Echo-Side Integrated Sensing and Communication via Space-Time Reconfigurable Intelligent Surfaces

TL;DR

The paper addresses integrated sensing and communication (ISAC) by enabling echo-side data embedding using space-time reconfigurable intelligent surfaces (ST-RIS) that apply time-varying phase modulation to radar echoes. By decomposing the ST-RIS phase into spatial and temporal components, the authors show a multiplicative coupling between sensing and communication, providing a framework to recover range information and uplink data from the same reflected signal. A closed-form modified Cramér–Rao bound (MCRB) for ST-RIS range estimation under unknown modulation is derived and used to quantify the phase-error accumulation that degrades data demodulation, while a generalized likelihood ratio test (GLRT) for frame synchronization accounts for residual frequency offsets. Under a fixed total bandwidth, the work reveals a convex Pareto frontier between sensing and communication, and provides a closed-form optimal bandwidth allocation that satisfies a minimum sensing requirement; numerical results validate the bounds and illuminate the trade-offs, highlighting practical implications for passive tagging and automotive radar applications.

Abstract

This paper presents an echo-side modulation framework for integrated sensing and communication (ISAC) systems. A space-time reconfigurable intelligent surface (ST-RIS) impresses a continuous-phase modulation onto the radar echo, enabling uplink data transmission with a phase modulation of the transmitted radar-like waveform. The received signal is a multiplicative composition of the sensing waveform and the phase for communication. Both functionalities share the same physical signal and perceive each other as impairments. The achievable communication rate is expressed as a function of a coupling parameter that links sensing accuracy to phase error accumulation. Under a fixed bandwidth constraint, the sensing and communication figures of merit define a convex Pareto frontier. The optimal bandwidth allocation satisfying a minimum sensing requirement is derived in closed form. The modified Cramer-Rao bound (MCRB) for range estimation is derived in closed form; this parameter must be estimated to compensate for the frequency offset before data demodulation. Frame synchronization is formulated as a generalized likelihood ratio test (GLRT), and the detection probability is obtained through characteristic function inversion, accounting for residual frequency errors from imperfect range estimation. Numerical results validate the theoretical bounds and characterize the trade-off across the operating range.

Figures (6)

• Figure 1: Echo-side ISAC scenario. A Sensing device illuminates an ST-RIS and $Q$ clutter targets. The ST-RIS communicates by impressing a time-varying phase modulation to the reflected signal.
• Figure 2: Timing diagram of echo-side ISAC. The radar transmits a sensing pulse (orange) that reaches the ST-RIS after one-way delay $\tau$. The ST-RIS applies phase modulation encoding data (blue), starting at offset $\tau_c$ relative to pulse arrival. At the receiver, the modulated echo (green) arrives after round-trip delay $2\tau$ and combines with unmodulated clutter returns (light orange).
• Figure 3: Pareto frontier of the sensing-communication trade-off. Markers denote numerical evaluation; solid lines represent the analytical expression \ref{['eq:pareto_frontier']}. With $h = 0.1$, the ratio $a/b \approx 53$ for $L = 2$ and $a/b \approx 5.3$ for $L = 10$, reflecting the increased modulation contribution to Fisher Information at larger alphabet sizes. Achieving $\tilde{\mathcal{S}} = 0.9$ limits communication to $\tilde{\mathcal{C}} \approx 0.15$.
• Figure 4: Delay estimation performance. (a) MSE versus SNR for $\beta \in \{0.1, 0.2, 0.5\}$; the DA estimator attains the MCRB (solid lines) across the SNR range. (b) MSE versus bandwidth allocation at SNR $\in \{-5, 5, 15\}$ dB; at high SNR, larger $\beta$ is tolerable without violating sensing constraints.
• Figure 5: Frame synchronization performance. (a) ROC curves for different SNR and bandwidth allocations; higher SNR and lower $\beta$ yield improved detection. (b) Detection probability at $P_{\rm fa} = 10^{-3}$; dashed lines: theory without residual CFO; solid lines: theory with $\sigma_{\epsilon_f}$ from MCRB; markers: simulation. The gap quantifies the sensing-synchronization coupling.