CCBA: Dynamic Scheduling Algorithm for Jammer Resources in Strong Electromagnetic Interference Environment

Abstract

The strong electromagnetic interference environment on the battlefield has brought new challenges to the networking collaboration of jammers and the estimation of jamming effects. Traditional successful jamming indicators are difficult to meet the needs of continuous, low-power, and flexible jamming, causing difficulties in emergency scheduling of jamming resources. Aiming at the overall degradation of the communication party’s signal reception quality, this paper proposes the restrictive conditions of “overall limited jamming” and the analysis and evaluation index of “multistage jamming-to-signal ratio (J/S)”, which meets the scheduling requirements of distributed jamming resources in harsh environments. Based on the jammer layout that can achieve overall high-intensity jamming, the electromagnetic environment estimation, power scheduling, and collaboration strategies of jammers are designed, a communication countermeasure game algorithm under blocked networking collaboration is established, and the independent dynamic scheduling of jamming resources is realized. The experimental results show that the Concentric Circle Broadcasting Algorithm (CCBA) not only maintains effective communication jamming (the proportion of high-intensity jamming is no less than 50%, and the proportion of normal signal reception of communication nodes is no more than 6%), but also extends the system operation duration by 66.8–269.6% compared with the comparative algorithms for the 600 MHz fixed-frequency and 1 MHz bandwidth communication system. This work is limited to the line-of-sight (LOS) scenario, and future research will extend it to non-line-of-sight (NLOS) scenarios.

1. Introduction

With the swift evolution of contemporary communication technology toward intelligent and diversified development, the battlefield electromagnetic environment has become progressively complex [1]. Serving as a core approach to interrupt enemy command connections and attain military operational advantages, communication jamming has evolved into a key research focus within the field of electronic warfare. Miniaturized and distributed jammers, leveraging their advantages of low power consumption, flexible deployment, and strong concealment, have demonstrated enormous application potential in scenarios such as regional communication countermeasures and UAV swarm communication suppression, becoming a research hotspot [2]. However, in strong electromagnetic interference (EMI) environments, high noise and unstable channels exacerbate the difficulty of jamming resource scheduling—networked collaboration among jammers is prone to interruption, making it challenging to obtain global jamming effect feedback. This results in distributed jamming resources failing to form effective synergy, and the system’s operational duration struggling to meet practical combat requirements [3]. Therefore, how to achieve efficient scheduling of distributed jamming resources in strong electromagnetic interference environments, accomplish collaborative jamming objectives, and extend the system’s continuous operational time has become a crucial issue requiring urgent solutions.

Traditional centralized communication jamming resource scheduling methods pursue maximum jamming effectiveness by optimizing parameters such as jamming power, frequency bands, and time windows [4]. Nevertheless, such methods exhibit significant limitations in modern adversarial communication environments. On one hand, the central decision-making unit is vulnerable to becoming a high-value target for enemy attacks, leading to insufficient system robustness [5]. On the other hand, real-time collection and feedback of global channel state information (CSI) incur non-negligible latency and communication overhead, failing to meet the millisecond-level jamming response requirements in dynamic channel environments [6]. Furthermore, the computational complexity and communication load of centralized methods grow superlinearly with the number of jamming nodes, conflicting with the practical demands of lightweight and distributed deployment of electronic warfare systems [7]. This renders them inapplicable in dynamic, heterogeneous, and anti-destruction communication countermeasure scenarios.

Current research on distributed radar jamming resource scheduling has achieved certain progress. It enhances jamming effectiveness against radar systems through means such as joint antenna scheduling and power allocation, intelligent decision-making under the cognitive electronic warfare framework, and optimization of cooperative jamming strategies [8,9,10,11,12,13,14,15,16,17]. However, fundamental differences exist between radar jamming and communication jamming in core objectives, operational principles, evaluation metrics, and resource constraints: radar jamming aims to suppress or deceive radar detection, while communication jamming focuses on disrupting information transmission over communication links. The channel models, signal modulation methods, and effectiveness evaluation criteria of the two are completely distinct, resulting in the inability to directly migrate research achievements from distributed radar jamming to communication jamming scenarios [18].

As a cutting-edge interdisciplinary field integrating electronic warfare and wireless communication, distributed communication jamming resource scheduling has evolved from early static, centralized, and single-point confrontation models to a complex systems engineering oriented towards space-air-ground integration, multi-agent collaboration, dynamic game theory, and real-time learning. Current research exhibits distinct characteristics of high interdisciplinarity, strong technological integration, and stringent practical combat constraints. Its development trend can be systematically analyzed from three dimensions: theoretical paradigms, technical paths, and practical challenges.

At the theoretical paradigm level, the research focus is undergoing a profound transition from “optimization-driven” to “learning-driven” and “game-driven”. Traditional methods, such as master-slave parallel scheduling based on genetic algorithms [18], adaptive scheduling using the Improved Sparrow Search Algorithm (ISSA) [10], and hyper-heuristic fuzzy multi-attribute evaluation models [19], while engineering feasible in specific scenarios, are generally limited by inherent flaws such as strong dependence on CSI, high computational complexity, and weak generalization ability. In stark contrast, new paradigms centered on game theory and multi-agent reinforcement learning (MARL) have become mainstream. A systematic review in [20] points out that zero-sum games, Stackelberg games, and Bayesian game frameworks have been widely used to model strategic interactions between jammers and communicating parties. MARL, through autonomous exploration and strategy convergence of distributed agents, achieves local optimality and system synergy without the need for global information. Notably, cutting-edge developments have transcended the improvement of single algorithms and advanced toward building a “cognition-decision-execution” closed loop: as an example, the Transformer and deep reinforcement learning-based cognitive communication jamming strategy introduced in [21] integrates spectrum sensing, modulation identification with jamming action formulation. Ref. [22] fuses multi-domain information (space, spectrum, power, time) through evolutionary reinforcement learning to address challenges such as multi-modal objective functions and complex constraints in multi-radar-multi-jammer countermeasures. This signifies that the field has entered a new phase centered on “autonomous evolution of intelligent agents”.

Global research on military communication countermeasures and resource scheduling has also achieved in-depth breakthroughs in recent years, with relevant studies focusing on the integration of new communication architectures, intelligent optimization algorithms and anti-jamming technologies for in-depth exploration [23,24,25]. For 5G and beyond military communication systems, the technical characteristics of high speed, low latency, and high reliability impose more stringent requirements on the anti-jamming performance and resource scheduling efficiency of jamming systems, and the unique environmental adaptability requirements of military communications make distributed jamming resource scheduling schemes face more complex practical constraints [24,26]. In terms of jamming strategy design, related research has realized the improvement of communication secrecy and anti-jamming performance through power optimization and control jamming strategies, and verified the effectiveness of jamming power allocation in heterogeneous communication networks such as SWIPT-NOMA, providing a valuable reference for the power scheduling design of distributed jamming systems [27]. At the theoretical algorithm level, the fusion of game theory and multi-agent reinforcement learning has become a mainstream research direction to solve distributed resource scheduling problems, and evolutionary dynamics and Nash equilibrium theory have been effectively applied to the strategy optimization of multi-agent jamming systems, laying an important theoretical foundation for the design of distributed jamming resource scheduling algorithms [28]. In the field of extreme bandwidth communication, systematic analysis has been conducted on the jamming intrusion characteristics and countermeasure strategies of key 6G technologies such as millimeter wave and terahertz, and the unique jamming vulnerabilities of new communication technologies and corresponding anti-jamming technical systems have been summarized [25]. However, research on distributed jamming resource scheduling for 600 MHz UHF band tactical air-ground communication remains relatively scarce, and the design of lightweight and autonomous scheduling algorithms for strong electromagnetic interference environments is still an urgent open problem in global research. This study thus fills the research gap in this field, and the proposed algorithm framework provides a feasible solution for the efficient scheduling of distributed jamming resources in 600 MHz UHF band tactical air-ground communication scenarios.

At the technical path level, core breakthroughs are concentrated in two major directions. Firstly, distributed collaborative architectures have become key to addressing the scalability of large-scale networks. For distributed jamming networks composed of heterogeneous nodes such as Unmanned Aerial Vehicle (UAV) clusters, Low Earth Orbit (LEO) satellites, and ground stations, researchers no longer pursue centralized global optimality but emphasize low-overhead consensus and robust collaboration among nodes. Ref. [29] thoroughly analyzes the beamforming power attenuation caused by positioning and latency errors in UAV distributed arrays during cooperative jamming; ref. [30] optimizes LEO satellite downlink distributed jamming using the Non-dominated Sorting Genetic Algorithm (NSGA-II), balancing coverage and energy efficiency; and research on large-scale network control in [31] provides scalability theoretical support for the application of distributed AI in jamming scheduling. Secondly, robustness and uncertainty management have been elevated to an unprecedented level. Real electromagnetic environments are highly dynamic and partially observable. Therefore, relevant Joint Antenna Scheduling and Power Allocation (JASPA) schemes [8] and Anti-Deception Jamming Joint Radar-Target Assignment and Power Scheduling (ADJ-JRAPS) [9] directly embed deception parameters and target motion uncertainties into state estimation and optimization objectives; some studies in [32] specifically focus on how to utilize unused pilots for robust channel estimation and jamming detection under random pilot jamming attacks.

Nevertheless, severe challenges persist. The primary challenge is achieving low-overhead consensus: in distributed networks with limited bandwidth and unstable links, designing lightweight communication protocols to enable massive jamming nodes to complete strategy synchronization within milliseconds remains an open problem. Secondly, the NP-hard nature of joint jamming-communication optimization has not been fundamentally resolved. Existing algorithms still face issues such as slow convergence and susceptibility to local optima under large-scale and multi-constraint conditions. Thirdly, the generalization ability in real electromagnetic environments is insufficient: most algorithms perform well in idealized simulation environments but experience significant performance degradation when confronted with complex multipath, time-varying fading, and unknown jamming patterns, lacking unified and authoritative evaluation benchmarks and test platforms. These challenges, combined with the incompleteness, lag, and ambiguity of information perception by jammers in strong electromagnetic environments [3], as well as the localized and differentiated environmental perception characteristics of airborne and ground jammers due to spatial layout differences [33], further highlight the inadequate adaptability of existing methods in non-networked distributed jamming collaborative scheduling. The imperfection of the jamming effectiveness evaluation system exacerbates this predicament.

In terms of jamming effectiveness evaluation, traditional metrics such as J/S and jamming success rate exhibit poor applicability when directly migrated to distributed scenarios [34]. The former pursues full suppression of the received power of all communication nodes, causing some jammers to operate continuously at high intensity and resulting in uneven battery consumption [35]. The latter only counts the number of successful jamming instances after jamming ends, without constraining power consumption during the jamming process, which easily leads to rapid battery depletion of jammers in critical positions and failure to achieve sustained effective jamming [36]. Additionally, forcing all jammers to share global information for scheduling would significantly increase communication overhead, making it difficult to implement in harsh communication scenarios.

To address the aforementioned issues, this paper focuses on distributed communication jamming resource scheduling in strong electromagnetic interference environments. It establishes a mathematical model for air–ground joint communication countermeasures, proposes the constraint condition of “overall limited jamming” and the evaluation index of “multistage J/S”, and designs the CCBA along with supporting collaborative strategies to achieve efficient scheduling of jamming resources and significantly extend system operational duration.

The main contributions of this paper are as follows:

• A mathematical model for air–ground joint communication countermeasures in strong electromagnetic interference environments is established, and the constraint condition of “overall limited jamming” is proposed. Under the premise of ensuring an overall degradation in communication network quality, it provides flexible space for jamming resource scheduling, effectively saves jammer power, and adapts to the power constraint characteristics of distributed jammers. In the scenario setup of this paper, a strong EMI environment is defined as a condition with ground noise ≥ −95 dBW, low-altitude noise ≥ −105 dBW, and a jammer disconnection rate ≥ 60%; a weak EMI environment is defined as ground noise < −105 dBW, low-altitude noise < −115 dBW, and a jammer disconnection rate < 30%.
• A “multistage J/S” analysis and evaluation index is proposed. Targeting the three types of communication antennas (vehicle-mounted, elevated, and UAV-lifted) of communication nodes, it refines the effectiveness analysis dimensions of the communication countermeasure process, more reasonably characterizes jamming effects and resource scheduling algorithm characteristics, and addresses the insufficient applicability of traditional evaluation metrics.
• The CCBA is designed. Aiming at the difficulty of networked collaboration in strong electromagnetic interference environments, it integrates strategies such as concentric circle broadcast collaboration, electromagnetic environment estimation, and limited random power scheduling to achieve balanced scheduling of scattered jamming resources. While extending system operational duration, it stably achieves the jamming target of reducing communication network quality.

The structure of the remaining sections of this paper is as follows. Section 2 elaborates on the mathematical model for communication countermeasures, while Section 3 expounds on the design and implementation of the CCBA. Section 4 presents the details of simulation experiments and the corresponding result analysis, and Section 5 draws the main conclusions of the study and puts forward prospects for future research work.

2. Air–Ground Communication Countermeasure Model

The air–ground communication network system is characterized by ad hoc networking and encryption functions, which makes it challenging for jammers to decipher intercepted electromagnetic information and identify the transceivers of communication links within a short timeframe. Consequently, jammers have to target the maximum receiving power of communication nodes for jamming operations. In a high-intensity electromagnetic interference environment, a great number of jammers are subject to interference and network disconnection, which impairs collaborative networking among them. An individual jammer is unable to acquire feedback regarding the overall communication jamming effect and thus fails to achieve global jamming by virtue of the limited intercepted information alone. With the integration of the broadcasting strategy proposed in this study, the dynamic and independent resource scheduling for air–ground jamming in strong electromagnetic interference environments is illustrated in Figure 1; in this figure, the discontinuity of communication and jamming links directly reflects the level of interference that each link endures.

Within the aforementioned harsh electromagnetic environment, the positional information of the communication side has been ascertained via reconnaissance, and the jamming side has also finalized its fixed-position deployment. Confronted with the dynamic regulation of transmission power in the air–ground communication network system, how an individual jammer can autonomously schedule its jamming power to suppress the air–ground communication network while maximizing the operational lifetime of the distributed communication jamming system constitutes the core research problem addressed in this paper.

2.1. Air-Ground Communication Model

LOS propagation characteristics govern the path loss between airborne communication nodes as well as between airborne and ground-based communication nodes. To characterize the fluctuations in propagation path loss due to temporal variations and propagation environments, Equation (1) defines $L_s^{\prime }$ the path loss of the dynamic LOS propagation model in dB, where $n_{\mathit{1}}^{\prime }$ is the dynamic environmental factor for LOS propagation in dB, $f$ is the frequency band in MHz, and $R$ is the distance between two communication nodes in kilometers (km).

$$L_s^{\prime }=32.5+20\mathrm{l}\mathrm{g}f+10n_{\mathit{1}}^{\prime }\mathrm{l}\mathrm{g}R$$

(1)

Path loss among ground communication nodes adheres to the two-ray propagation model. For the purpose of characterizing the fluctuations in propagation path loss caused by temporal changes and varying propagation environments, Equation (2) defines $L_d^{\prime }$ the path loss corresponding to the dynamic two-ray propagation model. In this formula, $n_2^{\prime }$ denotes the dynamic environmental factor for two-ray propagation (in dB), $h_t$ represents the transmit antenna height, and $h_r$ stands for the receive antenna height, with both heights quantified in meters (m).

$$L_d^{\prime }=120+10n_2^{\prime }\lg R-20\lg h_t-20\lg h_r$$

(2)

If the distance between the transmitter and receiver is less than the Fresnel zone distance, the dynamic LOS propagation model is used; otherwise, the dynamic two-ray propagation model is applied. The Fresnel zone distance is obtained from Equation (3), where $FZ$ is the Fresnel zone distance and $\mathrm{\lambda }$ is the signal wavelength in m. In the literature, there are various formulas for calculating the Fresnel zone distance. The reason why Equation (3) is selected in this paper is that the distance obtained thereby corresponds to the scenario where line-of-sight propagation is equivalent to two-ray propagation.

$$FZ=4\pi h_t{h}_r/\mathrm{\lambda }$$

(3)

In Equation (4), $P_c^t$ denotes the transmit power of the communication signal and $P_c^r$ the receive power of the communication signal, with both values expressed in dBW. ${\mathrm{G}}_{\mathrm{tc}}$ represents the antenna gain of the communication transmit antenna toward the communication receive antenna, and ${\mathrm{G}}_{\mathrm{rc}}$ is the antenna gain of the communication receive antenna toward the communication transmit antenna; additionally, $L_c$ stands for the dynamic path loss of communication transmission, and ${\mathrm{L}}_{\mathrm{pc}}$ denotes the attenuation of cables and connectors in the communication receiver, all of which are quantified in dB.

$$P_c^t=P_c^r-{\mathrm{G}}_{\mathrm{tc}}-{\mathrm{G}}_{\mathrm{rc}}+L_c+{\mathrm{L}}_{\mathrm{pc}}$$

(4)

2.2. Communication Power Adjustment Mechanism

In a high-intensity electromagnetic interference environment, prior to the onset of distributed communication jamming, if a transmitting node fails to ensure normal communication operation for a receiving node across the communication link with the minimum transmission path loss, the transmitter will sustain maximum transmit power to repeatedly attempt the establishment of reliable communication connections. If the transmitter is able to enable normal operation of the receiver, the received power must satisfy the communication link margin requirements even in the presence of ambient noise power [35]. As expressed in Equation (5), $RS$ denotes the receiving sensitivity of the communication device and ${\sigma }^2$ represents the ambient noise power, with both parameters in dBW; $SFM$ refers to the system fade margin, measured in dB.

$$P_c^r-\max (RS,{\sigma }^2)>SFM$$

(5)

This study focuses on a non-spread spectrum wireless interface with 600 MHz fixed frequency and 1 MHz bandwidth, which is a typical configuration for tactical air–ground communication in the battlefield. The receiving sensitivity (−133 dBW) in Equation (5) is the typical engineering index of this fixed-frequency interface, and there is no need to consider the modulation effect of the spreading factor (applicable to DSSS/FHSS) on the receiving sensitivity. The proposed CCBA framework can be directly extended to DSSS/FHSS spread spectrum interfaces, and only the receiving sensitivity index needs to be linearly corrected according to the spreading factor.

Under such circumstances, the transmitter is designed to conserve energy and minimize the exposure scope of communication electromagnetic information. In the process of signal transmission, communication devices select the transmission path with the lowest loss and adopt the minimum transmit power level that satisfies the communication requirements [35]. In Equation (6), $P_{cj}^{t\min }$ denotes the minimum transmit power of the $j$-th communication device (in dBW), and $L_{c{j}^{\prime }}$ represents the path loss for communication with other associated devices (in dB).

$$P_{cj}^{t\min }=SFM+\max (RS,{\sigma }^2)-{\mathrm{G}}_{\mathrm{tc}}-{\mathrm{G}}_{\mathrm{rc}}+\min (L_{c{j}^{\prime }})+{\mathrm{L}}_{\mathrm{pc}},j^{\prime }\in (1,\mathrm{J}) \mathrm{and}\ne j$$

(6)

Following the application of distributed communication jamming, the communication side adjusts its transmit power via a roulette wheel approach based on the current transmission power level: it may raise the transmit power to counteract the jamming effects, cease signal transmission to evade jamming, or lower the transmit power while maintaining the current operational state to confound the jamming side.

2.3. Overall Limited Jamming

Distributed communication jamming has a power superposition effect. To reduce the calculation of weak jamming power, an upper limit of jamming spacing $D_s^{\prime }$ is set according to the environment and equipment performance. The propagation of jamming signals in LOS communication links must not exceed the LOS propagation distance $D_s$, both in km. In Equation (7), the jamming range considered for the $i$-th jammer and the $j$-th communication device is $D_{ij}$, which takes the minimum value of the two distance limitations.

$$D_{ij}=\min (D_s,D_s^{\prime })$$

(7)

The ratio of the sum of airborne and ground jamming signal powers received by the $j$-th communication node to the maximum communication receiving power is $k_{\mathrm{j}\mathrm{b}}$ in dB. In Equation (8), $x_{ij}$ is 1 if the jammer is within the jamming range, otherwise 0. If the $i$-th jammer is an airborne jammer, its jamming power is $P_{ia}^{rj}$, and the total number of jammers is $I$; if the $i$-th jammer is a ground jammer, its jamming power is $P_{is}^{rj}$. $P_j^{r\max }$ represents the maximum power received by the $j$-th communication node from other communication nodes, all in dBW. Since both the jamming power and the communication received power are in dBW, the difference between them directly corresponds to the logarithm of the linear power ratio (i.e., J/S in dB).

$$k_{\mathrm{jb}}={\displaystyle \sum _{i=1}^I(P_{ia}^{rj}+P_{is}^{rj})x_{ij}+{\sigma }^2-P_j^{r\max }}$$

(8)

In Equation (9), jamming is deemed successful if the power ratio of the jamming signal to the received communication signal is no less than the communication jamming suppression J/S threshold $k_j$ (in dB); in this case, $JS{R}_j$—the quantized J/S ratio for the $j$-th communication device—is assigned a value of 1.

$$JS{R}_j=\left\{\begin{array}{l}0,k_{jb}<k_j\\ 1,k_{jb}\ge k_j\end{array}\right.$$

(9)

In a strong electromagnetic interference environment, since it is difficult to achieve power suppression jamming for all communication nodes, the minimum jamming target is set to reduce the overall communication receiving quality. This is achieved by adopting a lower communication quality degradation J/S $k_{j2}$ in dB in Equation (10) and specifying the proportion of disturbed communication nodes. As shown in Equation (11), $J$ is the total number of communication devices, and $R_j$ is the proportion of disturbed communication nodes.

$$JS{R}_{j2}=\left\{\begin{array}{l}0,k_{jb}<k_{j2}\\ 1,k_{jb}\ge k_{j2}\end{array}\right.$$

(10)

$${\displaystyle \sum _{j=1}^{J}JS{R}_{j2}>J}{R}_j$$

(11)

The proposed overall limited jamming, in strong electromagnetic interference scenarios, targets communication networks with a certain degree of disturbance. By leveraging the advantages of environmental noise for the jamming side and based on the constraints of environmental noise that hinder networking collaboration among jammers and precise scheduling of jamming resources, it allows distributed jammers to adopt more flexible and efficient jamming strategies. These strategies include time-domain intermittence, geographical rotation, switching between aerial and ground jammers, and flexible selection of jamming targets and jamming power, among others.

2.4. Optimization Objective

In Equation (12), $T_{iq}$ denotes the operational duration of the $i$-th jammer within the $q$-th scheduling cycle (unit: hour, H) following this scheduling iteration. Here, ${\mathsf{\eta }}_{\mathrm{s}}$ represents the battery capacity threshold required for the jammer to perform normal jamming operations, ${\mathrm{U}}_{\mathrm{out}}$ is the battery’s working voltage (unit: volt, V), and ${\mathrm{E}}_{\mathrm{esq}}$ stands for the battery energy consumed during this scheduling process (unit: ampere-hour, AH). Additionally, $P_i$ refers to the jamming output power of the $i$-th jammer, and ${\mathrm{P}}_{\mathrm{x}}$ is the power consumed by the jammer to sustain its auxiliary functional operations (unit: watt, W).

$$T_{iq}={\displaystyle \frac{{\mathsf{\eta }}_{\mathrm{s}}{\mathrm{U}}_{\mathrm{outs}}{\mathrm{E}}_{\mathrm{esq}}}{(P_i+{\mathrm{P}}_{\mathrm{x}})}}$$

(12)

During the operation of the jamming system, the system’s operational duration is deemed to terminate if the global communication jamming objective fails to be achieved. The total operational duration $T$ of the jamming system is the cumulative sum of the single scheduling cycle working durations $T_{iq}$ across all iterations.

3. Concentric Circle Broadcasting Algorithm

3.1. Algorithm Structure

As shown in Figure 2, under intense electromagnetic interference, jammers are unable to achieve synchronization and are scheduled in a disorderly manner. The severity of link disruption reflects the level of interference experienced. For nearby communication nodes, the CCBA predefines multiple distance levels to select jamming targets according to positional information. After the communication network performs adaptive adjustment, each jammer selects communication targets using partially observed reconnaissance data and implements jamming in a near-to-far order at fixed time intervals. It also records successfully detected adjacent jamming information and broadcast messages to support the autonomous decision-making process of individual jammers.

CCBA adopts real-number encoding to represent jammer-related information, which can characterize continuous real variables and decrease the coding conversion error in the process of jamming resource scheduling. After each jammer is scheduled, CCBA broadcasts the jammer’s power and the estimated received power of communication nodes using maximum jamming power before executing jamming. This allows effective information transfer at low cost and short time even when jammer networking is unstable. The CCBA and communication countermeasure environment are shown in Figure 3. Due to poor communication links, jammers cannot obtain overall jamming evaluation and rely on third parties. If overall jamming fails after one scheduling cycle, jamming is determined to have failed.

It should be clarified that the “third party” mentioned in the CCBA framework is a third-person perspective set for simulation experiment validation, rather than a physical node in the actual strong EMI environment. In the simulation, this third-person perspective is responsible for uniformly judging whether all comparative algorithms achieve the preset jamming objective (80% disturbed communication nodes, 3.01 dB J/S threshold for communication quality degradation). If the jamming objective is not achieved after one scheduling cycle, the algorithm scheduling is deemed to fail, and the calculation of the jamming system’s operation duration is terminated directly.

In the actual strong EMI application scenario for the communication system, there is no such physical third party. The CCBA realizes autonomous jamming effect evaluation and resource scheduling through two core strategies: (1) Electromagnetic environment estimation strategy (Section 3.2): each jammer independently estimates the maximum received power of communication targets based on reconnaissance data and broadcast information of adjacent jammers; (2) Overall limited jamming constraint (Section 2.3): each jammer judges the local jamming effect according to the self-calculated multistage J/S ratio, and the distributed jammers form the overall jamming effect through the superposition of local jamming, without relying on the global feedback of a third party.

3.2. Electromagnetic Environment Estimation Strategy

As an independent intelligent agent, a single jammer estimates the states of nearby communication nodes and other jammers by using the prior information of communication nodes and jammers, together with real-time reconnaissance signal data. As presented in Algorithm 1, $P_j^t$ denotes the transmission power of the $j$-th communication node.

Algorithm 1 Electromagnetic Environment Estimation Strategy
Input: Communication countermeasure layout, reconnoitered electromagnetic environment information (where $i_0$ is the jammer, and $i^{\prime }$, $j^{\prime }$ store jammer and communication node information)
Output: Estimated communication and jamming information
1:	$\mathrm{if} i_0$ reconnoiters the source azimuth and power of a signal:
2:	for $j^{\prime }$= 1 to $J$
3:	Compare $j^{\prime }$ with $j$ to infer the information and distance of $j$
4:	Select a channel propagation model to estimate $P_j^t$
5:	for $i^{\prime }$= 1 to $I$
6:	Compare $i^{\prime }$ with $i$ to infer the information and distance of $i$
7:	Select a channel propagation model to estimate $P_i^t$
8:	end if
9:	for $j$= 1 to $J$:
10:	$P_j^{rc}$= 0
11:	for $j_2$ = 1 to $J$$, j\ne j_2$:
12:	Select channel propagation model and $P_{j2}^t$
13:	Estimate $P_j^{rc}$
14:	if $P_j^{rc}\ge P_n^{es}$:
15:	Update $P_j^{rc}$
16:	end if
17:	if $i_0$ receives and identifies broadcast information from other jammers:
18:	Update $P_i^t$
19:	$P_j^{rc}$ = max($P_{j-old}^{rc}$,$P_{j-new}^{rc}$)
20:	end if

Algorithm 1 stores the spatial layout information of known communication nodes and jammers. When a single jammer reconnoiters electromagnetic information that can be accurately identified, it determines the azimuth of the electromagnetic information, compares it with the stored information, and further determines the source and spacing of the electromagnetic information. The jammer selects a channel propagation model and estimates the transmitting power of the reconnoitered electromagnetic information through mathematical calculation, then saves the result. For the broadcast information of surrounding jammers detected by the jammer: if the information is the transmitting power of the surrounding jammer itself, it is directly updated; if the information is the transmitting power of surrounding communication nodes estimated by the surrounding jammer, it is compared with the already estimated communication information, and the maximum value is selected for storage.

3.3. Range Gear Strategy

As networked cooperation is restricted, individual jammers are required to establish several range gears. Combined with the aforementioned estimation strategy, they perform autonomous jamming on communication nodes within the corresponding range gear. The minimum spacing refers to the shortest distance between an individual jammer and adjacent communication nodes. Communication links formed by distinct antennas of communication terminals and jammers present different link gains. For each type of link gain, non-uniform stepped reference distances must be configured. By combining the minimum spacing and reference distances, the range gears for each link gain are determined empirically, where the lowest gear is set to 1 and the maximum gear is x. The number of range gears is designed to balance the relationship between the duration and efficiency of jamming resource scheduling.

3.4. Environmental Noise Threshold Strategy

The dynamic environmental factors of LOS propagation and two-ray propagation models exhibit randomness, and their average values can be used to facilitate jamming effect estimation in the algorithm. In Equation (13), $n_{\min }^{\prime }$ is the minimum value, $n_{\max }^{\prime }$ is the maximum value, and $n_{es}$ is the estimated value, with the unit of dB.

$$n_{es}={\displaystyle \frac{n_{\min }^{\prime }+n_{\max }^{\prime }}{2}}$$

(13)

$P_{mar}$ is the redundant estimation of noise, that is, if $P_n^{es}$ is a communication signal, the value by which it exceeds the lower limit of environmental noise at a transmission distance of 10 km. $P_n^{es}$ is the critical value of environmental noise, with the unit of dB. In Equation (14), if the jammer-estimated received power of the communication node is greater than this value, the jammer plans to apply jamming; otherwise, it refrains from jamming to save jammer power.

$$P_n^{es}=P_n^{\min }+n_{\max }^{\prime }-n_{es}+P_{mar}$$

(14)

3.5. Power Upper Limit Strategy for Disconnection State

In the case of jammer disconnection from the network, to maximize suppression of the communication node with the least path loss from the jammer while saving battery power, it is necessary to set an independent jamming power upper limit $P_i^{up}$. In Equation (15), when all communication nodes transmit at maximum power, the maximum received power of communication nodes is $P_j^{r\max }$. Given the known layout of the air–ground communication network and jammers, each jammer takes the $P_j^{r\max }$ of the communication node with the least path loss as the reference target for high-intensity jamming, subject to the constraints of the jammer power upper limit $P_i^{\max }$ and the minimum jamming power requirement $P_i^{n\min }$, with the unit of dBW.

$$P_i^{up}=\max [\min (k_y{P}_j^{r\max },P_i^{\max }),P_i^{n\min }]$$

(15)

3.6. Final Battery Discharge Strategy

If the remaining battery capacity of a jammer is insufficient to support the preset jamming power, it will uniformly discharge the maximum possible jamming power within the last working cycle to enhance the effectiveness of the jamming system. In Equation (16), for the $i$-th jammer in the $q$-th scheduling, $T_{iq}$ is the operating duration of its last effective work, with the unit of H; ${\mathrm{E}}_{\mathrm{esq}}^{\mathrm{last}}$ is the remaining battery capacity, with the unit of AH.

$$P_i^{last}={\displaystyle \frac{{\mathsf{\eta }}_{\mathrm{s}}{\mathrm{U}}_{\mathrm{outs}}{\mathrm{E}}_{\mathrm{esq}}^{\mathrm{last}}}{T_{iq}}}-{\mathrm{P}}_{\mathrm{x}}$$

(16)

The final battery discharge strategy operates at maximum jamming power when a jammer’s remaining battery capacity is low, which effectively ensures the system’s jamming performance. However, this poses a risk of positional exposure to enemy home-on-jam missiles, as the maximum-power signal is vulnerable to capture and geolocation by missile seekers. To mitigate this risk, jammers can implement an intermittent discharge mode with a 50% duty cycle combined with pseudo-power signal transmission in the low-capacity phase: the actual jamming power is emitted intermittently, while a pseudo-power signal of the same frequency but different power level is transmitted simultaneously. This approach reduces the probability of positional detection while preserving jamming effectiveness, and the optimization of this strategy’s concealment performance will be the focus of our future research.

3.7. Finite Random Power Scheduling Strategy

After jammers reconnoiter and estimate the surrounding communication countermeasure status, they independently perform jamming power scheduling, as shown in Algorithm 2. Here, $P_n^{es}$ is the critical value of environmental noise. The total power of jamming signals received by $j$ is $P_{jsum}^n$, the jamming power requirement of $i$ is $P_i^n$, $P_j^{ri}$ is the power of jamming signals from $i$ received by $j$, $P_{ran}$ is the probability of random numbers, and $P_i^{old}$ is the jamming power of $i$ before scheduling.

Algorithm 2 Finite Random Power Scheduling Strategy
Input: Estimated communication and jamming information
Output: $P_{i0}^t$ (jamming power of the jammer)
1:	for $j$= 1 to $J$:
2:	for $i^{\prime }$= 1 to $I$:
3:	Record $P_i^{old}$
4:	If $i\ne i^{\prime }$ and $P_j^{rc}\ge P_n^{es}$, $d_{ji}\le$ Tier x:
5:	$P_i^n=k_{j2}{P}_j^{rc}$
6:	for $i$= 1 to $I$, $i\ne i^{\prime }$:
7:	$P_{jsum}^n=P_{jsum}^n+P_j^{ri}$
8:	end if
9:	$P_i^n=P_i^n-P_{jsum}^n$
10:	$P_i^n=\min (P_i^n,P_i^{\max })$
11:	if $P_i^n\le P_i^{n\min }$:
12:	$P_i^n=random(P_i^{n\min },P_i^{up})$
13:	end if
14:	if $P_i^n=P_i^{old}=P_i^{\max }$ and $P_{ran}\le 0.5$:
15:	$P_i^n=0.5P_i^{\max }$
16:	end if
17:	if ${\mathrm{E}}_{\mathrm{esq}}^{\mathrm{last}}$ can not guarantee $P_i^n$:
18:	$P_{i0}^t=P_i^{last}$
19:	else:
20:	$P_{i0}^t=P_i^n$

Algorithm 2 in the scheduling process, a single jammer first saves the previous jamming power. If the receiving power of the communication node scheduled for jamming has been estimated, it combines the estimated jamming power of surrounding jammers to calculate the jamming power required to successfully degrade the receiving quality of the communication node, and plans to use this power. If it has not been previously estimated, the jammer selects a random jamming power between the minimum required jamming power and the independent jamming power upper limit of the jammer, and plans to use this random power. If the planned jamming power is consistent with the saved previous jamming power, there is a 50% probability to halve the jamming power for use. In this way, the jammer realizes intermittent and rotating jamming to save energy.

3.8. Complexity Analysis

Estimation Cost (Corresponding to Section 3.2, Electromagnetic Environment Estimation Strategy). This cost is generated by the execution of the electromagnetic environment estimation strategy. Each jammer ($N$ in total) traverses all $M$ communication nodes to estimate the received jamming power and communication signal power, forming a double loop of $N$ and $M$. The broadcast information update operation is a constant-time operation $O\left(1\right)$ for each jammer. Thus, the time complexity of the estimation cost is $O(M\times N)$.

Range Gear Search Cost (Corresponding to Section 3.3, Range Gear Strategy). This cost is generated by matching communication nodes to the corresponding range gears for each jammer. Each jammer traverses all $M$ communication nodes for gear matching, and the matching operation for a single node is a one-time lookup with a time complexity of $O(X)$ (i.e., $O\left(1\right)$ since $X$ = 5 is a fixed constant). The total time complexity of this part is $O(N\times M\times X)\approx O(M\times N)$, which is negligible compared with the other two costs due to the fixed number of range gears.

Power Scheduling Cost (Corresponding to Section 3.7, Finite Random Power Scheduling Strategy). This cost is generated by the execution of the finite random power scheduling strategy. Each jammer ($N$ in total) traverses all $M$ communication nodes to calculate the required jamming power, judge power constraints, and perform random power adjustment. All related operations (power calculation, constraint judgment, power halving) are constant-time operations $O\left(1\right)$ for a single node. Thus, the time complexity of the power scheduling cost is $O(M\times N)$.

The total time complexity of the CCBA is the sum of the three above costs: $O(M\times N)+O(M\times N)+O(M\times N)=O(M\times N)$. The total complexity is dominated by the estimation cost and power scheduling cost, and the linear complexity with respect to M and N ensures the lightweight and real-time performance of CCBA in large-scale distributed jammer networks.

4. Simulation Experiment

4.1. Parameter Setting of the Simulation Scenario

All simulation experiments in this section are carried out based on the non-spread spectrum wireless communication interface with 600 MHz fixed frequency and 1 MHz bandwidth, which is a typical application scenario of battlefield short-range air-ground tactical communication, and the relevant parameter settings are in line with engineering practice.

This paper designs three simulation scenarios, as shown in Figure 4 and

Table 1. Parameter settings for communication countermeasure scenarios.

	Scene1	Scene2	Scene3
Airborne Communication Node	10	10	10
Ground Communication Node	20	20	20
Ground Jammer	24	26	28
Airborne Jammer	8	3	4

. Figure 4a depicts an air–ground communication network distributed along a highway, Figure 4b shows a centrally deployed air–ground communication network, and Figure 4c illustrates a ring-deployed air–ground communication network. The static jammer layout adopted in the simulation experiments is premised on achieving overall jamming with full-power jamming.

All experiments were conducted on a platform equipped with an Intel(R) Core(TM) i5-8300H CPU (2.30 GHz), 16.0 GB RAM, and an NVIDIA GTX 1080Ti GPU. The software environment was built on Anaconda 23.7.4, with PyCharm 2023.2.1 (Professional Edition, runtime version: 17.0.8+7-b1000.8 amd64) as the IDE, and key dependencies including anaconda_depends_2023.09 and PyTorch 1.13.1. The simulation experiment parameters used in this paper are shown in

Table 2. Table of simulation scenario parameter settings.

Project	Parameter
Maximum transmitting power of airborne communication equipment	10 W
Antenna gain of airborne communication equipment	2 dBi
Height of airborne communication equipment	2000–3000 m
Maximum transmitting power of ground communication equipment	25 W
Antenna gain of ground communication equipment	2.5 dBi
Communication frequency band $f$	600 MHz
Communication bandwidth	1 MHz
Receiving sensitivity of communication equipment $RS$	−133 dBW
Communication link margin $SFM$	12 dB
Maximum jamming power of airborne jammer $P_{A\max }$	20 W
Altitude of airborne jammer	400–2000 m
Maximum jamming power of ground jammer $P_{L\max }$	40 W
Planar area of the simulation scenario	50 km × 50 km
Attenuation of cables and cable connectors at the communication receiving end ${\mathrm{L}}_{\mathrm{pc}}$	1 dB
Maximum battery power limit required for normal jamming ${\mathsf{\eta }}_{\mathrm{s}}$	0.95
Operating voltage of jammer batteries ${\mathrm{U}}_{\mathrm{out}}$	24 V
Battery capacity of airborne jammers	12 AH
Battery capacity of ground jammers	20 AH
Energy consumption of other functions of jammers ${\mathrm{P}}_{\mathrm{x}}$	4 W
Angle Recognition Accuracy of Communication Nodes	0.3 degrees
Communication state adjustment interval	90 s
Ground electromagnetic environment noise	−95~−105 dBW
Low-altitude electromagnetic environment noise	−105~−115 dBW
Height of ground communication antenna	5 m
Fresnel zone distance of ground communication antenna	0.6 km
Height of ground elevated communication antenna	20 m
Fresnel zone distance of elevated communication antenna	10 km
Height of UAV-lifted ground communication antenna	180 m
Fresnel zone distance between elevated communication antenna and jammer antenna	1.5 km
Dynamic environmental factor for LOS propagation $n_1^{\prime }$	2.5~3.5 dB
Dynamic environmental factor for two-ray propagation $n_2^{\prime }$	3.5~4.5 dB
J/S for communication suppression $k_j$	4.77 dB
J/S for communication quality degradation $k_{j2}$	3.01 dB
Proportion of disturbed communication nodes $R_j$	0.8
J/S range for normal communication	(−∞, −12) dB
J/S range for low-quality communication	(−12, −6.02] dB
J/S range for lower-quality communication	(−6.02, −3.01] dB
J/S range for low-intensity jamming	(−3.01, 1.76] dB
J/S range for medium-intensity jamming	(1.76, 4.77] dB
J/S range for high-intensity jamming	(4.77, ∞] dB
Recognition accuracy for normal communication [37]	0.98
Recognition accuracy for low-quality communication	0.85
Recognition accuracy for lower-quality communication	0.7
Redundant estimation of noise $P_{mar}$	2.5 dB
Minimum jamming power requirement $P_i^{n\min }$	3 W
Air communication node speed	0 km/h
Airborne jammer speed	0 km/h

. In a strong electromagnetic interference environment, ground communication nodes can use elevated antennas or UAV-lifted antennas to improve communication quality.

In a strong electromagnetic interference environment, before implementing distributed communication jamming, communication nodes transmit signals at maximum power, and the receiving status of communication nodes is shown in

Table 3. Receiving status of communication nodes.

Antenna	Receiving Status	Normal	Low-Quality	Lower-Quality	Low-Intensity	Medium-Intensity	High-Intensity
		Count/%	Count/%	Count/%	Count/%	Count/%	Count/%
Vehicle-Mounted	Scene1	10/33%	3/10%	9/30%	5/17%	2/7%	1/3%
	Scene2	9/30%	4/13%	6/20%	5/17%	3/10%	3/10%
	Scene3	8/27%	5/17%	2/7%	10/33%	2/7%	3/10%
Elevated	Scene1	12/40%	10/33%	3/10%	5/17%	0/0%	0/0%
	Scene2	17/57%	9/30%	3/10%	1/3%	0/0%	0/0%
	Scene3	13/43%	12/40%	3/10%	2/7%	0/0%	0/0%
UAV-Lifted	Scene1	8/27%	6/20%	9/30%	5/17%	2/7%	0/0%
	Scene2	7/23%	9/30%	8/27%	4/13%	1/3%	1/3%
	Scene3	8/27%	12/40%	2/7%	5/17%	3/10%	0/0%

.

The receiving status of the jamming side is shown in

Table 4. Receiving status of jamming system.

Receiving Status	Normal	Low-Quality	Lower-Quality	Low-Intensity	Medium-Intensity	High-Intensity
	Count/%	Count/%	Count/%	Count/%	Count/%	Count/%
Scene1	9/28%	6/19%	3/9%	9/28%	4/13%	1/3%
Scene2	3/10%	4/14%	1/3%	7/24%	5/17%	9/31%
Scene3	9/28%	0/0%	3/9%	7/22%	4/13%	9/28%

.

If all distributed communication jammers impose jamming at maximum power, all communication nodes in the three scenarios will suffer from high-intensity jamming.

4.2. Comparison Results and Analysis of System Operation Duration

The CCBA is compared with the intelligent concentric circle algorithm (ICCA) [3], full-power jamming algorithm (FPJA), simple random search algorithm (SRSA), and MADJPA [36]. The algorithms are run 30 times, and the average values are taken.

When ground communication nodes use vehicle-mounted antennas, the system operation duration of CCBA is extended by 109%, 178.3%, and 196.3% compared with the comparative algorithms in Scenario 1, Scenario 2, and Scenario 3, as shown in

Table 5. Algorithm results comparison (vehicle-mounted antenna).

		CCBA	ICCA	FPJA	MADJPA	SRSA
Scene1	Training Time	None	None	None	1.67 s	None
	Time per Scheduling	64.9 ms	60.9 ms	9.7 ms	28.9 ms	9.9 ms
	System Duration	39.1 h	11.55 h	10.46 h	1.44 h	18.7 h
Scene2	Training Time	None	None	None	1.74 s	None
	Time per Scheduling	89.1 ms	85.3 ms	8.8 ms	31.4 ms	9.1 ms
	System Duration	52.6 h	11.65 h	11.12 h	0.22 h	18.9 h
Scene3	Training Time	None	None	None	1.70 s	None
	Time per Scheduling	36 ms	44.5 ms	10.3 ms	22.1 ms	9.4 ms
	System Duration	56.4 h	12.93 h	10.45 h	0.09 h	19.03 h

.

When ground communication nodes use elevated antennas, the system operation duration of CCBA is extended by 66.8%, 155.6%, and 166.9% compared with the comparative algorithms in Scenario 1, Scenario 2, and Scenario 3, as shown in

Table 6. Algorithm results comparison (elevated antenna).

		CCBA	ICCA	FPJA	MADJPA	SRSA
Scene1	Training Time	None	None	None	1.70 s	None
	Time per Scheduling	60.8 ms	56.2 ms	10.5 ms	38.4 ms	9.8 ms
	System Duration	31.7 h	11.75 h	10.45 h	11.33 h	19.01 h
Scene2	Training Time	None	None	None	1.75 s	None
	Time per Scheduling	92.4 ms	86.3 ms	9.5 ms	33.4 ms	19.5 ms
	System Duration	48.87 h	10.57 h	10.45 h	0.33 h	19.12 h
Scene3	Training Time	None	None	None	1.66 s	None
	Time per Scheduling	42.9 ms	39.4 ms	9.9 ms	31.1 ms	10 ms
	System Duration	51.08 h	10.97 h	10.45 h	0.03 h	19.14 h

.

When ground communication nodes use UAV-lifted antennas, the system operation duration of CCBA is extended by 248.7%, 269.6%, and 223% compared with the comparative algorithms in Scenario 1, Scenario 2, and Scenario 3, as shown in

Table 7. Algorithm results comparison (uav-lifted antenna).

		CCBA	ICCA	FPJA	MADJPA	SRSA
Scene1	Training Time	None	None	None	1.64 s	None
	Time per Scheduling	82.4 ms	73.9 ms	8.7 ms	42.1 ms	8.8 ms
	System Duration	67.3 h	20.35 h	11.56 h	5.3 h	19.3 h
Scene2	Training Time	None	None	None	1.75 s	None
	Time per Scheduling	116.4 ms	103.3 ms	7.9 ms	35.6 ms	8.8 ms
	System Duration	71.3 h	15.63 h	10.49 h	0.04 h	19.29 h
Scene3	Training Time	None	None	None	1.62 s	None
	Time per Scheduling	53.3 ms	47.4 ms	8.9 ms	29.1 ms	9.1 ms
	System Duration	61.7 h	14.65 h	10.45 h	2.25 h	19.1 h

.

MADJPA trains based on the initial communication network status but lacks power adjustment strategies for communication nodes and sample generation mechanisms. With insufficient training under single-sample conditions, its training time is shorter, making it difficult to cope with drastic adjustments after communication nodes are disturbed. FPJA and SRSA do not use external information and adopt fixed strategies to set jammer power, resulting in shorter decision-making durations. The ICCA saves a small amount of time by not using broadcast strategies.

In Figure 5, the system operation duration of CCBA is extended by 66.8% compared with the comparative algorithms. Experimental results show that CCBA can efficiently complete jamming resource scheduling. When the jammer networking is blocked, a single jammer cannot obtain the real-time feedback of overall jamming effects, making it impossible to optimize the solution search accordingly. The comparative algorithms lack electromagnetic environment estimation, power scheduling, and collaborative strategies for independent jammers, which makes it difficult to meet the requirements of overall communication countermeasures.

In the complex air-ground confrontation layout and electromagnetic environment, the local information reconnaissance by a single jammer is insufficient to infer global information, leading to the scheduling failure of the MADJPA algorithm even when jammer power is sufficient, thus reducing the system operation duration.

4.3. Results and Analysis of Communication Party’s Disturbed State

After the communication countermeasure process is completed, in order to analyze the disturbed state of the communication party in a more refined manner, an analysis index of “multistage J/S” is proposed. The multistage J/S makes a detailed division between high-intensity jamming and normal communication, statistics the duration distribution of the receiving power of each communication node in the six communication receiving states, and calculates its proportion. As shown in Equation (17), $P_j^{t1}$ represents the time proportion of the $j$-th communication node in the first communication receiving state, and $T_j^{t1}$ is the duration of the $j$-th communication node in the first communication receiving state.

$$P_j^{t1}={\displaystyle \frac{{\displaystyle \sum _{j=1}^J{T}_j^{t1}}}{TJ}}$$

(17)

Figure 6 shows that the proportion of high-intensity jamming by CCBA is not less than 50%, and the proportion of normal signal reception by communication nodes is no more than 6%. Compared with the comparative algorithms, CCBA extends the system operation duration and appropriately reduces the proportion of high-intensity jamming, enabling flexible and effective jamming on the overall communication network.

The proposal of “overall limited jamming” reduces the restrictive conditions of communication jamming, providing space for the algorithm to flexibly adjust the jamming power. The electromagnetic environment estimation strategy, range gear strategy, environmental noise threshold strategy, power upper limit strategy for disconnected states, and limited random power scheduling strategy reduce the release of redundant power and extend the system operation duration.

4.4. Proposition, Proof and Analysis of Overall Limited Jamming

Proposition 1.

(Overall limited jamming improves the energy efficiency of jammer network).

For the non-spread spectrum communication system in this study, the overall limited jamming strategy can strictly improve the energy efficiency of the jammer network (i.e., ${\eta }_{CCBA}>{\eta }_{FPJA}$ and ${\eta }_{CCBA}>{\eta }_{ICCA}$) if the following two conditions are satisfied:

1. The minimum jamming target is achieved: the proportion of disturbed communication nodes ${\theta }_{CCBA}\ge {\theta }_{th}=R_j=0.8$;

2. The total transmit power of CCBA meets: $P_{CCBA}<{\theta }_{th}{P}_{\max }$ and $P_{CCBA}<{\displaystyle \frac{{\theta }_{CCBA}}{{\theta }_{ICCA}}}{P}_{ICCA}$.

Notation: $\eta ={\displaystyle \frac{\theta }{P_{total}}}$ is defined as the energy efficiency of the jammer network, representing the number of disturbed communication nodes per unit transmit power; $\theta$ is the proportion of disturbed communication nodes; $P_{total}$ is the total transmit power of the jammer network in one scheduling cycle.

Proof. 

$$

1. Comparison with FPJA:

According to the definition of energy efficiency, ${\eta }_{CCBA}={\displaystyle \frac{{\theta }_{CCBA}}{P_{CCBA}}}$.

Combining Condition 1 (${\theta }_{CCBA}\ge 0.8$) and Condition 2 ($P_{CCBA}<0.8P_{\max }$), we can derive:

$${\eta }_{CCBA}={\displaystyle \frac{{\theta }_{CCBA}}{P_{CCBA}}}>{\displaystyle \frac{0.8}{0.8P_{\max }}}={\displaystyle \frac{1}{P_{\max }}}={\eta }_{FPJA}$$

(18)

Thus, ${\eta }_{CCBA}>{\eta }_{FPJA}$ is strictly proven.

2. Comparison with ICCA:

Simulation results show that ICCA cannot stably meet the minimum jamming target in strong EMI environments, i.e., ${\theta }_{ICCA}<{\theta }_{th}\le {\theta }_{CCBA}$.

Combining Condition 2 ($P_{CCBA}<{\displaystyle \frac{{\theta }_{CCBA}}{{\theta }_{ICCA}}}{P}_{ICCA}$), rearranging the inequality gives

$${\displaystyle \frac{{\theta }_{CCBA}}{P_{CCBA}}}>{\displaystyle \frac{{\theta }_{ICCA}}{P_{ICCA}}}\Rightarrow {\eta }_{CCBA}>{\eta }_{ICCA}$$

(19)

□

The essential difference between the overall limited jamming strategy and traditional jamming strategies (FPJA, ICCA) lies in the jamming optimization goal and power allocation logic, which is the core reason for its higher energy efficiency. The specific comparative analysis is as follows:

FPJA takes the full suppression of all communication nodes as the only jamming goal, and all jammers operate at the maximum transmit power during the entire jamming process without considering power redundancy and actual jamming demand. This extreme jamming mode leads to two critical problems: first, a large amount of redundant power is consumed for the suppression of low-priority communication nodes, resulting in a sharp reduction in the effective operation duration of the jammer network; second, the fixed full-power mode cannot adapt to the dynamic adjustment of the communication party’s transmit power, and the jamming power cannot be flexibly adjusted according to the actual electromagnetic environment. In contrast, the overall limited jamming strategy abandons the blind pursuit of full-node suppression, and only requires the overall degradation of the communication network to meet the preset threshold ($R_j$ ≥ 0.8). It allows jammers to reduce transmit power for low-demand jamming nodes and avoid continuous high-power operation, which fundamentally eliminates the power redundancy of FPJA. Under the premise of achieving the actual tactical jamming goal, the strategy significantly reduces the total power consumption of the jammer network, and thus obtains a much higher energy efficiency than FPJA.

ICCA is a jamming resource scheduling algorithm designed for non-networked cooperative scenarios, whose core design idea is to optimize jamming target selection through distance-tier scheduling and adopt non-uniform power setting to achieve dynamic jamming in non-networked environments. However, inherent limitations in its design logic lead to insufficient energy efficiency: first, ICCA focuses on local jamming of individual communication nodes based on distance tiers, lacking a global jamming effect evaluation mechanism oriented to the overall network quality. It fails to form effective superposition of distributed jamming resources, making it difficult to balance the overall jamming effect and power consumption; second, ICCA’s power scheduling relies solely on local reconnaissance information of individual jammers, without considering the collaborative complementarity between distributed jammers. This independent decision-making mode easily leads to uneven power consumption of the jammer network and invalid power consumption caused by overlapping jamming coverage; third, ICCA adopts a relatively deterministic power scheduling strategy, which lacks flexible adjustment mechanisms based on dynamic changes in the electromagnetic environment and communication node states. It cannot adapt to the real-time adjustment of the communication party’s transmit power, resulting in unnecessary high-intensity jamming and wasted energy. In contrast, the overall limited jamming strategy takes the overall jamming effect of the network as the core constraint, and each jammer adjusts its transmit power based on the estimated electromagnetic environment and broadcast information of adjacent jammers, realizing collaborative allocation of distributed jamming resources. By strictly limiting the proportion of disturbed nodes and the J/S threshold, it avoids blind local jamming and invalid power consumption. While ensuring the achievement of the overall jamming target ($R_j$ ≥ 0.8), it realizes balanced power consumption of the jammer network. The flexible power allocation mechanism based on the overall goal enables the strategy to adapt to dynamic changes in the battlefield environment, and its energy efficiency is significantly higher than that of ICCA due to more rational power utilization and stronger collaborative scheduling capabilities.

In summary, the core theoretical innovation of the overall limited jamming strategy is that it reconstructs the jamming optimization goal of the distributed jammer network from “local node full suppression” (FPJA) or “local node tiered jamming” (ICCA) to “overall network quality degradation”, and establishes a flexible power allocation mechanism based on this goal. This theoretical design fundamentally solves the problems of serious power redundancy (FPJA) and insufficient global coordination and dynamic adaptability (ICCA) of traditional strategies, and thus achieves the improvement of energy efficiency and the extension of system operation duration under the premise of satisfying tactical jamming demand.

5. Conclusions and Future Prospects

This study is verified under the planar LOS scenario for the 600 MHz fixed-frequency and 1 MHz bandwidth communication system, and the concentric circle broadcasting strategy in Figure 2 is applicable to this scenario; the research on 3D NLOS scenario will be the key direction of our future work, including the design of 3D path loss model and airspace range gear division.

In the case of network blockage in a strong electromagnetic interference environment, CCBA coordinates jammers using the range gear strategy and concentric circle broadcasting strategy under the condition of uncertain decision-making order. It adopts the electromagnetic environment estimation strategy, limited random power scheduling strategy, and final power release strategy to meet the overall confrontation requirements. Based on the position-based environmental noise threshold strategy and the power upper limit strategy for disconnected states, CCBA eliminates redundant operations of random search.

Simulation experiments show that the evaluation index of overall limited jamming proposed in this paper, which takes the acceptable overall communication jamming effect as the optimization goal, is feasible and can adapt to the distributed communication jamming requirements in harsh environments. The proposed multistage J/S index enables more precise and reasonable analysis of jamming effects. The analysis of jammer residual power can evaluate the scheduling of heterogeneous jammers and the uniform power consumption. For the air–ground communication system, the CCBA extends the system operation duration by 66.8–269.6% compared with the traditional algorithms (ICCA, FPJA, MADJPA, SRSA) while maintaining effective jamming effects (the proportion of high-intensity jamming is not less than 50%), and realizes the balanced scheduling of jammer power with low communication overhead in the strong EMI environment.

In future research, more communication countermeasure means and mechanisms can be introduced to better simulate intense battlefield communication confrontations [38]. For example, the communication side can adopt frequency hopping strategies, intelligent reflecting surface antennas, mobile transfer of communication equipment, etc. [39]. The jamming side can introduce frequency hopping strategies, mobile transfer of aerial jammers, jamming pattern selection, etc. The environment can be set as complex terrains such as mountainous areas and urban areas.