  In this paper, we investigate simultaneously transmitting and reflecting
reconfigurable intelligent surfaces (STAR-RIS), which enables to communicate
with users both sides by transmitting signals to users forward and reflecting
signals to users backward simultaneously. We consider a communicatio system
with a STAR-RIS, a base station (BS) and many users to maximize the minimum
user energy efficiency (EE) by jointly optimizing the active beamforming,
transmission and reflection coefficients with BS power consumption limited. To
solve this optimization problem efficiently, we divide it into two sub-problems
to optimize the transmitting beamforming matrix and phase shifts of STAR-RIS
seperately. With the two subproblems fixed, an Alternating Optimization (AO)
method is proposed to solve the maximize minmum user EE fair optimization
problem. Numerical results can demonstrate that STAR-RIS behaves better than
traditional reflecting-only RIS, and the algorithm we desigend can maximize the
minum EE problem efficienty to ensure user fairness.
