Mutual-Coupling-Aware Optimization of a Time-Floquet RIS for Harmonic Backscatter Communications

Abstract

This Letter studies the optimization of a wireless communications system empowered by a periodically time-modulated reconfigurable intelligent surface, coined time-Floquet RIS (TF-RIS), in the presence of mutual coupling (MC) among the RIS elements. In contrast to a conventional RIS whose elements may be reconfigured between signaling intervals, a TF-RIS periodically modulates its elements within a signaling interval, thereby inducing frequency conversion. Periodic time modulation is particularly attractive for harmonic backscatter communications to avoid self-jamming. Based on time-Floquet multiport network theory, we formulate an MC-aware optimization problem for binary-amplitude-shift-keying (BASK) harmonic backscatter communications with practical 1-bit-programmable TF-RIS elements. We propose a general discrete-optimization algorithm and evaluate its performance based on realistic model parameters. We systematically examine the performance dependence on the time resolution of the periodic modulation and the number of retained harmonics. Benchmarking against an MC-unaware approach reveals the importance of MC awareness for the more challenging optimization problem of simultaneous desired-harmonic-channel-gain maximization and undesired-harmonic-channel-gain minimization.

Figures (5)

• Figure 1: Left: MNT-based system model for a TF-RIS-parametrized radio environment. Right: Binary time-periodic load-modulation pattern.
• Figure 2: Considered TF-RIS setup based on kuznetsov2025multifrequency.
• Figure 3: Effect of the number of retained harmonics $|\mathcal{H}|$ on the TF-MNT accuracy, as a function of $Q$. We quantify the TF-MNT accuracy in terms of the 95th percentile of $\varepsilon_{|\mathcal{H}|}$ (see main text for details).
• Figure 4: Performance evaluation on \ref{['eq:on_only_opt']} as a function of (a) $Q$ (for $\theta_\mathrm{TX}=110^\circ$) and (b) $\theta_\mathrm{RX}$ (for various $Q$, see legend). In (a) we compare optimizations with different $|\mathcal{H}|$ as well as with and without MC awareness. The optimizations in (b) are performed with $|\mathcal{H}|=7$ and MC awareness.
• Figure 5: Selected examples of TF-RIS-empowered simultaneous harmonic beam steering and nulling (see \ref{['eq:on_only_opt_beamplusnull']}), for $Q=3$ (top row) and $Q=7$ (bottom row). The MC-aware (purple) and MC-unaware (black) optimizations both use $|\mathcal{H}|=11$. The optimized configurations are plotted with $|\mathcal{H}|=51$ and MC awareness. Key metrics are summarized in Table \ref{['tab:polar_gains']}.