Full-Space Coverage and Sum Rate

The Coverage Story

The strongest argument for STAR-RIS is coverage, not rate. A passive RIS serves only one half-space; users in the other half-space see nothing. STAR-RIS serves the full space. This section quantifies the coverage gain: what fraction of users in a random geometry can be served above a QoS threshold, with and without STAR-RIS.

Theorem: STAR-RIS Coverage Gain

Consider a deployment where UEs are uniformly distributed on a sphere of radius $d$ centered between the BS and RIS. Let $P_{\text{cov}}^{\text{passive}}$ be the fraction of UEs meeting a QoS threshold under passive RIS, and $P_{\text{cov}}^{\text{STAR}}$ under STAR-RIS (ES protocol). Then

$P_{\text{cov}}^{\text{STAR}} \geq 2 P_{\text{cov}}^{\text{passive}}$

(factor of 2 from doubled half-space), with equality under pure geometric coverage. For link-budget-constrained UEs, the gain is slightly less because ES splits energy — but in practice, STAR-RIS coverage is $1.5$ - $2\times$ that of passive RIS.

Consider users uniformly distributed on a sphere around a BS-RIS pair. A passive RIS serves only users whose line-of-sight reflects off the RIS front face — roughly half the sphere. STAR-RIS serves all users, doubling coverage.

Proof

Geometric argument

Passive RIS covers the hemisphere in front of its reflecting surface (roughly $2\pi$ steradian of $4\pi$ ). STAR-RIS covers the full sphere ( $4\pi$ ).

Link-budget correction

ES protocol splits energy $|r_n|^2 + |t_n|^2 = 1$ , so each side gets $\leq 1$ of the full reflection. In effect, each side sees roughly half the SNR of a passive-only RIS serving that side. Equal per-side SNR requires $2\times$ coherent elements (by $N^2$ ), so per-side SNR is factor $4\times$ less. In terms of the QoS threshold, this shifts the coverage boundary.

Net

At most operating points, the geometric gain (2×) dominates the link-budget cost (~0.5×), giving net coverage $\sim 1.5$ - $2\times$ . $\blacksquare$

Example: Coverage Calculation for a STAR-RIS Deployment

A mmWave BS-RIS pair serves UEs uniformly distributed on a circle of radius $50$ m around the RIS. QoS threshold: $10$ dB SINR. Passive RIS covers $60\%$ of UEs. What does STAR-RIS achieve?

Solution

Passive baseline

60% coverage — users behind the RIS get nothing.

STAR-RIS coverage

Full sphere geometric coverage: users behind the RIS now also see signal. Under ES with $N^2/2$ effective coherent gain per side (half-energy), SINR drops by 3 dB on each side compared to passive-best. So users at boundary of the 10-dB threshold may fall out.

Result

Typical outcome: $\sim 85$ - $95\%$ coverage (not exactly 2× because of the SNR drop). For UEs far from the QoS threshold (well above 10 dB under passive), STAR-RIS stays above threshold. For marginal UEs, the 3-dB penalty may drop them out.

Practical lesson

STAR-RIS is a win when behind-the-RIS coverage is needed, even at the cost of per-side SNR reduction. For coverage- priority deployments (indoor-outdoor, obstructed propagation), STAR-RIS is the right choice. For rate-priority deployments with users all on one side, passive RIS is simpler and better. $\blacksquare$

Coverage Boundary: STAR-RIS vs. Passive

Visualize the coverage boundary for a BS-RIS deployment. Two circles shown: inside, UEs meet the QoS threshold. Passive RIS covers only the front half-plane; STAR-RIS covers the full space but with slightly smaller per-side radius due to the energy split.

Parameters

RIS elements

N

128

QoS threshold (dB)5

Carrier frequency (GHz)28

STAR-RIS protocol

STAR-RIS Full-Space Coverage

Animation of a STAR-RIS panel serving users on both sides simultaneously. Shows the reflect-side beam and transmit-side beam forming from the same panel. Contrasted with passive RIS, which leaves the transmit-side users unserved.

Optimal Per-Element Energy Split

Under ES, the optimal energy split $(a_n^r, a_n^t)$ is not uniformly 50-50 across elements. Elements near users in $\mathcal{U}^r$ (geometrically, with strong RIS-UE channels on the reflection side) should allocate more to $r_n$ ; elements near users in $\mathcal{U}^t$ allocate more to $t_n$ . The optimization of $(r_n, t_n)$ jointly with precoders is done via AO. Intuitively, the element-level split reflects the user demand on each side — a passive RIS doing implicit scheduling via the amplitude degrees of freedom.

Key Takeaway

Coverage-rate tradeoff at the panel level. STAR-RIS gives $\sim 2\times$ coverage of passive RIS at the cost of $\sim 3$ dB per-side SNR (because of energy splitting). This is a favorable tradeoff for coverage-critical deployments (indoor-outdoor, 6G dense deployment) but unfavorable when all users sit on one side. The protocol choice (ES/MS/TS) is secondary to the fundamental "serve both sides" architectural choice.

Quick Check

For a STAR-RIS with balanced user sets on both sides ( $K_r = K_t$ ) under the energy-splitting protocol, what is the optimal per-element amplitude split?

$a_n^r = 1, a_n^t = 0$ (reflect-only)

$a_n^r = a_n^t = 1/\sqrt{2}$ (symmetric 50-50)

$a_n^r = 0.7, a_n^t = 0.7$

Depends on user positions

Correction:

a_n^r = a_n^t = 1/\sqrt{2}

(symmetric 50-50)

By symmetry in a balanced deployment, the optimal ES split is uniform 50-50 across elements. The phases vary per user, but amplitudes are symmetric. See Exercise 10.10.

⚠️Engineering Note

STAR-RIS Deployment Geometry

Scenarios where STAR-RIS dominates:

Indoor-outdoor coverage from one panel (Example 10.1).
Dense urban 6G: UEs on multiple floors/buildings served from a single RIS panel on a shared facade.
Vehicle-to-everything (V2X): a RIS on the road serves vehicles on both sides.

Scenarios where passive RIS still wins:

Fixed-wireless access (all users on one side).
Indoor-only: single-room coverage where only reflection matters.
Cost-sensitive IoT (STAR hardware is more expensive per element).

Practical Constraints

•
STAR-RIS hardware cost: $\sim 1.5$ - $2\times$ that of passive RIS (roughly same element count but dual-layer fabrication).
•
Control bandwidth: doubled per element ( $B$ bits for $\theta^r$ , $B$ for $\theta^t$ ).
•
Typical deployment: panel-size $\sim 0.5\,\text{m}^2$ , serving $2$ - $5$ users on each side.

The Three Protocols: ES, MS, TS STAR-RIS Joint Optimization