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The large scale reflector array of programmable metasurfaces is capable ofincreasing the power efficiency of backscatter communications via passivebeamforming and thus has the potential to revolutionize the low-data-ratenature of backscatter communications. In this paper, we propose to design thepower-efficient higher-order constellation and reflection pattern under theamplitude constraint brought by backscatter communications. For theconstellation design, we adopt the amplitude and phase-shift keying (APSK)constellation and optimize the parameters of APSK such as ring number, ringradius, and inter-ring phase difference. Specifically, we derive closed-formsolutions to the optimal ring radius and interring phase difference for anarbitrary modulation order in the decomposed subproblems. For the reflectionpattern design, we propose to optimize the passive beamforming vector bysolving a multi-objective optimization problem that maximizes reflection powerand guarantees beam homogenization within the interested angle range. To solvethe problem, we propose a constant-modulus power iteration method, which isproven to be monotonically increasing, to maximize the objective function ineach iteration. Numerical results show that the proposed APSK constellationdesign and reflection pattern design outperform the existing modulation andbeam pattern designs in programmable metasurface enabled backscattercommunications.

Amplitude-Constrained Constellation and Reflection Pattern Designs for Directional Backscatter Communications Using Programmable Metasurface