Repeater-Assisted Bi-Static ISAC System

• The paper demonstrates that repeater-assisted bi-static ISAC systems use an amplify-and-forward repeater to enhance radar sensing SINR and extend coverage in challenging areas.
• It shows that joint precoder and repeater gain optimization effectively balances improved target detection with manageable interference in downlink communications.
• Analytical results reveal that proper gain scheduling and comm-centric beamforming can yield up to 30% improvement in radar performance and 20% enhancement in user spectral efficiency.

A repeater-assisted bi-static integrated sensing and communication (ISAC) system is a wireless network architecture in which an amplify-and-forward (AF) repeater is strategically deployed to simultaneously enhance radio-sensing capabilities and communication performance by participating as an active analog scatterer. The repeater instantaneously amplifies and retransmits incident signals—both direct and target-reflected—to increase the effective sensing signal-to-interference-plus-noise ratio (SINR) at a sensing receiver, and extends coverage for downlink users in challenging areas such as coverage holes. The same mechanism introduces new trade-offs, as the power gain provided by the repeater also increases noise, interference, and cross-talk between the sensing and communication functionalities, necessitating a careful joint system design incorporating channel state information (CSI) and network constraints (Chowdhury et al., 22 Nov 2025, Jopanya et al., 23 Sep 2025, Åkesson et al., 26 Mar 2025).

1. System Model and Fundamentals

In a canonical bi-static MIMO ISAC configuration, the core elements include:

• A transmitting base station (BS) or AP with $M$ antennas, which emits a linear combination of downlink communication and sensing-specific waveforms.
• A dual-antenna or multi-repeater AF relay, each with $N_r$ receive and $N_t$ transmit antennas, realizing full-duplex operation.
• Multiple downlink users (e.g., $K$ single-antenna user equipment), and targets with unknown, random radar cross-section (RCS).
• A receive BS (bi-static receiver) with $N$ antennas for sensing; potentially the same as the transmitter (monostatic case) or a distinct node (bi-static).
• OFDM or single-carrier signaling, where the transmitted vector $x[\tau]\in\mathbb{C}^M$ fulfills a power constraint $\mathbb{E}\|x[\tau]\|^2\le\rho$.

The repeater processes its received signal (comprising direct transmission, target echo, and noise) through an amplification transformation $G$ (often diagonal/gain matrix), and re-emits it instantaneously: $$\begin{align*} y_R^{\rm in}[\tau] &= H_{BR}x[\tau] + \alpha H_{RT}H_{BT}x[\tau] + w_R^{\rm in}[\tau] \ y_R^{\rm out}[\tau] &= G\,y_R^{\rm in}[\tau] + w_R^{\rm out}[\tau]. \end{align*}$$ All links, including BS-to-users $f_n$, repeater-to-users $h_n$, and sensing/communication channels (e.g., $H_{BB}$, $C$, and $H_{RB}$), are modeled as complex baseband matrices or vectors, with zero-mean circularly symmetric Gaussian noise in each receiver (Chowdhury et al., 22 Nov 2025).

2. Sensing Signal Model and Detection Theory

The sensing receiver observes a composite signal comprised of four principal contributions:

• Target-reflected return via direct and repeater-assisted paths,
• Amplified BS–repeater–BS “leakage”,
• Environmental clutter ($C\,x[\tau]$),
• Aggregate noise comprising both native and repeater-reinjected terms: $$y_B[\tau] = r[\tau]\alpha + \bigl(C\,x[\tau] + H_{RB}G H_{BR}x[\tau]\bigr) + \bigl(w_B[\tau] + H_{RB}G w_R^{\rm in}[\tau]\bigr),$$ where $r[\tau]$ is the effective sensing steering vector incorporating both direct and repeater-echo channels.

Detection exploits a generalized likelihood ratio test (GLRT). Under the standard target-plus-interference model, the GLRT statistic is

$$T = y_B^H\,\Sigma_w^{-1} r \left( r^H\Sigma_w^{-1}r + 1/\sigma_{\rm RCS}^2 \right)^{-1} r^H\Sigma_w^{-1} y_B - y_B^H\,\Sigma_w^{-1} C (C^H\Sigma_w^{-1} C)^{-1} C^H\Sigma_w^{-1} y_B,$$

which under rank regularity yields a noncentral chi-squared distribution, with detection probability determined by the noncentrality

$\nu_T = \sigma_{\rm RCS}^2\, r^H \Sigma_w^{-1} r,$

interpreted as the system’s effective sensing SINR. Typical ROC curves (probability of detection $P_d$ vs. probability of false alarm $P_{\rm FA}$) demonstrate sensitivity enhancements as repeater gain $\nu$ increases, enabling confident detection of targets with a lower RCS (Chowdhury et al., 22 Nov 2025).

3. Communication Performance and Interference Coupling

Simultaneously, the downlink signal model at user $n$ captures both direct and repeater-amplified beams: $$y_{u,n}[\tau] = f_n^T x[\tau] + h_n\,G(H_{BR}\,x[\tau] + \alpha\,H_{RT}H_{BT}x[\tau] + w_R^{\rm in}) + w_{u,n}.$$ The instantaneous SINR at the user is

$$\mathrm{SINR}_n = \frac{\rho\,\pi_n\,|\dot f_n^T p_n|^2}{\rho \left( \sum_{k\neq n} \pi_k |\dot f_n^T p_k|^2 + \pi_T |\dot f_n^T p_T|^2 \right) + \sigma_u^2 + \|h_n G\|^2 \sigma_R^2 },$$

where $p_k$ and $p_T$ are the communication and sensing precoder weights, $\pi_k$ and $\pi_T$ their respective power splits. The ergodic user rate is $R_n = \log_2(1 + \mathrm{SINR}_n)$.

The repeater can substantially enhance coverage (e.g., median per-user spectral efficiency can increase by $\approx 20\%$), but if the sensing precoder is “target-centric”, downlink users may experience up to $5$ Mbps rate degradation due to increased cross-interference. “Comm-centric” sensing beams, i.e., ones projected orthogonally to user channels, mitigate this at a minor sensing SINR cost (Chowdhury et al., 22 Nov 2025).

4. Precoder Optimization and Sensing-Communication Trade-Offs

Optimal design involves the simultaneous selection of precoding vectors $\{p_n, p_T\}$ and repeater gain $\nu$ (or vector gains in the multi-repeater case) to jointly maximize detection performance and communication rates under a total power constraint. The trade-off is formally captured through (non-convex) multi-objective optimization: $$\max_{\{p_1,\dots,p_K,p_T\}} w_s P_d(\{p_\cdot\}) + w_c \sum_n R_n(\{p_\cdot\})$$ subject to $\sum_k \|p_k\|^2 + \|p_T\|^2 \le 1$, $R_n \ge R_{0,n}$, $P_d \ge P_{d,0}$ (Chowdhury et al., 22 Nov 2025).

In practice, regularized zero-forcing solutions on composite user channels are often used for data beams: $$p_n = \epsilon_n \left( \sum_k \dot f_k \dot f_k^H + \zeta_{\rm ZF} I \right)^{-1} \dot f_n$$ and two representative prescriptions for the sensing beam:

• Target-centric: $p_T\propto \dot f_T$;
• Comm-centric: $p_T$ projected onto the null of $\{\dot f_n\}$ (i.e., $p_T \propto (I-UU^H)\dot f_T$ for $U$ the user channel span).

Repeater gain is tuned to balance the SINR of both sensing and communication legs; over-amplification can degrade sensing by elevating noise covariance and can couple excessive sensing-induced interference to users (Åkesson et al., 26 Mar 2025).

5. Analytical Results and Numerical Guidelines

Empirical and analytical studies consistently reveal:

• Sensing SINR increases rapidly with moderate repeater gain ($10$–$15$ dB), with diminishing returns at excessive gain due to noise amplification and feedback instability (when multiple repeaters are coupled) (Chowdhury et al., 22 Nov 2025, Jopanya et al., 23 Sep 2025).
• With gain control and smart placement (e.g., within $100$ m of the target hotspot), a repeater-assisted ISAC system enables detection of targets with a radar cross-section $10\times$ smaller for fixed $P_d$ and $P_{\rm FA}$, or equivalently supports reliable detection at greater distances.
• In multi-repeater deployments, design reduces to linear-fractional programming: only repeaters with strong AP–repeater and repeater–target channels are activated at high gain, yielding power and stability savings (Jopanya et al., 23 Sep 2025). Dinkelbach’s algorithm is used to allocate gain vector entries.
• For communication, user SINR depends not directly on repeater gain, but on the power split (sensing vs. data). Keeping the sensing fraction low (e.g., $\pi_T\approx 0.2$ when $\nu\ge 10$ dB), together with “comm-centric” sensing beams, preserves user rates.
• Joint optimization of precoder and repeater gain under communication SINR constraint (via projected gradient descent) yields up to $20$–$30\%$ improvement in radar CRB compared to fixed-gain designs (Åkesson et al., 26 Mar 2025).

6. Design Considerations and Open Challenges

The system performance is governed by several critical implementation factors:

• Repeater placement: Positioning repeaters in sensing “hot-spots” or along direct/strong intermediate paths maximizes $\beta_{A,n}\beta_{AD,n}$ and combined SNR boosts.
• Gain allocation: Either full gain for all repeaters (when below the system geometry’s threshold) or selective activation (at high maximal gain) is recommended.
• Robustness: Imperfect CSI and hardware impairments (e.g., residual self-interference, repeater–repeater coupling) complicate practical deployment. Stability must be enforced, e.g., by limiting gain, especially in distributed repeater swarms (Jopanya et al., 23 Sep 2025).
• Power and scheduling: Joint power allocation between communication and sensing, subject to hardware constraints and overall budget, is essential. Harvest-and-forward schemes and robust scheduling are promising directions.
• Scalability: For multi-target scenarios or dense user deployments, advanced multi-user or multi-target precoding, and possibly additional repeaters, are required for angular diversity and interference management.

Future research is focused on robust and adaptive joint design techniques, stability analysis for large repeater swarms, energy-efficient gain scheduling, and integration with other intelligent reflecting or reconfigurable surface technologies (Chowdhury et al., 22 Nov 2025, Jopanya et al., 23 Sep 2025, Åkesson et al., 26 Mar 2025).

7. Summary Table: Key System Features and Trade-Offs

Feature/Metric	Repeater-Assisted Enhancement	Limiting Factors / Trade-Offs
Sensing SINR	Boosted by gain $\nu$; much lower RCS detectable	Excess gain raises noise, possible instability
Communication Coverage	Improved per-user spectral efficiency; coverage holes mitigated	Cross-interference if sensing beam is target-centric
Precoder Design Complexity	CSI-aware, nonconvex, regularized-ZF heuristics	Requires joint tuning of power/gain, stability risk
Power/Gain Optimization	Linear-fractional program, Dinkelbach iterations	Hardware constraints, need stability enforcement
Placement Strategy	Hot-spot proximity; line deployment (swarm) optimal	Geographic limitations, channel estimation error

Repeater-assisted bi-static ISAC systems are a rigorously established avenue for next-generation wireless networks, enabling joint improvements in radar sensing and communication through network-controlled active repeaters. Their effectiveness hinges on a subtle joint design balancing amplified signal power, noise injection, optimal precoding, and robust architecture—providing flexible, CSI-driven sensing-communication trade-off engineering (Chowdhury et al., 22 Nov 2025, Jopanya et al., 23 Sep 2025, Åkesson et al., 26 Mar 2025).