Design of IRS with Discrete Phase Shifts

Develop algorithms for configuring the phase shifts of an intelligent reflecting surface when each reflecting element’s phase is constrained to a finite discrete set of values rather than the ideal continuous [0, 2π) range, in order to enable practical IRS operation with quantized phase shifters.

Background

The paper analyzes joint active (AP) and passive (IRS) beamforming under the assumption that each IRS element can realize an arbitrary continuous phase shift in [0, 2π). This assumption enables characterizing fundamental limits and deriving tractable optimization methods but is idealized for practical hardware.

In practice, phase shifters on IRS elements typically have finite resolution and can take only a discrete set of phase values. Incorporating these discrete constraints fundamentally alters the beamforming design problem, turning the continuous optimization into a combinatorial one and potentially changing performance limits and algorithmic approaches.

References

To characterize the fundamental performance limits of IRS, we assume that the phase shifts can be continuously varied in [0, 2π), while in practice they are usually selected from a finite number of discrete values from 0 to 2π for the ease of circuit implementation. The design of IRS with discrete phase shifts is left for our future work .

— Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive Beamforming  (1810.03961 - Wu et al., 2018) in Footnote 1, Section 2.1 (System Model)