ICCA: Independent Multi-Agent Algorithm for Distributed Jamming Scheduling

Abstract

In extreme scenarios, to prevent the leakage of jamming coordination information, the jammers must proactively terminate their communication functions and implement jamming resource scheduling via Non-Networked Cooperation. However, current research on this non-networked jamming approach is relatively limited. Furthermore, existing algorithms either rely on networked interactions or lack cognitive strategies for the surrounding communication countermeasure situation. For example, they fail to adapt to dynamic changes in electromagnetic noise and struggle to determine jamming effectiveness, leading to low jamming efficiency and severe energy waste in non-networked scenarios. To address this issue, this paper establishes a game process and corresponding algorithm for non-networked communication countermeasures and designs cognitive, cooperative, and scheduling strategies for individual jammers. Meanwhile, a novel performance metric called the “Overall Communication Suppression Ratio (OCSR)” is proposed. This metric quantifies the relationship between “sustained full-suppression duration” and “ operating duration of the jamming system,” overcoming the defect that traditional metrics cannot evaluate the dynamic jamming effectiveness in non-networked scenarios. Experimental results indicate that although the OCSR of the proposed Intelligent Concentric Circle Algorithm (ICCA) is significantly lower than that of the Full-Power Jamming Algorithm (FPJA), ICCA extends the operating duration of the jamming system by 4.8%. This achieves non-uniform power setting of jammers, enabling flexible and dynamic jamming in non-networked scenarios and retaining more battery capacity for jammers after overall jamming failure.

1. Introduction

Wireless communication is a critical factor in modern military operations. Communication jamming technology, which can disrupt the enemy’s command chain and expand one’s own advantages, has therefore attracted the attention and development of major military powers worldwide [1,2,3]. High-power jammers represent the traditional development direction of communication jamming, but the continuous increase in jamming power and equipment scale has led to a decline in their battlefield mobility and survivability. In contrast, distributed communication jammers, with their low power and low cost, have become a research hotspot and new development trend due to their characteristics of wide distribution area, flexible jamming, and strong concealment. Distributed jammers rely on communication networking to achieve jamming coordination. However, complex electromagnetic environmental noise in modern battlefields can disrupt the communication links between jammers, rendering network-dependent jamming scheduling algorithms unable to achieve coordination due to information interruption. Furthermore, there is relatively little research on resource scheduling and coordination strategies for non-networked jammers.

Existing resource scheduling research has mainly focused on radar jamming [4,5,6,7,8,9,10,11,12], but its mathematical models and scheduling strategies are not applicable to communication jamming. In the research of communication jamming, more attention has been paid to the problem of static resource scheduling. Some studies using traditional optimization algorithms with global search [13], convex optimization theory [14], various genetic algorithms [15,16,17], intelligent optimization algorithms [18,19,20], and knowledge-based Bayesian neural network algorithms [21] have made progress. The rapidly developing machine learning technology has contributed to the algorithm research of communication countermeasures [22,23,24,25]. However, the difficulty in obtaining communication countermeasure datasets has limited the application of deep learning technology [26]. The above studies generally assume that all information of the communication parties is fully known and remains unchanged for a long time, without considering issues such as the usage timing of multiple jammers, resulting in poor applicability in dynamic communication countermeasure processes. Compared with traditional resource scheduling methods based on intelligent optimization algorithms, the proposed method in this paper adds jamming effectiveness evaluation and coordination strategies for non-networked scenarios. In contrast to traditional convex optimization-based methods, the proposed algorithm features a simple mathematical principle and is more suitable for scenarios with multiple distributed communication jammers. Compared with traditional deep learning-based methods, the method in this paper does not rely on pre-acquired communication party datasets, nor does it require tedious long-term adjustment and training processes of deep learning models.

Reinforcement learning algorithms can interact with the environment autonomously without prior information to learn the optimal strategies. Therefore, reinforcement learning technology has been widely used in dynamic resource scheduling [27,28,29,30,31,32,33,34], but most of them assume that the jammers can directly obtain the jamming effects. In reality, first, the implementation approaches (such as jamming index estimation and communication quality cognition) are ignored; second, the anti-jamming power and channel adjustment strategies of the communicating parties are not considered [35,36].

To address these issues, some scholars, based on the judgment principles of communication jamming, have modeled the communication countermeasure process as an MDP (Markov Decision Process) and proposed corresponding jamming methods [37]. They have taken channel alignment as an evaluation index for effective jamming [38] and used the Q-learning algorithm [39] to predict the changes in communication channels. They have also formulated jamming effectiveness measurement indicators by integrating the basic principles of jamming and the behavioral changes of communication targets [40].

However, there are still deficiencies in the evaluation of jamming effects. Firstly, The above strategies are established on the basis that jammers can normally detect and identify all communication information, without considering the masking interference of electromagnetic environmental noise. Secondly, they are based on mutually independent and deterministic two-way communication links, which is not applicable to complex communication networks. Thirdly, they rely on the search strategies of algorithms and fail to fully utilize the positional information of both communication and jamming parties as well as the roles of electromagnetic propagation characteristics.

The optimization objectives of most of the research content are the physical layer parameters such as the jamming styles and power of a single jammer, and there is very little research involving the scheduling of distributed jamming resources. References [41,42,43,44,45] have studied a small number of high-power and long-distance communication jammers deployed on the ground and adopted technologies such as multi-agent reinforcement learning and hierarchical reinforcement learning. Reference [46] has designed a proximal policy optimization algorithm to solve the problem of scheduling jamming resources when a small number of jammers are in the air and in a moving state. The above algorithms have shown good performance in small-scale scenarios.

The majority of prior works operate under the assumption of interconnected jammer networks, with minimal literature addressing autonomous coordination in non-networked scenarios involving standalone jamming units. Reference [47] proposed a cooperative jamming strategy based on self-confidence. Under the constraint of self-confidence, jamming cooperation is achieved at the cost of more interaction times, but the limited power of jammers is not considered. Reference [27] introduced a multi-agent reinforcement learning algorithm with centralized training and distributed decision-making. However, in a complex electromagnetic environment, the large environmental noise makes it impossible for jammers to identify all signals, thus it is difficult to meet the actual requirements of overall communication countermeasures. Compared with traditional reinforcement learning-based methods, the proposed method can obtain feasible solutions in a short time. It does not need to design reward functions according to scenarios, nor does it require long training time or a large number of interactions with the environment, making it more suitable for non-networked jammers with limited battery capacity.

Facing severe electromagnetic jamming in wireless communications, deep reinforcement learning (DRL) and multi-agent reinforcement learning (MARL) have become core frameworks for recent anti-jamming research, with notable advances in single/multi-user scenarios. For single-user frequency hopping (FH) systems, Li et al. proposed a Markov decision process (MDP) model with frequency-power action space and a dual-action network DRL algorithm, which considered energy and switching overhead and was validated in simulations and field tests [48]. To address insufficient exploration of traditional DRL in multi-user scenarios with external jamming and internal co-interference, Jing et al. established a Markov game model, discretized the soft actor-critic (SAC) algorithm, and extended it to the multi-agent discrete SAC (MA-DSAC) algorithm under the centralized training with decentralized execution (CTDE) framework, achieving over 25% performance improvement and reducing system instability [49]. For moving reactive jammers with hybrid modes, Li et al. designed a parallelized DRL strategy that decomposed action spaces and accelerated convergence, realizing nearly 90% normalized throughput gain while balancing concealment and anti-jamming [50].

Scenario-specific anti-jamming solutions have made breakthroughs in aerial networks and communication-computing integration. For multi-hop aerial networks, Ma et al. formulated a joint anti-jamming problem, constructed a decentralized partially observable Markov decision process (Dec-POMDP) model, and proposed a graph convolutional MARL algorithm with jammer adversarial pre-training and information temporal smoothing (ITS) mechanism, showing superior transmission success ratio and energy efficiency [51]. For unmanned aerial vehicle (UAV)-enabled semantic communication-mobile edge computing (MEC) integration under jamming, Liu et al. proposed a DRL algorithm optimizing UAV trajectories, user associations and channels, which captured jammer behavior and mitigated impacts on task offloading [52]. For multi-user spectrum sharing, Li et al. proposed the local knowledge diffusion and differential weighted fusion mechanisms (LKD-DWF-M) distributed strategy for low-overhead collaboration; theoretical analysis confirmed Nash equilibrium and convergence, and simulations showed significant throughput improvement under statistical jamming (SJ), dynamic sweeping jamming (DSJ) and intelligent comb jamming (ICJ) [53]. The aforementioned anti-jamming resource scheduling algorithms based on machine learning rely on known jammer information and long-term training time, belonging to the autonomous and intelligent anti-jamming adjustment behaviors of communication devices. However, in battlefield environments, a large number of communication devices are operated by personnel, which is prone to numerous unexplainable or irrational behaviors. To construct a simple and feasible jamming target for communication jamming algorithms, it is necessary to design a new communication party behavior simulation algorithm.

The wireless links of the air–ground communication network system are complex, and it has a strong self-organizing and adaptive ability. There are a large number of both communicating and jamming parties, and the jamming parties need to exert dynamic jamming on all communication receiving nodes. Prior art assumes networked topologies, consequently lacking real-time scheduling mechanisms for standalone jammers operating in geometrically sparse, dimensionally complex battlespaces with imperfect situational data because:

• In the face of unknown and dynamic communication power scheduling strategies, reinforcement learning-based algorithms have a long training time and require a large number of interactions. This delays the overall time to achieve jamming and consumes a large amount of energy.
• There is a lack of specific strategies for non-networked distributed jammers to perceive the environment using reconnaissance information and determine the jamming effects.
• There is a lack of applicable mathematical models and strategies, and there is insufficient research on issues such as the superposition, coordination, and usage order of jamming power.

In summary, the contributions of this paper are as follows:

• Based on the detected and prior location information, cognitive and power scheduling strategies for non-networked jammers are designed.
• Considering the requirements of high-speed and overall countermeasures, a deterministic strategy with strong robustness is adopted.
• The OCSR is defined as the normalized temporal ratio between the total sustained full-suppression jamming duration and the partial effectiveness periods (i.e., periods where communication quality degrades above a threshold but remains detectable).
• A simulation experiment for distributed communication countermeasures in a complex electromagnetic environment is designed and solved, and the problem of the indeterminate decision-making order of jammers is identified.

By virtue of the above contributions, this paper further focuses on addressing practical battlefield challenges: aiming at the three key challenges of non-networked distributed jamming—“incomplete information, long training time, and energy waste”—it designs a non-network-dependent jamming scheduling algorithm with low latency and high endurance. Meanwhile, a jamming effectiveness evaluation index suitable for dynamic scenarios is proposed, ultimately addressing the practicality issues of traditional methods in battlefield environments.

2. Communication Countermeasure Mode

The air–ground communication network system has self-organizing and encryption functions. It is difficult for the jamming side to obtain the transmitting and receiving ends of the communication link through reconnaissance. Therefore, it is necessary to apply jamming to the maximum receiving power of communication nodes. In a complex electromagnetic environment, a single jammer has limited information and cannot receive overall feedback for decision-making, which makes cooperation difficult, as shown in Figure 1.

2.1. Mathematical Model of the Air–Ground Communication Network System

In the air–ground communication scenario, the path loss between airborne devices and between airborne and ground devices is line-of-sight propagation, while the path loss between ground devices is two-ray propagation.

In Equation (1), $P_c^t$ is the transmission power of the communication signal, $P_c^r$ is the received power of the communication signal, and the unit of both is dBW. ${\mathrm{G}}_{\mathrm{tc}}$ is the antenna gain of the communication transmitting antenna in the direction of the communication receiving antenna, ${\mathrm{G}}_{\mathrm{rc}}$ is the antenna gain of the communication receiving antenna in the direction of the communication transmitting antenna, $L_c$ is the path loss of the communication transmission, ${\mathrm{L}}_{\mathrm{pc}}$ is the attenuation of the cable and cable head at the communication receiving end, and the unit of all of them is dB.

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

(1)

The received power of the communicating party’s receiving end needs to meet the communication link margin, and the environmental noise power needs to be taken into account. In Equation (2), $RS$ is the receiving sensitivity of the communication device, ${\sigma }^2$ represents the environmental noise power, and $SFM$ is the System Fade Margin.

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

(2)

When the communication device transmits a signal, it selects the path with the minimum transmission loss and uses the lowest power that meets the communication requirements. In Equation (3), $P_{cj}^{t\min }$ is the lowest transmitting power of the $j$-th communication device, $L_{c{j}^{\prime }}$ is the path loss of the communication transmission with the remaining devices, and the total number of communication devices is $\mathrm{J}$.

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

(3)

2.2. Mathematical Model of Air–Ground Joint Communication Jamming

2.2.1. Quantized Jammer-to-Signal Ratio

$$k_{jb}={\displaystyle \frac{P_j^n+{\displaystyle \sum _{i=1}^{\mathrm{I}}{P}_j^{in}}}{P_j^{rmax}}}$$

(4)

In Equation (4), the ratio of the sum of the airborne jammer, ground jammer, and electromagnetic environmental noise to the maximum power in the received signal of the communication device is $k_{jb}$. Among them, $P_j^{in}$ is the jamming signal released by the $i$-th jammer and received by the $j$-th communication device, where the $i$-th jammer is an airborne or ground jammer; $P^{jn}$ is the environmental noise at the $j$-th communication device; and $P_j^{\max r}$ is the actual maximum communication signal power received by the $j$-th communication device.

In Equation (5), if the power ratio of the interference signal to the communication received signal is not less than the jamming-to-signal ratio $k_j$, it is considered that the interference is successful, that is, the quantized jamming-to-signal ratio $JS{R}_j$ of the $j$-th communication device is 1.

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

(5)

2.2.2. Restriction Conditions

Under non-networked cooperation, it is necessary to impose interference on the received signals of communication devices to reduce their communication quality. As shown in Equation (6), where $JS{R}_j$ is the quantized jammer-to-signal ratio of the $j$-th communication device, and $J$ is the total number of communication devices, and $R_j$ is the proportion of communication nodes that are disturbed. If the constraints are satisfied, the equation holds; otherwise, it does not hold.

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

(6)

2.2.3. System Operating Duration

When the jamming system is operating, if the overall communication jamming cannot be achieved, it is considered that the operating duration of the jamming system ends at this time. The operating duration $T$ of the jamming system is the sum of the operating duration $T_{iq}$ of the jamming system in a single scheduling.

In Equation (7), after the $i$-th jammer undergoes the $q$-th scheduling, $T_{iq}$ is its operating duration this time, with the unit of hour (H). ${\mathsf{\eta }}_{\mathrm{s}}$ is the battery power limit required for normal jamming, ${\mathrm{U}}_{\mathrm{out}}$ is the battery operating voltage, with the unit of volt (V), ${\mathrm{E}}_{\mathrm{esq}}$ is the battery power consumed in this scheduling, with the unit of ampere-hour (AH), $P_i$ is the jamming output power of the $i$-th jammer, and ${\mathrm{P}}_{\mathrm{x}}$ is the power consumed by the jammer to maintain other functions, with the unit of watt (W).

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

(7)

2.2.4. Overall Communication Suppression Ratio

In non-networked jammer scenarios, achieving the overall jamming target (i.e., successfully applying power-suppressive jamming to the received power of all communication nodes) is relatively challenging. Consequently, traditional jamming effectiveness indicators (such as “jamming success rate”) cannot be simply used to determine “whether suppression is achieved”. In addition, traditional indicators have two shortcomings: first, they fail to reflect “suppression continuity” and “partial failure states” (e.g., degraded communication quality without complete interruption) in dynamic scenarios. However, “sustained suppression” is more critical than “instantaneous suppression” on the battlefield (for instance, the enemy’s communication can quickly recover after a brief interruption); second, they cannot reflect the proportion of “overall complete jamming” in the “operating duration of the jamming system”, that is, on the basis of meeting basic jamming requirements, measuring the achievement rate of overall effective jamming from the perspective of duration.

In the dynamic communication countermeasure game process, the overall communication suppression ratio is defined as the ratio of total interference duration to operating duration of the jamming system $T$, which is used to evaluate communication jamming effectiveness. In Equation (8), $R_{total}$ is the overall communication suppression ratio, and $T_{total}$ is total interference duration.

$$R_{total}={\displaystyle \frac{T_{total}}{T}}$$

(8)

If OCSR = 1, meaning jamming fully covers the period of quality degradation, this is defined as “ideal suppression”, but it also consumes more battery power of the jammer; if OCSR < 1, indicating gaps in jamming, scheduling optimization is required. This indicator not only covers “overall complete jamming” but also includes “partial failure states”, making it more in line with the actual needs of dynamic jamming on the battlefield.

Communication nodes with different JSR exhibit varying degrees of susceptibility to different types of communication signals. In the scenario of non-networked communication jamming, the minimum JSR for all communication nodes needs to be set to prevent individual nodes from maintaining normal bidirectional communication with the outside world. In Equation (9), if the power ratio of the interference signal to the communication received signal is not less than the jamming-to-signal ratio $k_{j2}$, it is considered that the interference achieves a low degree of success, that is, the quantized jamming-to-signal ratio $JS{R}_{j2}$ of the $j$-th communication device is 1.

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

(9)

The air–ground communication network system has anti-jamming measures such as multi-hop forwarding, and the jamming party needs to exert effective jamming on the received signals of all communication devices. As shown in Equation (9), where $JS{R}_{j2}$ is the quantized jammer-to-signal ratio of the $j$-th communication device, and $J$ is the total number of communication devices. If the constraints are satisfied, the equation holds; otherwise, it does not hold.

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

(10)

2.2.5. Configurable Range Gradation

In non-networked operations, individual jammers require configurable range gradation with multiple preset tiers. Using estimation strategies, these systems autonomously target communication nodes within designated ranges.

$$d_j^{\min }=\min (\sqrt{{(x_i-x_j)}^2+{(y_i-y_j)}^2+{(z_i-z_j)}^2}),i\in (1,I)$$

(11)

In Equation (11), the minimum spacing represents the shortest distance between a jammer and its nearest communication node.

Communication links between heterogeneous antennas (transmitter/receiver vs. jammer) exhibit differential link gains. For each gain category, non-uniform graduated reference distances must be established.

Based on the shortest distance between the integrated jammer and communication nodes as well as the reference distance, the range tiers for each type of link gain are set empirically, where Tier 1 represents the lowest tier and Tier X represents the highest tier. The number of range tiers needs to balance the relationship between the time consumption and effectiveness of non-networked collaborative scheduling of jammers.

2.3. Strategies of the Air–Ground Communication Party

The initial power allocation of communication nodes must balance “energy consumption” and “communication quality”. If a high-loss link is selected, higher transmission power is required, which will accelerate energy consumption and expose electromagnetic signals. Therefore, Algorithm 1 is designed to enable nodes to maintain communication with the minimum power (meeting the link margin of 12 dB, as shown in

Table 1. Statistics of the Number of Communication Nodes and Jammers in Simulation Scenarios.

	Scenario 1	Scenario 2	Scenario 3
Airborne Communication Nodes	10	10	15
Ground Communication Nodes	20	20	20
Ground jammers	8	26	32
Airborne jammer	24	4	12

). This strategy not only aligns with the battlefield requirements of “low exposure and long endurance” but also provides a benchmark for the subsequent “on-demand power scheduling” of the jamming party. The initial communication power allocation method for the air–ground network system is shown in Algorithm 1 ($j$ is the serial number of the communication device, $i$ is the serial number of the jammer).

Algorithm 1 The Initial Communication Power Allocation Method
Input: Communication Party Information
Output: New Communication Party Information
1:	Select $P_{cj}^t$ in order, for $j$= 1 to $J$
2:	Search for $j$ with $L_{c\min }$ as the receiving node (Iterate through all communication links with $j$ as the receiving end, aiming to filter out the link with the minimum transmission loss and avoid initial power redundancy caused by improper link selection)
3:	Estimate $P_{cj}^{t\min }$
4:	Select $P_{cj}^r$ in order, for $j$= 1 to $J$:
5:	Select $P_{c{j}^{\prime }}^t$ in order, for $j^{\prime }$= 1 to $J$:
6:	If $j\ne j^{\prime }$, or $P_{c{j}^{\prime }}^t\ne 0$:
7:	Estimate $P_{cj}^r$
8:	If $P_{cj}^r>P_{cj}^{rold}$:
9:	$P_{cj}^{rold}=P_{cj}^r$
10:	End if
11:	End if
12:	Select $P_{cj}^t$ in order, for $j$= 1 to $J$
13:	If $P_{cj}^{r\max }$ do not meet the demand for receiving signals:
14:	Search for $j^{\prime }$ with $L_{c\min }$ as the transmitting node
15:	Estimate $P_{c{j}^{\prime }}^t$
16:	If $P_{c{j}^{\prime }}^t>P_{c{j}^{\prime }}^{told}$:
17:	$P_{c{j}^{\prime }}^{told}=P_{c{j}^{\prime }}^t$
18:	End if
19:	End if

In Algorithm 1, each communication node is instructed to select the link with the minimum transmission path loss. Through the traversal calculation of the transmitting end and the receiving end, the initial transmitting power of the communication nodes is set.

After the overall communication jamming is achieved, the receiving power of all communication nodes is suppressed. Based on the current communication power, the communicating party adjusts the transmitting power in a roulette wheel selection manner. It can increase the transmitting power to counteract the communication jamming, stop transmitting to avoid the jamming, or reduce the transmitting power and maintain the status quo to confuse the jamming party, as shown in Algorithm 2 ($P_c^{t\lim it}$ is the upper limit of the transmitting power of the communication node, $P_{cj}^{t-ini}$ is the initial transmitting power).

Algorithm 2: Communication Power Scheduling Method for Countering Interference
Input: Communication Party Information
Output: New Communication Party Information
1:	Select $P_{cj}^t$ in order, for $j$= 1 to $J$
2:	If $P_{cj}^t$= 0:
3:	Adjust the transmitting state in a roulette wheel manner to be, lower than, higher than $P_{cj}^{t-ini}$, and no transmission
4:	End if
5:	If $P_{cj}^t\ne$ and $P_c^{t\lim it}$:
6:	Adjust the transmitting state in a roulette wheel selection method to reduce, increase, maintain $P_{cj}^t$, and stop transmitting
7:	End if
8:	If $P_{cj}^t=P_c^{t\lim it}$:
9:	$P_{cj}^t$= random($P_{cj}^t$, 0)
10:	End if

2.4. Strategies of the Air–Ground Jamming Party

As an independent intelligent agent, a single jammer estimates the states of surrounding communication nodes and jammers based on the prior information of the communication countermeasure location and the detected signal information, as shown in Algorithm 3. In this scenario, assuming all communication nodes operate at their maximum transmit power, the maximum received power at the communication node is defined as the theoretical maximum received power $P_j^{r\max }$. The environmental noise at the jammer $i$ is $P^{in}$.

Algorithm 3 Estimation Strategy of the Surrounding Electromagnetic Environment
Input: The layout of communication countermeasures and the information of the electromagnetic environment detected
Output: Estimated communication and jamming information
1:	If the $i$ detects the source azimuth and power of the signal from the $j$:
2:	Select $j^{\prime }$ in order, for $j^{\prime }$= 1 to $J$
3:	Compare $j^{\prime }$ and $j$, and infer the information and distance of $j$
4:	Estimate $P_{cj}^t$ or $P_{ji}^t$
5:	End if
6:	If $P_i^r$ contains only one communication signal:
7:	If $d_{ji}\le$ Tier 1:
8:	$P_j^r=P_j^{r\max }$
9:	End if
10:	End if
11:	Select $i$ in order, (signals within the Tier x and have not been detected)
12:	If $d_{ji}\le$ Tier 2:
13:	Set $P_j^{r\max }$ as the receiving power.
14:	End if
15:	If $d_{ji}\le$ Tier 3:
16:	Take $P^{in}$ as the received power, and estimate $P_i^t$
17:	End if
18:	Select $j$ in order, for $j$= 1 to $J$
19:	Update $P_c^{r\max }$

After a single jammer completes the environmental awareness, it independently conducts power scheduling, as shown in Algorithm 4. $P_j^{n-cri}$ is the critical value of the environmental noise, $P_{jsum}^n$ is the total power of the jamming signals received by $j$, $P_i^n$ is the jamming power requirement of $i$.

Algorithm 4: Independent Scheduling Strategy of Jamming Power
Input: Estimated communication information and real-time information of the interfering party
Output: Jammer Power Setting
1:	Select $j$ in order, for $j$= 1 to $J$
2:	Select $i^{\prime }$ in order, for $i^{\prime }$= 1 to $I$
3:	If $i\ne i^{\prime }$ and $P_j^{rc}\le P_j^{n-cri}$, $d_{ji}\le$ Tier x:
4:	Calculate $P_{jsum}^n$
5:	$P_j^n=P_c^r{k}_j-{\sigma }^2-P_{jsum}^n$
6:	End if
7:	Estimate $P_i^n$
8:	$P_{i\max }^n=\min (P_i^n,P_i^{\max })$, update
9:	If the battery power cannot guarantee $P_{i\max }^n$:
10:	Set the jamming power based on the current battery level
11:	Else:
12:	Set it as $P_{i\max }^n$

In Figure 2, in the non-networked state of the jammer, for the surrounding communication nodes, multiple ranges for selecting jamming targets are preset based on location information. After the communication network undergoes adaptive adjustment, a single jammer, based on part of the information it has detected through reconnaissance, selects communication targets and applies jamming at certain time intervals according to the jamming ranges from near to far. During this process, it will identify adjacent jamming information to assist the decision-making of a single jammer. In the non-networked scenario, the jammers cannot be synchronized and will be scheduled in a chaotic order. The ICCA and the communication countermeasure environment are as shown in Figure 3.

During the execution of ICCA, the communication nodes will be traversed first, and then the jammers will be traversed. Therefore, its time complexity is $O(n^2)$, where $n$ denotes the problem size.

The interference party information in ICCA employs real-number encoding, which can represent continuous real values, thereby reducing encoding conversion errors when scheduling interference resources. The ICCA adopts lightweight data structures to adapt to the low-latency requirement of non-networked scenarios: (1) Arrays are used to store communication node and jammer IDs for linear traversal, ensuring a time complexity of $O(n^2)$; (2) Structs encapsulate multi-dimensional state information (e.g., communication node type, coordinates, transmit power) for efficient data transmission during local decision-making; (3) Key-value pairs map scenario IDs to tier thresholds (Scenario 1: 3, Scenario 2: 2, Scenario 3: 5) to enable fast parameter lookup. All data structures are designed to minimize computational overhead, aligning with the core objective of ‘real-time scheduling for distributed jammers’.

3. Simulation Experiment

3.1. Parameter Setting of the Simulation Scenario

All simulations were conducted on a hardware platform equipped with an Intel(R) Core(TM) i5-8300H CPU @ 2.30 GHz, 16.0 GB of RAM, and an NVIDIA GTX 1080Ti graphics card. The software environment was built on Anaconda 23.7.4, with Python code implemented using PyCharm 2023.2.1 (Professional Edition) as the integrated development environment (IDE) and runtime version 17.0.8 + 7-b1000.8 amd64. The core third-party libraries utilized for the experiments included anaconda_depends_2023.09 and PyTorch 1.13.1, which provided reliable support for algorithm operation and data processing.

In the face of a complex electromagnetic environment, the communication party will raise the antenna to improve the communication quality. This paper adopts three simulation scenarios, where the ground height is uniformly set to 0, as shown in Figure 4, Figure 5 and Figure 6. The statistics of the number of communication nodes and jammers in each scenario are shown in Table 1. The static jammer layout used in the simulation experiment is based on the premise that the jamming target can be achieved with full-power jamming.

The parameters of the simulation experiment are shown in

Table 2. Table of Simulation Scenario Parameter Settings.

Project	Parameter
Maximum transmitting power of airborne communication equipment	10 dBW
Antenna gain of airborne communication equipment	2 dBi
Height of airborne communication equipment	2000–3000 m
Maximum transmitting power of ground communication equipment	13.98 dBW
Antenna gain of ground communication equipment	2.5 dBi
Height of ground communication equipment	10 m
Communication frequency band	600 MHz
Receiving sensitivity of communication equipment	−133 dBW
Communication link margin	12 dB
Ambient electromagnetic noise	−95–−115 dBW
Antenna gain of jammers	2 dBi
Maximum jamming power of airborne jammers	13 dBW
Height of airborne jammers	300–2000 m
Maximum jamming power of ground jammers	16 dBW
Height of ground jammers	3 m
Planar area of the simulation scenario	50 km × 50 km
Attenuation of cables and cable connectors at the communication receiving end	1 dB
Environmental factor for line-of-sight propagation	3
Environmental factor for two-ray propagation	3
The jamming-to-signal ratio when the communication quality deteriorates $k_{j2}$	1.76 dB [16]
The jamming-to-signal ratio for communication interference suppression $k_j$	4.77 dB [54]
Maximum battery power limit required for normal jamming	0.95
Operating voltage of jammer batteries	24 V
Battery capacity of airborne jammers	12 AH
Battery capacity of ground jammers	20 AH
Energy consumption of other functions of jammers	4 W
Minimum distance between jammers and communication equipment	500 m
Time limit for the first decision of intelligent optimization algorithms	10 s
Time limit for non-first interference decision	1 s
Communication state adjustment interval	90 s
Angle Recognition Accuracy of Communication Nodes	0.3 degrees
Tier X in scenario 1	3
Tier X in scenario 2	2
Tier X in scenario 3	5
The proportion of communication nodes that are disturbed $R_j$	0.9
The minimum distance between jammers and communication nodes [27]	500 m
The flexible update coefficient of MADJPA [27]	0.01
The number of training episodes of MADJPA [27]	5000
The number of interactions per episode of MADJPA [27]	500
The capacity of the experience replay buffer of MADJPA [27]	217
The discount factor of MADJPA [27]	0.98
The initial value of the entropy coefficient of MADJPA [27]	1
Fixed random number seed for Scenario 1 of MADJPA	36
Fixed random number seed for Scenario 2 of MADJPA	46
Fixed random number seed for Scenario 3 of MADJPA	40
The commit hash of the ICCA code	4a4c29994211a1 e2109bad2f2a75 a9f670634164
Fixed random number seed for Scenario 1 of ICCA	36
Fixed random number seed for Scenario 2 of ICCA	46
Fixed random number seed for Scenario 3 of ICCA	40
Random number generation module	NumPy’s numpy.random submodule
Threshold for airborne jammers targeting air–ground communication objectives	[2.8, 5.2, 7.8, 10.4, 15, 20] km
Threshold for ground jammers targeting ground communication objectives	[1.7, 3, 4.5, 6, 10, 16] km
Threshold for ground jammers targeting airborne communication objectives	[3.1, 6.2, 9.3, 12.4, 15, 20] km
Tier X in scenario 1 of ICCA	3
Tier X in scenario 2 of ICCA	2
Tier X in scenario 3 of ICCA	5

.

3.2. Results and Analysis of the Comparative Experiment

In this paper, the ICCA is compared with FPJA (Full-Power Jamming Algorithm), MADJPA (Multi-Agent Distributive Jamming Power Allocation) [27], SRSA (Simple Random Search Algorithm) and GA (Greedy Algorithm). MADJPA schedules ground distributed jamming resources, and its scenario is relatively similar to that of this paper, so it is used as a comparison algorithm. All algorithms are run 30 times independently, with the experimental results reported as the mean value plus/minus the 95% confidence interval.

In

Table 3. Comparison of the Algorithm Results.

	Algorithm	ICCA	FPJA	MADJPA	SRSA	GA
Indicator
Scenario 1	Training time (95% CI)	None	None	1.67 ± 0.44 s	None	None
	Time for each decision (95% CI)	64.2 ± 9.8 ms	10.2 ± 1.4 ms	40.3 ± 14 ms	None	None
	Operation duration of system (95% CI)	11.6 ± 0.7 h	10.4 ± 0 h	0.02 ± 0.02 h	None	None
	OCSR (95% CI)	0.16 ± 0.12	1 ± 0	0.92 ± 0.27	None	None
Scenario 2	Training time (95% CI)	None	None	1.73 ± 0.35 s	None	None
	Time for each decision (95% CI)	92.2 ± 11.2 ms	8.8 ± 1.6 ms	None	None	None
	Operation duration of system (95% CI)	11.1 ± 0.4 h	10.4 ± 0 h	None	None	None
	OCSR (95% CI)	0 ± 0.04	1 ± 0	None	None	None
Scenario 3	Training time (95% CI)	None	None	1.79 ± 0.31 s	None	None
	Time for each decision (95% CI)	112.6 ± 13.5 ms	9.71 ± 1.8 ms	None	None	None
	Operation duration of system (95% CI)	10.9 ± 0.4 h	10.4 ± 0 h	None	None	None
	OCSR (95% CI)	0.05 ± 0.03	1 ± 0	None	None	None

The bold text in the table indicates the comparative data of the algorithms.

, the comparison of the initial decision-making time reflects the advantages of the algorithm in this paper, such as a high solution rate and no need for training. “Time for each decision” refers to the time required for the jamming party to complete resource scheduling after the power of communication nodes in the air–ground communication network changes, which includes some communication nodes stopping transmission and some starting transmission. The variation in the system’s operating duration indicates that the scheduling of dynamically adjusted jammers is dependent on the static layout of the jammer deployment. The subdued overall communication suppression ratio demonstrates ICCA’s power-conservation approach to jamming.

In the non-networked scenario studied in this paper, individual jammers independently impose jamming on communication nodes based on reconnaissance information while minimizing jamming power consumption as much as possible. If the greedy myopic algorithm is adopted, each jammer only considers its own operating duration and lacks non-networked coordination with other jammers. This results in the total number of jammed communication nodes failing to meet the constraint requirements, thereby directly leading to jamming failure.

In Figure 7, the system operating duration of the algorithm in this paper is 4.8% longer than that of the compared algorithms. The experimental results show that the algorithm in this paper can complete the scheduling of jamming resources quickly and efficiently.

When the jammers are not networked, a single jammer cannot obtain the true feedback of the overall jamming effect and thus cannot optimize the search for the solution based on this. The compared algorithms lack the cognition, scheduling, and non-networked coordination strategies for independent jammers, making it difficult to meet the requirements of overall communication countermeasures. The complex air–ground confrontation layout and electromagnetic environment make it difficult for a single jammer to infer global information from the incomplete local information it has detected, leading to the failure of the MADJPA algorithm.

Non-networked distributed jamming aims to disrupt the enemy’s communication command chain rather than achieving “continuous full suppression” (which is the premise of OCSR = 1 for FPJA). The OCSR metric quantifies the ratio of “sustained full-suppression duration” to “system operating duration” (Equation (8) revised). For ICCA, the low OCSR values (0.16 in Scenario 1 and 0 in Scenario 2) do not indicate “ineffective jamming”—instead, they reflect its core design philosophy:

ICCA adopts non-uniform power scheduling (Algorithm 4) to dynamically adjust jamming intensity based on target distance tiers. It prioritizes maintaining “low-intensity suppression” for all communication nodes (meeting Equation (9) with JSR ≥ 1.76 dB) rather than pursuing “full suppression” (JSR ≥ 4.77 dB) at the cost of excessive energy consumption.

In battlefield scenarios, “low-intensity suppression” is sufficient to hinder the enemy’s communication signal recognition and command transmission (as verified by engineering practice in Section 2.2.5), which constitutes the “jamming effectiveness” claimed in the paper. FPJA achieves OCSR = 1 by adopting full-power continuous jamming, but this leads to rapid energy depletion and zero residual battery capacity after jamming failure (

Table 4. Comparison of Remaining Power Status of Communication Jammers.

	Algorithm	ICCA	FPJA
Indicator
Scenario 1	Ground jammer max	14 AH	0 AH
	Ground jammer mean	5.37 ± 3.67 AH	0 ± 0 AH
	Ground jammer failure ratio	0.18	1
	Air jammer max	4.55 AH	1.16 AH
	Air jammer mean	1.19 ± 1.27 AH	1.16 ± 0 AH
	Air jammer failure ratio	0.1	0
Scenario 2	Ground jammer max	15.89 AH	0 AH
	Ground jammer mean	6.6 ± 6.3 AH	0 ± 0 AH
	Ground jammer failure ratio	0.16	1
	Air jammer max	9.83 AH	1.16 AH
	Air jammer mean	6.6 ± 4.9 AH	1.16 ± 0 AH
	Air jammer failure ratio	0	0
Scenario 3	Ground jammer max	17.8 AH	0 AH
	Ground jammer mean	5.5 ± 4.9 AH	0 ± 0 AH
	Ground jammer failure ratio	0.15	1
	Air jammer max	5.2 AH	1.16 AH
	Air jammer mean	1.1 ± 1.2 AH	1.16 ± 0 AH
	Air jammer failure ratio	0	0

The bold text in the table indicates the comparative data of the algorithms.

), making it unsuitable for long-duration battlefield missions.

Both ICCA and FPJA can sustain jamming operations in non-networked scenarios. Post-jamming-failure, their residual energy levels are compared. The jammer failure ratio is defined as the proportion of depleted jammers.

In Table 3, ICCA demonstrates more balanced energy consumption than FPJA across both aerial and ground jammers, while maintaining higher residual energy reserves. In battlefield applications, this non-uniform power allocation strategy enhances operational flexibility and survivability compared to full-power jamming approaches.

Figure 8, Figure 9 and Figure 10 are the heatmaps of the transmit power of communication nodes in three simulation scenarios during a single run of the ICCA. The abscissa represents the serial number of communication nodes, and the ordinate denotes the number of adjustment intervals of the interferer. The first interval corresponds to the transmit power of communication nodes under the action of Algorithm 1, while the others correspond to that under the action of Algorithm 2. It can be observed that Algorithm 1 enables communication nodes to maintain bidirectional communication with the minimum transmit power; Algorithm 2 allows communication nodes to adjust their transmit power irregularly after being interfered.

Figure 11, Figure 12 and Figure 13 are the heatmaps of the JSR of communication nodes in three simulation scenarios during a single run of the ICCA. The abscissa represents the serial number of communication nodes, and the ordinate denotes the number of adjustment intervals of the interferer. It can be observed that the JSR distribution of each communication node varies with location and time, but it can satisfy the scenario constraint that a certain proportion of communication nodes are under high-intensity interference and all communication nodes are under low-intensity interference at the same time. In the simulation experiment, after the communication party makes a single adjustment, the interferer, under the decision-making of the ICCA, updates or maintains the jamming power of each individual jammer in a random-order and non-networked manner. The JSR at each communication node is output and recorded in real time by the relevant program in the simulation scenario.

Figure 14, Figure 15 and Figure 16 are the line charts of the average JSR of communication nodes in three simulation scenarios during a single run of the ICCA. The abscissa represents the number of adjustment intervals of the interferer, and the ordinate denotes the average JSR of all communication nodes. It can be observed that on the basis of meeting a relatively high intensity of communication JSR, the JSR under each adjustment interval of the interferer exhibits significant fluctuations, which is a combined result of the communication party’s power adjustment strategy and the ICCA.

4. Conclusions and Future Prospects

The algorithm proposed in this paper coordinates distributed jammers via distance-interval-based decision-making in non-networked, complex electromagnetic environments, even when the jammer decision-making sequence is uncertain. It adopts a reliable communication state estimation strategy to meet the overall countermeasure requirements. Power scheduling based on the deterministic strategy of location information eliminates the redundant operations of random search and the inefficient training links of reinforcement learning. This paper proposes an interference effectiveness analysis metric, namely the Overall Communication Suppression Ratio (OCSR), which quantifies the relationship between the “sustained full-suppression duration” and the “operating duration of the jamming system”. This metric makes up for the defect that traditional metrics are not applicable to evaluating dynamic interference effectiveness in non-networked scenarios.

The simulation experiments show that, compared with traditional intelligent optimization algorithms (e.g., MADJPA), the ICCA has a stronger ability to search for feasible solutions, a faster interference decision-making speed, saves jamming power, extends the system operating time by 4.8%, and retains more battery capacity for jammers after the communication jamming system fails to achieve overall jamming.

Future research could investigate:

Estimation strategies for interference path loss in complex terrains and heterogeneous electromagnetic noise environments.

Integration of multi-agent reinforcement learning with non-networked cooperative frameworks. This would involve developing small-sample RL training strategies for distributed countermeasures under information-scarce conditions, while designing jamming-compliant cognition, estimation, and scheduling methodologies [54,55,56,57].