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

For integrated sensing and communication (ISAC) systems, the channel information essential for communication and sensing tasks fluctuates across different timescales. Specifically, wireless sensing primarily focuses on acquiring path state information (PSI) (e.g., delay, angle, and Doppler) of individual multi-path components to sense the environment, which usually evolves much more slowly than the composite channel state information (CSI) required for communications. Typically, the CSI is approximately unchanged during the channel coherence time, which characterizes the statistical properties of wireless communication channels. However, this concept is less appropriate for describing that for wireless sensing. To this end, in this paper, we introduce a new timescale to study the variation of the PSI from a channel geometric perspective, termed path invariant time, during which the PSI largely remains constant. Our analysis indicates that the path invariant time considerably exceeds the channel coherence time. Thus, capitalizing on these dual timescales of the wireless channel, in this paper, we propose a novel ISAC framework exploiting the recently proposed delay-Doppler alignment modulation (DDAM) technique. Different from most existing studies on DDAM that assume the availability of perfect PSI, in this work, we propose a novel algorithm, termed as adaptive simultaneously orthogonal matching pursuit with support refinement (ASOMP-SR), for joint environment sensing and PSI estimation. We also analyze the performance of DDAM with imperfectly sensed PSI.Simulation results unveil that the proposed 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).