⚡ electrical engineering

Microwave Linear Analog Computer (MiLAC) for Simultaneous Active and Passive Beamforming

This paper proposes a dual-functionality framework for Microwave Linear Analog Computers (MiLACs) that simultaneously perform active beamforming for transmission/reception and passive beamforming as a reconfigurable intelligent surface, while providing an optimal reconfiguration strategy and characterizing the fundamental capacity trade-offs between these two modes.

Original authors: Matteo Nerini, Bruno Clerckx

Published 2026-06-01

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CC BY 4.0

Original authors: Matteo Nerini, Bruno Clerckx

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a high-tech radio tower that doesn't just shout messages at you, but also acts like a giant, intelligent mirror for other people's conversations. This is the core idea behind the paper's invention: a Microwave Linear Analog Computer (MiLAC) that does two jobs at once.

Here is a simple breakdown of how it works, using everyday analogies:

1. The Two Jobs: The "Megaphone" and the "Mirror"

Usually, a communication device has to choose a role:

Role A (Active Beamforming): It acts like a megaphone. It takes a message from its own computer, amplifies it, and shouts it directly to a specific user (like User 1).
Role B (Passive Beamforming): It acts like a smart mirror. It doesn't generate its own message; instead, it catches a signal bouncing off from someone else (User 1) and reflects it toward a different person (User 2) to help them talk.

The Innovation: The paper proposes a device that can do both at the same time. It can shout a message to User 1 while simultaneously acting as a mirror to help User 1 talk to User 2.

2. The Problem: The "Tug-of-War"

The paper explains that this device is built with very specific, "perfect" physics (it's lossless and reciprocal). Think of the device as a perfectly balanced seesaw.

If you push down hard on one side to make the "Megaphone" job super loud (maximizing the active rate), the "Mirror" side goes up and stops working well.
If you push down hard on the "Mirror" side to perfectly reflect User 1's signal to User 2, the "Megaphone" side goes up and stops working.

You cannot have the absolute maximum performance for both jobs simultaneously. There is a trade-off. If you want the device to be 100% a megaphone, it's 0% a mirror, and vice versa.

3. The Solution: Finding the "Sweet Spot"

The researchers figured out exactly how to balance this seesaw. They introduced a "dial" (mathematically called a parameter $t$ ) that lets you slide between the two extremes.

Turn the dial all the way left: The device is purely a megaphone.
Turn the dial all the way right: The device is purely a mirror.
Turn the dial to the middle: The device splits its energy. It shouts a message and reflects a signal, but neither is at its absolute maximum power.

The paper proves that by finding the perfect middle ground, you can get the highest total amount of data flowing through the system. It's like realizing that if you split your time 50/50 between shouting and mirroring, you actually help more people communicate overall than if you tried to do one thing perfectly and the other thing not at all.

4. The "Capacity Region" Map

The authors drew a map (called a "capacity region") that shows every possible combination of performance you can get.

Imagine a curve on a graph. The top-left corner is "All Megaphone," and the bottom-right is "All Mirror."
The curve connecting them shows every possible mix.
The paper provides a recipe to find the exact point on that curve where the total speed (the sum of both jobs) is the highest.

5. Why This Matters (According to the Paper)

The paper demonstrates that by using this "dual-function" approach, the system can handle twice as much data (a "multiplexing gain of 2") compared to just switching back and forth between the two jobs or doing only one.

In the simulations, they tested this with a device having 64 antennas. They found that even when there was no direct path for the users to talk to each other (User 1 couldn't see User 2), the MiLAC acting as a mirror was crucial. By splitting its attention perfectly (roughly 70% to one job and 30% to the other, or a 50/50 split in high-power scenarios), it maximized the total communication speed.

In short: The paper introduces a smart radio device that can talk and reflect at the same time. It proves that you can't be perfect at both simultaneously, but by finding the right balance, you can get the most out of the system overall.

Technical Summary: Microwave Linear Analog Computer (MiLAC) for Simultaneous Active and Passive Beamforming

Problem Statement

Microwave Linear Analog Computers (MiLACs) have recently been proposed to enable high-performance beamforming purely in the analog domain by processing signals via reconfigurable microwave networks. Traditionally, a MiLAC-aided transceiver performs active beamforming: precoding signals from RF chains for transmission or combining received signals from antennas for baseband detection. Separately, Reconfigurable Intelligent Surfaces (RISs), including Beyond-Diagonal RISs (BD-RISs), utilize reconfigurable microwave networks to perform passive beamforming by reflecting external incident signals.

The core problem addressed in this work is the potential for a single MiLAC-mounted transceiver to perform both functions simultaneously. When a MiLAC is implemented with lossless and reciprocal hardware, its scattering matrix is constrained to be unitary and symmetric. These physical constraints create a fundamental trade-off: the device cannot simultaneously maximize the rate of its own active transmission/reception and the rate of reflected passive communication. The paper seeks to characterize the fundamental limits of this trade-off and determine the optimal reconfiguration strategy to maximize system performance.

Methodology

The authors propose a dual-functionality framework where a MiLAC-aided transceiver simultaneously executes:

Active Beamforming: Processing signals between its own RF chains and a user (User 1).
Passive Beamforming: Reflecting signals from an external source (User 1) to a second destination (User 2), effectively acting as a BD-RIS.

System Model

The study focuses on a scenario where an $N$ -antenna transmitter equipped with a MiLAC communicates with User 1, while User 1 operates in full-duplex mode to communicate with User 2.

The MiLAC is modeled as a microwave network with $N+1$ ports (1 input from the RF chain, $N$ outputs to antennas).
The network is characterized by a scattering matrix $\bar{\Theta} \in \mathbb{C}^{(N+1)\times(N+1)}$ .
Due to lossless and reciprocal hardware, $\bar{\Theta}$ is constrained to be unitary ( $\bar{\Theta}^H \bar{\Theta} = I$ ) and symmetric ( $\bar{\Theta} = \bar{\Theta}^T$ ).
The matrix is partitioned into a reflection coefficient $\theta$ , a transmission vector $\theta$ , and a sub-matrix $\Theta$ governing the interaction between antenna ports.

Optimization Approach

The authors formulate the problem of optimizing $\bar{\Theta}$ to maximize the sum-rate $R = R_1 + R_2$ , where $R_1$ is the active link rate and $R_2$ is the passive link rate.

Individual Maximization: They first derive the conditions to maximize $R_1$ and $R_2$ independently. They demonstrate that these conditions require $\bar{\Theta}$ to map specific channel vectors to orthogonal directions, making simultaneous maximization impossible.
Capacity Region Characterization: To characterize the trade-off, the authors introduce a parameter $t \in [0, 1]$ . They define a compromise vector $\bar{h}$ that lies on the shortest arc of the unit $N$ -sphere connecting the optimal directions for active and passive beamforming. By optimizing $\bar{\Theta}$ to satisfy $\bar{\Theta}\frac{\bar{h}_1}{\|\bar{h}_1\|} = \bar{h}$ , they derive parametric expressions for $R_1(t)$ and $R_2(t)$ .
Sum-Rate Maximization: The authors prove that the frontier of the capacity region is defined by these parametric expressions. They derive a closed-form solution for the optimal $t^*$ that maximizes the sum-rate by solving a cubic equation derived from the first-order derivative of the sum-rate function.

Key Contributions

Dual-Functionality Framework: The paper introduces a novel framework where a MiLAC-aided transceiver acts simultaneously as a beamforming transmitter/receiver and a passive reflector (BD-RIS).
Fundamental Limits: The authors establish the capacity region for this dual-functional system, proving that a trade-off exists between active and passive rates due to the unitary and symmetric constraints of the scattering matrix. They show that the sum-rate upper bound (theoretical sum of individual maximums) is unachievable.
Optimal Reconfiguration Strategy: A global-optimal solution is provided to reconfigure the MiLAC to operate on the capacity region frontier. This includes a closed-form characterization of the capacity region and an algorithm to find the optimal operating point $t^*$ for sum-rate maximization.
High-SNR Insight: In scenarios where the direct link between users is obstructed ( $h_{21}=0$ ) and in the high-SNR regime, the optimal strategy converges to $t^* \approx \sqrt{1/2}$ . This indicates that uniform power allocation between active and passive modes yields a multiplexing gain of 2, superior to the gain of 1 achieved by time-sharing or using the device for only one function.

Results

Numerical simulations using Rayleigh distributed channels and $N=64$ antennas validate the theoretical findings:

Capacity Region: The proposed reconfiguration strategy achieves the theoretical frontier of the capacity region, significantly outperforming time-sharing schemes (which only achieve a multiplexing gain of 1).
Sum-Rate Performance: The optimal sum-rate capacity approaches the theoretical upper bound, achieving a multiplexing gain of 2.
Parameter Sensitivity: The results confirm that in the absence of a direct link and at high SNR, the optimal parameter $t$ is approximately $\sqrt{1/2}$ , balancing the active and passive links equally to maximize total throughput.

Significance

The paper claims that this work bridges the gap between MiLACs and RISs, demonstrating that a single hardware platform can support simultaneous active and passive beamforming. The significance lies in the characterization of the fundamental trade-offs imposed by reciprocal, lossless hardware and the provision of an optimal control strategy. By enabling a transceiver to simultaneously serve its own communication link and assist external links, the framework offers a scalable solution for large-scale MIMO systems in single-user, multi-user, and radar sensing contexts. The authors emphasize that for reciprocal MiLACs, the derived performance bounds are fundamental; relaxing symmetry constraints (using non-reciprocal hardware) would be required to improve these specific bounds, but within the reciprocal constraint, the proposed solution is optimal.