  This study considers the Joint Transmit/Reflect Beamforming and Power
Splitting (JTRBPS) optimization problem in a spectrum underlay setting, such
that the transmit sum-energy of the intelligent reflecting surface (IRS)-aided
secondary transmitter (ST) is minimized subject to the quality-of-service
requirements of the PS-simultaneous wireless information and power transfer
(SWIPT) secondary receivers and the interference constraints of the primary
receivers (PR). The interference at the PRs caused by the reception of
IRS-reflected signals sent by the primary transmitter is taken into account. A
coordinated channel state information (CSI) acquisition protocol is proposed.
Next, assuming availability at the ST of perfect CSI for all direct and
IRS-cascaded transmitter--receiver channels, two penalty-based iterative
algorithms are developed: an alternating minimization algorithm that involves
semi-definite relaxation in JTBPS design and successive convex approximation in
RB optimization, and a block coordinate descent algorithm that employs the
Riemannian conjugate gradient algorithm in RB updates. Finally, an
outage-constrained robust design under imperfect CSI is devised. Numerical
simulations highlight the performance gains of the proposed strategies over
benchmarks, corroborate the benefits of using an IRS, and provide valuable
insights.
