Experimental Validation of Provably Covert Communication Using Software-Defined Radio

TL;DR

A demonstration of provably-secure covert radio-frequency (RF) communication using software-defined radios (SDRs) validates theoretical predictions, opens practical avenues for implementing covert communication systems, and raises further research questions.

Abstract

The fundamental information-theoretic limits of covert, or low probability of detection/intercept (LPD/LPI), communication have been extensively studied for over a decade, resulting in the square root law (SRL): only $L\sqrt{n}$ covert bits can be reliably transmitted over time-bandwidth product $n$, for constant $L>0$. Transmitting more either results in detection or decoding errors. The SRL imposes significant constraints on hardware realization of mathematically-guaranteed covert communication. Indeed, they preclude using standard link maintenance operations that are taken for granted in non-covert communication. Thus, experimental validation of covert communication is underexplored: to date, only two experimental studies of SRL-based covert communication are available, both focusing on optical channels. Here, we report a demonstration of provably-secure covert radio-frequency (RF) communication using software-defined radios (SDRs). This validates theoretical predictions, opens practical avenues for implementing covert communication systems, and raises further research questions.

Figures (11)

• Figure 1: Discrete-time AWGN block broadcast channel. Alice modulates $x\in\mathcal{X}$ into a complex-valued pulse shape $\vec{u}(x)\in\mathbb{C}^{n_s}$ and transmits over $n_s$ uses of a channel corrupted by independent AWGN at legitimate receiver Bob and adversary (warden) Willie. Bob receives $h_{b}\vec{u}(x) + \vec{z}^{(b)}$ while Willie observes $h_{w}\vec{u}(x) + \vec{z}^{(w)}$, where the channel gain $h_{r}=a_re^{j\theta_r}$ from Alice to the receiver $r\in\{b,w\}$ contains attenuation $a_r>0$ and a random phase $\theta_r$. We model noise $\vec{z}^{(r)}$ by circularly-symmetric complex Gaussian random vectors.
• Figure 2: System model for covert communication. Alice either encodes, modulates, and transmits a message in $n_p$ pulses over $n = n_pn_s$ uses of the AWGN channel, or she remains silent. Here, $\vec{x}\in\left(\mathcal{X}\cup\{0\}\right)^{n_p}$ is the vector of QPSK and zero symbols, with the relative location of each selected using $\vec{t}$. After modulation, $\vec{u}(\vec{x})\in \mathbb{C}^n$ is the input pulse-shaped encoded signal from Alice. AWGN channel is characterized by additive noise $\vec{z}^{(w)}\in\mathbb{C}^{n}$ and channel gain $\vec{h}_b,\vec{h}_w \in \mathbb{C}^{n_p}$, as depicted in Fig. \ref{['fig:theoretical_channel']}. Here, each element of $\vec{h}_b,\vec{h}_w$ applies uniformly to one $n_s$ sample pulse slot. Then, $\vec{y}(\vec{x})\in\mathbb{C}^n$ (resp. $\vec{w}(\vec{x})\in\mathbb{C}^n$) is the output at Bob (resp. Willie). Willie's goal is to determine whether Alice is transmitting. Bob and Alice use a pre-shared secret $(\vec{s},\vec{t})$ to prevent this while communicating reliably.
• Figure 3: Pulse shape $\vec{u}(1)$. A strictly positive pilot segment $\vec{c_p}$ precedes the data segment $\vec{c_q}$, whose in-phase and quadrature components form the QPSK symbol $e^{\frac{j\pi}{4}}$ encoding $x=1$. The projections of the complex waveform onto the real and imaginary axes are overlaid with dotted red and blue lines, respectively, and the discrete time instants at which the Gaussian envelope is sampled for transmission are marked by $\star$.
• Figure 4: Covert communication experiment on COSMOS. Four Ettus USRP X310 radios -- Alice (Tx), Bob (Rx), Willie (warden), and a broadband noise source -- are linked by coaxial cables in a star topology using Mini-Circuits ZFSC-2-10G splitters/combiners. Tx-to-Rx and Tx-to-Tx path losses are 50 dB and 65 dB, respectively. All radios operate at $f_c = 915\,\text{MHz}$ with Alice, Bob, and Willie using a DAC/ADC sampling rate of $f_s = 12.5\times10^6$ samples/s and the noise generator $f_s = 22.5\times10^6$ samples/s. Alice, Bob, and Willie apply 0 dB Tx/Rx gain while the noise generator applies 15 dB gain. Each X310 connects over a 10 Gb/s SFP+ link to a dedicated control node (Intel Xeon E5-2640, 20 cores); Alice's node orchestrates the experiment via TCP messages to the other nodes and an eleven-node compute cluster of the same machines that performs real-time processing, while a 2 TB network-attached storage (NAS), mounted via NFS v4.2, provides a shared buffer.
• Figure 5: Measured spectrum at Willie's receiver. The Gaussian main lobe, expected to be centered at 915 MHz, is displaced by approximately $+300$ Hz, indicating a small carrier-frequency offset.