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Wideband probe-fed dielectric resonator antenna (DRA) arrays in an oversized dielectric loaded waveguide with hard horn excitation and radiating in free space are investigated for their use in waveguide-based spatial power-combining systems. A single embedded DRA element excited by a coaxial probe is analyzed first inside a hollow rectangular waveguide and a TEM waveguide. 1-D embedded DRA arrays are then studied inside the H- and E-plane sectoral hard horns. Finally, an entire spatial power-combining system with a 2-D embedded DRA array radiating in free space is analyzed. The analysis of the entire system is based on the finite-difference time-domain method with region-by-region discretization and subgridding schemes. The system's prototype of 2-D 3 times 3 embedded DRA array inside a pyramidal hard horn was fabricated and simulation results were compared with measurement results, showing a good agreement. Numerical results for radiation patterns are demonstrated for the examples of 2-D embedded dielectric resonator arrays excited by a pyramidal hard horn and radiating in free space.