Multi-Antenna Dual-Blind Deconvolution for Joint Radar-Communications via SoMAN Minimization

TL;DR

This work tackles the challenging problem of jointly recovering radar and communications signals and their continuous-valued channels from an overlaid, multi-antenna observation (dual-blind deconvolution). It casts the recovery as a 3-D sum of multivariate atomic-norm minimization (SoMAN), solved exactly via a semidefinite program (SDP) using positive hyperoctant trigonometric polynomials (PhTP). The authors prove a high-probability recovery guarantee: the required sample-antennna budget scales logarithmically with the larger of the radar-target or communications-path counts, rather than their sum, and show robustness to noise and steering-vector errors. They also provide a practical recovery workflow that includes regularized SDP formulations, dual certificates, and an alternating scheme to recover the transmitted radar waveform and communications messages. Numerical experiments validate exact parameter recovery across diverse JRC scenarios and demonstrate resilience to noise and array imperfections, underlining the method’s potential for passive, secure JRC reception.

Abstract

In joint radar-communications (JRC) applications such as secure military receivers, often the radar and communications signals are overlaid in the received signal. In these passive listening outposts, the signals and channels of both radar and communications are unknown to the receiver. The ill-posed problem of recovering all signal and channel parameters from the overlaid signal is termed as \textit{dual-blind deconvolution} (DBD). In this work, we investigate DBD for a multi-antenna receiver. We model the radar and communications channels with a few (sparse) \textit{continuous-valued} parameters such as time delays, Doppler velocities, and directions-of-arrival (DoAs). To solve this highly ill-posed DBD, we propose to minimize the sum of multivariate atomic norms (SoMAN) that depend on unknown parameters. To this end, we devise an exact semidefinite program using theories of positive hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show that the minimum number of samples and antennas required for perfect recovery is logarithmically dependent on the maximum of the number of radar targets and communications paths rather than their sum. We show that our approach is easily generalized to include several practical issues such as gain/phase errors and additive noise. Numerical experiments show the exact parameter recovery for different JRC scenarios.

Figures (7)

• Figure 1: The JRC ULA receive antenna admits a superposition of independently transmitted radar and communications signals that are reflected off scatterers along their respective paths.
• Figure 2: Channel parameter localization in the 3-D dual polynomials. The parameter estimates are localized in the 3-D delay-Doppler-DoA hyperplane when the polynomials' norm is unity. Here, we set $M = 13$, $P=9, N_R = 5$, $L=4$, and $J=3$. Top panel: (a) Scatter plot of 3-D $\mathbf{f}_r(\mathbf{r})$ polynomial with the color indicating the value of its norm evaluated at ${\tau, \nu, \beta}$ values. (b) As in (a), but for only 4 values of $\beta$ that correspond to the estimated DoAs of $L=4$ targets. These are the norm values of $\mathbf{f}_r(\mathbf{r})$ in the delay-Doppler plane for 4 fixed $\beta$ values. The rectangles with blue and red borders indicate the specific $\beta$ values of $0.14$ and $0.36$, for which the 2-D plot of $\Vert \mathbf{f}_r(\mathbf{r})\Vert_2^2$ is shown in (c) and (d), respectively. Bottom panel: (e) As in (a), but for $\mathbf{f}_c(\mathbf{c})$ with $Q=2$ communications propagation paths. (f) As in (b), but for $\Vert \mathbf{f}_c(\mathbf{c})\Vert_2^2$ with $Q=2$ delay-Doppler slices. The blue and red border rectangles indicate the specific $\beta$ values of $0.5$ and $0$, for which the 2-D plot of $\Vert \mathbf{f}_c(\mathbf{c})\Vert_2^2$ is shown in (g) and (h), respectively.
• Figure 3: As in Fig. \ref{['fig:results_dual']}, but for closely spaced channel parameters. Here, $M =17$ time samples, $P=11$ pulses/messages, $N_R=9$ number of receiver antennas and subspace size $J=3$.
• Figure 4: Success rate with respect to the (a) number of samples $M$ for fixed $P= 5, N_R = 5$ , (b) number of pulses/messages $P$ for fixed $M= 5, N_r = 5$ , and (c) number of antennas $N_R$ for fixed $M= 5, P = 5$ .
• Figure 5: Success rate with respect to the number of targets/paths $L=Q$ and subspace dimension $J$ for (a) radar and (b) communications. The curve in blue shows the theoretical performance as predicted by Theorem \ref{['th:main']}.

Theorems & Definitions (30)

• Remark 1
• Remark 2
• Remark 3
• Proposition 4
• proof
• Definition 5: Isotropy candes2011probabilistic
• Definition 6: Incoherence candes2011probabilistic
• Theorem 7
• proof
• Proposition 8