⚡ electrical engineering

Holographic Beamforming for Range-Doppler Sidelobe Suppression in OFDM-ISAC

This paper proposes a joint design of digital feed precoders and reconfigurable holographic surface (RHS) amplitudes using an alternating successive convex approximation method to suppress range-Doppler sidelobes in OFDM-based integrated sensing and communication systems, demonstrating that increasing the RHS aperture is more effective than adding feeds for sidelobe reduction.

Original authors: Amirhossein Azarbahram, Onel L. A. López

Published 2026-08-21

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CC BY 4.0

Original authors: Amirhossein Azarbahram, Onel L. A. López

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

Wireless technology is undergoing a quiet revolution, moving beyond simply sending messages to also acting as a set of eyes and ears for the world. This new approach, known as integrated sensing and communications, allows a single system to talk to your phone and simultaneously track the movement of objects, much like a lighthouse that both guides ships and watches the horizon. The challenge lies in the signals themselves. When these systems use a common method called orthogonal frequency-division multiplexing to send data, the signals naturally create a background of faint, ghostly echoes. These echoes, known as sidelobes, can hide weak targets, making it difficult to distinguish a small drone or a distant car from the noise of the transmission itself. To solve this, engineers must shape the signal so that the main beam is sharp and the surrounding noise is silenced, a task that becomes increasingly difficult as the system tries to do more things at once.

Researchers at the University of Oulu in Finland have tackled this problem by designing a new way to control these signals using a special type of surface called a reconfigurable holographic surface. Imagine a large, flat panel covered in thousands of tiny, adjustable elements that can change how radio waves bounce off them. This panel is fed by a smaller number of electronic sources, or feeds, which act like the heart of the system, pumping energy into the surface. The researchers discovered that by carefully coordinating the signals from these feeds with the precise settings of the surface elements, they could dramatically reduce those ghostly echoes. They developed a mathematical method to adjust both the feeds and the surface simultaneously, ensuring that the system remains powerful enough to talk to multiple users while keeping the radar view clear.

The team tested their idea through detailed computer simulations, creating a virtual environment where the system had to communicate with several users while tracking a moving target. They compared their new method against older approaches, such as using a fixed surface or a random arrangement of settings. The results showed that their joint design worked significantly better than the fixed or random methods, bringing the performance very close to that of a fully digital system, which is much more complex and expensive to build. The simulations revealed a clear pattern: making the surface larger, with more elements, consistently improved the ability to suppress the unwanted echoes. However, adding more electronic feeds to the system showed diminishing returns; after a certain point, adding more feeds did not help much, whereas increasing the size of the surface continued to yield better results.

The study also explored how the system behaves when the demands for communication become stricter. When the researchers required the system to maintain a higher quality of connection for its users, the ability to suppress the radar echoes naturally decreased, as more energy had to be diverted to ensure clear communication. Despite this trade-off, the new method remained robust, staying close to the performance of the ideal, fully digital benchmark across a wide range of conditions. The researchers concluded that by treating the electronic feeds and the holographic surface as a single, unified system rather than separate parts, they could achieve a level of control that was previously out of reach. This work suggests that future wireless networks could be designed to be both excellent communicators and precise sensors, provided the hardware is tuned with the right kind of mathematical care.

Technical Summary: Holographic Beamforming for Range-Doppler Sidelobe Suppression in OFDM-ISAC

Problem Statement
This paper addresses the challenge of Range-Doppler (RD) sidelobe suppression in Integrated Sensing and Communications (ISAC) systems utilizing Orthogonal Frequency-Division Multiplexing (OFDM). While OFDM is attractive for ISAC due to its time-frequency structure, the finite OFDM grid inherently generates non-negligible RD sidelobes. These sidelobes can mask weak targets, degrading sensing performance.

The specific context is a system employing a Reconfigurable Holographic Surface (RHS) as the transmitter. Unlike fully digital (FD) systems, RHS architectures use a limited number of digital feeds to excite a dense array of subwavelength radiating elements. This creates a "feed-to-aperture" mapping that couples the digital feed precoders with the analog surface amplitudes. This coupling prevents the direct application of standard FD precoding methods. Furthermore, while previous works have optimized spatial beam patterns or specific OFDM range sidelobes, RD sidelobe suppression for RHS-aided OFDM systems has not been previously investigated.

Methodology
The authors propose a joint design framework to minimize the Integrated Sidelobe Level (ISL) of the RD response. The optimization variables are the digital feed precoders ( $V_n$ ) and the RHS amplitude control vector ( $m$ ). The problem is formulated under three primary constraints:

Transmit Power: The total average power must not exceed a budget ( $P_t$ ).
Target Illumination: A minimum power must be radiated toward the target direction to ensure sufficient echo strength.
Communication Quality: Per-user Signal-to-Interference-plus-Noise Ratio (SINR) constraints must be met for multiuser communication.

The objective function (ISL) and the constraints are non-convex due to the multiplicative coupling between the precoders and the surface amplitudes, as well as the quartic nature of the ISL objective.

To solve this, the authors develop an Alternating Successive Convex Approximation (SCA) algorithm. The method iteratively updates two variable blocks:

Feed-Domain Update: With fixed RHS amplitudes, the problem is approximated using a proximal first-order model. The non-convex constraints are linearized or lower-bounded, transforming the subproblem into a convex Quadratically Constrained Quadratic Program (QCQP).
RHS-Amplitude Update: With fixed feed precoders, the problem is similarly reformulated. The authors introduce specific matrix constructions (e.g., $H(c)$ ) to handle the quadratic forms of the amplitude variables, again resulting in a convex QCQP subproblem.

The algorithm ensures feasibility at each step by using tight global lower bounds and employs a backtracking mechanism to adjust proximal parameters if constraints are violated. Convergence is guaranteed as the ISL is non-negative and non-increasing with each accepted update.

Key Contributions

Formulation: The paper formulates the joint optimization of digital feed precoders and RHS amplitudes specifically for RD ISL minimization, incorporating transmit power, target illumination, and multiuser SINR constraints.
Algorithm: It develops an alternating SCA method that updates both variable blocks through convex subproblems with feasible inner approximations, avoiding the rank-recovery issues often associated with semidefinite relaxation.
Numerical Validation: The study provides numerical evidence that the proposed joint design significantly outperforms baselines using random or fixed RHS configurations and approaches the performance of a fully digital (FD) benchmark.

Numerical Results
The authors evaluate the system using a monostatic OFDM-ISAC setup with a Uniform Linear Aperture (ULA) RHS. Key findings include:

Convergence: The proposed algorithm demonstrates rapid initial reduction in the objective function followed by slower refinement.
Aperture Size ( $M$ ): Increasing the number of RHS elements generally improves the achievable Normalized ISL (NISL). A larger aperture provides greater spatial and waveform-shaping flexibility, allowing for more effective sidelobe suppression.
Number of Feeds ( $N_f$ ): Increasing the number of feeds initially improves performance by offering more design flexibility. However, the paper notes "diminishing returns" as $N_f$ increases, suggesting that aperture size is a more effective lever for performance than simply adding more feeds.
SINR Constraints: Stricter communication SINR requirements degrade the achievable NISL, as more transmit resources are diverted to satisfy communication constraints. Nevertheless, the joint design remains close to the FD benchmark across the tested SINR range.
Baselines: The joint RHS-SCA method consistently outperforms a "Fixed" RHS (optimized precoders only) and a "Random" RHS (random amplitudes with optimized precoders).

Significance and Claims
The paper claims to be the first to investigate RD sidelobe suppression specifically for RHS-aided OFDM systems. It highlights that while hardware and spatial degrees of freedom are crucial for RD sidelobe suppression, previous works had not applied these concepts to RHS architectures.

The authors modestly conclude that their proposed joint design offers a practical solution that balances sensing and communication performance. They emphasize that increasing the aperture size is a more effective strategy for sidelobe suppression than increasing the number of feeds. The work demonstrates that despite the hardware constraints of RHS (coupled digital-analog control), it is possible to achieve sensing performance close to fully digital systems while maintaining multiuser communication guarantees.

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