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

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.