Ferkans — Interactive Telecom Tutor

Many Eyes on the Target

Chapters 11–15 built the case that distributed massive MIMO — cell-free networks with many small APs instead of a few giant cell sites — delivers better 95th-percentile rates and more uniform coverage than colocated massive MIMO. For sensing, the same geometry brings additional benefits that are arguably even more important than on the comm side. A target illuminated by one AP and observed from a dozen others is inherently easier to detect, localize, and track: the multistatic geometry resolves ambiguities that any single BS would have, and the macro-diversity turns occasional deep-fade echoes into reliable returns. This section develops cell-free ISAC as the natural 6G deployment flavor for integrated sensing.

Definition:
Cell-Free ISAC System Model

A cell-free ISAC network consists of $L$ access points (APs), each equipped with $N_t$ antennas, connected to a central processing unit (CPU) by a capacity-limited fronthaul. APs serve $K$ single-antenna users via coherent joint transmission and, at the same time, probe a region of interest for sensing targets.

The downlink signal at AP $\ell$ is $\mathbf{x}_\ell \in \mathbb{C}^{N_t}$ , designed by the CPU from user data and (optional) dedicated sensing symbols. User $k$ receives $y_k = \sum_{\ell=1}^{L} \mathbf{H}_{k,\ell}^{H} \mathbf{x}_\ell + n_k.$ A target at position $\mathbf{p}$ reflects the aggregated illumination back to AP $\ell'$ , producing the bistatic echo $\mathbf{z}_{\ell'} = \alpha(\mathbf{p}) \sum_{\ell=1}^{L} \mathbf{a}_{\ell'}(\mathbf{p})\mathbf{a}_\ell^H(\mathbf{p}) \mathbf{x}_\ell(t - \tau_{\ell \to \mathbf{p} \to \ell'}) + \mathbf{w}_{\ell'},$ where $\tau$ is the two-hop propagation delay from AP $\ell$ through the target $\mathbf{p}$ to AP $\ell'$ . The CPU collects all $L$ echoes over the fronthaul and performs joint detection.

Multistatic Sensing

A sensing configuration in which many spatially separated receivers observe echoes from the same target. Multistatic geometry provides spatial diversity against target RCS fluctuation and resolves range–angle ambiguities that any single receiver would have. Cell-free ISAC is multistatic by construction.

Definition:
Joint Detection Probability in Cell-Free ISAC

Assume a Swerling-I target: the complex reflectivity $\alpha$ is $\mathcal{CN}(0, \sigma_\alpha^2)$ , constant across one dwell but independent across dwells. Each AP $\ell'$ observes a returned SNR $\rho_{\ell'} = N_t^{2} \sigma_\alpha^2 P_t_\ell / (\sigma^2\, d_{\ell\to\mathbf{p}\to\ell'}^4)$ proportional to its own link gain. The central processor's optimal square-law detector against white noise has overall detection SNR $\rho_{\text{tot}} = \sum_{\ell'} \rho_{\ell'}$ . With $P_{\text{fa}}$ fixed by a threshold $\tau$ , the detection probability is $P_d(\rho_{\text{tot}}, P_{\text{fa}}) = \exp\!\left(-\tfrac{-\ln P_{\text{fa}}}{1 + \rho_{\text{tot}}}\right).$ Adding more APs increases $\rho_{\text{tot}}$ additively, which is the quantitative expression of macro-diversity for sensing.

Theorem: Macro-Diversity Gain for Target Detection

In a cell-free ISAC network with $L$ independent, equally-powered APs and Swerling-I target fading, the detection probability satisfies $1 - P_d(L) \;\sim\; \mathcal{O}\!\left(\rho_{\text{avg}}^{-L}\right)$ at high SNR, where $\rho_{\text{avg}}$ is the per-AP mean returned SNR. Equivalently, the sensing diversity order is $L$ : each additional AP reduces the outage of the detector by one order in SNR, exactly as cooperative diversity does in distributed MIMO comm.

A miss event requires every one of the $L$ APs to see a weak echo simultaneously. For independent Swerling-I reflectivities, this probability factors and the miss probability decays as the product of $L$ single-AP miss probabilities. The exponent $L$ is the textbook diversity order; it translates a fluctuating single-AP detection probability into reliable joint detection.

Show Hint

Write $1 - P_d(L) = \\Pr(\\max_\\ell \\rho_\\ell < \\tau)$ for a threshold $\\tau$ .

For i.i.d. exponential $\rho_\ell$ , the CDF at $\tau$ is $1 - e^{-\tau/\rho_{\text{avg}}}$ and the joint miss probability factorizes.

At high SNR, $1 - e^{-\tau/\rho_{\text{avg}}} \approx \tau/\rho_{\text{avg}}$ , so the product scales as $(\tau/\rho_{\text{avg}})^L$ .

Proof

Set up miss event

Under Swerling-I, per-AP echo power $|\alpha_\ell|^2$ is exponential with mean $\bar{\rho}_\ell$ . Assume i.i.d. means $\bar{\rho}_\ell = \rho_{\text{avg}}$ . For a square-law detector thresholded at $\tau$ , $P_d^{(\ell)} = \Pr(|\alpha_\ell|^2 > \tau) = e^{-\tau/\rho_{\text{avg}}}$ .

Joint miss factorizes

Under independent reflectivities (reasonable when APs view the target from angularly separated directions $> \lambda/$ aperture), the joint miss probability is $1 - P_d(L) = \prod_{\ell=1}^L (1 - P_d^{(\ell)}) = (1 - e^{-\tau/\rho_{\text{avg}}})^L.$

High-SNR expansion

For $\rho_{\text{avg}} \gg \tau$ , $1 - e^{-\tau/\rho_{\text{avg}}} \approx \tau/\rho_{\text{avg}} - O((\tau/\rho_{\text{avg}})^2)$ . Substituting, $1 - P_d(L) \approx (\tau/\rho_{\text{avg}})^L = \mathcal{O}(\rho_{\text{avg}}^{-L}). \qquad \blacksquare$

🎓CommIT Contribution(2024)

Bistatic Cell-Free ISAC Architecture

J. Liu, K. Wan, G. Caire — IEEE Transactions on Wireless Communications

Liu, Wan, and Caire (CommIT group, TU Berlin) developed the first system-level treatment of cell-free ISAC as a bistatic multistatic sensing network fused with cell-free communication. Their main contributions:

Joint uplink–downlink duality for ISAC. They show that the cell-free uplink–downlink duality of Chapter 13 extends to ISAC: the optimal downlink transmit covariance for joint comm+sense is the dual of the optimal uplink combiner for joint comm+sense, with an explicit Lagrange multiplier linking the two.
Joint fronthaul compression. They derive a distortion–rate tradeoff on the fronthaul for forwarding compressed echoes and comm samples jointly, extending the information-theoretic fronthaul analysis of Chapter 14.
Macro-diversity order $L$ theorem (shown above). The formal statement that each AP adds one order of diversity to target detection is their Theorem 2, with experimental validation on a testbed with $L = 8$ APs.

The architecture they propose sidesteps the monostatic self-interference problem (Section 24.3, Engineering Note 24.3) by keeping Tx and Rx on different APs: AP $\ell$ transmits the downlink waveform while APs $\ell' \neq \ell$ receive the echo, with zero full-duplex constraint. Each AP is simultaneously a comm-only node and a sensing-only node for a different subset of the targets.

isaccell-freecairebistaticView Paper →

⚠️Engineering Note

Joint Comm+Sensing Fronthaul Budget

Cell-free ISAC doubles the load on the fronthaul: each AP must forward both its communication uplink samples and its sensing echo samples to the CPU. Three design points matter:

Sample rate. Communication uplink samples at the ADC rate ( $\sim 100$ Msps for a 100 MHz channel) are forwarded as I/Q data. Sensing echoes can be pre-match-filtered at the AP, reducing the rate to the range-bin resolution ( $\sim 1$ Msps for 100 m unambiguous range).
Quantization. Communication samples need 10–12 bit ADC resolution to preserve MMSE combining gain. Sensing echo quantization can be more aggressive (4–6 bits) because detection is a non-coherent thresholding decision that is tolerant to coarse quantization.
Centralization level. Fully centralized processing maximizes both comm and sensing gain at the cost of maximum fronthaul bandwidth. Partially centralized operation (each AP does its own local sensing detection and reports only "target yes/no with confidence") dramatically reduces fronthaul but loses multistatic diversity. The tradeoff is the same one studied in Chapter 14 for comm-only fronthaul, now with a second axis.

Practical Constraints

•
Typical eCPRI fronthaul link: 10–100 Gbps per AP.
•
Raw monostatic echo sample rate: ADC rate $\sim$ comm rate.
•
Match-filtered echo rate: range resolution / max unambiguous range $\sim 10\times$ reduction.

📋 Ref: eCPRI v2.0, IEEE 1914.3

Cell-Free ISAC: Target Detection Probability Heatmap

Detection probability as a function of target position in a cell-free ISAC deployment with $L$ APs on a uniform grid. Each AP contributes one order of diversity via multistatic processing.

Parameters

APs

L

9

Antennas per AP

N_t

16

Tx power per AP (dBm)23

Service area size (m)500

\log_{10} P_{\text{fa}}

-6

Example: Diversity Gain from 1 AP to 4 APs

A single AP achieves a target detection probability of 0.90 at a certain target range; the per-AP SNR margin above threshold corresponds to a miss probability of 0.10. In a cell-free deployment with 4 independent APs at the same range, what is the joint detection probability?

Solution

Independence assumption

Independent Swerling-I reflectivities imply independent per-AP miss events. This requires angular separation between APs large enough that the target appears as independent scattering realizations — typically $\Delta\theta > \lambda/D_{\text{target}}$ where $D_{\text{target}}$ is the target extent.

Joint miss probability

$1 - P_d(4) = (1 - 0.90)^4 = 10^{-4}$ , so $P_d(4) = 0.9999$ . The detection probability went from 0.9 to 0.9999 — a factor of $10^4$ reduction in miss rate — by adding three more APs. That is the diversity order 4.

Comparison with coherent gain

If the four APs were instead combined coherently (phase-aligned, perfect sync), they would give a $4\times$ SNR gain instead of a diversity gain. Coherent gain improves the average but not the outage; the macro-diversity effect is specifically about protecting against deep fades. In practice, cell-free ISAC exploits both: coherent comm combining across APs (for throughput) and incoherent sensing fusion (for diversity). $\blacksquare$

Cell-Free Multistatic Sensing Fusion

Complexity: Fronthaul:

\mathcal{O}(L \cdot B_{\text{FH}})

. CPU:

\mathcal{O}(N_{\text{cells}} \cdot L^2)

per dwell.

Input: Per-AP pre-processed echoes

\{\mathbf{z}_\ell\}_{\ell=1}^L

, reference waveform

\mathbf{s}

, candidate target cells

\{\mathbf{p}_i\}

, fronthaul budget

B_{\text{FH}}

.

Output: Detection map

\{d_i\}_{i=1}^{N_{\text{cells}}}

.

1. for each AP

\ell

do

2.

\quad

Match-filter local echo:

\mathbf{r}_\ell \leftarrow \text{MF}(\mathbf{z}_\ell, \mathbf{s})

3.

\quad

Compress

\mathbf{r}_\ell

to rate

B_{\text{FH}}/L

(uniform quant.)

4.

\quad

Forward to CPU

5. end for

6. at CPU:

7. for each candidate cell

\mathbf{p}_i

do

8.

\quad

Compute expected delay

\tau_{\ell \to i \to \ell'}

for each AP pair

9.

\quad

Coherently sum contributions over pairs:

y_i \leftarrow \sum_{\ell,\ell'} r_{\ell'}(\tau_{\ell \to i \to \ell'})

10.

\quad

Threshold:

d_i \leftarrow \mathbb{1}[|y_i|^2 > \tau]

11. end for

12. return

\{d_i\}

Step 9 assumes phase-coherent fusion across APs, which requires sub-wavelength synchronization. If only frame-level sync is available, replace step 9 with a non-coherent energy sum — recovering the macro-diversity argument of the theorem but losing coherent gain.

Coherent vs Noncoherent AP Fusion

Phase-coherent fusion across APs is a stringent requirement: it demands wavelength-scale timing accuracy ( $\sim 10$ ps for 100 GHz carrier) shared over the network. Typical deployments achieve this over fiber with White Rabbit or PTP + hardware timestamping at sub-ns, which is enough for sub-6 GHz coherent fusion but becomes the limiting factor at mmWave. Noncoherent fusion is the conservative choice: it keeps the diversity order $L$ from the theorem but sacrifices the $L^2$ -style coherent sum. The upshot is that the incremental cost of coherent network synchronization — already needed for cell-free comm — directly enables better sensing as a side effect, a rare example of free engineering synergy.

Common Mistake: Do Not Forward Raw Echoes

Mistake:

A first-cut cell-free ISAC implementation forwards the raw echo samples from every AP to the CPU at the Nyquist rate of the receive band.

Correction:

The fronthaul is the bottleneck. Match-filtering at the AP typically reduces the data rate by $\text{time-bandwidth product} \sim 10^2$ – $10^3$ , and subsequent coarse quantization of the match-filter output is tolerable because detection is a non-coherent threshold decision. Empirically, 4–6 bit quantization of the match-filter output loses less than 0.5 dB of detection SNR, while reducing the fronthaul load by an order of magnitude over raw 12-bit I/Q forwarding.

Cell-Free ISAC Geometry: One Target, Many APs — In a cell-free ISAC network, one AP illuminates while several others observe the echo. Each (Tx, Rx) pair defines an iso-range ellipse through the target; the intersection of ellipses localizes it. Macro-diversity against target fading scales as the number of APs.

Why This Matters: Cell-Free ISAC in 3GPP Release 19+

3GPP Rel-19 study items on ISAC (TR 22.837) list "multi-TRP sensing" as a baseline architecture — essentially cell-free ISAC for the subset of deployments with dense TRPs (Transmission Reception Points). ITU-R's IMT-2030 draft frames 6G sensing as "ubiquitous sensing layer" with many distributed nodes jointly covering the service area. The Liu-Wan-Caire cell-free ISAC paper is the most cited academic reference behind these standardization efforts.

Cell-Free ISAC and Multistatic Detection