Ferkans — Interactive Telecom Tutor

The Network IS the Radar

In Sections 29.1--29.4 we considered monostatic ISAC: the same base station transmits and receives echoes. But a cellular network has many base stations, each transmitting communication signals. Bistatic and multi-static ISAC turns the entire network into a distributed radar system, where base stations serve as illuminators and receivers simultaneously.

This is precisely the multi-sensor imaging scenario of Chapter 11 (MIMO radar) --- but now the illumination signals carry communication data, and the sensing receivers may not know the transmitted waveform. The Liu/Wan/Caire framework addresses this fundamental challenge via blind interference management.

Definition:
Bistatic ISAC Architecture

In bistatic ISAC, the transmitter (BS $_i$ ) and sensing receiver (BS $_j$ ) are at different locations. BS $_i$ sends communication signals; BS $_j$ captures target echoes.

The bistatic range for a target at $\mathbf{p}_t$ is:

$R_b = \|\mathbf{p}_t - \mathbf{p}_i\| + \|\mathbf{p}_t - \mathbf{p}_j\| - \|\mathbf{p}_i - \mathbf{p}_j\|$

The target lies on an ellipse with foci at BS $_i$ and BS $_j$ (iso-range contour). Multiple baselines resolve the 2D/3D position.

The received signal at BS $_j$ is:

$\mathbf{y}_j(t) = \underbrace{\mathbf{H}_{ij}\mathbf{x}_i(t - \tau_d)}_{\text{direct path}} + \underbrace{\sum_k \alpha_k \hat{\mathbf{a}}(\hat{\theta}_k) \mathbf{a}^{H}(\theta_k) \mathbf{x}_i(t - \tau_k)}_{\text{target echoes}} + \mathbf{w}_{j}(t)$

where $\tau_d$ is the direct-path delay and $\tau_k$ is the target round-trip delay.

In bistatic ISAC, BS $_j$ typically does not know the data transmitted by BS $_i$ (different cells, different schedulers). This means data-symbol compensation is impossible, and the communication signal acts as unknown interference for sensing.

🎓CommIT Contribution(2023)

Blind Interference Management for Bistatic ISAC

F. Liu, K. Wan, G. Caire — IEEE Trans. Wireless Communications

Liu, Wan, and Caire addressed the fundamental challenge of bistatic ISAC: the sensing receiver does not know the communication data, so the transmitted signal acts as interference. Their contributions:

Deterministic-random signal decomposition: The transmitted ISAC signal has a deterministic part (pilots, preambles) known to all receivers and a random part (data) known only to the transmitter. Sensing uses only the deterministic part, while communication benefits from both.
Blind interference management: Instead of trying to subtract the unknown data (impossible without cooperation), the sensing receiver treats it as coloured noise and designs the sensing estimator accordingly. The key result: the sensing performance loss relative to a known-waveform radar is bounded by the sensing-communication power ratio.
Multi-static ISAC networks: They showed that with $N_b$ base stations, the spatial diversity from $N_b(N_b-1)/2$ bistatic pairs compensates for the per-pair SNR loss from blind processing, and the overall imaging quality can exceed monostatic ISAC.

This directly connects to the multi-sensor imaging framework of Chapter 11: each bistatic pair provides a different $\mathbf{A}_{ij}$ , and the joint sensing matrix is the vertical concatenation --- exactly as in the MIMO radar virtual array.

ISACbistaticblind-interferencemulti-staticCommIT

Definition:
Multi-Static ISAC Network

A multi-static ISAC network uses $N_b$ base stations, each transmitting communication signals and receiving echoes from all transmitters. For pair $(i, j)$ :

$y_{ij}(t) = \sum_k \alpha_k^{(ij)} \, x_i\!\left(t - \frac{R_{ik} + R_{jk}}{c}\right) + n_{ij}(t)$

The total number of independent bistatic baselines is $N_b(N_b-1)/2$ , providing rich spatial diversity.

The joint sensing matrix stacks all bistatic measurements:

$\mathbf{A}_{\mathrm{joint}} = \begin{bmatrix} \mathbf{A}_{12} \\ \mathbf{A}_{13} \\ \vdots \\ \mathbf{A}_{(N_b-1)N_b} \end{bmatrix}$

Each $\mathbf{A}_{ij}$ contributes a different viewing geometry, improving the condition number of $\mathbf{A}_{\mathrm{joint}}$ and the imaging resolution isotropy.

Multi-static ISAC creates an imaging system from existing cellular infrastructure. Each BS pair provides a different viewing angle --- equivalent to multi-view imaging (Chapter 11) but using communication signals of opportunity.

Bistatic ISAC Network Geometry

Visualise a multi-static ISAC network with configurable BS positions. The plot shows bistatic ellipses for each pair, their intersection (target position), and the resulting spatial diversity for imaging.

Parameters

Number of Base Stations3

Target X (m)30

Target Y (m)80

Show Bistatic Ellipses

Example: Bistatic ISAC for Urban Imaging

Three 5G base stations at $(0, 0)$ , $(500, 0)$ , and $(250, 400)$ m form a multi-static ISAC network. A target is at $(200, 150)$ m. Compute the bistatic ranges for all three pairs and explain 2D localisation.

Solution

Ranges to target

$R_1 = \sqrt{200^2 + 150^2} = 250$ m. $R_2 = \sqrt{300^2 + 150^2} = 335.4$ m. $R_3 = \sqrt{50^2 + 250^2} = 255$ m.

Bistatic ranges

Pair (1,2): $R_b^{(12)} = R_1 + R_2 - 500 = 85.4$ m. Pair (1,3): $R_b^{(13)} = R_1 + R_3 - \sqrt{250^2 + 400^2} = 250 + 255 - 472 = 33$ m. Pair (2,3): $R_b^{(23)} = R_2 + R_3 - 472 = 118.4$ m.

2D localisation

Each bistatic range defines an ellipse with foci at the two BSs. The target is at the intersection of the three ellipses. Two ellipses give two candidate positions; the third resolves the ambiguity. Localisation accuracy depends on the GDOP, which is best when BSs surround the target.

Common Mistake: Direct-Path Interference in Bistatic ISAC

Mistake:

Processing bistatic echoes without suppressing the direct-path signal from the transmitter to the sensing receiver.

Correction:

The direct path is 60--100 dB stronger than target echoes. Suppression methods:

Reference signal subtraction: Reconstruct the direct path from the known pilot/preamble structure.
Spatial filtering: Beamform at the receiver to null the transmitter direction.
Adaptive filtering: CLEAN or LMS-based cancellation.

Two-stage cancellation (analog + digital) typically achieves 80--90 dB suppression.

Theorem: Diversity Gain of Multi-Static ISAC

For a multi-static ISAC network with $N_b$ base stations and a single point target, the Fisher information for target position estimation satisfies:

$\operatorname{tr}(\mathbf{J}_{\mathrm{multi}}) \geq \sum_{i < j} \operatorname{tr}(\mathbf{J}_{ij})$

where $\mathbf{J}_{ij}$ is the FIM for bistatic pair $(i,j)$ . The improvement in localisation accuracy over a single pair scales as $\sqrt{N_b(N_b-1)/2}$ in the high-SNR regime.

Moreover, the condition number of $\mathbf{A}_{\mathrm{joint}}$ improves with the number of BSs, leading to more isotropic imaging resolution when BSs span diverse viewing angles.

Each bistatic pair provides a different "view" of the target. Combining views is equivalent to increasing the effective aperture, which directly improves resolution. This is the multi-view imaging principle from Chapter 11, now applied to communication infrastructure.

Proof

FIM additivity

For independent observations (separate bistatic pairs with independent noise), the total FIM is the sum of individual FIMs: $\mathbf{J}_{\mathrm{multi}} = \sum_{i < j} \mathbf{J}_{ij}$ . The trace (total information) is additive.

Localisation accuracy

CRB for position: $\mathrm{CRB} = \operatorname{tr}(\mathbf{J}_{\mathrm{multi}}^{-1})$ . By the matrix inequality $\operatorname{tr}(\mathbf{A}^{-1}) \geq d / \operatorname{tr}(\mathbf{A})$ (for $d \times d$ PSD matrix $\mathbf{A}$ ), the CRB decreases inversely with the number of pairs.

Isotropy

A single monostatic system has elongated PSF (range vs. cross-range asymmetry). Multi-static baselines spanning $> 90^\circ$ of viewing angles balance the eigenvalues of $\mathbf{A}^{H}\mathbf{A}$ , reducing the condition number and making the PSF more isotropic. $\blacksquare$

⚠️Engineering Note

Synchronisation Requirements for Multi-Static ISAC

Multi-static ISAC requires time and frequency synchronisation between base stations:

Time sync: For range resolution $\Delta R$ , the clock offset must satisfy $\Delta t < \Delta R / c$ . At $\Delta R = 1$ m: $\Delta t < 3.3$ ns. GPS-disciplined oscillators achieve $\sim 10$ ns; tighter sync requires wired backhaul timing (IEEE 1588 PTP achieves $< 1$ ns).
Frequency sync: Phase coherence between BSs requires $\Delta f < 1/(2T_{\mathrm{obs}})$ . For $T_{\mathrm{obs}} = 10$ ms: $\Delta f < 50$ Hz. This is achievable with rubidium oscillators but not with standard crystal oscillators.
Non-coherent alternative: Process each bistatic pair independently (magnitude only, no phase) and fuse the intensity images. Avoids frequency sync but loses $\sim 3$ dB.

Quick Check

What is the primary advantage of bistatic ISAC over monostatic ISAC for cellular networks?

No dedicated radar hardware is needed --- communication terminals serve as sensing receivers

Bistatic ISAC achieves better range resolution

Bistatic ISAC avoids the ISAC tradeoff entirely

Correction:

No dedicated radar hardware is needed --- communication terminals serve as sensing receivers

Bistatic ISAC uses existing communication infrastructure (base stations, UEs) as both illuminators and receivers, eliminating the need for dedicated radar hardware.

Bistatic ISAC

ISAC configuration where the transmitter and sensing receiver are at different locations. The communication signal serves as the radar illumination, and target echoes are captured by a separate receiver (another BS or a UE).

Multi-Static ISAC Network

An ISAC network with $N_b$ base stations, each serving as both illuminator and receiver. Provides $N_b(N_b-1)/2$ independent bistatic baselines for spatial diversity in imaging.

Related: Bistatic ISAC

Key Takeaway

Bistatic and multi-static ISAC turn the cellular network into a distributed radar. The Liu/Wan/Caire framework handles the fundamental challenge of unknown data interference via blind processing. With $N_b$ BSs, the $N_b(N_b-1)/2$ bistatic baselines provide rich spatial diversity --- directly connecting to the multi-sensor imaging framework of Chapter 11. Direct-path interference suppression (80--90 dB) is the primary practical challenge.

Bistatic and Multi-Static ISAC