  We introduce a novel system setup where a backscatter device operates in the
presence of an intelligent reflecting surface (IRS). In particular, we study
the bistatic backscatter communication (BackCom) system assisted by an IRS. The
phase shifts at the IRS are optimized jointly with the transmit beamforming
vector of the carrier emitter to minimize the transmit power consumption at the
carrier emitter whilst guaranteeing a required BackCom performance. The unique
channel characteristics arising from multiple reflections at the IRS render the
optimization problem highly non-convex. Therefore, we jointly utilize the
minorization-maximization algorithm and the semidefinite relaxation technique
to present an approximate solution for the optimal IRS phase shift design. We
also extend our analytical results to the monostatic BackCom system. Numerical
results indicate that the introduction of the IRS brings about considerable
reductions in transmit power, even with moderate IRS sizes, which can be
translated to range increases over the non-IRS-assisted BackCom system.
