Md Tarek Hassan | PhD Researcher in 6G Wireless, RIS and ISAC

Operating Principle

An RIS controls the boundary condition seen by an incident electromagnetic wave. In simple wireless-system models, each RIS element is represented by a complex coefficient:

\Gamma_n = a_n\, e^{j\phi_n}, \qquad 0 \le a_n \le 1,\quad \phi_n \in [0, 2\pi)

Phase: determines where reflected contributions add or cancel.
Amplitude: tells how much of the incoming field remains after loss.
Model versus hardware: ideal continuous, unit-amplitude control is often an approximation; real states can be quantized and lossy.

Beam steering with 1, 2 or 3-bit elements

1. Formula and symbols

\Delta\phi=2\pi/2^b,\quad\phi_n=Q_b(\phi_{n,\rm ideal})

g(\theta)=\frac1{N^2}\left|\sum_ne^{j(\phi_n+\psi_n(\theta))}\right|^2

$b$ : control bits
$\Delta \phi$ : phase-step spacing
$Q_b$ : nearest allowed phase
$\psi_n$ : propagation phase for element n in the selected direction
$N$ : elements
$g$ : normalized power

Quantization changes coherent addition.

Phase states per element

Wave arrives from (other side)30°

Compare with a plain mirror

Target direction0°

2. Work with the current inputs

Why are the phases rounded at all?

Each element’s phase comes from a physical switch. A PIN diode is either on or off, so one diode gives two states: 1 bit. Two or three diodes, or a varactor driven with a few voltage levels, give 4 or 8 states. Every extra bit costs more diodes, control lines and loss, so real surfaces round the ideal phase to the nearest state they have. That rounding is quantisation.

Why does 1 bit create a ghost beam?

With 1 bit the only phases are 0° and 180°, so every element weight is +1 or −1: a real number. The pattern of any set of real weights is mirror-symmetric in u = sin θ + sin θ_in. Whatever beam forms at u_t must also form at −u_t:

\mathrm{AF}(u) = \sum_{n} w_n e^{\,j\pi n u},\quad w_n \in \{+1, -1\} \;\Longrightarrow\; \mathrm{AF}(-u) = \mathrm{AF}(u)^{*} \;\Longrightarrow\; |\mathrm{AF}(-u)| = |\mathrm{AF}(u)|

Another way to see it: the ±1 pattern is a square wave, and a square wave is mostly two opposite phase ramps added together. Each ramp steers its own beam, each with amplitude 2/π, so each beam is (2/π)², about 3.9 dB, below an ideal one. That is the 1-bit main-lobe loss shown above.

w_n = \operatorname{sgn}\cos(\pi n u_t) \approx \frac{4}{\pi}\cos(\pi n u_t) = \frac{2}{\pi}\Big(\underbrace{e^{\,j\pi n u_t}}_{\text{ghost at } -u_t} + \underbrace{e^{-j\pi n u_t}}_{\text{beam at } u_t}\Big)

Setting −u_t = sin θ_g + sin θ_in gives where the ghost lands:

\sin\theta_g = -\sin\theta_t - 2\sin\theta_{\text{in}} = -\sin(0^\circ) - 2\sin(-30^\circ) = 1.000 \;\Rightarrow\; \theta_g = 90.0^\circ

Is the ghost simply at −θ_t, the opposite side?

Only when the wave hits the surface head-on (θ_in = 0°). The mirror symmetry lives in u = sin θ + sin θ_in, not in the angle itself, and its centre (u = 0) is the mirror direction, not 0°. With head-on illumination the centre is 0°, so sin θ_g = −sin θ_t and the ghost sits exactly opposite. Tilt the illumination and the centre moves to the mirror angle; the target and ghost then sit equally far from it in sine, which is not equally far in degrees. Set the arrival angle to 0° above to see the ghost land at −θ_t.

\underbrace{\sin\theta_t - \sin\theta_{\text{mirror}}}_{-0.500} = -\underbrace{\left(\sin\theta_g - \sin\theta_{\text{mirror}}\right)}_{0.500}, \qquad \theta_t - \theta_{\text{mirror}} = -30.0^\circ \ \ne\ \theta_{\text{mirror}} - \theta_g = -60.0^\circ

The ghost disappears in two cases: when the target sits exactly at the mirror angle (u_t = 0, the two beams merge) and when sin θ_g falls outside ±1. With 2 or more bits the weights become complex, the symmetry breaks, and the rounding error spreads into weak scattered lobes instead of one ghost: the average loss drops to about 0.9 dB for 2 bits and 0.2 dB for 3.

The model behind the plot

\phi_n^{\text{ideal}} = -\pi n\left(\sin\theta_{t} + \sin\theta_{\text{in}}\right), \qquad \phi_n = \frac{2\pi}{2^{b}}\,\operatorname{round}\!\left(\frac{2^{b}\phi_n^{\text{ideal}}}{2\pi}\right)

G(\theta) = \frac{1}{N^{2}}\left|\sum_{n=0}^{N-1} e^{\,j\left(\phi_n + \pi n(\sin\theta + \sin\theta_{\text{in}})\right)}\right|^{2}

3. Result

Target0°sweeping

Main-lobe loss3.0 dBvs ideal phases

Mirror toward the target-50.0 dBits beam stays at 30°

Ghost beam (measured)-3.0 dBat 83°

Ghost predicted by theory90.0°sin θ_g = −sin θ_t − 2 sin θ_in

Phase states2 (180° steps)

A 16-element RIS (half-wavelength spacing) lit from 30° on the other side, so a plain mirror would send the wave to 30°. The coloured strip shows the phase each element actually applies. The dashed curve is a plain metal plate of the same size: with no phase control it always reflects to the mirror angle, however you move the target. The beam sweeps slowly; pause it or move the slider to steer by hand. The explanation below the controls says why the phases are rounded and where the 1-bit ghost beam comes from.

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Beam Steering vs Beam Focusing

Beam steering sends energy in a desired direction. It is often described using far-field planar-wave models.

Beam focusing sends energy to a specific point in space. It becomes important for near-field RIS, where the user is close enough that spherical wavefront curvature cannot be ignored.

Far field: a direction-based phase gradient is often sufficient.
Near field: element-to-user distances differ enough that a direction-only model can miss range information.
Design consequence: focus phases for each complete path to the target point, not just one departure angle.

Mode	Best model	Main control target
Far-field steering	Plane wave	Angle
Near-field focusing	Spherical wave	Range and angle

Near-field operation is increasingly important in 6G because large surfaces and high carrier frequencies make the Rayleigh distance large.

Steering a direction vs focusing on a point

1. Formula and symbols

\phi_n=-ky_n\sin\theta\ \text{(steer)},\quad\phi_n=kr_{nF}\ \text{(focus)}

E(P)=\sum_n\frac{e^{j(\phi_n-kr_{nP})}}{r_{nP}},\quad k=2\pi/\lambda

$y_n$ : cell coordinate
$\theta$ : steering angle
$r_{nF}$ : Distance from cell n to the chosen focus
$r_{nP}$ : Distance from cell n to the observation point
$\phi_n$ : selected phase
$\lambda$ : wavelength

The field includes spherical 1/r spreading

the map normalizes power to its stated reference peak.

Phase profile

Beam angle15°

Focal distance70 λ

2. Work with the current inputs

\text{steer: } \phi_n = -k\,y_n\sin\theta \qquad \text{focus: } \phi_n = k\,\lVert \mathbf{p}_F - \mathbf{e}_n \rVert \qquad E(\mathbf{p}) = \sum_{n=1}^{64} \frac{e^{\,j(\phi_n - k\lVert \mathbf{p}-\mathbf{e}_n\rVert)}}{\lVert \mathbf{p}-\mathbf{e}_n\rVert}

3. Result

Aperture D32 λ34.3 cm at 28 GHz

Rayleigh distance2048 λ21.93 m at 28 GHz

Peak power at1 λ1.1 cm at 28 GHz

−3 dB depth along the beam1–2 λ

Top view of the field in front of a 64-element surface (32 λ tall), computed by adding every element's spherical wave. Its Rayleigh distance 2D²/λ is 2048 λ, so this whole picture is the near field. Steering applies a linear phase and the beam keeps going; focusing applies the exact path-length phase to one point and the energy concentrates there, giving range control as well as angle. Colour: power over 25 dB, scaled to the strongest point beyond 12 λ (the strip hugging the surface is brighter still).

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Main RIS Architectures

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Passive Reflective RIS

This is the most common concept. The surface reflects signals and changes their phase with very low power consumption.

Best for: coverage extension, interference control, passive beam shaping.

Challenge: double path loss and passive channel estimation.

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Active RIS

Active RIS elements include reflection-type amplifiers. This can compensate for the severe multiplicative path loss, but it introduces noise, power consumption, and hardware complexity.

Best for: longer RIS-assisted links and sensing scenarios where passive reflection is too weak.

Challenge: amplifier noise, stability, cost, and power constraints.

Passive or active RIS: which gives the higher SNR?

1. Formula and symbols

\gamma_p=PN^2h_1h_2/\sigma^2

\gamma_a=\frac{P_BP_ANh_1h_2}{P_Ah_2\sigma_v^2+\sigma^2(P_Bh_1+\sigma_v^2)}

$P$ : total RF budget
$P_B$ : RF power allocated to the BS
$P_A$ : RF power allocated to the active surface
$N$ : cells
$h_{1}$ : Power gain of the first per-cell path
$h_{2}$ : Power gain of the second per-cell path
$\sigma ^2$ : receiver noise
$\sigma v^2$ : amplifier noise. γp/γa are passive/active linear SNR under the equal-budget model
$\gamma_p$ : Passive-surface linear receive SNR
$\gamma_a$ : Active-surface linear receive SNR

Total power budget30 dBm

Share for active-RIS amplifiers10%

BS → RIS distance20 m

RIS → user distance10 m

Elements N1,024

2. Work with the current inputs

\gamma_{\text{passive}} = \frac{P\,N^{2}\varrho_f^{2}\varrho_g^{2}}{\sigma^{2}} \qquad \gamma_{\text{active}} = \frac{P_{\text{BS}}\,P_{\text{A}}\,N\,\varrho_f^{2}\varrho_g^{2}}{P_{\text{A}}\varrho_g^{2}\sigma_v^{2} + \sigma^{2}\left(P_{\text{BS}}\varrho_f^{2} + \sigma_v^{2}\right)}

P_{\text{BS}} = 29.5\ \text{dBm},\quad P_{\text{A}} = 20.0\ \text{dBm},\quad \varrho_f^{2} = -82.4\ \text{dB},\quad \varrho_g^{2} = -76.4\ \text{dB},\quad \sigma^{2} = \sigma_v^{2} = -87.0\ \text{dBm}

\gamma_{\text{passive}} \ge \gamma_{\text{active}} \iff N \ge \frac{P_{\text{BS}}P_{\text{A}}\sigma^{2}}{P\left(P_{\text{A}}\varrho_g^{2}\sigma_v^{2} + \sigma^{2}(P_{\text{BS}}\varrho_f^{2} + \sigma_v^{2})\right)} \approx 1.21\times10^{7}

3. Result

Passive SNR18.3 dB

Active SNR59.1 dB

Better hereActiveby 40.7 dB

Passive wins fromN ≈ 1.2 × 10⁷

Single-antenna BS and user, ideal phases, same total power for both designs. Passive: the BS gets all of it and the surface only reflects, so SNR grows with N². Active: part of the budget feeds reflection amplifiers, which beat the double path loss but add their own noise, so SNR grows only with N. Model after Zhang et al., “Active RIS vs. passive RIS: Which will prevail in 6G?”, IEEE TCOM 2023, with free-space per-element channels at 28 GHz, 100 MHz bandwidth and amplifier noise equal to receiver noise. Amplifier DC power is not counted.

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

STAR-RIS

STAR-RIS means Simultaneously Transmitting and Reflecting RIS. It can serve users on both sides of the surface, acting like a programmable smart window.

Best for: indoor/outdoor coverage, full-space service, building-mounted deployments.

Challenge: energy splitting, mode switching, coupled transmission/reflection design.

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Hybrid or Multifunctional RIS

Hybrid RIS contains some active sensing/receiving elements or additional radio modules. This is useful because a fully passive RIS cannot observe the channel directly.

Best for: channel estimation, sensing-assisted control, RIS-assisted ISAC.

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Pros

Low-power infrastructure: Passive RIS consumes much less power than active relays.
Coverage improvement: It can create controllable virtual LoS paths.
Interference control: It can redirect useful energy and suppress unwanted directions.
Localization support: A known RIS position can act as a virtual anchor.
Sensing support: A large aperture can help illuminate targets or improve angular resolution.

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Cons and Open Challenges

Cascaded channel estimation: The BS-RIS and RIS-user channels appear as a combined channel.
Training overhead: Large RIS panels require careful pilot design.
Hardware nonidealities: Mutual coupling, finite resolution, element losses, and bandwidth effects matter.
Placement sensitivity: A poorly placed RIS gives little benefit.
Optimization complexity: Joint active beamforming and RIS phase design is usually nonconvex.

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Practical Design Variables

When designing an RIS system, researchers usually optimize:

Number of RIS elements.
Element spacing.
Phase shifts.
Amplitude states.
RIS location and orientation.
BS beamforming.
User scheduling.
Pilot patterns.
Control latency.

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Takeaway

RIS is best understood as a programmable boundary for radio propagation. Its promise is large, but practical performance depends on accurate channel knowledge, realistic hardware, good placement, and low-overhead control.

References for this section3

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Check your understanding

0 of 4 answered

Which phase profile makes an RIS focus on a point instead of steering toward a direction?
Why does near-field focusing matter more for 6G surfaces?
In the passive vs active comparison, how does SNR grow with N?
What does a STAR-RIS add?

Complete references and further reading

M. Di Renzo et al., "Smart Radio Environments Empowered by Reconfigurable Intelligent Surfaces", IEEE JSAC, 2020.
X. Mu, J. Xu, Y. Liu, and L. Hanzo, "Reconfigurable Intelligent Surface-Aided Near-Field Communications for 6G: Opportunities and Challenges", IEEE Vehicular Technology Magazine, 2024.
M. Rihan, A. Zappone, S. Buzzi, and G. Fodor, "Passive vs. Active Reconfigurable Intelligent Surfaces for Integrated Sensing and Communication: Challenges and Opportunities", IEEE Network, 2023.

Operating Principle

Beam steering with 1, 2 or 3-bit elements

1. Formula and symbols

2. Work with the current inputs

Why are the phases rounded at all?

Why does 1 bit create a ghost beam?

Is the ghost simply at −θt, the opposite side?

The model behind the plot

3. Result

Beam Steering vs Beam Focusing

Steering a direction vs focusing on a point

1. Formula and symbols

2. Work with the current inputs

3. Result

Main RIS Architectures

Passive Reflective RIS

Active RIS

Passive or active RIS: which gives the higher SNR?

1. Formula and symbols

2. Work with the current inputs

3. Result

STAR-RIS

Hybrid or Multifunctional RIS

Pros

Cons and Open Challenges

Practical Design Variables

Takeaway

Check your understanding

Complete references and further reading

Is the ghost simply at −θ_t, the opposite side?