Ferkans — Interactive Telecom Tutor

From Theory to Practice: The RIS Reality Check

The theoretical results of Sections 28.1--28.4 paint an attractive picture: an RIS achieves $N^2$ SNR scaling with no power amplifiers and no RF chains. However, translating these gains into practical deployments requires confronting several hardware and system-level limitations. This section analyses the most important practical constraints and quantifies their impact on RIS performance. We conclude with a discussion of open problems that remain active research topics.

Definition:
Phase Quantisation

In practice, each RIS element can only realise a discrete set of phase shifts drawn from a codebook of $2^b$ levels:

$\mathcal{F}_b = \left\{0, \frac{2\pi}{2^b}, \frac{2 \cdot 2\pi}{2^b}, \ldots, \frac{(2^b - 1) \cdot 2\pi}{2^b}\right\}$

where $b$ is the number of quantisation bits per element. The quantised phase shift for element $n$ is:

$\hat{\theta}_n = \arg\min_{\theta \in \mathcal{F}_b} |\theta - \theta_n^*|$

where $\theta_n^*$ is the ideal continuous phase. The quantisation error is $\Delta\theta_n = \hat{\theta}_n - \theta_n^*$ , which is uniformly distributed on $[-\pi/2^b, \pi/2^b]$ when $\theta_n^*$ is uniformly distributed on $[0, 2\pi)$ .

Common configurations:

1-bit ( $b = 1$ ): two states, $\{0, \pi\}$ (ON/OFF or $\pm 1$ reflection)
2-bit ( $b = 2$ ): four states, $\{0, \pi/2, \pi, 3\pi/2\}$
3-bit ( $b = 3$ ): eight states
Continuous ( $b \to \infty$ ): ideal case

The number of quantisation bits directly affects the hardware complexity. A 1-bit RIS requires only a single PIN diode per element (two states), while a 3-bit RIS requires a more complex varactor or multi-diode circuit. The trade-off between hardware simplicity and beamforming performance is a central design decision.

Theorem: Phase Quantisation Loss

For an $N$ -element RIS with $b$ -bit phase quantisation, the average beamforming gain loss relative to continuous phase control is:

$\frac{\mathbb{E}[\text{SNR}_{b}]}{\text{SNR}_\infty} = \mathrm{sinc}^2\!\left(\frac{\pi}{2^b}\right) = \left(\frac{\sin(\pi/2^b)}{\pi/2^b}\right)^2$

In decibels, the loss is:

Bits $b$	Loss (dB)
1	3.92
2	0.91
3	0.22
4	0.056
$\infty$	0

The quantised RIS preserves the $N^2$ scaling law; only the multiplicative constant is reduced. Specifically:

$\text{SNR}_{b} \approx \frac{P}{\sigma^2} \mathrm{sinc}^2\!\left(\frac{\pi}{2^b}\right) N^2 \mu_h^2 \mu_g^2$

Each element's phase error $\Delta\theta_n$ causes a projection loss $\cos(\Delta\theta_n)$ . Averaging over the uniform distribution of errors: $\mathbb{E}[\cos(\Delta\theta)] = \frac{2^b}{2\pi}\int_{-\pi/2^b}^{\pi/2^b} \cos(\theta)\,d\theta = \mathrm{sinc}(\pi/2^b)$ . Since the SNR involves the square of the coherent sum, the loss factor is $\mathrm{sinc}^2(\pi/2^b)$ . Even 2-bit quantisation ( $< 1$ dB loss) is remarkably effective, which is why practical RIS prototypes often use 1--3 bit resolution.

Proof

Quantisation error model

The ideal phase is $\theta_n^* = -\angle(h_{r,n}^* g_n)$ , uniformly distributed on $[0, 2\pi)$ . With $b$ -bit quantisation, the quantised phase $\hat{\theta}_n$ is the nearest point in $\mathcal{F}_b$ . The error $\Delta\theta_n = \hat{\theta}_n - \theta_n^*$ is uniformly distributed on $[-\pi/2^b, \pi/2^b]$ .

Effect on coherent combining

With quantised phases, the $n$ -th element's contribution to the coherent sum is:

$h_{r,n}^* e^{j\hat{\theta}_n} g_n = |h_{r,n}||g_n| e^{j\Delta\theta_n}$

The coherent sum becomes:

$S_b = \sum_{n=1}^N |h_{r,n}||g_n| e^{j\Delta\theta_n}$

Expected power

$\mathbb{E}[|S_b|^2] = \sum_{n=1}^N \mathbb{E}[|h_{r,n}|^2|g_n|^2] + \sum_{n \neq m} \mathbb{E}[|h_{r,n}||g_n|] \mathbb{E}[|h_{r,m}||g_m|] \mathbb{E}[e^{j\Delta\theta_n}] \mathbb{E}[e^{-j\Delta\theta_m}]KATEXPLACEHOLDER0END\mathbb{E}[e^{j\Delta\theta}] = \frac{2^b}{2\pi} \int_{-\pi/2^b}^{\pi/2^b} e^{j\theta}\,d\theta = \frac{\sin(\pi/2^b)}{\pi/2^b} = \mathrm{sinc}\!\left(\frac{\pi}{2^b}\right)KATEXPLACEHOLDER1END\mathbb{E}[|S_b|^2] \approx N^2 \mu_h^2 \mu_g^2 \,\mathrm{sinc}^2\!\left(\frac{\pi}{2^b}\right)$ $Therefore:$ \mathbb{E}[\text{SNR}{b}] / \text{SNR}\infty \approx \mathrm{sinc}^2(\pi/2^b) $.$ \blacksquare$

⚠️Engineering Note

Hardware Constraints for RIS Element Design

The phase-shifting capability of each RIS element is realised through tunable impedance components. The dominant technologies and their constraints:

PIN diodes (1-2 bit): Fastest switching ( $< 1\;\mu$ s), lowest insertion loss (0.5--1 dB), but limited to discrete phase states. A 1-bit RIS uses one PIN diode per element; 2-bit requires two diodes with combinatorial control. Power consumption is 1--5 mW per element (bias current).

Varactor diodes (continuous phase): Voltage-controlled capacitance enables continuous phase tuning over $\sim 300°$ range at 5 GHz. Higher insertion loss (1.5--3 dB) than PIN diodes. Nonlinear response requires careful calibration. Phase range decreases with frequency; at 28 GHz, achieving full $360°$ coverage typically requires multi-varactor designs.

Liquid crystals (continuous, slow): Voltage-controlled dielectric constant enables continuous phase tuning with very low loss ( $< 1$ dB at mmWave). However, switching time is $\sim 1$ --10 ms, limiting use to quasi-static scenarios. Promising for sub-THz RIS.

Practical loss budget: A realistic RIS element at 28 GHz has $\beta_n \approx 0.7$ -- $0.85$ ( $-3$ to $-1.5$ dB) reflection efficiency, reducing the effective $N^2$ gain by $(0.7)^2 N^2$ to $(0.85)^2 N^2$ .

Practical Constraints

•
PIN diode: 1-5 mW per element, < 1 us switching, 1-2 bit
•
Varactor: continuous phase, 1.5-3 dB loss, nonlinear calibration
•
Liquid crystal: < 1 dB loss, 1-10 ms switching time
•
Typical reflection efficiency: 0.7-0.85 at 28 GHz

⚠️Engineering Note

RIS Control Link and Update Rate

Configuring the RIS phase shifts requires a control link from the BS (or a dedicated controller) to the RIS. This introduces practical overhead:

Control data volume: For an $N = 256$ element RIS with 2-bit phase resolution, each configuration requires $2 \times 256 = 512$ bits. At a coherence time of 1 ms (vehicular), the control rate is 512 kbps per RIS panel.

Control link options:

Dedicated wired link (fibre, Ethernet): low latency ( $< 10\;\mu$ s), reliable, but requires physical infrastructure
Wireless control channel: flexible but consumes spectrum and adds latency ( $\sim 100\;\mu$ s with scheduling)
Embedded in-band signalling: the RIS extracts control data from the BS signal using a simple energy detector, avoiding a separate control link but limiting update rate

Update granularity: The RIS phase configuration can be updated at different timescales:

Per-slot ( $\sim 0.5$ ms in 5G NR): tracks fast fading, highest overhead but best performance
Per-frame ( $\sim 10$ ms): tracks user mobility, moderate overhead
Semi-static ( $\sim 1$ s): based on user location only, minimal overhead but loses fast-fading gains

Most practical systems adopt per-frame or semi-static updates, accepting some performance loss to reduce control overhead.

Practical Constraints

•
512 bits per configuration for 256-element, 2-bit RIS
•
Control link latency < 100 us for per-slot updates
•
Semi-static updates (1 s) sufficient for pedestrian users

Wideband Operation and Beam Squint

The RIS phase shifts are typically frequency-flat: the same phase $\theta_n$ is applied to all frequency components of the incident signal. This creates a beam squint effect in wideband (OFDM) systems.

Consider a wideband signal spanning bandwidth $B$ around carrier frequency $f_c$ . The optimal phase for subcarrier $k$ at frequency $f_k = f_c + k\Delta f$ is:

$\theta_{n,k}^* = -2\pi f_k \tau_n / c$

where $\tau_n$ is the propagation delay difference for element $n$ . Since the RIS applies frequency-flat phases, the actual phase at subcarrier $k$ is $\theta_n$ (independent of $k$ ), causing a mismatch of:

$\Delta\theta_{n,k} = \theta_n - \theta_{n,k}^* \approx 2\pi k\Delta f \, \tau_n$

This mismatch grows with $|k|$ (distance from the centre frequency) and causes the reflected beam to point in slightly different directions at different frequencies — the beam squint.

The fractional bandwidth $B/f_c$ determines the severity:

Sub-6 GHz ( $B/f_c < 1\%$ ): negligible squint
mmWave ( $B/f_c \sim 5\%$ ): moderate squint, edge subcarriers lose $\sim$ 1--3 dB
Sub-THz ( $B/f_c > 10\%$ ): severe squint, may require frequency-dependent phase control or true-time-delay elements

Mitigation strategies:

Optimise $\theta_n$ to maximise the average rate across all subcarriers (robust design)
Use sub-connected RIS architectures with per-subband phase control
Employ true-time-delay (TTD) elements instead of pure phase shifters

Active RIS versus Passive RIS

The passive RIS described so far reflects signals without amplification ( $|\phi_n| \leq 1$ ). An active RIS incorporates a low-noise amplifier per element, allowing $|\phi_n| > 1$ . This addresses the double path loss problem but introduces key trade-offs:

Active RIS model:

$y = \mathbf{h}_r^H \boldsymbol{\Theta}_{\text{active}} \mathbf{G} \mathbf{w} x + \mathbf{h}_r^H \boldsymbol{\Theta}_{\text{active}} \mathbf{n}_{\text{RIS}} + n$

where $\mathbf{n}_{\text{RIS}} \sim \mathcal{CN}(\mathbf{0}, \sigma_a^2 \mathbf{I})$ is the amplifier noise at the RIS elements. This noise is also amplified and reflected towards the user.

Comparison:

Feature	Passive RIS	Active RIS
Reflection gain	$\|\phi_n\| = 1$	$\|\phi_n\| > 1$
Noise amplification	No	Yes ( $\sigma_a^2$ per element)
Power consumption	$\sim$ mW (control)	$\sim$ W (amplifiers)
Hardware cost	Low	Moderate
SNR scaling (optimal)	$N^2$	$N^2$ (with noise penalty)
Double path loss	Full penalty	Partially compensated

When does active RIS help? Active RIS provides the most benefit when: (i) the cascaded path loss is severe (long BS-RIS or RIS-user distances), (ii) $N$ is moderate (insufficient passive gain to overcome double path loss), (iii) the amplifier noise figure is low ( $< 5$ dB).

For very large $N$ with short RIS-user distances, the passive $N^2$ gain typically suffices, and the additional noise and power of the active architecture become unnecessary burdens.

Phase Quantisation Loss

Simulate the beamforming gain loss due to discrete phase shifts. The plot shows the empirical CDF (over many random channel realisations) of the normalised beamforming gain $|S_b|^2 / |S_\infty|^2$ for 1-bit, 2-bit, 3-bit, and continuous phase control. The vertical dashed lines indicate the theoretical mean loss $\mathrm{sinc}^2(\pi/2^b)$ . Observe that 2-bit quantisation loses less than 1 dB on average, and the distribution concentrates around its mean as $N$ grows (due to the law of large numbers). Increasing $N$ reduces the variance of the normalised gain, confirming the asymptotic result.

Parameters

N

elements64

MC realisations500

🎓CommIT Contribution(2023)

Multiuser Multibeam Array-Fed RIS for Sub-THz

G. Caire, G. D. Gonzalez, R. Salihu — IEEE Transactions on Wireless Communications

The CommIT group proposed an array-fed RIS architecture that addresses both the cost and the multiuser limitations of conventional RIS designs. The key idea:

A small active antenna array (e.g., $M = 4$ -- $16$ elements with full RF chains) is placed at the focal point of a large passive RIS ( $N = 256$ -- $4096$ elements).
Each active antenna illuminates the RIS from a different angle, creating an independent reflected beam. With $M$ active feeds, the system generates $M$ simultaneous beams serving $M$ users.
The RIS applies a fixed or slowly-varying phase profile (e.g., a parabolic reflector profile), while the active array handles fast beamforming and multiuser precoding.

This architecture achieves near-optimal multiuser sum rates at sub-THz frequencies (100--300 GHz) with dramatically lower hardware cost than a fully digital massive MIMO array of the same physical aperture. The array-fed RIS effectively converts a large passive surface into a high-gain, multi-beam antenna — bridging the gap between reflect-array antenna engineering and communication- theoretic RIS optimisation.

array-fed-rissub-thzmultibeamCommIT

Open Problems and Future Directions

Despite significant progress, several fundamental questions remain open:

1. Standardisation and protocol integration. How should RIS be integrated into existing cellular standards (5G NR and beyond)? Key open questions include: the signalling protocol for RIS configuration updates, the control channel between the BS and the RIS controller, and the time granularity of phase updates.

2. Electromagnetic-compliant channel modelling. Most theoretical work uses simplified models (Rayleigh fading, far-field assumption, no mutual coupling). Physically accurate models based on electromagnetic theory — including near-field effects, element mutual coupling, and polarisation — are needed to validate the predicted gains.

3. Deployment optimisation. Where should an RIS be placed to maximise network-level performance? This involves jointly optimising the RIS location, orientation, and phase configuration for multiple users. The problem is combinatorial and geometry-dependent.

4. Multi-RIS coordination. In dense deployments with multiple RIS panels, inter-RIS interference and coordinated phase design create new optimisation challenges.

5. RIS for sensing and localisation. Beyond communication, RIS can enable or enhance radar sensing and user localisation by creating controllable multipath. Joint communication and sensing with RIS (ISAC-RIS) is an emerging topic.

6. Energy harvesting RIS. Self-sustaining RIS that harvest energy from incident RF signals to power their control circuitry, eliminating the need for external power supplies.

Beam Squint

The phenomenon where a frequency-flat RIS phase configuration creates beams that point in slightly different directions at different frequencies within a wideband signal. Caused by the frequency-dependent relationship between phase shift and physical delay. Severe at mmWave and sub-THz with large fractional bandwidth.

Active RIS

An RIS variant where each element includes a low-noise amplifier, allowing $|\phi_n| > 1$ (signal amplification). Addresses the double path loss but introduces amplifier noise, higher power consumption, and greater hardware complexity compared to passive RIS.

Quick Check

A 2-bit RIS (4 discrete phase levels per element) has a theoretical average beamforming gain loss of approximately:

6 dB (factor of 4 loss, since only 4 levels available)

3 dB (half the power is lost due to quantisation)

0.91 dB, given by $-20\log_{10}(\mathrm{sinc}(\pi/4))$

0 dB (quantisation has no effect on average gain)

Correction:

0.91 dB, given by

-20\log_{10}(\mathrm{sinc}(\pi/4))

The average loss factor is $\mathrm{sinc}^2(\pi/2^b)$ where $b = 2$ . We have $\mathrm{sinc}(\pi/4) = \sin(\pi/4)/(\pi/4) = (\sqrt{2}/2)/(0.7854) = 0.9003$ . The power loss is $0.9003^2 = 0.8105$ , or $-10\log_{10}(0.8105) = 0.91$ dB. This remarkably small loss explains why 2-bit RIS designs are popular in practice — the hardware simplicity of 4 discrete states per element costs less than 1 dB.

Practical Limitations and Open Problems