This paper proposes, for the first time, a new radiation pattern synthesis for fractal antenna array that combines the unique multi-band characteristics of fractal arrays with the adaptive beamforming requirements in wireless environment with high-jamming power. In this work, a new adaptive beamforming method based on discrete cbKalman filter is proposed for linear Cantor fractal array with high performance and low computational requirements. The proposed Kalman filter-based beamformer is compared with the Least Mean Squares (LMS) and the Recursive Least Squares (RLS) techniques under various parameter regimes, and the results reveal the superior performance of the proposed approach in terms of beamforming stability, Half-Power Beam Width (HPBW), maximum Side-Lobe Level (SLL), null depth at the direction of interference signals, and convergence rate for different Signal to Interference (SIR) values. Also, the results demonstrate that the suggested approach not only achieves perfect adaptation of the radiation pattern synthesis at high jamming power, but also keep the same SLL at different operating frequencies. This shows the usefulness of the proposed approach in multi-band smart antenna technology for mobile communications and other wireless systems.