Singh, Abhay Raj2026-07-082026-06-1751p.http://hdl.handle.net/10263/7750This dissertation has been completed under the supervision of Professor Sasthi C. GhoshEnsuring reliable sensing coverage is a fundamental challenge in wireless sensor networks (WSNs), particularly when multiple sensors are monitoring each location to provide robustness against node failures. In this work, we address the problem of deterministic k-coverage in planar WSN by proposing a hierarchical triangular lattice-based deployment strategy that organizes sensor locations across di↵erent refinement levels and guarantees coverage of every point in the sensing domain by at least k sensors. Each lattice is three-colorable, and selective activation of color classes ensures adjustable coverage guarantees. We prove that activating a single color class at refinement level t guarantees at least 4t-coverage inside a triangular region. Using a base-4 decomposition of the required coverage level k, we construct a deployment scheme that achieves arbitrary k-coverage while minimizing the number of sensors. For finite irregular hexagonal (IRH) domain, we drive closed-form expressions for the exact number of sensors and minimum sensor spacing required to ensure k-coverage. Analytical comparison with existing IRH edge-overlap, IRH inner-diamond and square-band based deployment strategies show that the proposed method either reduces the required number of sensors or increases the minimum sensor spacing while maintaining the similar coverage guarantees. The analytical results are also validated against extensive simulations. The proposed framework provides a constructive and scalable approach for efficient sensor deployment in large-scale wireless sensing systems.enWSNTriangular LatticeK-coverageIRHHierarchical DeploymentThesis