information related to both type characteristics and individual unintentional modulation characteristics. By intercepting radar signals, tasks such as emitter sorting, type identification, individual fingerprint extraction, and threat assessment can be performed. Most traditional RER studies are based on the ideal-channel assumption of line-of-sight and distortion-free transmission, under which the signal characteristics received by the reconnaissance receiver are assumed to be consistent with those transmitted by the emitter. In this case, inter-pulse and intra-pulse features are usually extracted from the intercepted signal, with noise being the main factor considered. However, in tropospheric OTH transmission scenarios, electromagnetic waves may experience channel distortion caused by tropospheric turbulent scattering or multipath refraction in atmospheric ducts. Such distortion may affect the signal features used by RER methods and reduce recognition accuracy in OTH scenarios, making it difficult for existing algorithms to satisfy practical requirements in complex and adversarial electromagnetic environments. Therefore, it is necessary to systematically investigate the influence mechanisms and distortion characteristics of tropospheric OTH transmission on radar signal features and to explore radar emitter features that remain robust under OTH channel conditions. This is of theoretical and engineering significance for subsequent RER tasks in OTH scenarios.

With the evolution of battlefield environments and the increasing demand for radar countermeasure reconnaissance, tropospheric OTH propagation has attracted extensive research attention, and various experiments have been conducted, including studies on propagation loss, fading characteristics, and diversity reception. Reference [1] reviews experiments and research progress in tropospheric radio-wave propagation. Reference [2] summarizes the research history and applications of atmospheric ducts. Reference [3] discusses the influence of atmospheric refraction on radar accuracy and proposes ideas for correcting atmospheric refraction errors. Reference [4] reviews recent progress in atmospheric refraction, with emphasis on the measurement and calculation of atmospheric refraction, mainly in optical applications. Reference [5] focuses on the application of artificial intelligence to atmospheric ducts, including atmospheric duct inversion. Radar emitter recognition is also an important research topic in electronic countermeasures, and its integration with deep learning has provided new approaches for this field. Reference [6] discusses the mechanisms and recent methods of RER in detail. Reference [7] focuses on the combination of specific emitter identification (SEI) and artificial intelligence. Reference [8] emphasizes feature extraction methods for SEI.

The remainder of this paper is organized as follows. Section 2 introduces the mechanism of tropospheric OTH propagation for radar emitters. Section 3 summarizes tropospheric OTH propagation models. Section 4 analyzes the characteristics of OTH propagation. Section 5 summarizes and discusses the signal signatures required for radar emitter recognition. Section 6 identifies the main research challenges and possible improvement directions, with the aim of promoting further integration between tropospheric OTH propagation theory and radar emitter research.

To clarify the scope of this review, the related literature was mainly collected from Web of Science, IEEE Xplore, Engineering Village, and CNKI. This review covers classic studies on tropospheric propagation as well as recent studies on radar emitter recognition, with a main focus on publications from 2016 to 2026. The search terms included “tropospheric over-the-horizon propagation”, “troposcatter”, “atmospheric duct”, “evaporation duct”, “radar emitter recognition”, “specific emitter identification”, “radar emitter signature”, and “channel distortion.” Studies closely related to tropospheric OTH propagation mechanisms, propagation modeling, channel effects, radar emitter signature analysis, and radar emitter recognition were included, whereas duplicated or weakly relevant studies were excluded.

2. Mechanism of Tropospheric Over-the-Horizon Propagation for Radar Emitters

Radio waves in the VHF band and above can interact with atmospheric inhomogeneities and vertical stratification during tropospheric propagation, leading to two typical propagation phenomena: reradiation and super-refraction. Tropospheric reradiation is generally referred to as troposcatter, whereas tropospheric super-refraction may form atmospheric ducts under specific meteorological conditions, allowing radio waves to be trapped and guided within the duct layer. The composite propagation mechanism of tropospheric OTH propagation is illustrated in Figure 1. Troposcatter and atmospheric ducts are the principal physical mechanisms that enable tropospheric OTH propagation [2]. Reference [9] analyzes the mechanism of offshore microwave OTH propagation and summarizes related OTH propagation experiments.

In practical battlefield environments, it is often difficult for a passive reconnaissance receiver to determine whether the received signal has propagated through troposcatter, a specific type of atmospheric duct, or a combined propagation path. Therefore, the received signal can generally be regarded as the result of the combined effects of these mechanisms. Understanding the mechanisms of tropospheric OTH propagation provides a basis for analyzing changes in radar signal characteristics after OTH transmission and offers theoretical support for RER in OTH systems.

2.1. Mechanism of Tropospheric Scattering

Affected by the combined influence of the ground surface and the atmosphere, the troposphere contains numerous refractive-index inhomogeneities and irregular air masses. The shape, density, velocity, and direction of motion of these scatterers vary randomly in space and time, and their refractive indices differ from those of the surrounding medium [10]. When radio waves interact with these inhomogeneities, induced charges are generated and secondary radiation is produced. This process gives rise to troposcatter, which can support OTH propagation under a wide range of meteorological conditions. At present, the mechanism of troposcatter is commonly described using the generalized scattering theory proposed by Minggao Zhang. This theory classifies tropospheric scattering into three mechanisms: turbulent incoherent scattering, incoherent reflection from irregular layers, and coherent reflection from stable layers.

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The turbulent incoherent scattering theory suggests that troposcatter OTH propagation originates from atmospheric turbulence in the troposphere. Multiscale eddy structures generated by turbulent motion form numerous local inhomogeneities with randomly distributed dielectric constants. Scatterers located within the common volume of the transmitting and receiving antenna beams interact with incident radio waves and can be approximately regarded as dipoles, which reradiate part of the electromagnetic energy into regions beyond the line of sight. Because turbulence-induced scatterers move randomly and are mutually independent, the scattered components are incoherently superimposed at the receiver.

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The incoherent reflection theory of irregular layers suggests that abrupt variations in atmospheric temperature, humidity, and pressure at the boundaries of meteorological transition zones can produce sharp-gradient layers, or irregular layers, in the atmospheric refractive index. These layers differ in shape and intensity, exhibit strong irregularity, and evolve with meteorological conditions. Such stratified structures do not have stable spatial forms and may change rapidly as the atmospheric environment varies. They can generate incoherent reflections of incident radio waves, thereby contributing additional energy components to OTH propagation. This theory has been used to explain occasional enhancements of scattered signal levels in meteorologically complex regions at middle and low latitudes.

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The coherent reflection theory of stable layers suggests that persistent and smooth stratified structures, such as inversion layers, may form in the troposphere. Under such conditions, thin-layer structures with dielectric constants varying nonlinearly with height can be produced. Multiple thin layers within the common volume may coherently reflect radio waves, and the received OTH field is formed through coherent superposition, including both amplitude and phase relationships among different components. This theory has been used to explain persistent and significant enhancements of signal levels in long-distance OTH scattering links.

In field measurements and simulation studies, the atmospheric refractive-index structure constant, modified atmospheric refractivity, vertical refractivity gradient, and atmospheric refractive index are key parameters of interest. The specific symbols used for these parameters may differ across studies and are therefore not discussed in detail here. Existing studies generally regard turbulent incoherent scattering as the dominant mechanism of troposcatter OTH propagation [11], and this mechanism has been the most extensively developed in current research. However, a single theory is unlikely to explain all troposcatter propagation phenomena and experimental observations. In practical propagation environments, the received field may result from the combined effects of the three mechanisms described above.

Because tropospheric turbulence is highly uncertain, a major difficulty in troposcatter research lies in the fact that dynamic variations in the tropospheric environment can alter radio-wave propagation characteristics and produce different propagation phenomena. Random disturbances, unpredictable atmospheric parameters, and extreme weather conditions may reduce the applicability of physical models. These uncertainties can affect the long-term stability and reliability of measured data and limit the generalization capability of propagation models [12].

Since Reynolds initiated modern turbulence research in 1883, the study of turbulence has made substantial progress, but a universal theoretical framework for turbulence has not yet been established. In mainstream troposcatter research, turbulence is often used as a physical explanation for phenomena such as troposcatter OTH propagation and amplitude scintillation of received signals. However, related analyses are still largely based on statistical fitting of observational results. Quantitative characterization of the conditions under which turbulence occurs remains insufficient, and it is still difficult to accurately evaluate the influence of turbulence on radar propagation characteristics when turbulence is modeled as an irregular continuous or discontinuous refractive-index distribution [10]. In addition, turbulent motion is intrinsically anisotropic, although it may exhibit macroscopic isotropic behavior under the random superposition of turbulence clusters. Therefore, quantitative methods for distinguishing anisotropic and isotropic models of tropospheric turbulence remain an important issue for future research.

2.2. Mechanism of Tropospheric Atmospheric Duct

A tropospheric atmospheric duct is a special super-refractive layered structure formed in the troposphere, particularly within the tropospheric boundary layer. When electromagnetic waves are trapped and guided within the duct layer, they can propagate beyond the line of sight with relatively low loss [13,14].

Atmospheric ducts can be classified according to different criteria. Based on their formation mechanisms, they can be divided into evaporation ducts, advection ducts, subsidence ducts, radiation-cooling ducts, and other types. Based on duct height, they are commonly classified into evaporation ducts, surface ducts, and elevated ducts [5]. The latter classification is adopted in most studies.

Evaporation ducts are tropospheric ducts formed over large water surfaces, where water-vapor evaporation causes atmospheric humidity to decrease sharply with height. They usually exhibit pronounced diurnal variation. Air temperature, relative humidity, and wind speed are the main factors affecting evaporation duct height (EDH). Meteorological conditions with low relative humidity and high wind speed are generally favorable for seawater evaporation. However, the effect of air temperature on EDH depends on wind speed. Under high-wind-speed conditions, air temperature is positively correlated with EDH, whereas under low-wind-speed conditions, a negative correlation may occur.

Surface ducts and elevated ducts are both atmospheric stratification structures formed by temperature inversion or by the combined effects of temperature inversion and a sharp decrease in humidity with height. The main difference between these two types lies in altitude: elevated ducts generally occur at higher altitudes than surface ducts. The key characteristic parameters in duct studies include duct height, duct thickness, and duct strength. These parameters provide the basis for evaluating the ability of ducts to confine electromagnetic waves and for analyzing changes in electromagnetic-wave propagation characteristics. The formation mechanisms of atmospheric ducts have been discussed in detail in References [2,5,15], and are therefore not further expanded here.

Compared with surface ducts and elevated ducts, evaporation ducts have a higher occurrence probability and relatively greater application value. Consequently, duct-related research has mainly focused on evaporation ducts, for which many classical models have been developed. Representative classical evaporation duct models are listed in

Table 1. Classical models of evaporation duct.

Model	References
Jeskes model, Rothera model, Fairall model, LKB model, PJ model, MGB model, BYC model, NPS model, pseudo-refractive index model, NWA model, multi-parameter model, RSHMU model, etc.	1973: [16]; 1974: [17]; 1985: [18]; 1979: [19]; 1985: [20]; 1992: [20]; 1997: [21]; 2002: [22]; 2001: [23]; 1984: [24]; 2003: [24]; 2007: [25].

.

Tropospheric refractivity is a key parameter for characterizing atmospheric ducts, and the variation of tropospheric refractivity with height is usually described by the tropospheric refractivity profile. Surface refractivity and tropospheric refractivity profiles are commonly derived from meteorological sounding data and ground-based observations from meteorological stations [16]. The range of atmospheric refractivity gradients is given in

Table 2. Atmospheric refraction gradient.

Layer Type	N 1 Gradient (N Unit/km)	M 2 Gradient (M Unit/km)
Duct	N/dz ≤ −157	M/dz ≤ 0
Super-refraction	−157 < dN/dz ≤ −79	0 < dM/dz ≤ 78
Standard Refraction	−79 < dN/dz ≤ 0	78 < dM/dz ≤ 157
Sub-refraction	dN/dz > 0	dM/dz > 157

¹ N is the refractive index. ² M is the modified refractive index.

, and the corresponding schematic is shown in Figure 2. Tropospheric refractivity profiles are often used to analyze refractivity variations at different heights or within different layers of the troposphere. However, because of the complexity of tropospheric conditions, the refractive-index structure of evaporation ducts in real marine environments often exhibits strong inhomogeneity. Reference [26] analyzes the disturbance effect of anisotropic turbulence on atmospheric refractivity, and the resulting model shows improved accuracy. Therefore, incorporating the effects of anisotropic turbulence is necessary for improving the accuracy of refractivity-profile modeling.

In engineering applications, the main empirical models for tropospheric refractivity profiles include the linear model, exponential model, piecewise model, and Hopfield model [27,28]. The influence of refractivity varies with radio-wave frequency, and absorption peaks may occur in the atmospheric medium. In general, higher frequencies are associated with stronger atmospheric absorption attenuation. Therefore, in the quantitative calculation and theoretical analysis of tropospheric radio-wave propagation characteristics, the atmospheric complex refractive index should be introduced to describe both the refractive and absorptive effects of the atmosphere on electromagnetic waves.

3. Over-the-Horizon Propagation Models for Radar Emitters

The propagation path of radar signals provides the basis for analyzing the meteorological environment along the signal path and assessing the influence of OTH propagation. Tropospheric propagation models mainly include the parabolic equation (PE) model, the ray tracing (RT) model, and empirical or semi-empirical models.

Empirical and semi-empirical models are not derived from first-principles solutions of Maxwell’s equations. Instead, they are developed from large amounts of field-measured propagation-loss data and establish regression relationships between propagation loss and relevant influencing factors, such as propagation distance, operating frequency, meteorological parameters, and antenna height, through statistical fitting.

Pure empirical models generally adopt a black-box fitting strategy and rely mainly on the statistical patterns of measured data. In contrast, semi-empirical models introduce partial constraints from propagation mechanisms into the fitting framework and model loss terms associated with physical mechanisms such as atmospheric duct trapping and tropospheric scattering in a decoupled manner. This approach preserves the convenience of engineering implementation while improving model generalizability.

The underlying assumption of this class of models is the statistical stationarity of the atmospheric propagation environment. Specifically, the fitting parameters are calibrated using long-term and large-scale field measurements of meteorological and propagation characteristics. Therefore, these models usually provide statistical predictions of propagation loss, such as annual-mean or monthly-mean transmission loss.

Accordingly, in conventional marine environments with sufficient data coverage and strong scenario consistency, empirical and semi-empirical models can provide rapid and cost-effective propagation-loss prediction without complex numerical calculations or real-time meteorological inputs. However, for sudden and non-stationary atmospheric duct events, as well as scenarios not covered by the calibration data, such as extreme meteorological conditions and special sea areas, model prediction accuracy may decrease.

To address the limited generalizability of pure empirical models, Reference [29] proposes a semi-empirical annual-mean transmission-loss prediction model and provides a path-loss prediction method that considers both tropospheric scattering and atmospheric ducts. Reference [30] presents a semi-empirical tropospheric-scattering loss prediction model, and measured data indicate that the model has good stability.

The RT model is based on geometrical optics and Fermat’s principle under the high-frequency approximation. When the wavelength of radar electromagnetic waves is much smaller than the characteristic scale of the propagation environment, Maxwell’s equations can be simplified using the geometrical-optics approximation. Under this approximation, radio-wave propagation can be represented by the propagation of multiple independent rays, whose trajectories follow Fermat’s principle; that is, a ray propagates along a path with a stationary optical length.

Based on Fermat’s principle, the eikonal equation describing the ray trajectory can be derived. By numerically solving the eikonal equation, parameters associated with each ray, including propagation path, amplitude, phase, time delay, and incident angle, can be obtained. This constitutes the main modeling principle of the RT model. Accordingly, the RT model is often used in scenarios where parameters such as channel delay spread and propagation angle need to be estimated.

Reference [31] models the radio-wave propagation path using a ray-tracing algorithm based on Taylor-series approximation and quantitatively analyzes the delay characteristics of different ducts. Reference [32] points out that, based on the Hamiltonian canonical form, the ray-tracing problem can also be transformed into the numerical solution of extended Hamiltonian equations in phase space.

The PE model is derived from the Helmholtz equation under time-harmonic field conditions and reduces the dimensionality of the second-order partial differential equation through the parabolic approximation.

The key to solving the PE model lies in the forward parabolic approximation. Under the assumption that radar electromagnetic waves propagate mainly in the forward horizontal direction and that the variation of the field in the vertical direction is much weaker than that in the horizontal direction, the Helmholtz equation can be decomposed into forward- and backward-propagation operators. By neglecting the backward-scattering component, the original second-order elliptic partial differential equation is transformed into a first-order parabolic partial differential equation, allowing the propagation field to be solved iteratively in range.

This modeling feature enables the PE model to simulate inhomogeneous variations in atmospheric refraction in both the horizontal and vertical directions, and to calculate the effects of complex atmospheric environments on the amplitude and phase of radio-wave propagation. It is therefore well suited for numerical simulations of atmospheric-duct and troposcatter propagation, while offering a favorable compromise between computational accuracy and efficiency. The PE model can be used to solve radio-wave propagation problems in large-scale and complex environments and is currently one of the widely used models for tropospheric radio-wave propagation [11].

With the continued development of the PE model, several improved methods have been proposed, including the two-way parabolic equation [33], the three-dimensional parabolic equation algorithm [34], and the parabolic equation algorithm integrated with wavelet transform [35]. These methods can improve the accuracy of propagation-path prediction. Reference [36] models radio-wave propagation under inhomogeneous evaporation-duct conditions using an odd-even split-step Fourier-transform algorithm based on the three-dimensional parabolic equation, which improves the performance evaluation of OTH radar. Reference [37] derives the forward parabolic equation in cylindrical coordinates and predicts radio-wave propagation characteristics in space through orthogonal mode excitation and split-step Fourier transform. This method can be used to evaluate the effective detection range and detection performance of radar in marine environments.

In addition, various improved methods have been developed, including the odd-even decomposition method, the three-dimensional high-order parabolic equation method [38], the PE-PO hybrid method [39], the alternating direction implicit (ADI) method, the bending-coefficient-improved ADI-PE method [40], and the alternating direction decomposition (ADD) split-step Fourier algorithm [41,42]. These algorithms provide approximate predictions of propagation paths rather than exact solutions. In addition, atmospheric refractivity variations caused by temporal and spatial changes in the marine environment remain an important factor limiting the reliability of PE-based prediction models.

Reference [43] introduces an improved fractal sea-surface model into marine propagation prediction and establishes a propagation model using the two-way PE method, which can be used to characterize the influence of atmospheric ducts on radio-wave propagation. Reference [44] constructs a radio-wave propagation model that combines the parabolic equation with an adaptive absorption window regulated by the angular spectrum, which can be used to solve radio-wave propagation problems in three-dimensional atmospheric-duct environments. Reference [45] derives a three-dimensional two-way parabolic approximation solution of the wave equation. Reference [46] proposes a Greene-approximation wide-angle parabolic equation (WAPE) radio-wave prediction model based on a non-local boundary condition (NLBC), which is suitable for predicting electromagnetic-wave propagation characteristics in long-distance and complex tropospheric environments. Reference [47] constructs a radar echo-signal simulation model based on the semi-deterministic facet scattering model shooting and bouncing ray (SDFSM-SBR) method. The forward-propagation simulation and analysis process in this model also provides a useful reference for analyzing changes in radar signal characteristics.

From the perspective of signal-distortion analysis for radar emitter recognition, the applicability of the above propagation models should not be evaluated solely by their accuracy in predicting propagation loss. It is also necessary to consider whether their outputs can support the analysis of phase instability, group-delay spread, Doppler broadening, polarization variation, waveform distortion, and contamination of SEI features.

Empirical and semi-empirical models are mainly based on long-term observational data fitting or statistically averaged propagation characteristics. They are therefore more suitable for macroscopic assessments of propagation loss, fading statistics, average SNR degradation, and link availability. These models can provide an initial basis for evaluating the difficulty of signal interception and processing under OTH conditions. However, because their outputs usually do not include pulse-level delay, phase, or frequency-evolution information, they are difficult to use directly for explaining fine-grained waveform distortion, phase perturbation, or the degradation mechanisms of individual-specific features.

The RT model can provide physical quantities such as propagation path, angle of arrival, path delay, amplitude, and phase. It is therefore more suitable for analyzing atmospheric-duct multipath propagation, TOA/PRI bias, group-delay spread, and deterministic phase shifts under relatively stable refractive conditions. However, standard RT models rely on the high-frequency geometrical-optics approximation and have limited capability in describing diffuse turbulent scattering, diffraction-dominated regions, caustic regions, and rapidly time-varying stochastic effects. Therefore, they should not be used alone to analyze random Doppler broadening or subtle signal distortions under scattering-dominated conditions.

In contrast, the PE model can describe the evolution of electromagnetic-field amplitude and phase with range and height in inhomogeneous refractive-index environments. It can provide relatively high-fidelity numerical support for modeling propagation loss, amplitude fluctuation, phase perturbation, and channel response under atmospheric-duct or mixed-propagation conditions. Therefore, it is more suitable for waveform-level studies, such as pulse-compression performance degradation, modulation-feature distortion, and feature degradation after channel filtering. Nevertheless, conventional scalar, static, or quasi-static PE models still cannot directly characterize Doppler broadening or polarization variation, nor can they distinguish channel-induced distortion in the received signal from the transmitter’s intrinsic unintentional modulation features.

Therefore, empirical and semi-empirical models are more suitable for link-level feasibility assessment, RT models are more suitable for explaining multipath and delay mechanisms, and PE models are more suitable for simulating waveform-level propagation distortion. For issues such as phase instability, group delay, Doppler broadening, polarization variation, waveform distortion, and SEI-feature contamination in OTH radar emitter recognition, a comprehensive analysis is required that integrates the specific propagation scenario, meteorological parameters, channel-modeling results, and received-signal data, rather than relying on a single propagation model to draw deterministic conclusions.

4. Research on Propagation Channel Characteristics of Radar Emitters

OTH propagation will introduce large transmission loss due to its long propagation distance. Reference [48] analyzes the total transmission loss of radar OTH reconnaissance based on tropospheric scattering. Reference [49] constructs a Weather Forecast-Enabled tropospheric Scattering Path Loss Channel Model (WPE) with the parabolic equation (PE) as the core, which can characterize the influence of turbulence on tropospheric scattered wave propagation and predict tropospheric transmission loss more accurately. Reference [50] proposes an improved Advanced Propagation Model considering Free-Space propagation (IAPMFS), which achieves more accurate prediction of path loss.

OTH propagation introduces more pronounced propagation delays than line-of-sight propagation, resulting in the destruction of the coherence of the inter-pulse echo phase, the damage to the consistency of intra-pulse modulation characteristics, and the contamination of the inherent intra-pulse characteristics of the transmitter. Tropospheric delay cannot be eliminated by multi-frequency combination, and is usually compensated by empirical models [51]. Reference [52] compares various existing tropospheric delay models. Reference [53] establishes a time-varying envelope model of tropospheric delay residual error using extreme value analysis based on the geographical and seasonal variation characteristics of the residual error after model correction. Reference [12] calculates tropospheric time delay by combining tropospheric ray tracing and the numerical weather model, and verifies the influence of the troposphere on signal propagation. Reference [54] improves the estimation algorithm for tropospheric scattering slant delay. Existing compensation methods can only compensate for large-scale and slow-varying delay components, and have very limited compensation effect on small-scale, intra-pulse, and fast-varying turbulent components.

When the same signal arrives at the receiving end through different paths, the received signal is the superposition of multiple copies in the time domain [5], resulting in fading characteristics of amplitude/power, phase offset, and delay dispersion. The multipath effect of tropospheric scattering has a more serious impact than that of the atmospheric duct effect. In addition, the random motion of tropospheric turbulent scatterers and the dynamic changes of the duct layer atmosphere will lead to Doppler shift and spectrum broadening of the radar received signal. The interference caused by the superposition of multiple signals puts forward very high requirements for the signal processing module. Therefore, in engineering, it is necessary to use high-sensitivity receivers and perform signal processing such as diversity reception.

The non-stationary and non-laminar complex atmospheric structure in the troposphere is usually attributed to turbulent fluid, and statistical characteristic analysis is carried out using the structure function or spectral function in the random field theory, which can better evaluate the overall statistical characteristics of the scattering link. However, this method ignores the discontinuous characteristics of the “junction area” between randomly moving fluids, as well as the continuous change characteristics inside the randomly flowing fluids.

Optimization can be carried out from two aspects: one is to incorporate the interlayer reflection of the turbulent interface and the continuous gradient scattering inside the turbulence into a unified engineering model; the other is to combine deep learning technology, use the measured link data and meteorological sounding data to fit the nonlinear correction term of the multi-mode coupling effect, replacing the traditional linear empirical correction term. To explore the omnidirectional propagation characteristics of radar waves on the sea surface, Reference [55] introduces the turbulent scattering cross section, refractive turbulence structure constant and radar equation based on the PE equation, and simulates the detection performance of radar.

The difficulty in atmospheric duct research lies in analyzing the influence of trapped refraction on radar signal propagation. The boundary conditions involved in this type of refraction are relatively complex, requiring the use of sophisticated numerical methods and modeling techniques. Atmospheric duct height and transmission distance are important factors for the change of radar signal characteristics. Reference [56] analyzes the influence of rough sea surface on electromagnetic wave propagation loss in the evaporation duct environment. Reference [57] deeply studies the influence of inhomogeneous evaporation duct conditions on electromagnetic wave propagation characteristics. Reference [58] analyzes the relationship between signal strength and evaporation duct height. Reference [59] gives the modified radar equation under evaporation duct, and analyzes the radar detection performance based on measured data. Reference [60] studies the influence of evaporation duct on radar OTH jamming, which has high reference value for the field of radar countermeasures. Reference [61] analyzes the influence of atmospheric duct on radar detection area according to the attenuation of radar electromagnetic wave propagation. Reference [62] analyzes the detection characteristics of radar from the perspective of the influence of atmospheric duct on electromagnetic wave propagation. Reference [63] analyzes the abnormal sea surface echo of weather radar during an atmospheric duct process, which has reference value for studying the influence of atmospheric duct on radar surface echo.

It should be noted that when the duct structure is relatively clear, the refractivity-profile information is sufficiently available, the propagation path is mainly constrained by a single duct structure, and variations in sea-surface and meteorological conditions are relatively slow, atmospheric-duct propagation usually has relatively well-defined physical boundaries and path constraints. Its effects can therefore be more readily modeled using parameters such as duct height, duct thickness, duct strength, propagation distance, operating frequency band, and antenna height. Under such conditions, some propagation effects may mainly appear as systematic variations in propagation loss, arrival time, phase response, and amplitude response. Their influence on conventional parameters and some coarse-scale inter-pulse and intra-pulse structures is therefore relatively tractable.

In contrast, troposcatter is more strongly affected by refractive-index inhomogeneities, turbulent structures, the random motion of effective scatterers, and spatiotemporal variations in atmospheric structure. The received signal often contains the superposition of multiple random scattering components and may exhibit low SNR, rapid fading, random phase perturbation, Doppler broadening, delay spread, and frequency-selective fading. Therefore, the effects of troposcatter on phase-sensitive features, coherent inter-pulse features, intra-pulse modulation structures, and weak individual fingerprint features are usually more complex and more difficult to model deterministically or compensate stably.

However, this distinction does not imply that radar emitter features necessarily remain stable under atmospheric-duct conditions. In non-stationary marine environments, in particular, the height, thickness, and strength of evaporation ducts are jointly affected by temperature, humidity, wind speed, sea state, and underlying-surface conditions, and may vary rapidly in time and space. Evaporation ducts, surface ducts, elevated ducts, scattering propagation, and sea-surface reflection paths may also coexist or alternately dominate, leading to multimode propagation, multipath coupling, and nonlinear channel distortion. In such cases, atmospheric ducts may also introduce frequency-selective fading, phase perturbation, delay spread, polarization mismatch, and feature-estimation bias, thereby affecting the performance of radar emitter recognition.

5. Analysis of Radar Emitter Signal Signatures

Radar emitter recognition (RER), also referred to as emitter recognition, originated in the 1940s. It identifies radar type, signal waveform, individual emitter, and operating state by intercepting radar signals, extracting characteristic parameters [64], and performing database comparison and classification. RER is a key technology in electronic countermeasures and can support threat analysis and early warning in complex electromagnetic environments.

A major research topic in RER is specific emitter identification (SEI), which aims to distinguish individual emitters even when they have the same type and nominal parameters. RER mainly focuses on conventional features, inter-pulse features, and intentional intra-pulse modulation features, such as LFM, NLFM, BPSK, and FSK. In contrast, SEI places greater emphasis on unintentional modulation on pulse (UMOP) [25]. Although modern RER studies have expanded beyond conventional features [65], most of them are still based on line-of-sight reconnaissance scenarios and assume that radar signatures remain essentially unchanged during transmission.

The framework of emitter recognition is relatively mature, as shown in Figure 3. After a passive reconnaissance receiver intercepts a radar radio-frequency (RF) signal, preprocessing operations such as denoising and screening are first performed to improve data quality. Feature extraction is then conducted on the pulse data. The extracted features are generally divided into conventional features, inter-pulse features, and intra-pulse features. Intra-pulse features can be further classified into intentional modulation features and unintentional modulation features. Among them, intra-pulse unintentional modulation is regarded as an individual signature [66,67], which is mainly associated with the physical-layer characteristics of the radar equipment. Finally, the extracted feature data are compared with a database, and different recognition methods are used for classification and identification.

Conventional features, inter-pulse features, and intra-pulse features focus on different indicators, and several representative indicators are listed in

Table 3. Classification of radar signatures.

Classification	Indicators
Conventional Features	RF, PW, PRF, PA, DOA, TOA, etc.
Inter-Pulse Features	Fixed PRI, Staggered PRI, Jittered PRI, Sliding PRI, Grouped PRI, etc. [68]
Intra-Pulse Features	Intentional modulation: LFM, NLFM, FSK, PSK, composite modulation, etc. [67,69]
	Unintentional modulation: local oscillator phase noise, transmitter switching transient characteristics, amplitude-phase characteristics of filters, etc. [7]

. With the increasing complexity of radar systems and modulation schemes, corresponding recognition technologies have continued to develop toward multidimensional and multi-domain feature analysis [8]. Polarization, as a basic attribute of radar pulses, is usually classified as a conventional feature. If inter-pulse polarization coding or polarization agility is used, it can also be regarded as an inter-pulse feature. It should be noted that troposcatter may cause depolarization, which requires techniques such as channel polarization compensation.

Current research mainly focuses on several major effects of tropospheric OTH propagation, including multipath propagation, Doppler spread, and fading. These effects may alter radar emitter signatures and reduce the accuracy and efficiency of recognition. Therefore, analyzing the distortion characteristics of radar emitter signatures and identifying features with relatively high stability are important for RER. The effects of tropospheric OTH propagation on different types of signatures are discussed as follows.

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Conventional Features

The influence of tropospheric OTH propagation on conventional features is mainly reflected in deviations in received parameter measurements [70], reduced estimation accuracy [71], fading [72], and spectral or temporal broadening [73]. The influence of atmospheric ducts is often manifested as systematic deviations, which may be corrected through modeling [74]. In contrast, troposcatter signals are usually non-stationary and have low signal-to-noise ratio (SNR) [70], making them more difficult to analyze quantitatively [75]. Reference [72] constructs a fading model for received signals in troposcatter scenarios based on the analytical method of the scattering transfer function. This model can be applied to passive sensing of non-cooperative emitters in troposcatter scenarios, and experimental results demonstrate its effectiveness for OTH passive detection.

(2)

Inter-Pulse Features

Pulse repetition interval (PRI) [76] is an important inter-pulse feature [77], and PRI patterns contain rich and compact structural information about radar pulse trains [78]. With the increasing complexity of radar systems, PRI modulation types have also become more diverse [68]. The timing regularity of PRI sequences is strongly affected by missing pulses and false pulses [79]. Multipath propagation may disrupt the timing regularity of PRI sequences and damage sequence integrity. After such disturbance, the modulation patterns of complex PRI sequences become more difficult to recover [78], which represents a major influence of OTH propagation on inter-pulse features. In OTH scenarios, severe noise and interference, together with very low SNR, make PRI feature extraction difficult. The interval characteristics of staggered and sliding PRI patterns may be masked by random errors, while the non-stationarity of the intercepted signal further increases the difficulty of inter-pulse feature extraction [70].

(3)

Intra-Pulse Features

Intra-pulse features are sensitive to channel distortion. Specifically, for pulse signals with phase coding system, multipath time delay and time-varying channel will cause random disturbance of the intra-pulse phase of the received signal [70], destroying its inherent correlation structure. This mismatch will further lead to the broadening of correlation peaks, the rise of side lobes and the reduction in processing gain, thereby reducing the discrimination of intra-pulse features and recognition accuracy, and weakening the separability of individual difference features of emitters.

For frequency-modulated pulse signals, time-varying multipath and frequency selective fading will lead to uneven amplitude-frequency response and nonlinear phase-frequency response of the channel, thereby reducing the reliability of instantaneous frequency trajectory estimation and frequency point decision. At the same time, Doppler spread will not only reduce the pulse compression performance, but also cause spectrum expansion and decreased time-frequency focusing, further raising the requirements for intra-pulse feature extraction.

Compared with the single-modulation schemes discussed earlier, composite modulation places higher requirements on channel stability during recognition. Its recognition depends on the stable preservation and joint discrimination of multiple modulation dimensions. Distortion in any one of these dimensions may reduce recognition accuracy. It should be noted that the adverse effects of channel distortion may be further amplified under low-SNR conditions. In such cases, the fine features of intra-pulse modulation may already be masked by additive noise, while random distortion introduced by the OTH propagation channel may further disturb the intrinsic feature structure, making accurate and stable extraction of intra-pulse features more difficult.

Reference [67] proposes a clustering algorithm that combines inter-pulse parameters with intra-pulse bispectrum features. This algorithm was verified using real data and can reduce the influence of multipath effects to some extent. Reference [80] proposes an evaluation method for intra-pulse features in complex electromagnetic environments, which can provide a reference for selecting appropriate features for recognition under different environmental conditions.

In terms of signal manifestations, spectral broadening, multipath-component superposition, and low-SNR reception caused by OTH propagation may lead to degradation phenomena in the time-frequency domain that are similar to signal overlap and unknown interference in complex spectral environments. Chen et al. studied frequency-modulated continuous-wave (FMCW) radar recognition and parameter estimation in unknown and complex spectral environments. They pointed out that co-frequency operation of multiple FMCW radars can cause time-frequency overlap in the received signals, while unexpected signals in unknown spectral environments may further degrade radar signal cognition performance [81].

Because unintentional modulation features usually have weaker amplitudes and are more sensitive to hardware characteristics and channel disturbances, they are more difficult to extract stably under low-SNR OTH conditions. According to their signal manifestations, these features can be divided into transient features and steady-state features [8]. Even under line-of-sight conditions, SEI faces inherent difficulties: the transient process is short in duration, while steady-state fingerprint features are often deeply embedded in the received data and noise, making them difficult to extract reliably [8].

OTH conditions are generally more challenging than line-of-sight conditions. Radar reconnaissance systems often use wideband receivers, and the intercepted signals may contain substantial out-of-band noise, which can affect subsequent signal recognition and parameter estimation [69]. Under complex and non-ideal channel conditions, unintentional modulation features become more vulnerable to noise and channel distortion. At very low SNR, intrinsic fingerprint features may be largely masked by channel noise, making stable feature extraction difficult [73].

It should be noted that quantitative results concerning tropospheric OTH propagation effects are strongly scenario-dependent across different studies and should generally not be directly combined into a unified numerical range. Metrics such as propagation loss, delay spread, Doppler spread, coherence bandwidth, and fading statistics are jointly affected by carrier frequency, propagation distance, antenna height, signal bandwidth, dominant propagation mechanism, duct parameters, sea state, meteorological conditions, and model assumptions [13,29,49,57,82].

For example, some studies on troposcatter predict and analyze transmission loss or path loss under specific frequency bands, propagation distances, and model settings [29,49,82]. In contrast, some studies on atmospheric-duct channels analyze path loss, delay spread, coherence bandwidth, or fading characteristics under given duct height, duct strength, antenna height, propagation distance, or marine environmental conditions [13,57]. These results provide important references for understanding specific propagation mechanisms, but they are not universally comparable across frequency bands, propagation distances, propagation mechanisms, and meteorological conditions.

The previous section classified radar emitter signatures into conventional features, inter-pulse features, and intra-pulse features. The distortion of these signatures, however, is closely associated with specific tropospheric OTH propagation mechanisms. To illustrate this relationship more clearly,

Table 4. Influence of propagation mechanisms on radar emitter signatures.

Propagation Mechanisms	Physical Origin	Affected Signature Categories
Multipath propagation	Superposition of multiple delayed components caused by scattering, duct-guided propagation, reflection, or mixed propagation paths.	TOA, PRI, phase-coded signals, LFM/NLFM signals, composite intra-pulse modulation, UMOP features, etc.
Doppler spread and random phase fluctuation	Motion of effective scatterers, time-varying propagation paths, and dynamic atmospheric structures.	RF, spectral features, coherent inter-pulse features, phase-coded signals, LFM/NLFM signals, and UMOP features, etc.
Propagation loss and low SNR	Long-range OTH transmission loss, fading, and receiver noise accumulation.	All feature categories, especially PRI and weak UMOP-based individual features, etc.
Depolarization and polarization mismatch	Scattering, multipath coupling, and variation of the propagation medium.	Polarization features, conventional features, and inter-pulse polarization coding features if used, etc.

summarizes the mapping between major propagation mechanisms and the affected radar emitter signatures.

Specifically, multipath propagation mainly affects TOA, PRI, phase-coded signals, LFM/NLFM signals, composite intra-pulse modulation, and UMOP features. The superposition of multiple delayed components may cause pulse-edge distortion, correlation-peak broadening, increased sidelobe levels, frequency-selective fading, and nonlinear phase-frequency response. As a result, TOA estimation, PRI reconstruction, pulse compression, modulation recognition, and intra-pulse feature extraction may become less reliable.

Doppler spread and random phase fluctuations mainly affect RF and spectral features, coherent inter-pulse features, phase-coded signals, LFM/NLFM signals, and UMOP features. Doppler spread may lead to spectral broadening and reduced time-frequency concentration, whereas random phase fluctuations may weaken the original phase relationships within or between pulses. These effects are particularly unfavorable for frequency estimation, coherent integration, phase-sensitive modulation recognition, and individual feature extraction.

Severe propagation loss and very low SNR can affect almost all feature categories, but their influence is more pronounced for PRI extraction and weak UMOP-based individual features. Under low-SNR conditions, weak pulses may fall below the detection threshold, while noise or multipath components may be incorrectly detected as pulses. Consequently, missing pulses, false pulses, unstable parameter estimation, and masking of weak fingerprint features may occur.

Depolarization and polarization mismatch mainly affect polarization features, conventional features related to received power, and inter-pulse polarization coding features when such coding is used. The received polarization state may deviate from the transmitted state, resulting in polarization mismatch and additional received-power loss. Since polarization-related RER under tropospheric OTH propagation has not been sufficiently investigated, its specific influence requires further targeted analysis.

In summary, different radar emitter features exhibit different levels of robustness under tropospheric OTH propagation conditions. Conventional features are susceptible to propagation loss, time delay, and angle deviation, although some of these effects may be compensated through modeling when atmospheric-duct propagation is dominant. Inter-pulse features are mainly affected by missing pulses, false pulses, and unstable time delay, which may disrupt the regularity of PRI sequences. Intra-pulse intentional modulation features are more sensitive to multipath effects, Doppler spread, and random phase perturbations. UMOP-based individual features are particularly vulnerable because their weak amplitudes can be easily masked by low SNR and channel distortion. Therefore, RER under OTH conditions cannot simply adopt feature-extraction methods developed for line-of-sight scenarios. Instead, feature selection and compensation should be performed according to the dominant propagation mechanism and channel state.

6. Conclusions

At present, radar emitter recognition (RER) under tropospheric OTH conditions still faces several key bottlenecks.

(1)

Current research on atmospheric ducts, especially evaporation ducts, is relatively mature. However, the influence of troposcatter OTH propagation on radar emitter features has not yet been fully clarified.

(2)

For signal samples received by passive reconnaissance systems, it remains difficult to distinguish the propagation segments or conditions dominated by scattering from those dominated by atmospheric ducts, or to identify their corresponding distortion effects. An integrated theoretical framework has not yet been established.

(3)

Existing propagation studies mainly focus on propagation characteristics such as propagation loss, coverage range, and delay. In contrast, the signal features required for RER, including phase stability, group delay, spectral broadening, polarization variation, intra-pulse modulation structure, and individual fingerprint features, still lack in-depth quantitative correlation analysis.

(4)

Laboratory environments generally cannot reproduce OTH propagation conditions. Field experiments, meanwhile, impose strict requirements on weather and other environmental factors. Meteorological conditions are difficult to control, multivariable isolation is challenging, experimental repeatability is limited, and sufficient high-confidence labeled measured data remain scarce.

Based on these issues, the following aspects may become important directions for future research.

(1)

Feature-distortion mechanisms for radar emitter recognition.

Existing studies on tropospheric propagation mainly focus on propagation loss, coverage range, delay, and field-strength distribution. By contrast, RER is more concerned with the stability of conventional parameters, inter-pulse timing, intra-pulse modulation structures, and individual fingerprint features during propagation. Therefore, future research should move beyond propagation-performance analysis alone and place greater emphasis on feature-distortion mechanisms. Particular attention should be paid to the effects of troposcatter, atmospheric ducts, and their coupled propagation on phase stability, group delay, spectral broadening, polarization variation, intra-pulse modulation structures, and unintentional modulation features.

(2)

Propagation-aware data systems and validation methods.

In tropospheric OTH scenarios, signal distortion is often jointly affected by meteorological conditions, sea-state conditions, propagation paths, receiver status, and individual differences among transmitters. Therefore, relying only on the received signal makes it difficult to accurately explain the sources of feature variation. Future studies should consider establishing propagation-aware radar emitter datasets. In addition to radar signal parameters and recognition labels, such datasets should synchronously record meteorological parameters, refractivity profiles, atmospheric-duct parameters, turbulence-related indicators, link distance, operating frequency band, antenna height, and receiver status. Since high-confidence labeled data are difficult to obtain in large quantities from real field experiments, field-measured data, propagation-simulation data, and partially labeled data may be combined for real-scenario validation, controlled-variable analysis, and sample-coverage expansion, respectively.

(3)

AI-assisted channel inversion, feature robustness enhancement, and uncertainty assessment.

Artificial intelligence methods can provide useful tools for RER in complex nonlinear propagation environments, but their role should be defined within specific tasks. In tropospheric OTH scenarios, AI methods may be particularly useful for channel-state estimation and inversion, robust feature extraction under low-SNR and multipath conditions, complex modulation recognition, domain adaptation across sea areas and meteorological conditions, and uncertainty assessment of recognition results. It should be noted that the effectiveness of AI methods still depends on reliable labels, sufficiently representative training samples, and cross-scenario validation. In the absence of channel ground truth, true individual-emitter labels, or OTH reference samples, deep learning models alone may learn spurious features related to the environment or receiver conditions. Therefore, a more appropriate development path is to integrate AI methods with propagation models, environmental observations, and field validation, rather than treating them as an independent and mature solution.