Antenna Coding Approach

• Antenna coding is a technique that reconfigures antenna elements using spatial, temporal, and electromagnetic codewords to improve reliability and security.
• It integrates hardware-based designs like pixel antennas with algorithmic codebook optimization to achieve significant SNR and capacity gains.
• Practical implementations demonstrate enhanced performance in MIMO and 6G systems, paving the way for robust, secure, and energy-efficient wireless links.

Antenna coding is an approach in wireless communications that directly exploits electromagnetic, spatial, temporal, and switching degrees of freedom at the physical antenna or antenna array to encode, process, and transmit information for improved performance, capacity, or security. Modern antenna coding techniques transcend conventional modulation and code construction by leveraging physical reconfigurability, pattern programmability, spatial indexing, or selection of codewords in the spatial and beamspace domains. These methods encompass both electromagnetic (hardware-embedded) and algorithmic (codebook, feedback, or learning-based) architectures, and are foundational to emerging paradigms such as reconfigurable intelligent surfaces, pixel antennas, fluid antennas, and spatiotemporally coded arrays.

1. Fundamental Principles of Antenna Coding

Antenna coding refers to the use of programmable antenna structures, spatial codebooks, port- or pattern-level switching, or code-diverse physical-layer signal processing to achieve enhanced reliability, multiplexing, spatial selectivity, or security compared to traditional statically configured MIMO systems. The defining aspect of antenna coding is the direct utilization of the physical reconfigurability or indexing of antenna ports, pixel elements, or antenna states, resulting in instantaneous channel shaping or pattern diversity.

Key elements include:

• Physical codewords: Binary or multi-level switch states that configure the topology or radiation pattern of reconfigurable antennas (e.g., pixel antennas) (Han et al., 5 Dec 2025, Shen et al., 11 Nov 2024).
• Spatial index coding: Codeword selection or mapping over antennas, ports, or virtual positions, for example in spatial coded modulation (SCM) or index-modulated fluid antenna systems (Luo et al., 2019, Faddoul et al., 11 Mar 2024).
• Pattern coding and codebook design: Optimizing over pattern-weight vectors or pattern codebooks, often using precalculated offline sets for efficient online selection (Li et al., 11 Dec 2025, Shen et al., 11 Nov 2024).
• Feedback and diversity selection: Adaptive or code-diversity schemes using limited feedback to choose among code families, phase rotations, or induced-coding variants to maximize diversity/coding gains (0809.2639).
• Spatiotemporal coding: Control of programmable metamaterial arrays or leaky-wave antennas through digital sequences over space and time to achieve specific physical-layer objectives such as directional modulation (Nooraiepour et al., 2022).

2. Pixel Antennas and Electromagnetic-Based Antenna Coding

Pixel antennas represent a canonical hardware realization of antenna coding. A continuous or patch antenna aperture is discretized into Q sub-wavelength pixels. These are interconnected by programmable switches (PIN diodes or MEMS), which determine the instantaneous radiation pattern, impedance, and spatial/frequency behavior of the antenna (Shen et al., 11 Nov 2024, Han et al., 5 Dec 2025, Li et al., 11 Dec 2025).

• Multiport network modeling: A pixel antenna is modeled as a (Q+1)-port microwave network, characterized by its full impedance matrix. The on/off state of each switch is represented by a binary vector $b\in\{0,1\}^Q$, altering the load and thus the port currents and far-field pattern.
• Beamspace representation: The overall channel between a transmit and receive pixel antenna, with fixed excitation, is represented as $h(b) = e(b)^H H_V e_T$, where $e(b)$ is the coded far-field pattern and $H_V$ is the virtual (beamspace) propagation channel (Shen et al., 11 Nov 2024).
• Antenna coder and pattern coder: The binary antenna coder $b$ specifies the switch states, while the pattern coder (a function of $b$) determines the basis-pattern weights in an SVD-decomposed pattern space (Han et al., 5 Dec 2025).
• Optimization and codebook design: The code $b$ is either optimized instantaneously (e.g., via SEBO or genetic algorithms), or drawn from an offline-designed codebook maximizing gains or orthogonality, significantly reducing computational complexity (Han et al., 5 Dec 2025, Shen et al., 11 Nov 2024, Li et al., 11 Dec 2025).

Antenna coding with pixel antennas can multiply the average SISO gain by up to 5.4× and MIMO capacity by up to 3.1× compared to conventional designs, approaching the theoretical upper bound set by the effective aerial degrees of freedom (Shen et al., 11 Nov 2024).

3. Spatial, Index, and Fluid Antenna Coding Paradigms

Spatial coded modulation (SCM) and index-modulated fluid antenna (IM-FA) systems employ antenna coding principles at the codebook or signaling layer:

• Spatial Coded Modulation (SCM): SCM codes information bits directly onto the activation pattern (codeword) of the transmit antennas using binary (M,k,d_min) codes, where minimum Hamming distance $d_{\min}$ governs detection reliability (Luo et al., 2019). Larger $d_{\min}$ increases system capacity and reduces BER, at the cost of reduced spatial rate.
• Index-Modulated Fluid Antenna (IM-FA) Systems: FA ports (locations) are indexed via coded bits, with set-partition coding (SPC) ensuring maximal physical separation in the port mapping, hence tolerance to spatial correlation (Faddoul et al., 11 Mar 2024). Turbo-coded modulation extends this principle, concatenating recursive systematic convolutional codes at the antenna index layer for multi-dB coding gain under strong spatial correlation.

Both SCM and IM-FA frameworks demonstrate that combining physical antenna selection with code-based redundancy or partitioning mechanisms yields both improved error rates and spectral efficiency under diverse fading and correlation regimes.

4. Algorithmic Methodologies: Codebook Optimization and Complexity Reduction

Antenna coding system design faces a high-dimensional, discrete, often NP-hard optimization landscape due to the exponential number of possible switch states or codeword selections:

• Alternating optimization: Iteratively updating precoders and per-user antenna coders to maximize sum-rate or capacity in multi-user MISO/MIMO settings. Auxiliary variables (fractional programming) relax the objective, while block search (e.g., SEBO) addresses each user's binary search domain (Li et al., 11 Dec 2025).
• Offline codebook and hierarchical design: Generalized Lloyd or k-means-based clustering creates a small set of codewords (patterns) that partitions the possible channel states, enabling real-time pattern selection at negligible fraction of the full search complexity. Hierarchical structures further compress search overhead by tree search over codebook layers (Li et al., 11 Dec 2025).
• Genetic and iterative switch-reduction: Starting from a full-switch codebook, switches with invariant settings or minimal impact are progressively fixed, drastically reducing hardware and computational requirements while maintaining coding gain (Han et al., 5 Dec 2025).

These techniques enable practical exploitation of the latent coding and diversity potential in reconfigurable antenna platforms, while trading between performance and implementation complexity.

5. Applications in Physical-Layer Security and Directional Modulation

Antenna coding can provide robust security guarantees rooted in the physics of wireless propagation:

• Spatiotemporal digital coding metamaterial antennas: Programmable leaky-wave or metasurface arrays, with unit cells governed by real-time digital patterns, can shape radiation both spatially (beam angle) and spectrally (harmonic content), enabling directional modulation (DM) (Nooraiepour et al., 2022).
• Directional Modulation (DM): By constructing coding sequences ${q_u}$ (state of each unit cell in each time slot) and solving a mixed-integer nonlinear program, the system ensures that only a receiver at the target angle observes clean, harmonics-free OFDM signaling, while off-target directions are contaminated by strong harmonics or shaped interference. A machine-learning-accelerated branch-and-bound solver enables real-time optimization (Nooraiepour et al., 2022).
• Experimental validation: FPGA-controlled prototypes with time-modulated varactor-loaded unit cells confirm the theoretical predictions. BER below $10^{-3}$ is achieved solely at the target direction, while all other directions see BER near 0.5, demonstrating strong physical-layer security.

This approach leverages the high-dimensional code space of reconfigurable antennas, directly encoding physical-layer secrecy into the propagation medium.

6. MIMO, Cooperative, and Networked Antenna Coding Frameworks

Antenna coding is foundational in several advanced multi-antenna wireless network scenarios:

• Distributed and coordinate-interleaved coding: In relay networks, coordinate interleaved distributed space-time coding (CIDSTC) leverages intra-relay in-phase/quadrature interleaving prior to space-time encoding, exceeding previous DSTC coding gains under minimal per-relay complexity (0806.1577).
• Adaptive coding with feedback/code diversity: Families of structurally related space–time block codes, with selection guided by limited receiver-side CSI feedback, achieve maximal diversity and coding gains across a wide range of fading states. Code diversity through phase/parameter selection or circulant code families enables low-complexity decoding (e.g., Fourier-based linear decoders), with diversity orders and coding performance that can match or exceed ML decoding of static codes (0809.2639).
• Uplink with low-resolution ADCs: A coding-theoretic uplink MIMO framework uses the quantizer-augmented channel as an auto-encoder, with detection reduced to a minimum-distance decoding in codeword space. Weighted MDD exploiting the reliability of each spatial-quantization pipe reduces BER exponentially in the minimum code distance, yielding substantial SNR improvement compared to conventional detection (Hong et al., 2017).
• Buffer-aided and adjustable space–time coding: Cooperative relay systems equipped with adjustable STC matrices at each relay, subject to buffer-aware link selection and iterative SGD optimization, achieve improved coding gain and diversity under realistic Rayleigh fading and relay constraints (Peng et al., 2015).

In these settings, antenna coding acts as a unifying technical framework, encompassing physical index modulation, adaptive state selection, pattern-level redundancy, and structured lattice designs for ergodic channels (Hindy et al., 2017).

7. Impact, Opportunities, and Future Directions

Antenna coding unlocks an additional layer in the communication-theoretic and physical design of wireless systems, with concrete implications:

• Significant SNR, BER, and spectral efficiency gains are evidenced across SISO, MIMO, multi-user, and relay topologies, often with orders-of-magnitude improvement in channel gain, capacity, and energy efficiency (Han et al., 5 Dec 2025, Shen et al., 11 Nov 2024, Li et al., 11 Dec 2025).
• The approach is robust to device/array geometry, hardware nonidealities, spatial correlation, and channel fading statistics, and can be implemented with tractable hardware and search complexity due to hierarchical codebook and offline optimization frameworks.
• Antenna coding is central to future 6G and beyond architectures, including programmable intelligent surfaces, secure wireless links, ultra-massive MIMO, and dynamic electromagnetic environments.
• Fundamental limits are currently being established in terms of aerial DoF, switch/resource scaling, and codebook capacity bounds, with opportunities for further research in joint EM-algorithm design, learning-based online optimization, and multi-tenant security.

Antenna coding thus constitutes a new, physically grounded axis for the control and optimization of wireless systems, bridging hardware programmability, information theory, and spatial signal processing in ways not achievable by traditional antenna or code design alone (Shen et al., 11 Nov 2024, Han et al., 5 Dec 2025, Li et al., 11 Dec 2025, Luo et al., 2019, Nooraiepour et al., 2022).