Pixel Antennas for Reconfigurable 6G MIMO

• Pixel antennas are reconfigurable structures composed of sub-wavelength pixels interconnected by RF switches to dynamically control radiation patterns.
• They enable increased spatial degrees of freedom in MIMO systems, achieving up to 12 bit/s/Hz spectral efficiency gains and significant power reductions in 6G scenarios.
• Advanced optimization techniques, including genetic algorithms and alternating switch reduction, are used to minimize pattern coder cross-correlation for enhanced performance.

Pixel antennas constitute a class of general reconfigurable antennas in which an arbitrarily shaped radiating structure is discretized into sub-wavelength elements (pixels), interconnected by a set of radio-frequency (RF) switches. By configuring the switch states, the surface current distribution—and consequently the far-field radiation pattern—of the antenna can be dynamically reconfigured, yielding new degrees of freedom for beamspace spatial multiplexing and digital-pattern modulation. This approach enables efficient exploitation of spatial degrees of freedom (DoF) in compact hardware, offering significant gains in spectral and energy efficiency for multiple-input multiple-output (MIMO) communication systems, with particular promise for ultra-massive MIMO and 6G scenarios (Han et al., 5 Dec 2025).

1. Pixel Antenna Structure and Coding Abstractions

A pixel antenna consists of an arbitrarily shaped metallic or conductive radiating surface discretized into $Q$ sub-wavelength pixels. Each pixel can be connected to its neighbors or left open via RF switches (e.g., PIN diodes). Electrically, this structure is modeled as a $(Q+1)$-port network, comprising a single feed port and $Q$ switch-terminated pixel ports.

• Antenna Coder: The switch configuration is encoded by a binary vector $\mathbf{b} \in \{0,1\}^Q$, where $b_i=0$ denotes a closed (ON) switch (short-circuit the $i$-th pixel), and $b_i=1$ denotes an open (OFF) switch.
• Pattern Coder: For each switch state, define the resulting current excitation and far-field as $e(\mathbf{b})$. The set of open-circuit port radiation patterns is stacked into a matrix $E_{\mathrm{oc}} \in \mathbb{C}^{2K \times (Q+1)}$, whose singular value decomposition (SVD) yields an orthonormal basis $U$ for the radiation space and associated singular coefficients.
• Degrees of Freedom (DoF): The radiation pattern for a given $\mathbf{b}$ is represented as $e(\mathbf{b}) = U w(\mathbf{b})$, where $w(\mathbf{b}) \in \mathbb{C}^R$ is the so-called "pattern coder" (projections onto the $R$ most significant singular vectors). The mapping $\mathbf{b} \to w(\mathbf{b})$ provides additional spatial DoF beyond conventional array modes, enabling transmission of $\log_2 P$ additional bits per antenna for $P$ distinct switch states.

2. Beamspace MIMO Modeling with Pixel Antennas

In a MIMO system comprising $N$ transmit pixel antennas and $M$ (non-pixel) receive antennas, each transmit pixel antenna generically radiates a pattern $e_n(\mathbf{b}_n)$ parameterized by its switch configuration. The system is modeled in the beamspace domain as follows:

• The receive and transmit pattern bases are $F = [f_1, \dots, f_M]$ and $E = [e_1, \dots, e_N]$.
• The physical (virtual) channel is $H_V \in \mathbb{C}^{2K \times 2K}$, mapping radiation modes from transmit to receive basis.
• The compound channel under per-symbol antenna-coding is $H(\mathbf{B}) = F^\mathsf{T} H_V E(\mathbf{B})$, where $E(\mathbf{B})$ stacks the $N$ radiated patterns, with each $e_n(\mathbf{b}_n) = U_n w_n(\mathbf{b}_n)$.
• Projecting onto the beamspace receive basis yields the equivalent beamspace channel $H_{\mathrm{b}} = F^H H_V U_{\mathrm{BS}}$, where $U_{\mathrm{BS}} = [U_1,\dots,U_N]$ and $T = W(\mathbf{B})$ is the block-diagonal matrix of per-antenna pattern coders.

The end-to-end linear MIMO system is then

$y = H_{\mathrm{b}} T s + n$

with $s$ the digital symbol vector, and $T = W(\mathbf{B})$ jointly mapping digital and pattern-index bits.

3. Spectral Efficiency Quantification

For jointly Gaussian signaling over the system described above, with $s \sim \mathcal{CN}(0, S)$ and transmit power constraint $\mathrm{tr}(T S T^H)=P$, the spectral efficiency (SE) in bits/s/Hz is

$$C(H_{\mathrm{b}}, T) = \log_2 \det \left[ I + \frac{1}{\sigma^2} H_{\mathrm{b}} T S T^H H_{\mathrm{b}}^H \right]$$

For uniform power allocation $S = (P/N)I$, this simplifies to

$$C = \log_2 \det \left[ I + \frac{P}{N \sigma^2} H_{\mathrm{b}} T T^H H_{\mathrm{b}}^H \right]$$

The achievable $C$ is enhanced by both spatial mode multiplexing and the increase in DoF due to dynamic digital-pattern modulation via pixel antenna coding.

4. Antenna Coder (Pattern Codebook) Optimization

Maximizing SE requires selection of $P$ distinct, as-orthogonal-as-possible antenna-coder vectors $$\{ \mathbf{b}_{C,1}, \dots, \mathbf{b}_{C,P} \} \subset \{ 0, 1 \}^Q$$. The objective is to minimize mean squared cross-correlation between pattern coders:

$$g(\mathbf{b}_{C,1}, ..., \mathbf{b}_{C,P}) = \frac{2}{P(P-1)} \sum_{j<k} | w(\mathbf{b}_{C,j})^H w(\mathbf{b}_{C,k}) |^2$$

Optimization proceeds via:

• Genetic Algorithm (GA): Candidate codebooks are evolved across generations using closed-form evaluation of $g$. Typical parameters: $N_{\text{pop}} \approx 200$, $\approx 300$ generations, convergence to a good local minimum $g^\star$ in $O(P^2 R)$ per candidate.
• Switch-Count Reduction (Alternating Optimization): Starting with the GA solution, iteratively identify switch positions fixed across all $P$ codewords, freeze them, and re-optimize the reduced codebook until $g$ ceases to improve by more than a threshold $\Delta g$.

Typical runtimes for $Q \approx 40$ switches are 8–10 alternating steps with $\Delta g \approx 0.05$.

5. Numerical Results and Physical Implementation

Pixel antenna prototypes at 2.4 GHz (e.g., $5\times 5$ copper pixels, $Q=40$ switches) yield $R=8$ effective aerial DoF (capturing 99.5% of radiated power in the first 8 SVD modes). For codebooks of $P=4$ and $P=8$ switch patterns:

• With $Q=40$, $P=4$ achieves $g^\star \approx 0.005$ (fully unconstrained), which can be maintained with as few as $N_{\mathrm{sw}}=3$ active switches.
• For $P=8$, $g^\star \approx 0.05$ baseline, $N_{\mathrm{sw}}=5$ suffices for $g\leq 0.1$.

In a $4 \times 4$ MIMO with Rayleigh beamspace channel, at $30$ dB SNR, antenna coding with $P=8$, $N_{\mathrm{sw}}=15$ increases SE by up to $12$ bit/s/Hz over conventional fixed arrays. Alternatively, to sustain the same MIMO capacity as a conventional array, a transmit power reduction of approximately $10$ dB ($\approx 90\%$) is achieved.

Energy efficiency (EE = SE/total-power, including all RF and switch power) is maximized for moderate numbers of switches ($N_{\mathrm{sw}}=2\text{–}3$ for $P=4$, $N_{\mathrm{sw}}\approx 7$ for $P=8$).

6. Implications for 6G Wireless

Pixel antenna coding provides several key advantages for future 6G systems:

• Spatial Multiplexing Scaling: Pixel-antenna coding increases the number of exploitable spatial modes from $K$ to $K \times P$ without requiring additional RF chains, enabling ultra-massive MIMO with compact hardware.
• Spectral and Energy Efficiency: Dynamically coded radiation patterns enable flexible trade-offs between SE and EE, accommodating stringent power and form-factor constraints.
• Cost and Complexity: The hardware overhead remains minimal, requiring only a modest number of PIN diode switches.
• New Modulation Paradigm: Joint digital-pattern modulation (embedding information directly in the reconfigured radiation pattern) constitutes a new dimension of index modulation, orthogonal to conventional QAM/PSK for 6G (Han et al., 5 Dec 2025).

7. Conclusion

Pixel antennas, when combined with optimized digital antenna coding, offer an efficient and scalable means of exploiting spatial multiplexing in compact form factors. The approach directly enhances both the spectral and energy efficiency of MIMO systems and is particularly suited for the ultra-massive scale and power constraints of next-generation (6G) wireless communication infrastructures. Simulation and physical design results confirm the practical benefits of the paradigm, including SE gains up to $12$ bit/s/Hz in $4\times 4$ MIMO and $90\%$ reductions in required transmit power at target rates, establishing antenna coding in pixel arrays as a key enabler for high-dimensional, flexible 6G wireless (Han et al., 5 Dec 2025).