  This paper investigates a novel intelligent reflecting surface (IRS)-based
symbiotic radio (SR) system architecture consisting of a transmitter, an IRS,
and an information receiver (IR). The primary transmitter communicates with the
IR and at the same time assists the IRS in forwarding information to the IR.
Based on the IRS's symbol period, we distinguish two scenarios, namely,
commensal SR (CSR) and parasitic SR (PSR), where two different techniques for
decoding the IRS signals at the IR are employed. We formulate bit error rate
(BER) minimization problems for both scenarios by jointly optimizing the active
beamformer at the base station and the phase shifts at the IRS, subject to a
minimum primary rate requirement. Specifically, for the CSR scenario, a
penalty-based algorithm is proposed to obtain a high-quality solution, where
semi-closed-form solutions for the active beamformer and the IRS phase shifts
are derived based on Lagrange duality and Majorization-Minimization methods,
respectively. For the PSR scenario, we apply a bisection search-based method,
successive convex approximation, and difference of convex programming to
develop a computationally efficient algorithm, which converges to a locally
optimal solution. Simulation results demonstrate the effectiveness of the
proposed algorithms and show that the proposed SR techniques are able to
achieve a lower BER than benchmark schemes.
