A Sub-Channel Spatial Homogeneity-Based Channel Estimation Method for Underwater Optical Densely Arrayed MIMO Systems

The limited surface area and structural constraints of small underwater communication devices necessitate a dense placement of transmitting and receiving array elements in optical multiple-input multiple-output (MIMO) systems. The compact layout leads to the formation of sub-channels that exhibit notable spatial correlation and a tendency toward homogeneity. Although sub-channel spatial homogeneity (SSH) may diminish the communication capacity of MIMO systems, it provides a significant advantage by reducing the pilot overhead. In this study, we exploit the inherent SSH and the natural time-domain sparsity of channel impulse response (CIR) in the underwater optical densely arrayed MIMO (UODA-MIMO) system to propose an innovative SSH-based channel estimation (SSH-CE) method. We model the underwater optical CIR at Gbaud rates and integrate it with SSH characteristics. This approach transforms the reconstruction targets of compressive sensing (CS) from conventional CIR samples to prior CIR model parameters and the fitting residuals of the homogeneous sub-channels, reducing the pilot overhead. The simulation results of photon tracing for UODA-MIMO sub-channels in turbid harbor water indicate a monotonic, exponential decay in CIR at Gbaud rates, with transmission delays exceeding 5 nanoseconds for distances over 8 m. Moreover, the correlation coefficients among sub-channels reach a minimum of 0.975, confirming the presence of SSH in UODA-MIMO systems. In comparison to existing CS methods that rely on known sparsity, sparsity adaptation, and the structural sparsity of MIMO channels, the SSH-CE method achieves a lower degree of sparsity in reconstruction targets and a reduced lower bound for pilot requirements under the SPARK criterion. Specifically, the SSH-CE method achieves a reduction in the pilot overhead for reconstructing Nt sub-channels of K-sparse to 2Nt irrespective of CIR residual compensation.