  This work gives a blind beamforming strategy for intelligent reflecting
surface (IRS), aiming to boost the received signal-to-noise ratio (SNR) by
coordinating phase shifts across reflective elements in the absence of channel
information. While the existing methods of IRS beamforming typically first
estimate channels and then optimize phase shifts, we propose a conditional
sample mean based statistical approach that explores the wireless environment
via random sampling without performing any channel estimation. Remarkably, the
new method just requires a polynomial number of random samples to yield an SNR
boost that is quadratic in the number of reflective elements, whereas the
standard random-max sampling algorithm can only achieve a linear boost under
the same condition. Moreover, we gain additional insight into blind beamforming
by interpreting it as a least squares problem. Field tests demonstrate the
significant advantages of the proposed blind beamforming algorithm over the
benchmark algorithms in enhancing wireless transmission.
