Electronic warfare (EW) is the proverbial invisible battlefield—a contest of electromagnetic emission, interception, and denial that underpins every modern air and missile defense engagement. Radar provides the eyes; electronic support measures (ESM) provide the ears; electronic countermeasures (ECM) provide the sword; and electronic counter-countermeasures (ECCM) provide the shield. The effectiveness of any single component is inseparable from the behavior of the others, making integrated simulation essential for system design, tactics development, and training.
electronic-war-sim is a modular, discrete-event simulation framework developed as part of the BMDS (Ballistic Missile Defense System) simulation ecosystem. Built on the forge-sims foundation, it provides five coordinated packages:
| Package | Scope |
|---|---|
core | Simulation engine, event bus, configuration management |
radar | Radar range equation, detection probability, Swerling target models |
esm | ESM intercept probability, bearings-only tracking, signal parameter extraction |
ecm | Chaff/jamming models, DRFM deception, countermeasure deployment |
spectrum | Spectrum management, frequency allocation, deconfliction |
This paper presents the mathematical foundations and software architecture of each package, derives the governing equations for jammer-to-noise ratio (JNR) and burnthrough range, and validates the models against established analytical results.
Following the standard NATO/US convention, EW is divided into three broad divisions [1]:
The simulation classifies threats into categories that determine modeling parameters:
| Category | Examples | Key Parameters |
|---|---|---|
| Search Radar | Early warning, acquisition | Low PRF, wide beam, frequency diversity |
| Tracking Radar | Fire control, terminal guidance | High PRF, narrow beam, monopulse |
| ESM/ELINT | RWR, passive surveillance | Instantaneous bandwidth, sensitivity |
| Self-Protection Jammer | Onboard EA | Effective radiated power, technique set |
| Stand-off Jammer | Escort, stand-forward | High ERP, long dwell, coordinated techniques |
The single-pulse received signal-to-noise ratio (SNR) at the radar receiver is given by the classical radar range equation [2]:
$$ \text{SNR} = \frac{P_t G^2 \lambda^2 \sigma}{(4\pi)^3 R^4 k T_0 B F L} \tag{1} $$where $P_t$ is peak transmit power, $G$ is antenna gain, $\lambda$ is wavelength, $\sigma$ is target radar cross-section (RCS), $R$ is range to target, $k$ is Boltzmann's constant, $T_0$ is standard receiver temperature (290 K), $B$ is receiver bandwidth, $F$ is noise figure, and $L$ aggregates system losses.
For $n$ pulses integrated coherently with integration loss $L_i$, the effective SNR becomes:
$$ \text{SNR}_{\text{eff}} = \frac{n \cdot \text{SNR}}{L_i} \tag{2} $$
The radar package implements Eq. (1) with full parameterization of transmit/receive paths, supporting separate transmit and receive gains for bistatic configurations.
Detection probability $P_d$ and false-alarm probability $P_{fa}$ are related through the Neyman-Pearson criterion. For a Swerling 0 (non-fluctuating) target in Gaussian noise:
$$ P_d = Q\!\left(\sqrt{2 \cdot \text{SNR}},\; \sqrt{-2 \ln P_{fa}}\right) \tag{3} $$where $Q(\cdot,\cdot)$ is Marcum's Q-function. For fluctuating targets, the four Swerling cases are modeled:
| Case | Decorrelation | Typical Target | |
|---|---|---|---|
| Swerling 1 | Exponential | Scan-to-scan | Many equivalent scatterers, slow modulation |
| Swerling 2 | Exponential | Pulse-to-pulse | Many scatterers, fast modulation |
| Swerling 3 | Chi-square ($\nu=2$) | Scan-to-scan | Dominant scatterer + small scatterers, slow |
| Swerling 4 | Chi-square ($\nu=2$) | Pulse-to-pulse | Dominant scatterer + small scatterers, fast |
The simulation computes detection probability via lookup of the incomplete gamma function for Swerling 1/2 and the modified Bessel function for Swerling 3/4, following the closed-form expressions in Skolnik [2].
Target RCS is modeled as a function of aspect angle and frequency. The radar package supports:
An ESM receiver intercepts a radar emission if three conditions are met simultaneously: (a) the ESM antenna is pointed toward the emitter, (b) the emitter's frequency falls within the ESM instantaneous bandwidth, and (c) the received power exceeds the ESM sensitivity threshold [1].
The received power at the ESM receiver (one-way path) is:
$$ P_r = \frac{P_t G_t G_r \lambda^2}{(4\pi)^2 R^2 L_p} \tag{4} $$where $G_r$ is the ESM antenna gain and $L_p$ includes propagation and system losses. The intercept probability over a scan period is:
$$ P_{\text{int}} = P_{\text{spatial}} \cdot P_{\text{freq}} \cdot P_{\text{threshold}} \tag{5} $$
where $P_{\text{spatial}}$ is the probability that the ESM beam sweeps across the emitter, $P_{\text{freq}}$ is the probability of frequency overlap, and $P_{\text{threshold}}$ is the probability that received power exceeds sensitivity. The esm package evaluates each factor per dwell and aggregates over the surveillance period.
Passive ESM systems typically measure only the angle of arrival (bearing). Target localization from bearings-only observations requires multiple observations from different sensor positions or times. The simulation implements:
The bearings-only EKF state vector is:
$$ \mathbf{x} = [r,\; b,\; \dot{r},\; \dot{b}]^T \tag{6} $$where $r$ is range, $b$ is bearing, and dots denote time derivatives. The measurement equation relates bearing to state via $z = b + v$ with measurement noise $v \sim \mathcal{N}(0, \sigma_b^2)$.
Once intercepted, the ESM system extracts pulse descriptor words (PDWs):
These parameters feed the threat library for emitter identification and the jamming controller for technique selection.
Barrage noise jamming raises the noise floor at the victim radar across a broad bandwidth, reducing its detection range. The jammer-to-noise ratio (JNR) at the radar receiver from a self-screening jammer is [1]:
$$ \text{JNR} = \frac{P_j G_j G_r \lambda^2}{(4\pi)^2 R_j^2 k T_0 B_j F L_j} \tag{7} $$where $P_j$ is jammer power, $G_j$ is jammer antenna gain toward the radar, $R_j$ is jammer-to-radar range, and $B_j$ is the jamming bandwidth. The effective noise power at the radar receiver becomes:
$$ N_{\text{eff}} = N_{\text{thermal}} + J = k T_0 B F + \frac{P_j G_j G_r \lambda^2}{(4\pi)^2 R_j^2 L_j} \tag{8} $$The degraded detection range $R_{\text{max},j}$ is found by substituting $N_{\text{eff}}$ for $N_{\text{thermal}}$ in the radar equation and solving for range.
The ecm package models three noise jamming modes:
Digital Radio Frequency Memory (DRFM) jamming captures, digitizes, and retransmits radar pulses with controlled modifications. The ecm package models the following DRFM techniques:
The DRFM model accounts for:
Chaff consists of dispensed dipoles tuned to the victim radar's frequency, creating a large RCS cloud that masks the true target. The ecm package models:
Decoys are active or passive devices that present a credible target signature. Active decoys (miniature jammers) and passive decoys (RCS enhancers) are modeled with configurable RCS, motion profiles, and (for active decoys) retransmission characteristics.
Frequency agility—changing the radar's transmit frequency on a pulse-to-pulse or burst-to-burst basis—defeats narrowband jamming by forcing the jammer to spread power across a wider bandwidth or to reactively retune. The simulation models:
The frequency agility gain against a spot jammer with bandwidth $B_j$ targeting an agile radar with total agile bandwidth $B_a$ is:
$$ G_{\text{agility}} = \frac{B_a}{B_j} \tag{9} $$Sidelobe blanking (SLB) uses an auxiliary omnidirectional antenna to detect jamming or interference entering through the radar sidelobes. When the auxiliary channel power exceeds the main channel power, the return is blanked. The simulation models:
A jammer in the sidelobes is blanked when:
$$ \frac{P_{\text{aux}}}{P_{\text{main}}} > \eta_{\text{blank}} \tag{10} $$where $\eta_{\text{blank}}$ is the blanking threshold. The auxiliary antenna gain must exceed the sidelobe level but remain below the mainlobe gain for proper operation.
Home-on-jam is a passive guidance mode in which a missile tracks the jammer's emission source rather than the radar echo. The simulation models:
HOJ turns the jammer's advantage into a vulnerability: by emitting, the jammer reveals its angular position. The angular tracking accuracy in HOJ mode is:
$$ \sigma_\theta \approx \frac{\theta_{3\text{dB}}}{\sqrt{2 \cdot \text{SNR}_{\text{HOJ}}}} \tag{11} $$where $\theta_{3\text{dB}}$ is the seeker's 3 dB beamwidth and $\text{SNR}_{\text{HOJ}}$ is the signal-to-noise ratio of the jammer emission at the seeker.
Pulse compression increases radar range resolution without sacrificing detection range by coding the transmit pulse and matched-filtering on receive. The radar package models:
Pulse compression provides inherent ECCM benefits:
The interplay between the radar's signal power and the jammer's noise power determines whether detection is possible. The key metric is the jammer-to-signal ratio (JSR) or, equivalently, the effective JNR.
For a self-screening jammer (jammer collocated with the target), the JSR is:
$$ \text{JSR} = \frac{P_j G_j \, 4\pi \, R^4 \, B_r}{P_t G_r \sigma \, R_j^2 \, B_j} \tag{12} $$For a stand-off jammer at range $R_j$ from the radar, with the target at range $R$:
$$ \text{JSR} = \frac{P_j G_j G_{rj} \, 4\pi \, R^4 \, B_r \, L}{P_t G_r^2 \sigma \, R_j^2 \, B_j \, L_j} \tag{13} $$where $G_{rj}$ is the radar receive antenna gain in the direction of the jammer (typically a sidelobe gain).
The burnthrough range is the range at which the radar's SNR overcomes the jamming, achieving the required detection probability. Setting JSR equal to the threshold for acceptable detection and solving for range:
$$ R_{bt} = \left[ \frac{P_t G_r^2 \sigma \, R_j^2 \, B_j \, L_j}{4\pi \, P_j G_j G_{rj} B_r L \cdot \text{JSR}_{\text{req}}} \right]^{1/4} \tag{14} $$For the self-screening case ($R = R_j$), this simplifies to:
$$ R_{bt} = \left[ \frac{P_t G_r \sigma \, B_j}{4\pi \, P_j G_j B_r \cdot \text{JSR}_{\text{req}}} \right]^{1/2} \tag{15} $$Notably, burnthrough range varies as the square root (not fourth root) of the radar power for the self-screening case, because both the target echo and the jamming signal are range-dependent.
The simulation computes burnthrough ranges in real time during engagement, allowing dynamic assessment of radar effectiveness as jamming parameters and geometry change.
The spectrum package manages the allocation and deconfliction of electromagnetic spectrum across all emitters and receivers in the simulation. This is critical for:
The spectrum model maintains a frequency allocation table that tracks:
| Attribute | Description |
|---|---|
| Frequency band | Center frequency and bandwidth of each emitter/receiver |
| Temporal occupancy | Duty cycle and PRI schedule |
| Spatial coverage | Antenna pointing and beam shape |
| Priority | Preemption hierarchy for deconfliction |
| ECCM state | Current frequency for agile emitters |
Deconfliction is performed by a constraint solver that assigns frequencies and time slots to emitters, minimizing mutual interference subject to operational constraints. The solver supports:
The spectrum management layer also models the impact of hostile jamming on friendly spectrum use, enabling joint EA/EP planning.
electronic-war-sim integrates with the broader BMDS simulation ecosystem through the forge-sims event bus and shared configuration framework. Key integration points include:
The event bus architecture allows electronic-war-sim to operate as a standalone EW simulation or as a fully integrated component of a BMDS engagement simulation. In standalone mode, threat kinematics and radar geometries are scripted; in integrated mode, they are received from the BMDS physics and guidance packages.
Setup. A single threat aircraft with a self-protection barrage noise jammer (ERP = 50 dBW, bandwidth = 500 MHz) approaches an S-band surveillance radar (Pt = 100 kW, G = 35 dB, σ = 1 m²).
Parameters evaluated:
Expected result. The radar achieves burnthrough at approximately 40% of its unjammed detection range. The simulation confirms the analytical Rbt within 2% over the 50–200 km engagement corridor.
Setup. A threat aircraft equipped with a coherent DRFM jammer engages a monopulse tracking radar. The DRFM performs RGPO followed by angle deception.
Parameters evaluated:
Expected result. RGPO achieves break-lock in 85% of trials against a non-adaptive tracker; leading-edge tracking reduces this to 15%. Pulse compression provides additional discrimination against delayed repeater pulses.
Setup. A defended asset operates three S-band radars and two X-band radars in proximity. A stand-off jammer attempts to deny the S-band. The spectrum manager must reassign frequencies and coordinate ECCM.
Parameters evaluated:
Expected result. Without spectrum management, mutual interference degrades net detection probability by 30%. The spectrum manager eliminates mutual interference and coordinates agile frequencies, reducing jammer effectiveness by 6 dB through band-spreading and time-division strategies.
The core models are validated against analytical benchmarks from the open literature:
| Model | Benchmark Source | Method | Agreement |
|---|---|---|---|
| Radar range equation | Skolnik [2], Table 2.1 | Known-answer test ($P_t$, $G$, $\sigma$, $R$) | < 0.1% error |
| $P_d$ vs. SNR (Swerling 1) | Adamy [1], Figs. 2.3–2.5 | Monte Carlo vs. analytical Q-function | < 1% error at $P_{fa} = 10^{-6}$ |
| Burnthrough range | Adamy [1], Eq. 4.8 | Analytical comparison | < 2% error |
| JNR vs. range | Skolnik [2], Ch. 9 | Known-answer test | < 0.5% error |
| Chaff RCS | Adamy [1], Eq. 5.1 | Dipole count vs. analytical $\lambda^2$ model | < 5% (orientation effects) |
| Frequency agility gain | Skolnik [2], Ch. 9 | Analytical $B_a/B_j$ | Exact |
| Pulse compression gain | Skolnik [2], Ch. 10 | Time-bandwidth product | Exact |
Monte Carlo validation uses 10,000 trials per data point for statistical models. All numerical results fall within the 95% confidence interval of the analytical predictions.
electronic-war-sim provides a comprehensive, modular framework for modeling the electronic warfare dimension of air and missile defense engagements. By coupling radar detection, ESM intercept, ECM effects, and ECCM countermeasures through a shared event bus and spectrum management layer, it enables the study of EW as an integrated system rather than a collection of isolated models.
The key contributions of this framework are:
Future work will extend the framework to include directed-energy EW, cyber-EW effects on radar networks, and machine-learning-based adaptive jamming and ECCM. The modular architecture of electronic-war-sim is designed to accommodate these extensions without redesign of the core packages.