You’re supposed to be solving problem (1) per Algorithm 1 in https://www.researchgate.net/profile/Trang-Mai-6/publication/327297753_Pilot_Power_Control_for_Cell-free_Massive_MIMO/links/61e95a3ddafcdb25fd3c59e9/Pilot-Power-Control-for-Cell-free-Massive-MIMO.pdf . I’ll let you sort out what that all means. iI you do need to use inv_pos, you should incorporate it directly into the constraint in which it appears, and there would be no equality constraint with it (nonlinear equality constraints are non-convex and not allowed by CVX).
I recommend you carefully read CVX Users’ Guide and Why isn't CVX accepting my model? READ THIS FIRST! rather than aimlessly trying stuff in hopes you get something CVX accepts, to implement an algorithm you may not understand.