Beamforming of an adaptive array antenna often becomes effective for the precise localization of nodes in wireless sensor networks. In an erratic channel, a link with possibly a narrower beamwidth is always suitable for sending data to target nodes. It can also cancel interference from other nearby nodes while steering deep nulls and keeping the lower sidelobe level in the pattern. This paper presents a custom design for such a beamforming network on a reconfigurable architecture. It includes all the desired attributes of the beam on a reference template characterized by the parabolic function. It also considers a linear array with non-uniform element excitations. Using the Particle Swarm Optimization (PSO) algorithm, the weight vector containing the excitations of the array elements is iteratively optimized. It is then implemented adopting the concept of the Finite State Machine with Datapath (FSMD) model and using appropriate COordinate Rotation DIgital Computer (CORDIC) blocks. Its performance is tested on a dedicated Field Programmable Gate Array (FPGA) board with multiple fixed-point hardware-level simulations for beamforming accuracy and computational overhead. The results corroborate its competence comparable to existing systems.