Compared to traditional omnidirectional systems, in-band full-duplex (IBFD) phased arrays provide higher antenna gains and offer the ability to electronically steer beams spatially to improve communications/radar links and enable multifunction operation. While a variety of approaches have successfully incorporated self-interference cancellation (SIC) into arrays, their techniques do not scale beyond the limited sizes demonstrated. In addition to providing an overview on state-of-the-art IBFD arrays, this paper presents a novel complexity reduction method that uniquely applies infinite impulse response (IIR) filter modeling for the purpose of compensating for the dispersion effects of the array hardware. Using measured statistical performance, this process is demonstrated for a scalable array design covering 2700 to 3500 MHz, and exhibits a 10x reduction in computations for an array with 1000 elements. Additionally, the distribution of on-array SIC adaptive processing is discussed for aperture-level IBFD designs, including the use of cache-oblivious algorithms that can help facilitate real-time processing and lead to the realization of large-scale IBFD arrays.