Sensing Within Ultra-Short Duration: Extended Subspace Algorithms With Insufficient Snapshots

In pursuit of real-time sensing within ultra-short duration, conventional sensing algorithms are gradually failing to fulfill the stringent latency demands. Specifically, traditional subspace-based methods such as multiple signal classification (MUSIC) are hindered by their need for an extensive number of snapshots to accumulate the rank of the spatial covariance matrix (SCM), resulting in poor real-time performance. Moreover, advanced techniques like compressed sensing and machine learning are constrained by requirements for high signal sparsity or suffer from limited generality. To handle these challenges, this paper proposes an innovative extension of subspace theory tailored to insufficient-snapshot scenarios, leveraging the concept of spatio-temporal exchangeability. Based on the defined spatio-temporal correlation predicated on the space translation invariance characteristic of uniform linear arrays, we engineer a pseudo SCM that inherently possesses sufficient rank. This methodology not only resolves the rank-deficiency issue but also fully exploits the array aperture and significantly reduces the noise level. Simulation results are presented, substantiating the feasibility and enhanced performance of the proposed algorithms, marking a significant advancement over existing methodologies.