1-bit Phase Resolution LIS

• 1-bit Phase Resolution LIS is a reconfigurable intelligent surface that toggles reflection phases between 0 and π to enable low-cost, energy-efficient wave manipulation.
• It employs simple hardware components such as PIN diodes and RF switches, achieving robust phase control and enhanced network coverage in MIMO/MISO systems.
• Advanced optimization methods—including mixed-integer programming, deep reinforcement learning, and genetic algorithms—mitigate quantization losses while maximizing energy efficiency and capacity.

A 1-bit phase resolution Large Intelligent Surface (LIS), also discussed as a 1-bit Reconfigurable Intelligent Surface (RIS), is an array of nearly passive or weakly active electromagnetic scatterers, each capable of toggling its reflection phase between two discrete values (0 and π, or equivalently +1 and –1). This severe phase quantization enables low-cost, low-power, and scalable hardware suitable for smart reconfigurable radio environments, wireless MIMO/MISO communications, and wave-based sensing. Despite its coarse granularity, such 1-bit LIS/RIS designs enable substantial performance gains in terms of energy efficiency, network coverage, and robust phase control, while facilitating robust signal processing algorithms operating at the fundamental information-theoretic limits.

1. Physical and System Architecture

In 1-bit phase resolution LIS implementations, each element (or "unit cell") manipulates the phase of incident electromagnetic waves by discrete switching—typically achieved by toggling PIN diodes, RF switches, or MEMS between open and grounded states. The resulting phase shift per element is either 0° or 180°, corresponding to reflection coefficients of +1 or –1. Practical architectures employ cost-effective PCB technology, spring-contact or pin-feed structures, and simple bias networks, allowing high-density deployment over large surfaces for 5G/6G wireless bands (Heinrichs et al., 19 Feb 2026, Rezaei et al., 10 Jun 2025).

Insertion losses per element range from 2.5 to 4 dB, and reflection phase differences close to 180° are practically achievable over bandwidths up to 500 MHz (e.g., for n78 3.6 GHz 5G). Power consumption is extremely low: less than 0.02 mW per 1-bit switch, facilitating the construction of meter-scale walls with energy consumption below 10 mW for thousands of elements (Heinrichs et al., 19 Feb 2026).

2. Mathematical Model and Performance Metrics

In a multi-user MISO wireless downlink scenario, the system comprises an M-antenna base station (BS), K single-antenna users, and an N-element LIS acting as a programmable reflector. The received signal model at user k is:

$y_k = (h_{2,k}\,\Phi\,H_1 + h_{1,k})\,x + n_k,$

where $h_{1,k}$ and $h_{2,k}$ are the direct and LIS channels, $H_1$ is the BS-to-LIS channel, $x$ is the transmit vector, and $\Phi = \mathrm{diag}(\phi_1,\ldots,\phi_N)$ with $\phi_n \in \{+1, -1\}$ is the 1-bit phase matrix (Huang et al., 2018). The effective channel is $h^{\mathrm{eff}}_k = h_{2,k}\,\Phi\,H_1 + h_{1,k}$. The instantaneous SINR for user k follows:

$$\gamma_k = \frac{p_k\,|h^{\mathrm{eff}}_k\,g_k|^2}{\sum_{i \neq k} p_i\,|h^{\mathrm{eff}}_k\,g_i|^2 + \sigma^2}.$$

Energy efficiency (EE) is measured as the ratio of sum-rate to total power consumption:

$$\eta(\Phi,P) = \frac{\sum_k \log_2(1+\gamma_k)}{\sum_k \mu_k p_k + K P_c + N P_n(1)},$$

where $h_{1,k}$0 denotes 1-bit LIS element power (Huang et al., 2018).

In array-level beamforming, the main-lobe array gain with 1-bit control is reduced by $h_{1,k}$1 ($h_{1,k}$23.9 dB), and first sidelobes remain below –13 dB relative to the main lobe (Heinrichs et al., 19 Feb 2026, Rezaei et al., 10 Jun 2025).

3. Optimization and Control of 1-Bit LIS

Mixed-Integer Optimization

The main challenge in 1-bit LIS design is combinatorial: with $h_{1,k}$3 elements, the set of feasible $h_{1,k}$4 is of size $h_{1,k}$5. To maximize EE or capacity while satisfying rate and power constraints, the canonical approach alternates between:

1. Optimizing $h_{1,k}$6 given fixed power allocation $h_{1,k}$7: This is tackled via a relaxation (allowing $h_{1,k}$8 on $h_{1,k}$9), then quantization of the optimal continuous phases back to 0 or π (Huang et al., 2018).
2. Optimizing $h_{2,k}$0 given fixed $h_{2,k}$1: Formulated as a quasi-convex fractional program and efficiently solved by Dinkelbach's algorithm.

This alternating procedure is near-optimal for moderate $h_{2,k}$2, especially when the continuous-then-quantize step is used for the 1-bit phase matrix (Huang et al., 2018).

Learning-Based 1-Bit Configurations

For online adaptation and scalability to very large $h_{2,k}$3, binary-action vector representations are paired with deep reinforcement learning (DRL) agents such as binarized Deep Q-Networks (bin-DQN) and binarized Deep Deterministic Policy Gradient (bin-DDPG). These methods scale linearly with $h_{2,k}$4, in contrast to the exponential scaling of enumerative approaches, and achieve near-optimal reflection configuration in large-scale (up to $h_{2,k}$5) deployments (Stylianopoulos et al., 2022).

Genetic and Heuristic Optimization

For high-frequency (e.g., mmWave 28 GHz) hardware where phase errors and unintended specular reflections degrade ideal performance, genetic algorithms (GAs) seeking to maximize coherent beamforming gain (minimize phase quantization error) can restore up to 50% of quantization-induced main-lobe loss, offering 2–3 dB improvement compared to naive quantization. Chromosome representation is binary, and fitness is defined through the magnitude of the coherent field sum (Rezaei et al., 10 Jun 2025).

4. Information-Theoretic and Algorithmic Aspects

1-Bit Phase Retrieval and Recovery

1-bit phase quantization models correspond to an extreme compressed sensing and phase retrieval regime—only the sign of pairwise measurement differences is preserved. Precisely, for $h_{2,k}$6 measurement pairs,

$h_{2,k}$7

is the datum available for recovery (Mroueh et al., 2013, Mroueh, 2014). The leading eigenvector of the empirical signed difference matrix provides a near-optimal estimator of $h_{2,k}$8, with sample complexity $h_{2,k}$9 and robust recovery guarantees, even under rank-preserving nonlinearities, clipping, or Poisson noise (Mroueh et al., 2013, Chen et al., 2024, Mroueh, 2014). These guarantees are extended to the super-resolution setting, where random masks coupled with 1-bit quantization enable recovery well beyond conventional diffraction limits (Mroueh, 2014).

For $H_1$0-sparse signals, thresholded gradient descent with 1-bit measurements achieves $H_1$1 error $H_1$2, matching 1-bit compressed sensing in rate, revealing the non-necessity of phase information in sparse regimes (Chen et al., 2024).

Alternating Minimization and Greedy Refinement

A standard alternating minimization (AM) scheme, initialized by the spectral method above, further accelerates convergence. AM alternates between estimating unknown phases and solving least-squares, with convergence rates and sample complexity improved when initialized by 1-bit spectral estimators (Mroueh et al., 2013).

5. Capacity, Energy Efficiency, and Quantization Trade-Offs

The impact of 1-bit phase resolution on achievable capacity, beamforming gain, and energy efficiency is quantifiable. For realistic MISO/MIMO downlinks:

• Energy Efficiency: Representative results show $H_1$3 improvement in EE using 1-bit LIS relative to amplify-and-forward relays across practical scenarios (e.g., $H_1$4, $H_1$5), with modest sum-rate loss (up to 20 bits/s/Hz at high SNR) (Huang et al., 2018).
• Ergodic Capacity Degradation: Under Rician fading, analytic bounds show that 1-bit quantization (b=1) can lead to capacity losses exceeding 1 bit/s/Hz at moderate $H_1$6 and SNR, while 2 bits suffices to constrain degradation to 1 bit/s/Hz. The lower bound on coherent gain is zero for 1-bit due to $H_1$7, so complete phase coherence is lost (Han et al., 2018).
• Beamforming: 1-bit RISs at 3.6 GHz and 28 GHz exhibit main-lobe degradation by approximately 4 dB and increased sidelobe levels, but maintain practical scanning ranges ($H_1$8) and array efficiencies of 30–40% (Heinrichs et al., 19 Feb 2026, Rezaei et al., 10 Jun 2025).
• Specular Reflection and Hardware Constraints: At mmWave, hardware design must address parasitic specular reflections (from metallic layers) and nonideal phase shifts (Δϕ < 180°), which further degrade effective array gain. Careful geometric and biasing network calibration is essential (Rezaei et al., 10 Jun 2025).

6. Practical Implementations and Scalability

Advances in RF switch technology (e.g., SPDT switches drawing <20 μW per element) and PCB-based unit-cell architectures enable construction of RIS walls covering multiple square meters, with straightforward mechanical assembly and minimal thermal footprint (Heinrichs et al., 19 Feb 2026). Low-complexity binarized RL controllers provide feasible real-time optimization for thousand-element arrays (Stylianopoulos et al., 2022). Genetic algorithms complement hardware limitations by recovering beamforming fidelity lost to quantization and nonideal tolerance (Rezaei et al., 10 Jun 2025). Hybrid bit-resolution (mixing 1-bit with higher-resolution cells) presents a future direction to optimize the cost-performance-power envelope.

7. Applications, Limitations, and Outlook

1-bit phase resolution LIS/RIS is suited for green MISO/MIMO downlink, smart radio environments, lensless imaging (including super-resolution and compressed coded diffraction), and energy-constrained IoT deployments. Coarse quantization constrains sum-rate and capacity, especially at high SNR and under strong LoS conditions, but EE and robustness are high, and practical costs are minimal (Huang et al., 2018, Han et al., 2018). Information-theoretic and empirical results confirm that 1-bit phase control saturates the minimal information scenario for phase retrieval and robust MIMO channel shaping (Mroueh et al., 2013, Mroueh, 2014). The main limitations remain phase quantization loss, hardware non-idealities, and the need for accurate channel state information (CSI) in joint optimization. Ongoing research explores adaptive mixed-resolution architectures, integrated absorber design to suppress specular backgrounds, and scalable learning-based configuration for dynamic and large-scale environments.