Directional SDR Jamming: Methods & Optimization

• Directional SDR jamming is a technique that selectively interferes with unauthorized receivers using controlled beamforming and precise spatial nulling via SDR platforms.
• It integrates trajectory optimization, closed-form phase adjustments, and agile antenna control to maximize interference at target locations while avoiding friendly nodes.
• Performance simulations and operational insights demonstrate that dynamic UAV platforms can achieve enhanced jamming efficacy and maintained nulling at designated client positions.

Directional software-defined radio (SDR) jamming refers to the technique of electronically denying wireless communications to unauthorized receivers (e.g., eavesdroppers) using targeted jamming signals whose spatial interference pattern is precisely controlled via digital signal processing and agile antenna configuration. Directional jamming contrasts with omnidirectional approaches by seeking to maximize interference specifically in target directions, while minimizing collateral impact to friendly nodes. A notable methodology is the integration of trajectory optimization, beamforming, and phase control on a mobile platform such as a UAV equipped with multiple SDR-controlled antennas, enabling highly selective and adaptable jamming with explicit spatial nulling toward non-adversarial entities (Fotiadis et al., 24 Aug 2025).

1. System and Signal Modeling

The canonical architecture involves a UAV equipped with two omnidirectional antennas separated by a fixed distance $D$, each controlled by an independent SDR transmit chain. Let the UAV position be $p_g = [x_g, y_g]^T \in \mathbb{R}^2$, while the client and eavesdropper reside at fixed locations $p_c$ and $p_e$ respectively. The antennas are positioned as

$$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$

where $\theta_g$ is the array orientation.

Each transmit chain emits a broadband jamming waveform $s(t)$, with per-antenna envelopes

$$s_1(t) = \sqrt{P_0} \, e^{j\phi_1(t)} s(t),\quad s_2(t) = \sqrt{P_0} \, e^{j\phi_2(t)} s(t),$$

where $P_0$ is the transmit power per antenna and $\phi_i(t)$ are programmable phase offsets. Received wideband jamming power at a generic location $p_g = [x_g, y_g]^T \in \mathbb{R}^2$0 is determined by the array geometry, free-space propagation loss $p_g = [x_g, y_g]^T \in \mathbb{R}^2$1 for $p_g = [x_g, y_g]^T \in \mathbb{R}^2$2, and the path-dependent complex channel coefficients

$p_g = [x_g, y_g]^T \in \mathbb{R}^2$3

The baseband received signal at $p_g = [x_g, y_g]^T \in \mathbb{R}^2$4 is

$p_g = [x_g, y_g]^T \in \mathbb{R}^2$5

with beampattern gain

$p_g = [x_g, y_g]^T \in \mathbb{R}^2$6

The resulting received jamming power is

$p_g = [x_g, y_g]^T \in \mathbb{R}^2$7

This formalism enables rigorous analysis and synthesis of spatial jamming patterns (Fotiadis et al., 24 Aug 2025).

2. Closed-Form Nulling via Phase Selection

An essential feature of directional SDR jamming is the ability to impose spatial nulls—directions where the jamming impact is exactly zero—by suitably adjusting transmission phases. To null the jamming signal at the client $p_g = [x_g, y_g]^T \in \mathbb{R}^2$8, the phases must satisfy

$p_g = [x_g, y_g]^T \in \mathbb{R}^2$9

implying

$p_c$0

Thus, the required phase for the second antenna is given in closed form by

$p_c$1

The base phase $p_c$2 is arbitrary with respect to nulling but can be selected for practical exigencies such as Doppler compensation: $p_c$3 This explicit phase relationship guarantees zero jamming power at the client under ideal propagation (Fotiadis et al., 24 Aug 2025).

3. Beampattern and Orientation Optimization

With the nulling constraint encoded, the jamming beampattern at an arbitrary target becomes

$p_c$4

In the far-field ($p_c$5), this simplifies to an angle-only function: $p_c$6 The optimal orientation maximizing $p_c$7 is

$p_c$8

This framework enables pointwise maximization of interference toward an eavesdropper while respecting the client null (Fotiadis et al., 24 Aug 2025).

4. Optimal Control of Platform Trajectory

Maximizing directional jamming efficacy over time requires optimal coordination of the UAV’s position and array orientation. Denote UAV kinematics as

$p_c$9

with acceleration bound $p_e$0. The joint objective integrates control effort and jamming performance: $p_e$1 where $p_e$2 is a smooth approximation of a denial-of-service reward. The optimal control is derived from Pontryagin’s Minimum Principle, leading to

$p_e$3

with costate evolution: $p_e$4 and $p_e$5. The associated boundary-value problem is solved numerically (e.g., MATLAB’s bvp4c or direct collocation). Analytical closed-form expressions for $p_e$6 are available in the referenced work (Fotiadis et al., 24 Aug 2025).

5. SDR Implementation Specifics

Implementation utilizes two SDR transmitters (e.g., USRP X310, LimeSDR), each providing a feed to an antenna. Practical considerations include:

• Phase programming: Baseband phase offsets $p_e$7, $p_e$8 are programmed directly into the signal sample streams, e.g.,

$p_e$9

• Time/frequency synchronization: Both SDRs share a 10 MHz reference and PPS via hardware interconnect, ensuring phase coherency.
• Real-time update loop: $$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$0 and $$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$1 are recomputed at rates exceeding 10 Hz, with updates transferred from a companion computer over Ethernet.
• Calibration: Initial calibration uses fixed offsets and a known reference target to remove static delay and phase bias; RF group delay flattening is performed via digital FIR pre-equalization.
• DSP chain: The signal processing sequence is: noise generation → per-antenna phase rotation → IQ upconversion → amplification → antenna emission.

This establishes a fully programmable, phase-coherent 2-element array for dynamic directional jamming and null steering (Fotiadis et al., 24 Aug 2025).

6. Performance, Simulation, and Operational Insights

With representative parameters ($$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$2 MHz, $$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$3 m, $$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$4, $$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$5 W), simulated execution demonstrates that the UAV optimally deviates from the straight client-eavesdropper axis to maximize the angular separation $$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$6, thus enhancing beamforming discrimination. The client experiences a perfect null at all times, while the eavesdropper receives jamming power increasing from 0 to 4 (beampattern gain scale). Jamming at $$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$7 crosses the denial-of-service threshold ($$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$8 dBm) at approximately $$p_1 = p_g - \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T, \quad p_2 = p_g + \frac{D}{2}[\cos\theta_g,\, \sin\theta_g]^T,$$9 s, compared to omnidirectional jamming that never exceeds $\theta_g$0 dBm under identical conditions. Figure outputs include time series of phases/orientations/power and two-dimensional beampattern visualizations showing the evolving spatial selectivity. These results substantiate the efficacy and precision of joint beamforming and trajectory control in mobile, SDR-based jamming contexts (Fotiadis et al., 24 Aug 2025).