⚡ electrical engineering

Microwave Linear Analog Computers (MiLACs) for Communications: Opportunities and Challenges

This paper proposes Microwave Linear Analog Computers (MiLACs) as a scalable solution for future wireless MIMO systems by offloading complex matrix operations, such as zero-forcing beamforming, to the analog domain to reduce hardware costs and computational complexity while overcoming the scaling limitations of conventional digital architectures.

Original authors: Matteo Nerini, Bruno Clerckx

Published 2026-07-27

📖 7 min read🧠 Deep dive

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 you are trying to solve a massive, tangled knot of strings. In the world of modern wireless internet, these "strings" are the invisible radio waves carrying your videos, games, and messages. To make sure these waves reach your phone without crashing into each other, computers have to do a lot of heavy lifting. They take the data, twist it, and aim it in the right direction using complex math. But here's the catch: as we try to connect more devices and send faster data, the number of these "strings" is exploding. The computers trying to untangle them are getting so big, hot, and power-hungry that they might soon hit a wall. They simply can't process the math fast enough to keep up with the future of 6G.

This is where a clever idea called "analog computing" steps in. Think of it like this: instead of using a calculator to figure out how to fold a piece of paper, you just fold the paper with your hands. The paper knows how to fold because of its physical shape, not because a brain told it to. In wireless tech, this means letting the radio waves themselves do the math as they travel through a special circuit, rather than stopping to ask a digital computer to calculate the answer first. It's like letting a river carve its own path through a canyon instead of trying to dig the canyon out with a spoon.

The paper you are about to read explores a new kind of "river path" called a Microwave Linear Analog Computer, or MiLAC. The authors, Matteo Nerini and Bruno Clerckx, are asking a big question: Can we build a physical device made of tiny electronic parts that instantly solves the complex math needed for wireless signals just by letting the waves pass through it? They suggest that by moving some of the heavy lifting from the digital brain to the analog "body" of the network, we could build super-fast, super-efficient wireless systems that don't melt down from heat or cost a fortune. They show that these devices can perform tricky math tricks, like reversing complex equations, much faster than our current computers can, potentially unlocking the door to the next generation of global connectivity.

The Magic of the "Instant" Math Machine

So, what exactly is this MiLAC? Imagine a black box with many doors on one side and many doors on the other. You shout a message into the doors on the left, and because of the special maze of wires and components inside the box, the sound comes out of the doors on the right already rearranged, mixed, and aimed perfectly. You didn't have to tell the box how to rearrange the sound; the box just did it because of how it was built.

In the world of wireless, this "black box" is a network of microwave components. The paper explains that these networks can be fixed (like a permanent maze) or reconfigurable (like a maze with moving walls). If you change the settings of the moving walls—using tiny switches called tunable parameters—you can change the math the box performs. Here is the really cool part: even though the box itself is "linear" (meaning it follows simple, straight rules), the way the settings change the output is actually nonlinear. It's like turning a dial on a radio: the dial moves in a straight line, but the station you land on jumps around in a complex way. This allows the MiLAC to do much more than just simple mixing; it can actually perform advanced math like matrix inversion (a fancy way of saying "undoing" a complex mix of signals) in a flash.

Why This Changes Everything

The authors show that using these MiLACs could solve three huge headaches in wireless technology:

Fewer Expensive Parts: Currently, every antenna on a tower needs its own expensive, power-guzzling computer chain to do the math. With MiLACs, the math happens in the air or in a simple circuit board. This means you might only need one computer chain for every single stream of data, rather than one for every single antenna. It's like replacing a hundred individual calculators with one giant, magical abacus that does the work for all of them instantly.
Cheaper, Simpler Converters: Digital computers need very precise tools to turn digital numbers into radio waves (and back again). These tools are expensive and use a lot of power. Because MiLACs do the heavy math in the analog world, the digital tools at the start and end of the process can be much simpler and lower-resolution. The paper notes that for certain types of signals, you might only need a 1-bit or 2-bit converter instead of a high-end one, saving a ton of energy.
Instant Speed: In a digital computer, solving a complex math problem with a huge list of numbers takes time. The time grows cubically, meaning if you double the size of the problem, it takes eight times longer to solve. But in a MiLAC, the "computation" happens as fast as the wave travels through the box. Since waves travel near the speed of light, the math is effectively instant. The paper suggests that tasks that usually take cubic time (very slow) can be done in quadratic time (much faster) just by configuring the right knobs on the MiLAC.

The Hurdles on the Road

Of course, this isn't a magic wand that fixes everything overnight. The authors are very clear that there are still big challenges to figure out.

Real-World Messiness: In the perfect world of the math models, these devices are "lossless" (no energy is lost) and "reciprocal" (they work the same way forward and backward). But in the real world, components have tiny flaws, lose a bit of energy, and don't always behave perfectly. The paper suggests we need better models to understand how these imperfections affect the final signal.
The "Wideband" Problem: Right now, the math works great for narrow bands of radio waves. But future internet will use wide bands. The paper points out that the MiLAC might behave differently at different frequencies, which could cause the signal to get messy. We need to figure out how to make these devices work reliably across a whole range of frequencies, not just one.
Complexity vs. Simplicity: The most flexible MiLAC designs require a huge number of tiny switches, which makes the circuit board very complex and expensive to build. The authors suggest that maybe we don't need every possible connection to get great results. Finding the "sweet spot" where the device is simple enough to build but smart enough to work is a key area for future research.

The Bottom Line

This paper doesn't claim to have built the perfect 6G tower today. Instead, it lays out a promising roadmap. It suggests that by letting the physics of microwaves do the heavy lifting, we can build wireless systems that are faster, cheaper, and less power-hungry than anything we have now. While there are still engineering puzzles to solve—like dealing with real-world imperfections and wideband signals—the idea of a "microwave computer" that solves math problems just by letting waves flow through it is a powerful new way to think about the future of how we connect. It turns the signal processing problem from a digital bottleneck into an analog opportunity, potentially paving the way for the massive, high-speed networks of tomorrow.

Technical Summary: Microwave Linear Analog Computers (MiLACs) for Communications

1. Problem Statement

Future wireless systems, particularly in the context of 6G and beyond, are projected to utilize massive antenna arrays (hundreds to thousands of elements) to achieve high data rates and spectral efficiency. However, conventional digital Multiple-Input Multiple-Output (MIMO) architectures face a critical scalability bottleneck. These systems rely heavily on digital baseband processing, requiring a dedicated radio frequency (RF) chain for every antenna. Each RF chain includes expensive and power-hungry components such as digital-to-analog converters (DACs) and analog-to-digital converters (ADCs). Furthermore, the matrix operations required for precoding and combining (e.g., zero-forcing, MMSE) become computationally prohibitive as the array dimensions increase, scaling cubically with the matrix size. The paper posits that offloading a portion of this processing from the digital domain to the analog RF domain is a necessary evolution to overcome these hardware and computational constraints.

2. Methodology and Framework

The paper introduces and reviews the concept of Microwave Linear Analog Computers (MiLACs). A MiLAC is defined as a linear microwave network designed to perform mathematical operations directly using communication signals at radio frequency (RF) through wave propagation.

A. General Model

The authors model a MiLAC as a multi-port linear network with $N$ input ports and $M$ output ports.

Fixed Networks: A fixed linear network performs a single, predetermined linear transformation $v = Wu$, where $W$ is a constant matrix. The computation occurs instantaneously via wave propagation, effectively taking $O(1)$ time relative to the signal speed of light.
Reconfigurable Networks: By incorporating tunable components (e.g., PIN diodes, varactors, tunable phase shifters), the network's behavior becomes a function of tunable parameters $h = [h_1, \dots, h_P]$ . The output is $v = W(h)u$ .
Structural Nonlinearity: A key theoretical insight is that while the relationship between the input signal $u$ and output $v$ remains linear, the relationship between the output and the tunable parameters $h$ can be nonlinear. This "structural nonlinearity" allows linear microwave networks to compute nonlinear functions with respect to their configuration parameters, enabling complex operations like matrix inversion.

B. Implementation Architectures

The paper categorizes MiLAC implementations into two domains:

Over-the-Air (OTA): Computation occurs through the wireless propagation channel. Examples include:
- Fixed wireless channels.
- Reconfigurable Intelligent Surfaces (RIS) and Stacked Intelligent Metasurfaces (SIM) to modify the channel response.
On-the-Board: Computation occurs on Printed Circuit Boards (PCBs) or microstrip circuits. Examples include:
- Fixed circuits (e.g., Butler matrices for DFT).
- Hybrid digital-analog beamforming networks (power dividers/combiners with phase shifters).
- General Reconfigurable Networks: A fully interconnected network of tunable impedance components (Fig. 2f) that offers the highest flexibility.

3. Key Contributions and Results

A. Computational Complexity Reduction

The paper demonstrates that MiLACs can perform matrix operations with significantly lower computational complexity compared to digital processing:

Matrix-Vector Product: Digital complexity is $O(MN)$; MiLAC complexity is effectively $O(1)$ (instantaneous propagation).
Matrix Inversion: Digital inversion scales as $O(N^3)$ . Using a MiLAC with interconnected tunable impedances, matrix inversion and pseudo-inversion can be achieved with complexity scaling as $O(N^2)$ . This is derived from the fact that the tunable parameters (impedance values) are linear combinations of the input data, requiring only $O(N^2)$ digital operations to configure the network, after which the inversion is performed physically.
LMMSE Estimator: Similarly, the Linear Minimum Mean Square Error (LMMSE) estimator, crucial for regularized zero-forcing beamforming, scales from $O(MN^2)$ digitally to $O(MN)$ in the analog domain.

B. MIMO Architecture Enhancements

The paper reviews MiLAC-aided transmitting and receiving architectures:

Basic MiLAC-Aided MIMO: In single-user systems, lossless and reciprocal MiLACs can achieve the same performance as fully digital beamforming. However, in multi-user systems, these basic architectures are limited to semi-unitary transformations due to reciprocity constraints.
Advanced Architectures: To overcome multi-user limitations without returning to full digital processing, the authors propose:
1. Hybrid Digital-MiLAC: Combining digital precoding with analog MiLAC precoding to achieve arbitrary precoding with $N_{RF} = N_{streams}$ .
2. Two-Layer MiLAC: Cascading two MiLACs with power amplifiers in between. This architecture can realize arbitrary precoding (fully digital performance) using only $N_{RF} = N_{streams}$ , even with lossless and reciprocal components, by decomposing the desired precoding matrix via Singular Value Decomposition (SVD).

C. System-Level Benefits

The paper identifies three primary advantages of adopting MiLAC-aided architectures:

Reduced RF Chains: The number of RF chains can be reduced to match the number of data streams (rather than the number of antennas), drastically lowering hardware cost and power consumption.
Low-Resolution Converters: Since beamforming is performed in the analog domain, the signals at the DACs and ADCs correspond directly to the transmitted symbols or combined detection signals. This allows for the use of low-resolution DACs (e.g., 1-bit for 4-QAM) and ADCs, avoiding the exponential power growth associated with high-resolution converters in fully digital systems.
Low Computational Complexity: By shifting matrix-vector multiplications to the analog domain, the system eliminates symbol-by-symbol digital matrix computations. Furthermore, the configuration complexity for advanced beamforming (like R-ZFBF) is reduced from cubic to quadratic scaling.

4. Challenges and Future Directions

The paper concludes by outlining several open research problems:

Hardware Impairments: Practical components suffer from discrete tuning steps, insertion losses, mutual coupling, and impedance mismatches. Accurate modeling of these non-idealities is required for robust optimization.
Channel Estimation: Estimating channels in systems where processing occurs in the analog domain is challenging. Early work suggests MiLACs could be used to accelerate channel estimation itself.
Wideband Operation: Current models focus on narrowband systems. Wideband operation introduces frequency-dependent variations (e.g., beam squinting) that must be modeled and mitigated.
Low-Complexity Architectures: While fully interconnected tunable networks offer maximum flexibility, they require $O(N^2)$ components. Research is needed to determine if simpler, sparsely connected architectures can achieve near-optimal performance with reduced hardware complexity.

5. Significance

The paper positions MiLAC as a promising solution to the scalability crisis in future wireless networks. By leveraging the physical properties of wave propagation in linear microwave networks, MiLACs offer a pathway to "gigantic MIMO" systems that are not constrained by the power, cost, and computational limits of current digital architectures. The ability to perform complex linear algebra (including matrix inversion) with quadratic complexity and to reduce the reliance on high-resolution converters represents a fundamental shift in how signal processing for communications can be architected. The authors frame MiLAC not just as a beamforming tool, but as a new class of analog computers with potential applications extending beyond communications into broader signal processing domains.