Integrated Sensing and Channel Estimation by Exploiting Dual Timescales for Delay-Doppler Alignment Modulation

Abstract

For integrated sensing and communication (ISAC) systems, channel information that is essential for communication and sensing tasks fluctuates at different timescales. Specifically, the composite channel state information (CSI) for wireless communication is static during channel coherence time. However, this concept is less appropriate for describing the wireless channel for sensing. To this end, in this paper, we first introduce a new timescale to study the real-time variations of the path state information (PSI) (e.g., delay, angle, and Doppler) of individual multi-path, termed path-invariant time, during which the PSI remains constant. As the goal of environment sensing for PSI essentially aligns with the channel estimation for the recently proposed delay-Doppler alignment modulation (DDAM) technique, we introduce a novel framework for a bi-static ISAC system, which refers to as DDAM-based ISAC. To acquire the PSI, in this paper, by capitalizing on the dual timescales of wireless channels, we propose a novel algorithm, termed as adaptive simultaneously orthogonal matching pursuit algorithm with support refinement (ASOMP-SR). The performance of DDAM with the imperfectly sensed PSI is analyzed, where the signal-to-interference-plus-noise ratio (SINR) and the achievable spectral efficiency are derived. Numerical results unveil that the proposed ASOMP-SR algorithm achieves better sensing performance than the conventional orthogonal matching pursuit (OMP) algorithm, in terms of the normalized mean squared error (NMSE) and the number of multi-paths resolved. In addition, DDAM-based ISAC can achieve superior spectral efficiency and a reduced peak-to-average power ratio (PAPR) compared to standard orthogonal frequency division multiplexing (OFDM).