Ferkans — Interactive Telecom Tutor

Two Architectures, One Answer

Cell-free massive MIMO and reconfigurable intelligent surfaces (RIS) were developed in separate communities for separate reasons. Cell-free came from academia wanting to eliminate cell boundaries and guarantee uniform coverage. RIS came from metamaterial researchers who realized that a passive electromagnetic surface could be made programmable at low cost. For five years these two communities published in parallel without intersecting.

They are converging. A RIS is, operationally, a passive AP — it has no transmit chain, but it has spatial DoF it can allocate to beamforming. A cell-free network with a few active APs plus many passive RIS panels looks architecturally identical to a sparse active network densified by cheap reflectors. The open problem is how to jointly design the active APs, the RIS phase profiles, and the user scheduling in a way that scales and that handles the channel estimation burden honestly. This section surveys what is known and what is not.

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Definition:
Cascaded Tx-RIS-Rx Channel

Consider a link with $N_t$ transmit antennas, $N_r$ receive antennas, and a single RIS with $N_{\text{RIS}}$ reflecting elements. The end-to-end signal model is

$\mathbf{y} = \left(\mathbf{H}_{d} + \mathbf{H}_{2} \mathbf{\Theta} \mathbf{H}_{1}\right) \mathbf{x} + \mathbf{w},$

where:

$\mathbf{H}_{d} \in \mathbb{C}^{N_r \times N_t}$ is the direct Tx-Rx channel (possibly blocked or weak).
$\mathbf{H}_{1} \in \mathbb{C}^{N_{\text{RIS}} \times N_t}$ is the Tx-to-RIS channel.
$\mathbf{H}_{2} \in \mathbb{C}^{N_r \times N_{\text{RIS}}}$ is the RIS-to-Rx channel.
$\mathbf{\Theta} = \mathrm{diag}(e^{j\phi_1}, \ldots, e^{j\phi_{N_{\text{RIS}}}})$ is the diagonal RIS phase profile (unit-modulus constraint).

The cascaded channel $\mathbf{H}_{2} \mathbf{\Theta} \mathbf{H}_{1}$ has a rank bounded by $\min(N_r, N_t, N_{\text{RIS}})$ and its Frobenius norm is bilinear in $(\mathbf{H}_{1}, \mathbf{H}_{2})$ — not linear, which is the source of most technical difficulties in RIS channel estimation.

Despite superficial resemblance to a two-hop relay, a RIS is not an amplify-and-forward relay: it does not regenerate the signal, it only applies a phase shift, and it adds no noise. The pathloss therefore multiplies (not adds), which is why RIS-assisted links typically need $N_{\text{RIS}} \gtrsim 10^3$ elements to compensate for the double-pathloss penalty.

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Definition:
RIS as a Passive Access Point

In a joint RIS-and-cell-free deployment, a set of $N_{\text{AP}}$ active APs and $N_{\text{RIS}}$ passive surfaces jointly serve $K$ users. From the point of view of the central processing unit, a RIS behaves as an access point with:

Zero transmit-chain cost (no RF chains, no DACs, no amplifiers)
Zero per-element computation cost (just diode/varactor control)
Zero fronthaul data rate (control channel only)
Spatial DoF count equal to $\min({N_t}_{\text{nearest active AP}}, N_{\text{RIS}})$
Channel estimation cost proportional to $N_{\text{RIS}} \cdot {N_t}_{\text{nearest active AP}}$ (cascaded channel)

The "passive AP" abstraction motivates treating RIS panels and active APs uniformly in the scheduling and beamforming optimization. In practice, the orders-of-magnitude different estimation costs and the bilinear structure of the cascaded channel create separate sub-problems.

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Theorem: Cascaded RIS Pathloss Scaling

Consider a RIS-aided link where the Tx-RIS distance is $d_1$ , the RIS-Rx distance is $d_2$ , and both links are in the far field of the RIS ( $d_1, d_2 \gg L_{\text{RIS}}$ , where $L_{\text{RIS}}$ is the physical RIS size). With optimal (phase-aligned) RIS configuration, the end-to-end pathloss is

$\beta_{\text{cascade}} \propto \frac{1}{d_1^2 \cdot d_2^2} \cdot N_{\text{RIS}}^2,$

in contrast to a traditional single-hop link's $1/d^2$ and a two-hop relay's $1/(d_1^2) + 1/(d_2^2)$ . The $N_{\text{RIS}}^2$ factor reflects the coherent combining of $N_{\text{RIS}}$ reflected paths at the receiver. For the passive RIS to match the pathloss of a direct link at distance $d \approx d_1 + d_2$ , the number of elements must satisfy

$N_{\text{RIS}} \gtrsim \frac{d_1 d_2}{d \cdot \sqrt{G_{\text{element}}}},$

where $G_{\text{element}}$ is the per-element effective gain.

Each RIS element contributes a fraction $1/N_{\text{RIS}}$ of the total reflected amplitude — this is the element-level loss. Phase alignment coherently sums $N_{\text{RIS}}$ contributions at the receiver, squaring back to $N_{\text{RIS}}^2$ . But the pathloss multiplies over the two hops because the RIS does not re-transmit at full power. The quadratic-in- $N_{\text{RIS}}$ requirement is why practical RIS panels need hundreds to thousands of elements to be useful.

Show Hint

Compute the power received at each RIS element from the Tx, then the power radiated by each element, then coherent combining at the Rx.

The element-level effective gain $G_{\text{element}}$ sets the per-element pathloss; phase alignment creates the $N_{\text{RIS}}^2$ coherent gain.

The product of two $1/d^2$ factors (Tx-RIS and RIS-Rx) replaces the single $1/d^2$ of a direct link.

Proof

Tx-to-element power

The power received at element $n$ of the RIS from a Tx at distance $d_1$ with transmit power $P_t$ is approximately $P_{\text{elem}} = P_t \cdot G_t G_{\text{element}} (\lambda/(4\pi d_1))^2$ , using the Friis formula for a link to a single RIS element.

Element-to-Rx power

Each element re-radiates its incident power (with no gain or loss beyond a phase shift, assuming a lossless RIS) toward the Rx at distance $d_2$ . The per-element contribution to the Rx power is $P_{\text{elem,Rx}} \propto P_{\text{elem}} \cdot G_{\text{element}} (\lambda/(4\pi d_2))^2$ .

Coherent combining

Under the optimal RIS phase profile, all $N_{\text{RIS}}$ element contributions add in phase at the Rx. The total received amplitude scales as $N_{\text{RIS}}$ , so the power scales as $N_{\text{RIS}}^2 \cdot P_{\text{elem,Rx}}$ . Collecting terms:

$P_{\text{Rx}} \propto P_t \cdot N_{\text{RIS}}^2 \cdot G_{\text{element}}^2 \cdot \frac{\lambda^{4}}{(4\pi)^4 \, d_1^2 d_2^2}.$

The $d_1^2 d_2^2$ denominator is the characteristic product pathloss of a RIS link, distinct from the sum pathloss of a relay. $\blacksquare$

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Coverage CDF with and without RIS Assistance

Compare the per-user SINR cumulative distribution for a cell-free deployment with only active APs versus one where some APs are replaced with or augmented by passive RIS panels. Adjust the AP/RIS counts to see when RIS assistance closes coverage holes.

Parameters

Active APs

N_{\text{AP}}

20

RIS panels

N_{\text{RIS,panel}}

10

Elements per RIS

N_{\text{RIS}}

256

Users

K

50

Example: When Is a RIS Panel Cheaper Than an AP?

An operator considers two options for extending coverage into an indoor dead zone that is 30 m from the nearest active AP (32 antennas, 23 dBm per antenna, $f_0 = 3.5$ GHz). Option A: add a second active AP of equal size inside the dead zone. Option B: add a $16 \times 16 = 256$ -element passive RIS panel at the midpoint. Compute the received power for a user at the far side of the dead zone ( $d = 30$ m from the main AP, $d_1 = 15$ m from AP to RIS, $d_2 = 15$ m from RIS to user) for option B, assuming element gain $G_{\text{element}} = 3$ dBi.

Solution

Direct link (no assistance)

At $f_0 = 3.5$ GHz, $\lambda = 0.086$ m. Free-space path loss for $d = 30$ m: $\beta_{d} = (4\pi d/\lambda)^2 \approx 19.2 \times 10^{6} \approx 72.8$ dB. With $P_t = 23 + 10\log_{10}(32) = 38$ dBm total, received power without beamforming: $38 - 72.8 = -34.8$ dBm (before beamforming gain).

RIS-assisted pathloss

$\beta_{1} = (4\pi \cdot 15 / 0.086)^2 \approx 66.8$ dB, same for $\beta_{2} = 66.8$ dB. Cascaded pathloss without coherent combining: $66.8 + 66.8 = 133.6$ dB. With $N_{\text{RIS}}^2 = 256^2$ coherent combining gain $= 20\log_{10}(256) = 48.2$ dB, and $G_{\text{element}}^2 = 6$ dB, effective cascaded loss: $133.6 - 48.2 - 6 = 79.4$ dB.

Compare

Direct: $-34.8$ dBm. RIS-assisted: $38 - 79.4 = -41.4$ dBm. The RIS path is $6.6$ dB worse than the direct path in this geometry, purely because the double pathloss penalty is not compensated. For RIS to win, the direct link must be blocked (e.g., a concrete wall with $20$ dB penetration), at which point the direct link becomes $-54.8$ dBm and RIS wins by $13.4$ dB. The operational lesson: RIS panels are only useful when they replace a blocked direct link, not when they supplement an unblocked one. $\blacksquare$

The Channel Estimation Cost

A RIS cannot estimate its own channels — it has no baseband hardware. Every coefficient of $\mathbf{H}_{1}$ and $\mathbf{H}_{2}$ must be estimated through the RIS by the active endpoints, using pilot protocols that cycle through RIS configurations. For a $N_{\text{RIS}} = 256$ -element panel with $N_t = 32$ and $N_r = 1$ , the number of pilot symbols required is at least $N_{\text{RIS}} \cdot N_t/N_r = 8192$ — more than a coherence block at typical mobility. The open research question is whether the bilinear structure of the cascaded channel $\mathbf{H}_{2} \mathbf{\Theta} \mathbf{H}_{1}$ can be exploited to reduce this cost to manageable levels, and whether sparse or parametric models of the RIS channel let the estimator scale.

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⚠️Engineering Note

Joint Active-AP / RIS Optimization Is an SDP with $N_{\text{AP}} + N_{\text{RIS}}$ Variables

Computing the jointly optimal active-AP precoders and RIS phase profiles for a given set of user SINR constraints is a non-convex optimization. The standard relaxation to a semidefinite program (SDP) has $\mathcal{O}(N_{\text{AP}}^2 K + N_{\text{RIS}} K)$ variables. For a deployment with $N_{\text{AP}} = 20$ active APs of $M = 8$ antennas and $N_{\text{RIS}} = 10$ RIS panels of $N_{\text{RIS,panel}} = 256$ elements, that is approximately $10^5$ SDP variables — beyond what CVX or Mosek can handle in real time. The open question is whether an iterative block-coordinate scheme (alternately optimizing AP beamformers with RIS fixed and vice versa) converges to a near-optimal point quickly enough, and whether learning-based warm starts can reduce the iteration count.

Practical Constraints

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Joint SDP variables scale as $N_{\text{AP}} M^2 K + N_{\text{RIS,total}}K$
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Real-time constraint: full optimization within one coherence block (~1 ms at 3.5 GHz)
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RIS phase resolution: typically 1-3 bits per element
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Channel estimate refresh: every coherence block for active paths, slower (every 10-100 ms) for stable cascaded paths

📋 Ref: 3GPP Release 19 study item on RIS (SI RP-240794, 2024)

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Common Mistake: A RIS Is Not a Relay

Mistake:

Analyses that model a RIS as an amplify-and-forward relay predict linear $N_{\text{RIS}}$ gain and conclude that RIS is always a cheaper substitute for a relay.

Correction:

A RIS is passive: it does not add power. The element gain is bounded by the individual element's physical aperture ( $\lambda^{2}/(4\pi)$ for an isotropic element) and coherent combining squares the amplitude to give $N_{\text{RIS}}^2$ power gain — but this gain is against a cascaded pathloss, not a single-hop one. The correct baseline for comparison is a blocked direct link; comparing against an unblocked direct link typically shows RIS losing.

Historical Note: From Metasurface to RIS: The 2017-2020 Pivot

2017-present

Programmable metasurfaces were developed by electromagnetics researchers throughout the 2000s and 2010s as imaging and holography tools, with no communication context. Around 2017-2018, Marco Di Renzo, Chongwen Huang, and Ertugrul Basar (each independently) proposed repurposing them as "intelligent reflectors" for wireless channels, initially as a supplement to mmWave systems that struggle with blockage. By 2020 the idea had crystallized into the RIS acronym and a rapidly growing literature. By 2022, RIS was a 3GPP Release 19 study item.

The timeline is unusual for wireless: five years from initial proposal to standardization study. The speed reflects both the simplicity of the RIS concept and the fact that metasurface hardware already existed. What remains open is not the architecture but the joint algorithm and estimation questions treated in this section.

The Convergence Question

The open question is what the "unified" RIS + cell-free architecture should look like:

Scheduling: do RIS panels serve groups of users in TDMA, or do multiple RIS panels support the same user simultaneously?
Channel estimation: is the pilot overhead for $N_{\text{RIS}}$ cascaded channels reducible to $o(N_{\text{RIS}})$ via sparsity or low-rank structure?
Backhaul: is the control channel to each RIS panel dimensioned per-cell or per-cluster?
Joint beamforming: is there a low-complexity algorithm that jointly configures active-AP precoders and RIS phase profiles, scalable to $N_{\text{AP}} + N_{\text{RIS}} \gtrsim 100$ ?
Deployment economics: when does replacing an active AP with several RIS panels win, and under what propagation environments?

Each of these sub-questions is an active research topic in 2026. The convergence happens in the answers, not the problem statement.

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Why This Matters: Cross-Reference to the RIS Book

The broader theory of reconfigurable intelligent surfaces is developed in the RIS book of this library. There, the RIS is studied in isolation: channel models, phase-shift design, fundamental limits, and active vs passive comparisons. Section 27.5 treats the RIS only as one component of a larger cell-free deployment. Readers interested in the RIS-specific open problems (full-rank vs rank-deficient channels, near-field RIS holography, nonlinear active RIS) should consult the RIS book's final chapter for the corresponding research agenda.

Cascaded Channel

In RIS-assisted systems, the effective channel seen by the receiver equals $\mathbf{H}_{2} \mathbf{\Theta} \mathbf{H}_{1}$ , a bilinear function of the Tx-RIS channel $\mathbf{H}_{1}$ and the RIS-Rx channel $\mathbf{H}_{2}$ . Its bilinearity makes channel estimation from pilots substantially harder than estimating a linear channel.

Passive Access Point

Conceptual abstraction treating a RIS panel as an AP with zero transmit-chain cost, zero compute cost, and zero data fronthaul — only a control channel for phase configuration. Unifies RIS and cell-free scheduling frameworks when the cascaded channel estimation cost is amortized across multiple coherence blocks.

Quick Check

A 256-element passive RIS replaces a direct LOS link of total length 60 m with two 30-m hops. Which statement about the end-to-end pathloss is correct?

Same as a 60-m direct link (RIS does not add loss)

Same as a 30-m direct link (the RIS restores one hop)

Product of two free-space losses, offset by $N_{\text{RIS}}^2$ coherent gain

Always better because RIS is passive