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We develop a two-dimensional (2-D) superconducting quantum interference filter (SQIF) array based on the recently introduced high-linearity tri-junction bi-SQUIDs (superconducting quantum interference device). Our bi-SQUID SQIF array design is based on a tight integration of individual bi-SQUID cells sharing inductances with adjacent cells. We provide extensive computer simulations, analysis, and experimental measurements, in which we explore the phase dynamics and linearity of the array voltage response. The nonuniformity in inductances of the bi-SQUIDs produces a pronounced zero-field single antipeak in the voltage response. The antipeak linearity and size can be optimized by varying the critical current of the additional junction of each bi-SQUID. The layout implementation of the tight 2-D array integration leads to a distinct geometrical diamond shape formed by the merged dual bi-SQUID cells. Different-sized 2-D arrays are fabricated using the standard HYPRES niobium 4.5 kA/cm2 fabrication process. The measured linearity, power gain, and noise properties will be analyzed for different array sizes and the results will be compared with circuit simulations. We will discuss a design approach for the electrically small magnetic field antenna and low-noise amplifiers with high bandwidth based on these 2-D bi-SQUID SQIF arrays. The results from this work will be used to design chips densely and completely covered in bi-SQUIDs that have optimized parameters such as linearity and power gain.