  The spectrum shift from the sub-6G band to the high-frequency band has posed
an ever-increasing demand on the paradigm shift from narrowband beamforming to
wideband beamforming. Despite recent research efforts, the problem of wideband
beamforming design is particularly challenging in reconfigurable intelligent
surface (RIS)-assisted systems, due to that RIS is not capable of performing
frequency-dependent phase shift, therefore inducing high signal processing
complexity. In this paper, we propose a simple-yet-efficient wideband
beamforming design for RIS-assisted systems, in which a transmitter sends
wideband signals to a desired target, through the aid of the RIS. In our
proposed design, we exploit space-frequency Fourier transformation and
stationary phase method to yield an approximate closed-form solution of the RIS
phase shifts which significantly reduces the signal processing complexity,
compared to the existing approaches. The obtained solution is then used to
generate a large and flat beampattern over the desired frequency band. Through
numerical results, we validate the effectiveness of our proposed beamforming
design and demonstrate how it can improve system performances in terms of
communication rate and sensing resolution. Beyond generating the flat
beampattern, we highlight that our proposed design is capable of mimicking any
desired beampattern by matching the RIS phase shift with the amplitude
modulation function, thus providing valuable insights into the design of novel
wideband beamforming for RIS-assisted systems.
