Spectrum scarcity in a highly congested radio environment call for simultaneous transmit and receive (STAR) radios. A key challenge in STAR radios is the self-interference cancellation (SIC) of the signals that leak from the transmitter into the receiver. With this in mind, this paper presents an ultra-wideband (UWB) RF-SIC filter capable of more than 20dB cancellation across 1GHz bandwidth. This SIC is part of a multistage cancellation scheme achieving more than 100dB of STAR isolation. Our presented SIC employs a filter bank with weight optimization to reach the noted unprecedented bandwidth. This design ensures phase linearity estimating the minimum number of filter stages. For optimization, a discrete-gradient descent algorithm is used to arrive at a practical SIC filter bank.