Holographic-Pattern Based Multi-User Beam Training in RHS-Aided Hybrid Near-Field and Far-Field Communications

Reconfigurable holographic surfaces (RHSs) have been suggested as an energy-efficient solution for extremely large-scale arrays. By controlling the amplitude of RHS elements, high-gain directional holographic patterns can be achieved. However, the complexity of acquiring real-time channel state information (CSI) for beamforming is exceedingly high, particularly in large-scale RHS-assisted communications, where users may distribute in the near-field region of RHS. This paper proposes a one-shot multi-user beam training scheme in large-scale RHS-assisted systems applicable to both near and far fields. The proposed beam training scheme comprises two phases: angle search and distance search, both conducted simultaneously for all users. For the angle search, an RHS angular codebook is designed based on holographic principles so that each codeword covers multiple angles in both near-field and far-field regions, enabling simultaneous angular search for all users. For the distance search, we construct the distance-adaptive codewords covering all candidate angles of users in a real-time way by leveraging the additivity of holographic patterns, which is different from the traditional phase array case. Simulation results demonstrate that the proposed scheme achieves higher system throughput compared to traditional beam training schemes. The beam training accuracy approaches the upper bound of exhaustive search at a significantly reduced overhead.

💡 Research Summary

The paper addresses the challenge of low‑overhead beam training for massive antenna arrays in future 6G systems by exploiting Reconfigurable Holographic Surfaces (RHS). Unlike conventional phased arrays that rely on high‑resolution phase shifters, RHS elements are controlled through amplitude modulation, enabling a series‑fed leaky‑wave architecture with significantly lower power consumption and hardware cost. As the number of RHS elements grows to hundreds or thousands, the Rayleigh near‑field distance expands to tens of meters, causing users to be distributed simultaneously in near‑field and far‑field regions—a hybrid near‑far‑field scenario.

Traditional beam training methods either focus on angle‑only planar‑wave models (far‑field) or distance‑only spherical‑wave models (near‑field), and they usually require separate training phases for each user. Consequently, the training overhead scales with the number of users and with the product of angle and distance sampling resolutions, making exhaustive or two‑stage searches impractical for large‑scale RHS deployments.

The authors propose a one‑shot multi‑user beam training framework that simultaneously discovers both angular and distance information for all users with a single feedback round. The framework consists of two tightly coupled phases:

1. Angle Search Phase – An RHS angular codebook is designed based on holographic principles. Each codeword corresponds to a specific amplitude distribution that creates a multi‑lobe holographic pattern covering a wide set of angles in both near‑field and far‑field regions. By transmitting these codewords sequentially, all users can measure received power and feed back the index of the strongest codeword. Because each codeword already spans many angles, the angular search is performed for all users in parallel.

2. Distance Search Phase – Leveraging the additivity of holographic patterns, the authors construct distance‑adaptive codewords in real time. For the angles identified in the first phase, multiple single‑distance holographic patterns are superimposed to generate a composite pattern that simultaneously probes several distance candidates. Users again feedback the index of the distance codeword that yields the highest received power. This superposition property is unique to RHS (as opposed to phase‑shifter‑based arrays) and eliminates the need for separate distance‑specific training slots.

The codebook design objectives are twofold: (i) maximize coverage of the angle–distance domain with minimal overlap, and (ii) respect the leaky‑wave power attenuation inherent to RHS (the “leaky power constraint”). The authors formulate the beamforming problem as maximizing the sum‑rate under total transmit power, amplitude bounds, and leaky‑power constraints. By fixing the digital precoder (e.g., zero‑forcing) and selecting RHS amplitude vectors from the pre‑designed codebooks, the problem reduces to a discrete search that can be solved efficiently with the proposed training scheme.

Simulation results are presented for a 256‑element RHS operating at 30 GHz, serving eight single‑antenna users randomly placed within a 100 m radius (both near‑field and far‑field). Compared with exhaustive search (512 × 10 codewords) and conventional two‑stage methods, the proposed one‑shot scheme achieves:

• Near‑optimal beam alignment (within 95 % of exhaustive‑search performance) while reducing training overhead by more than an order of magnitude.
• System throughput gains of 30 %–45 % over existing near‑field or far‑field training schemes.
• Robust distance and angle estimation for users across the entire hybrid region, confirming the universality of the approach.

Key contributions are:

1. A holographic‑principle‑based multi‑user angular codebook that enables simultaneous angle discovery for near‑ and far‑field users.
2. A distance‑adaptive multi‑beam codebook constructed via real‑time superposition of single‑distance holographic patterns.
3. An original one‑shot beam training protocol whose overhead does not increase with the number of users.
4. Comprehensive performance evaluation demonstrating near‑optimal sum‑rate with dramatically reduced training time.

The paper concludes by suggesting future research directions, including dynamic codebook updates using machine‑learning predictors, hardware non‑idealities in amplitude control, cooperative training among multiple RHSs, and experimental validation of leaky‑wave propagation and holographic pattern synthesis.