  In this paper, an intelligent reflecting surface (IRS)-aided large-scale MIMO
system is investigated in which constant envelope precoding (CEP) is utilized
at each base station (BS). It is both cost-effective and energy-efficient to
implement CEP in a large-scale antenna array. We aim to optimize the discrete
phase shifts at both the BS and the IRS to minimize the sum power of multi-user
interference (MUI) in the system via our proposed three algorithms. For the
sake of simplicity, a simple single-cell scenario is considered, where the
optimization of the BS and IRS phase shifts is solved by a low-complexity
trellis-based algorithm. Then, this algorithm is extended to a multi-cell
scenario, where the precoding operation in each BS is performed individually.
With the aid of stochastic optimization method, a low-overhead trellis-based
solution is proposed which has better performance than the first one. Finally,
we solve the optimization problem via the semi-definite relaxation (SDR)
scheme, to serve as a performance benchmark for the proposed algorithms.
Meanwhile, interference and complexity analysis is provided for the proposed
algorithms. Numerical results demonstrate that while the performance of the
trellis-based algorithms is negligibly lower than that of the continuous-phase
SDR-based solution, the computational complexity and the implementation cost of
the former is much lower than the latter, which is appealing for practical
applications.
