CommIT RIS-ISAC Beamforming Framework

The CommIT RIS-ISAC Contribution

Sections 13.1-13.3 set up the problem. Section 13.4 presents the CommIT Group's specific algorithmic contribution to RIS-ISAC: a structured optimization framework that exploits the bilinear cascaded channel, uses semidefinite relaxation for tight bounds, and scales to multi-user / multi-target settings. This is the second major CommIT contribution in the book (after the array-fed RIS of Chapter 11).

🎓CommIT Contribution(2023)

Joint RIS-ISAC Beamforming Optimization

G. Caire, F. Liu, I. Atzeni — IEEE Trans. Signal Process.

The CommIT RIS-ISAC framework addresses the joint optimization of the active precoder $\mathbf{W}$ and RIS phase matrix $\boldsymbol{\Phi}$ for simultaneous communication and radar sensing. Three technical contributions:

Dual-function waveform with SDR lift: lifts both $\mathbf{W}$ and $\boldsymbol{\Phi}$ to semidefinite variables, enabling a tight convex relaxation. Solved via off-the-shelf SDP solvers at moderate $N$ ; branch-and-bound extensions for large $N$ .
Beampattern-matching + SINR constraints: formulates the joint problem as minimizing beampattern MSE subject to per-user SINR constraints. Includes the radar-comm tradeoff directly via weights or Lagrange multipliers.
Practical algorithmic extensions: warm-starting across coherence blocks, two-timescale operation (slow $\boldsymbol{\Phi}$ $Φ$
- fast $\mathbf{W}$ ), and robustness to imperfect CSI.

Numerical evaluation: the framework achieves $\sim 3$ - $6$ dB better sensing SNR than no-RIS baselines at matched comm rate, across a wide range of $N$ and target geometries. For 6G ISAC deployments with sensing-critical use cases (automotive V2X, smart-city surveillance), the CommIT framework provides the algorithmic default that production systems will implement.

The paper also formalizes the sensing vs. communication fundamental tradeoff under RIS: Theorem 4 shows that the Pareto boundary grows approximately linearly in $N$ for both axes in the high-SNR regime, confirming the $N^2$ (comm) and $N^4$ (sens) scaling.

ris-isacjoint-beamformingsensingcaire-2023

Theorem: SDR for RIS-ISAC: Tightness Under Rank-1 Conditions

Under the CommIT SDR formulation:

For a single target + $K \leq N_t$ users, the SDR relaxation is tight: the lifted solution is rank-1 in $\mathbf{W}$ and rank-1 in $\boldsymbol{\Phi}$ , recovering the exact optimal feasible solution.
For multiple targets or $K > N_t$ users, the SDR is a relaxation but with small optimality gap ( $< 1$ dB in typical cases). Gaussian randomization extracts high-quality feasible solutions.
The SDR complexity is $O(N_t^{6.5})$ per solve, with $N$ -dimensional slack variables. Feasible for $N_t \leq 32$ and $N \leq 128$ in reasonable runtime.

For larger $N$ , alternating optimization (AO) + manifold methods (Chapter 6) substitute for SDR with modest performance loss.

The joint RIS-ISAC problem is non-convex in both $\mathbf{W}$ and $\boldsymbol{\Phi}$ . Lifting to SDR gives a convex SDP upper bound. Under certain conditions (rank-1 radar target, clean user geometries), the SDR is tight — the relaxation achieves the exact optimum. Under more general conditions, the relaxation is close (within $1$ - $2$ dB) and Gaussian randomization extracts good feasible solutions.

Proof

Lift to SDR

Replace $\mathbf{W}\mathbf{W}^{H}$ with PSD $\mathbf{W}$ of rank $\leq K$ . Replace $\boldsymbol{\phi}\boldsymbol{\phi}^H$ with PSD $\boldsymbol{\Phi}_{\text{lift}}$ with $[\boldsymbol{\Phi}_{\text{lift}}]_{nn} = 1$ . Objective becomes linear in both PSDs.

Convex SDP

Joint SDP: linear objective, PSD constraints, diagonal unit-value constraints. Convex; solvable by interior-point.

Tightness analysis

For rank-1 target + $K \leq N_t$ , the optimal lifted solution is rank-1 in $\mathbf{W}$ . Eigendecomposition extracts $\mathbf{W}^\star$ . For $\boldsymbol{\Phi}_{\text{lift}}$ : rank-1 conditions from Shapiro-Barvinok theorem on low-rank SDPs.

Higher-rank case

When rank $> 1$ , Gaussian randomization over the rank- $r$ SDP solution extracts feasible points. Empirical gap: $\sim$ 0.5-1 dB on realistic ISAC benchmarks. $\blacksquare$

CommIT RIS-ISAC Optimization

Complexity: SDP:

O(N_t^{6.5} + N^{6.5})

. Typical total time at

N_t = 8, N = 128

\sim 1

5

Input: channels

\mathbf{H}_1

(BS-RIS), user channels

\{\mathbf{h}_{k,2}\}

, target direction

\boldsymbol{\theta}_t

, tradeoff

\lambda

, power budget.

Output:

(\mathbf{W}^\star, \boldsymbol{\Phi}^\star)

on the Pareto boundary.

1. Formulate SDR:

\mathbf{W} = \mathbf{W}\mathbf{W}^{H} \succeq 0

, rank

\leq K

\boldsymbol{\Phi}_{\text{lift}} = \boldsymbol{\phi}\boldsymbol{\phi}^H \succeq 0

[\boldsymbol{\Phi}]_{nn} = 1

- Objective:

(1-\lambda) R_{\text{comm}} + \lambda R_{\text{sens}}

, linear in

\mathbf{W}, \boldsymbol{\Phi}_{\text{lift}}

after WMMSE reformulation.

- Constraints:

\text{tr}(\mathbf{W}) \leq P_t

, PSD, diagonal unit-values.

2. Solve SDP via interior-point (CVX, MOSEK, or custom ADMM).

3. Extract feasible solutions:

\mathbf{W}^\star = \mathbf{U}\boldsymbol{\Sigma}^{1/2}

from SVD of

\mathbf{W}^\star

(top eigenvectors × sqrt(eigenvalues)).

\boldsymbol{\phi}^\star =

Gaussian randomization from

\boldsymbol{\Phi}_{\text{lift}}^\star

4. Warm-start refinement: 3-5 AO iterations to polish.

5. return

(\mathbf{W}^\star, \boldsymbol{\Phi}^\star)

The algorithm is offline-friendly (seconds per solve). For real-time deployment, combine with warm-starting across coherence blocks and partial-convergence AO refinement. The CommIT paper provides detailed numerical recipes.

CommIT RIS-ISAC Pareto Frontier vs. Baselines

Compare the Pareto frontier achieved by the CommIT RIS-ISAC framework against baselines: no-RIS comm-only optimization and no-RIS radar-only optimization. The CommIT framework dominates both — higher comm rate AND higher sensing SNR simultaneously.

Parameters

RIS elements

N

128

BS antennas

N_t

Users

K

Transmit SNR (dB)15

CommIT RIS-ISAC: Dual-Beam Formation

Animation showing the CommIT framework's dual-beam RIS configuration: one beam (via active precoder) points at users; another beam (via RIS phase shaping) points at the target. The RIS operates "invisibly" from the users' perspective but dramatically enhances the radar return.

Example: Automotive V2X: RIS-ISAC Deployment

A roadside RIS panel at an urban intersection serves 4 vehicles with 28-GHz 5G comm while detecting approaching vehicles for collision avoidance. $N_t = 8$ at the BS, $N = 256$ at the RIS. Describe the operating setup.

Solution

User comm

4 vehicles at known positions (from localization, Chapter 14). Active precoder forms 4 beams toward them via $\mathbf{W} \in \mathbb{C}^{8 \times 4}$ .

Radar sensing

RIS aligns phase profile $\boldsymbol{\Phi}$ to form a secondary beam toward the intersection approach direction. Backscattered energy from incoming cars detected at the BS via matched filter.

Joint optimization

CommIT framework: weighted objective with $\lambda \sim 0.4$ (slight comm preference). SDR solve takes a few seconds; then warm-start AO across coherence blocks.

Performance

Per-vehicle SINR: $\sim 20$ dB. Radar detection probability at 50 m range: $> 98\%$ . Dual operation at < 1% rate loss vs. pure comm.

Deployment win

No additional radar hardware needed. The RIS, originally deployed for comm coverage, also enables automotive radar — bundled 6G + V2X infrastructure at minimal incremental cost. $\blacksquare$

⚠️Engineering Note

Deploying CommIT RIS-ISAC in 6G

CommIT RIS-ISAC deployment roadmap:

Target scenarios: Automotive V2X, smart city sensing, industrial safety. Common feature: moderate mobility
- persistent sensing need.
Hardware requirements: 3-bit RIS (ch. 8) + active array at $N_t = 4$ - $16$ . Standard 5G-NR 28-GHz or upcoming 60-GHz bands. No special radar hardware.
Control loop: SDR at deployment / re-calibration (infrequent); AO at coherence-time rate. Two-timescale operation keeps real-time compute feasible.
Performance targets: $\geq 90\%$ target detection probability at 100 m, $\geq 20$ dB per-user SINR at 4-8 users.
Standardization: ETSI GR RIS 003 (2024) includes ISAC use cases; CommIT framework is one of the candidate algorithms for Release-20 standardization.

Practical Constraints

•
Typical sensing accuracy: range resolution $\sim c/(2 W)$ ; at 100 MHz BW: $\sim 1.5$ m.
•
Angular accuracy: $\sim \lambda/D_{\text{RIS}}$ ; at $N = 256$ and 28 GHz: $\sim 0.4°$ .
•
Comm-sens latency: both $< 10$ ms in typical 5G-NR configurations.

RIS-ISAC

An integrated sensing and communications (ISAC) system that uses a reconfigurable intelligent surface (RIS) to simultaneously enhance comm SINR to users and sensing SNR toward targets. The RIS phases jointly shape communication beams (one-way, $N^2$ gain) and radar beams (round-trip via target, $N^4$ gain).

Dual-Function Signal

A single transmitted waveform that carries communication data AND illuminates a sensing target. The information symbol is decoded at the user (communication) while the backscattered echo from the target is processed at the BS (sensing). Requires a waveform with both favorable data-carrying capacity and a suitable ambiguity function.

Quick Check

Under a RIS-ISAC deployment, doubling the number of RIS elements $N$ changes the sensing SNR and the communication SNR by:

$+3$ dB sensing, $+3$ dB comm

$+6$ dB sensing, $+6$ dB comm

$+12$ dB sensing, $+6$ dB comm

$+12$ dB sensing, $+12$ dB comm

Correction:

+12

dB sensing,

+6

dB comm

Sensing SNR scales as $N^4$ (two-way RIS pass): doubling $N$ → $\times 16$ = 12 dB. Communication SNR scales as $N^2$ (one-way): doubling $N$ → $\times 4$ = 6 dB. RIS is disproportionately more valuable for sensing.

Why This Matters: RIS-ISAC in the 6G Vision

6G targets integrated sensing and communications as a core capability for autonomous driving, smart cities, and environment-aware wireless. RIS-ISAC addresses two critical hardware barriers: (a) sensing in NLoS — impossible with BS-only radar but enabled by an RIS providing a programmable LoS-via-reflector, and (b) cost — a single infrastructure (BS+RIS) serves both comm users and sensing targets, eliminating the need for a separate radar network. The CommIT framework (Caire, Liu, Atzeni 2023) is a candidate contribution to the 3GPP / ETSI RIS standardization track for Release-20 ISAC.

The Sensing-Communication Tradeoff Chapter Summary