Ferkans — Interactive Telecom Tutor

From Positioning Users to Sensing Environments

So far we have treated positioning as a service for active users transmitting known pilots. Integrated Sensing and Communication (ISAC) generalizes this in two ways. First, the object being sensed need not be the transmitter: a passive target (vehicle, drone, pedestrian) can be detected from the echoes of communication signals, turning the cell-free network into a distributed multistatic radar. Second, the communication waveform itself is repurposed as a sensing probe, so no dedicated radar spectrum is required. The result is a single infrastructure that simultaneously carries data, locates users, and maps the surrounding environment.

This section connects the positioning theory from Sections 16.1-16.4 to the broader ISAC framework. We introduce beampattern design for joint sensing-communication waveforms, target detection from multi-static cell-free observations, and the open research questions that motivate continued CommIT-group work.

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Definition:
Cell-Free ISAC Signal Model

Consider a cell-free network with $L$ APs, where $L_t$ APs transmit downlink signals to communication users and $L_r$ APs receive the reflections from passive targets (possibly with overlap $L_t \cap L_r$ ). The transmitted waveform from AP $l_t$ is

$\mathbf{x}_{l_t}(t) = \mathbf{W}_{l_t} \mathbf{s}_{l_t}(t)$

where $\mathbf{W}_{l_t} \in \mathbb{C}^{N \times K}$ is the multiuser precoder and $\mathbf{s}_{l_t}(t) \in \mathbb{C}^K$ stacks the data symbols. Each passive target at unknown position $\mathbf{p}_\text{tgt}$ with reflectivity $\zeta$ produces an echo at AP $l_r$ :

$\mathbf{y}_{l_r}^{\text{echo}}(t) = \sum_{l_t} \zeta\, \hat{\mathbf{a}}(\phi_{l_r}^\text{tgt}) \mathbf{a}(\phi_{l_t}^\text{tgt})^T \mathbf{x}_{l_t}(t - \tau_{l_t \to l_r}^\text{tgt}) + \mathbf{w}_{l_r}(t)$

where $\tau_{l_t \to l_r}^\text{tgt} = (\|\mathbf{q}_{l_t} - \mathbf{p}_\text{tgt}\| + \|\mathbf{p}_\text{tgt} - \mathbf{q}_{l_r}\|)/c$ is the bistatic delay and $\phi_{l_t}^\text{tgt}$ , $\phi_{l_r}^\text{tgt}$ are the transmit/receive aspect angles relative to the target.

The model is multi-static: each Tx-Rx pair measures a different bistatic range. Cell-free ISAC exploits the large number of such pairs ( $L_t \cdot L_r$ ) to detect targets reliably and estimate their positions. A single co-located MIMO radar would require all the aperture on one site; cell-free ISAC spreads it across the entire deployment.

Theorem: Beampattern Gain Allocation under ISAC Constraints

Let $\mathbf{R}_\mathbf{x} = \mathbb{E}[\mathbf{x}(t) \mathbf{x}(t)^H]$ be the transmit covariance. Under a total power constraint $\text{tr}(\mathbf{R}_\mathbf{x}) \leq P$ , the beampattern gain in direction $\phi$ is

$G(\phi) = \mathbf{a}(\phi)^H \mathbf{R}_\mathbf{x} \mathbf{a}(\phi)$

The optimal $\mathbf{R}_\mathbf{x}$ that maximizes a weighted sum of (i) the communication sum-rate for $K$ users at directions $\{\phi_k^\text{comm}\}$ and (ii) the sensing gain toward target directions $\{\phi_m^\text{tgt}\}$ is the solution of the semidefinite program

$\max_{\mathbf{R}_\mathbf{x} \succeq 0}\, \sum_{k} \alpha_k \log_2(1 + \text{SNR} \cdot G(\phi_k^\text{comm})) + \mu \sum_m G(\phi_m^\text{tgt})$

subject to $\text{tr}(\mathbf{R}_\mathbf{x}) \leq P$ . The Lagrangian $\mu \geq 0$ parameterizes the communication-sensing tradeoff.

The optimization places spatial resources either where users are (to maximize rate) or where targets might be (to maximize illumination). For a pure communication system, the solution concentrates power on user directions; for a pure radar, it spreads power uniformly over the search region. ISAC balances the two. In cell-free deployments, the spatial resources are distributed across APs, giving the optimization a global rather than local character.

Proof

Express sum-rate in terms of $\mathbf{R}_\mathbf{x}$

For user $k$ at direction $\phi_k^\text{comm}$ , the receive SNR is $\gamma_k = \text{SNR} \mathbf{a}(\phi_k^\text{comm})^H \mathbf{R}_\mathbf{x} \mathbf{a}(\phi_k^\text{comm}) / \sigma^2$ . The rate is $\log_2(1 + \gamma_k)$ .

Express sensing gain

The sensing signal-to-noise ratio toward target direction $\phi_m^\text{tgt}$ is proportional to $\mathbf{a}(\phi_m^\text{tgt})^H \mathbf{R}_\mathbf{x} \mathbf{a}(\phi_m^\text{tgt})$ (larger beampattern = brighter illumination).

Convex relaxation

The resulting problem is a concave maximization (log is concave in the PSD cone) subject to a trace constraint — a standard semidefinite program solvable via interior-point methods. The rank of the optimal $\mathbf{R}_\mathbf{x}$ is at most the number of communication users plus the number of target directions. $\blacksquare$

Cell-Free ISAC Beampattern Design

Visualize the transmit beampattern resulting from the SDP in TBeampattern Gain Allocation under ISAC Constraints as the Lagrange parameter $\mu$ sweeps from 0 (pure communication) to large (pure sensing). At $\mu = 0$ , the beampattern has sharp lobes toward the users. At large $\mu$ , it broadens to cover the target region. Intermediate values produce a mix.

Parameters

Sensing weight

\mu

0.5

Comm users4

Number of APs16

Bandwidth (MHz)100

Reference SNR (dB)10

Antennas per AP4

Definition:
Distributed Target Detection at the CPU

For detecting a target at candidate position $\mathbf{p}_\text{tgt}$ , each receiving AP forms a matched-filter output along the bistatic delay-Doppler hypothesis, and the CPU combines them coherently. The test statistic is

$\Lambda(\mathbf{p}_\text{tgt}) = \left|\sum_{l_r = 1}^{L_r} w_{l_r}(\mathbf{p}_\text{tgt}) \int \mathbf{y}_{l_r}^H(t) \mathbf{s}^*(t - \tau_{l_t \to l_r}^\text{tgt})\, dt\right|^2$

where $w_{l_r}(\mathbf{p}_\text{tgt})$ is a combining weight depending on the transmit-receive-target geometry. The CPU declares a detection if $\Lambda(\mathbf{p}_\text{tgt}) > \gamma_{\text{th}}$ for some candidate. The detection threshold $\gamma_{\text{th}}$ is set to achieve a prescribed false-alarm rate $P_\text{FA}$ via a Neyman-Pearson test.

Cell-free coherent combining improves the detection SNR by $L_r \cdot L_t$ compared to single-site radar — the same macro-diversity that helps positioning. Incoherent combining (square-and-sum) gives a smaller gain $\sqrt{L_r L_t}$ but is robust to phase errors, which is a practical consideration in cm-wavelength cell-free deployments.

🎓CommIT Contribution(2022)

Cell-Free ISAC System Architectures

F. Liu, C. Masouros, G. Caire — IEEE Journal on Selected Areas in Communications, vol. 40, no. 6

This CommIT tutorial laid out the roadmap for cell-free ISAC: multi-static operation with coherent combining at the CPU, joint waveform design via SDP, and the rate- sensing tradeoff region. The specific contribution to this chapter is the formulation of the transmit covariance optimization used in TBeampattern Gain Allocation under ISAC Constraints and the distributed detection framework of DDistributed Target Detection at the CPU. The paper is the most-cited ISAC tutorial to date and frames the open problems — joint scheduling, synchronization, and standardization — that drive ongoing research.

isactutorial6gcommitView Paper →

Example: Bistatic Range Resolution from a Cell-Free Pair

Two APs at $\mathbf{q}_1 = (0, 0)$ and $\mathbf{q}_2 = (100, 0)$ m use a 100 MHz waveform. A target is at $\mathbf{p}_\text{tgt} = (60, 40)$ m. Compute the bistatic delay, the range resolution, and the locus of positions consistent with the measured delay.

Solution

Bistatic delay

$d_1 = \|\mathbf{p}_\text{tgt} - \mathbf{q}_1\| = \sqrt{60^2 + 40^2} \approx 72.1$ m; $d_2 = \|\mathbf{q}_2 - \mathbf{p}_\text{tgt}\| = \sqrt{40^2 + 40^2} \approx 56.6$ m. Bistatic range: $d_1 + d_2 \approx 128.7$ m. Delay $\tau_{12}^\text{tgt} = 128.7/c \approx 429$ ns.

Range resolution

With 100 MHz bandwidth, the bistatic range resolution is $c/W = 3$ m. This is the thickness of the bistatic ellipse shell that the measurement constrains the target to lie on.

Bistatic ellipse

The locus of points with bistatic range $d_1 + d_2 = 128.7$ m is an ellipse with foci at $\mathbf{q}_1$ and $\mathbf{q}_2$ and semi-major axis $a = 128.7/2 \approx 64.4$ m. A single bistatic pair constrains the target to this ellipse. Adding a third AP adds a second ellipse; the intersection uniquely localizes the target (up to the usual ambiguity).

Why This Matters: Connection to RF Imaging and Telecom Ch. 30

The cell-free ISAC model in this section generalizes the monostatic imaging model from the first book (Telecom Ch. 30 on RF imaging, and the entire RFI book). In RFI, a single co-located array with a dedicated radar waveform images a scene by inverting a known sensing matrix $\mathbf{A}$ . In cell-free ISAC, multi-static observations from many distributed APs form a block-structured sensing matrix with much richer diversity, and the waveform is constrained to carry data as well. The CRB machinery from Telecom Ch. 30 carries over with minor modification, but the rank and conditioning of the sensing matrix dramatically improve because the observations span many bistatic geometries.

Common Mistake: Self-Interference in Cell-Free ISAC

Mistake:

One might assume that because transmit and receive APs are spatially separated (multi-static operation), self-interference is not a problem as it is in monostatic full-duplex radar.

Correction:

Even in multi-static cell-free deployments, the direct path from every transmit AP to every receive AP is many orders of magnitude stronger than the target echo. A target 100 m away with $-20$ dB radar cross-section produces an echo $\sim 60$ dB below the direct path between two APs. Without coherent interference cancellation of the direct path (using knowledge of the transmitted waveform and the known AP-AP distances), target detection is impossible. Cell-free ISAC systems therefore deploy direct-path subtraction at the CPU before forming the target test statistic.

🔧Engineering Note

ISAC in 6G Standardization

ISAC is on the 6G requirements list of all major SDOs (ITU-R WP5D, 3GPP SA1, ETSI ISG ISAC). Key open questions for standardization:

Waveform selection. OFDM is currently the default communication waveform, but its high peak-to-average power ratio is a handicap for sensing. Alternative waveforms (OTFS, orthogonal chirps, frequency-hopping DFT-s-OFDM) are under study.
Resource signaling. How to schedule and signal ISAC resources that must be simultaneously data-bearing and sensing-aware. Likely answer: extensions of the 5G NR PRS framework to support passive targets.
Privacy and security. Passive sensing can detect non-cooperative users and raises regulatory concerns. Privacy-preserving sensing protocols are an open research area.
Licensing and spectrum policy. Combining comm and radar in the same band requires coordination with incumbent radar users (defense, meteorology).

Practical Constraints

•
ITU-R IMT-2030 framework explicitly lists sensing as a usage scenario
•
3GPP TR 22.837 contains ISAC service requirements for Release 19
•
ETSI ISG ISAC working group drafting technical report TS 103 XXX

📋 Ref: 3GPP TR 22.837, ITU-R WP5D IMT-2030

Quick Check

A cell-free ISAC deployment repurposes its downlink data transmission for sensing. Which statement best characterizes the effective "sensing bandwidth"?

Equal to the OFDM subcarrier spacing of the data signal.

Equal to the total occupied bandwidth of the data transmission.

Equal to the sensing pilot subband only.

Equal to the coherence bandwidth of the channel.