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Antenna array-based multi-dimensional infinite-impulse response (IIR) digital beamformers are employed in a multitude of radio frequency (RF) applications ranging from electronically-scanned radar, radio telescopes, long-range detection and target tracking. A method to design 3D IIR beam filters using 2D IIR beam filters is described. A cascaded 2D IIR beam filter architecture is proposed based on systolic array architecture as an alternative for an existing radar application. Differential-form transfer function and polyphase structures are employed in the design to gain an increase in the speed of operation to gigahertz range. The feasibility of practical implementation of a 4-phase polyphase 2D IIR beam filter is explored. A digital hardware prototype is designed, implemented and tested using a ROACH-2 Field Programmable Gate Array (FPGA) platform fitted with a Xilinx Virtex-6 SX475T FPGA chip and multi-input analog-to-digital converters (ADC) boards set to a maximum sampling rate of 960 MHz. The article describes a method to build a 3D IIR beamformer using polyphase structures. A comparison of technical specifications of an existing radar application based on phased-array and the proposed 3D IIR beamformer is also explained to illustrate the proposed method to be a better alternative for such applications.