⚡ electrical engineering

Microwave Linear Analog Computer (MiLAC)-Aided MIMO Radar Sensing: Transmit Beamforming Design and DoA Estimation

This paper proposes a Microwave Linear Analog Computer (MiLAC)-aided MIMO radar framework that achieves fully-digital-level transmit beamforming and direction-of-arrival estimation performance while significantly reducing hardware cost and power consumption by shifting linear operations to the analog domain.

Original authors: Ziang Liu, Zheyu Wu, Bruno Clerckx

Published 2026-05-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ziang Liu, Zheyu Wu, 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

The Big Picture: The "Analog Computer" for Radar

Imagine you are trying to take a high-resolution photo of a busy city street at night using a massive camera with hundreds of lenses. To get a perfect picture, you need to coordinate every single lens perfectly (this is beamforming) and then process the data to figure out exactly where every car and person is (this is Direction-of-Arrival or DoA estimation).

In a traditional radar system, this is like having a super-computer in the back of the camera. Every lens sends its signal to the computer, which does billions of calculations to combine them and find the targets. This requires a lot of power, expensive hardware, and takes time.

This paper introduces a new gadget called a MiLAC (Microwave Linear Analog Computer). Think of MiLAC not as a computer that calculates numbers, but as a smart, physical filter or a magic lens that does the math while the signal is traveling through it. It moves the heavy lifting from the digital brain (software) to the physical hardware (analog waves).

The Problem: Too Many Lenses, Too Much Power

The authors explain that modern radars want to use "massive arrays" (hundreds of antennas) to see tiny details. But this creates two big problems:

Cost and Power: You need a dedicated electronic chain for every single antenna to convert signals. If you have 256 antennas, you need 256 expensive, power-hungry converters. It's like needing 256 separate chefs to cook one meal; it's inefficient.
Complexity: Processing the data from all those antennas digitally is incredibly slow and complex. It's like trying to solve a massive jigsaw puzzle in your head while running a marathon.

The Solution: The "Magic Filter" (MiLAC)

The paper proposes using MiLAC to solve these problems on both the sending and receiving ends of the radar.

1. The Transmitter: Shaping the Beam without the Brain

The Goal: The radar needs to send out a focused beam of energy toward specific targets (like shining a flashlight exactly where a car is).
The Old Way: A digital computer calculates the perfect pattern, then sends instructions to every antenna.
The MiLAC Way: The paper shows that you can use the MiLAC as a physical "shaper." You feed the signal in, and the MiLAC's internal structure (a network of adjustable electrical components) naturally shapes the wave into the perfect beam as it passes through.

The Big Claim: The authors proved a surprising mathematical fact: Even though the MiLAC is a physical "analog" device with strict rules (it can't lose energy and must work the same way in both directions), it can shape the beam just as perfectly as a super-computer could. It achieves the exact same "sensing accuracy" (measured by something called the Cramér–Rao Bound) as the fully digital version, but with much less hardware.

Analogy: Imagine trying to fold a piece of paper into a specific origami crane. The digital way is to calculate every fold, then use a robot arm to fold it. The MiLAC way is to put the paper in a special mold that, when you press it, the paper automatically folds into the perfect crane shape. The result is identical, but the mold is cheaper and faster.

2. The Receiver: Reading the Map without the Computer

The Goal: After the signal bounces off a target and comes back, the radar needs to figure out the angle of the target. The standard way to do this is a mathematical operation called a 2D Discrete Fourier Transform (2D-DFT).
The Old Way: The radar collects all the signals, sends them to a digital processor, and runs a complex algorithm (like a massive spreadsheet calculation) to find the angle.
The MiLAC Way: The authors show that the MiLAC can be built to act as a physical 2D-DFT machine. When the signals enter the MiLAC on the receiving end, the device physically rearranges the waves so that the output is the answer.

The Big Claim: You don't need a digital computer to do the math anymore. The math happens in the air and the wires.

Analogy: Imagine you have a room full of people shouting different notes. To find the "pitch" of the room, a digital computer would record everyone, write down the notes, and calculate the average. The MiLAC is like a room with special acoustic panels that naturally sort the sound waves so that the loudest sound comes out of a specific door, instantly telling you the pitch without anyone doing a single calculation.

Why This Matters (According to the Paper)

The paper runs simulations to prove their theory, and the results show:

Same Performance: The MiLAC radar sees targets just as clearly and accurately as the expensive, fully digital radar.
Less Hardware: Because the MiLAC does the work, you don't need a digital processor for every antenna. You can use cheaper, lower-resolution parts.
Zero Digital Math: The receiver doesn't need to run the heavy "2D-DFT" algorithm. The hardware does it instantly.
Speed: Because the processing happens in the analog domain (physically), it is incredibly fast, which is great for things like self-driving cars that need to react instantly.

Summary

This paper is about building a radar that uses a smart physical filter (MiLAC) instead of a digital super-computer to shape its signals and find targets. The authors proved that this "analog" approach is just as accurate as the digital one but is much cheaper, uses less power, and is faster because it skips the heavy digital calculations entirely.

Technical Summary: Microwave Linear Analog Computer (MiLAC)-Aided MIMO Radar Sensing

Problem Statement
Multiple-input multiple-output (MIMO) radar offers high-resolution sensing through waveform diversity and large spatial degrees of freedom (DoFs). However, scaling these systems to massive arrays introduces significant bottlenecks:

Hardware Cost and Power Consumption: Fully digital architectures require one RF chain (including high-resolution DACs and ADCs) per antenna. For large arrays (e.g., 256 antennas), power consumption becomes prohibitive (e.g., ~256 W for 12-bit ADCs).
Computational Complexity: Digital processing for transmit beamforming and receiver-side parameter estimation (such as Direction-of-Arrival (DoA) estimation via Discrete Fourier Transform (DFT)) scales poorly with array size. Subspace methods like MUSIC require $O(N^3)$ complexity, creating latency issues for real-time applications like automotive radar.

Existing solutions, such as low-resolution ADCs/DACs or hybrid beamforming, often incur irreversible information loss or reduced waveform diversity. While analog processing (e.g., Stacked Intelligent Metasurfaces) has been proposed, a unified framework that maintains the flexibility of digital beamforming while operating in the analog domain has been lacking.

Methodology
This paper proposes a unified MiLAC-aided MIMO radar framework that moves linear operations from the digital to the analog domain under practical physical constraints (losslessness and reciprocity).

System Model: The system employs a co-located Uniform Planar Array (UPA). The transmitter uses a MiLAC to perform beamforming, and the receiver uses a second MiLAC to perform 2D DFT for DoA estimation.
Transmit Beamforming Design:
- The authors formulate a weighted Cramér–Rao Bound (CRB) minimization problem for multi-target 2D angle estimation.
- The optimization is subject to total transmit power constraints and the specific constraints of the MiLAC impedance network (lossless and reciprocal).
- To solve the resulting non-convex problem (due to the coupling between the beamforming matrix $W$ and the covariance matrix $R_x = WW^H$ ), a Penalty Dual Decomposition (PDD) based iterative algorithm is developed. This algorithm alternates between updating the beamforming matrix, power allocation, and auxiliary variables.
Receiver-Side Processing:
- The paper demonstrates that a lossless reciprocal MiLAC can exactly implement a 2D DFT matrix in closed form.
- This enables analog-domain DoA estimation without digital optimization or per-symbol digital processing.
- To enhance resolution, a fractional 2D DFT approach is proposed, where the MiLAC is reconfigured across time slots to generate finer spatial-frequency bins.

Key Contributions

First MiLAC Radar Framework: This is the first work to investigate MiLAC-aided MIMO radar sensing under practical lossless and reciprocal constraints, addressing both transmitter and receiver sides.
Theoretical Equivalence: The authors prove that MiLAC-aided beamforming achieves the same optimal CRB as fully-digital beamforming. The key insight is that the CRB depends on the beamforming matrix only through the transmit covariance matrix ( $R_x$ ), and the set of achievable covariance matrices is identical for both architectures under the given constraints.
Algorithm Development: A PDD-based iterative algorithm is proposed to solve the non-convex transmit beamforming problem, with convergence analysis showing it reaches a KKT point.
Analog 2D DFT Implementation: A closed-form solution is derived showing that a lossless reciprocal MiLAC can implement the 2D DFT exactly, eliminating the need for digital DFT operations at the receiver.
Performance Validation: Numerical results confirm that the proposed approach matches the CRB and Mean Squared Error (MSE) of fully-digital benchmarks while drastically reducing hardware and computational costs.

Results

Sensing Performance: Simulations with $N=64$ antennas show that the MiLAC-aided design generates beampatterns identical to fully-digital designs and achieves the same CRB across various SNR levels and target counts.
DoA Estimation: The MiLAC-aided receiver successfully implements 2D DFT, producing angular spectra and MSE performance comparable to fully-digital 2D DFT processing.
Complexity and Hardware:
- Transmitter: Requires only low-resolution DACs as the RF chains carry radar-modulated signals directly.
- Receiver: Eliminates RF chains and ADCs entirely, as signal processing occurs in the analog domain.
- Computation: The analog implementation of the 2D DFT reduces computational complexity from $O(LN \log N)$ (digital) to effectively zero digital operations for the transform, offering ultra-low latency.

Significance
The paper claims that MiLAC-aided MIMO radar offers a promising hardware architecture that resolves the trade-off between performance and efficiency in massive array systems. By leveraging the analog domain for linear operations, the system achieves:

Performance Parity: It matches the sensing performance (CRB and DoA accuracy) of fully-digital systems.
Resource Efficiency: It significantly reduces hardware cost and power consumption by removing high-resolution ADCs/RF chains at the receiver and using low-resolution DACs at the transmitter.
Latency Reduction: It eliminates digital DFT operations and per-symbol digital processing, making it particularly suitable for real-time, latency-sensitive applications such as automotive radar.

The authors conclude that while current results focus on DFT-based estimation, the framework opens the door for future exploration of high-resolution algorithms (e.g., MUSIC) within the MiLAC architecture.