6G Green IoT Network: Joint Design of Intelligent Reflective Surface and Ambient Backscatter Communication

Algorithm 3

The alternate optimization algorithm.

1:Initialize: number of backscattering coefficient levels , number of Gaussian randomization , and threshold .

2:for to do

3:random IRS phase shifts

4:While the change of the objective function (12a) is higher than the threshold do

5:Optimize problem (P4) by CVX and get .

6:Get and , where

7:Get , where is uniformly distributed. On the unit sphere.

8:Scaling so as to satisfy constraints (14b)–(14d).

9:Relax the constraint (23d), then optimize problem (P7) by CVX and get .

10:Perform eigenvalue decomposition

11:for to do

12:Get a rank-one solution of (P7),

end for

13:Obtain the target value of problem (P7), where .

14:Obtain the target value of problem (P5), where .

15:Set for the next iteration.

16: end while

17:.

18:end for

19:Return: optimized beamforming vector , optimized phase shift vector , optimized reflection coefficient