Cooperative ISAC Networks: Performance Analysis, Scaling Laws and Optimization

I. INTRODUCTION

• Prior ISAC research mainly addressed link- or system-level design, while network-level analysis must account for random BS locations, topologies, and fading.The paper also identifies limited study of tight intercell S&C cooperation and CRLB-based network sensing analysis.Source: §I · pp. 1–2

A. Cooperative ISAC Network Model

• Communication and sensing use dynamically formed BS clusters, but larger clusters can increase processing, feedback, signaling, and backhaul demands.Too-small clusters may miss cooperation gains, while limited backhaul can constrain the benefit of larger clusters.Source: §I · p. 2, A. Cooperative ISAC Network Model · p. 3

I. INTRODUCTION

• The proposed framework combines CoMP joint transmission and distributed radar, with stochastic geometry used to derive tractable S&C performance expressions.The framework is designed to operate under limited backhaul capacity and is reported to improve average data rate and sensing accuracy.Source: §I · p. 2
• The average cooperative sensing CRLB scales with ln^2 N, below the N^2 geometry gain because distant BSs contribute less under higher path loss.The comparison concerns random BS locations versus the stated geometry gain.Source: §I · p. 2
• The paper derives effective channel gains and signal and interference Laplace transforms, then obtains a communication-rate expression and an optimal cluster size accounting for BS acceptance probability.The supplied passages do not provide the rate expression's values.Source: §I · pp. 2–3
• The authors formulate a performance-boundary optimization and compare it with an inner bound; they also optimize cooperative cluster sizes and S&C power for a flexible network-level tradeoff.Simulations report greater improvement than time-sharing when more time/frequency resource blocks and backhaul capacity are available.Source: §I · pp. 2–3

B. Cooperative Sensing Model

• The CRLB lower-bounds the mean squared location error of an unbiased target-position estimator.The estimated target position is represented by its two-dimensional coordinates.Source: B. Cooperative Sensing Model · p. 4
• Non-coherent MIMO radar is assumed because cell-delay synchronization is adequate for non-coherent processing, whereas coherent distributed radar synchronization is expensive.The sensing cluster comprises N BSs, whose transmitted radar signals are assumed approximately orthogonal over delays of interest.Source: B. Cooperative Sensing Model · p. 4
• Because target RCS fluctuates, the analysis forms the Fisher information matrix using the average RCS to make CRLB analysis tractable.The target is assumed stationary during the short processing interval and follows a Swerling-I RCS model.Source: B. Cooperative Sensing Model · p. 4
• The expected CRLB is evaluated over random ISAC-transceiver locations, with the model describing target-channel path loss and bearing angles.The target position is estimated by maximum likelihood using the ranges of monostatic and bistatic links.Source: B. Cooperative Sensing Model · p. 4

C. Cooperative Communication Model

• In non-coherent CoMP, the closest BS requests cooperation from nearby BSs, which accept according to their traffic load.The closest BS initiates a user-centric cluster of L BSs.Source: C. Cooperative Communication Model · p. 4
• The communication analysis assumes a dense, interference-limited network, disregards noise, and evaluates the typical user's SIR.The closest BS's large-scale path loss follows the stated distance-power model.Source: C. Cooperative Communication Model · p. 4

D. Limited Backhaul Capacity Model

• Backhaul capacity constrains average communication rate plus sensing-cooperation traffic, while CSI-sharing traffic is excluded, yielding a best-case backhaul assessment.Sensing traffic covers transmission of preprocessed echo results.Source: D. Limited Backhaul Capacity Model · p. 5
• The paper proposes an analytical cluster-size selection method using prior BS load, BS-to-user density ratio, and path-loss exponents, with parameters calculable offline and updateable online.It is presented as less computationally complex than iterative clustering schemes.Source: D. Limited Backhaul Capacity Model · p. 5

A. Geometry Gain of Cooperative Sensing

• With equal BS-to-target distances and link measurement gains ignored, the analysis isolates the localization gain from sensing-direction diversity.The section first treats geometry-based gain, then considers random BS and target locations for expected CRLB analysis.Source: A. Geometry Gain of Cooperative Sensing · p. 5, §III · p. 5
• Expected GDoP is inversely proportional to the square of the number of cooperating BSs.This geometry-based result considers random sensing directions.Source: A. Geometry Gain of Cooperative Sensing · p. 5

B. Performance Gain of Cooperative Sensing

• The expected CRLB approximation is determined only by the expected distance from a BS to the typical target.The derivation uses a tractable approximation to handle the complex operations involved in the CRLB.Source: B. Performance Gain of Cooperative… · pp. 5–6
• CRLB scales inversely with ln N, with diminishing accuracy gains because distant BS measurements contribute only modestly under excessive propagation loss.The theorem establishes the random-location scaling law for an infinite cooperative cluster.Source: B. Performance Gain of Cooperative… · p. 6

C. Cooperation Acceptance Probability for Limited Resource Blocks

• Acceptance probability decreases with target-BS density ratio and cluster size, but increases with the maximum BS load ψ.The acceptance analysis assumes independent request counts across BSs.Source: C. Cooperation Acceptance Probability… · p. 6
• Under limited resource availability, the CRLB first decreases and then increases as N grows.When average requests exceed ψ, some requests are denied, increasing the average distance of participating BSs and eroding collaboration gain.Source: C. Cooperation Acceptance Probability… · p. 6
• The optimal sensing cluster generally has κs ≈ 1 and average BS service load no greater than ψ.When average requests exceed ψ, κs falls below one and BSs must deny some requests.Source: C. Cooperation Acceptance Probability… · p. 6

IV. COMMUNICATION PERFORMANCE ANALYSIS

• The communication section derives a tractable performance expression and an approximate method for finding the optimal cooperative cluster size.Source: §IV · p. 6

• The analysis formulates the BS acceptance probability when each user requests L BSs, with the closest BS always serving the typical user.Source: A. Expression of Communication Rate · p. 6
• The expected data rate is formulated from Laplace transforms of cooperative transmission power and interference components.The analysis distinguishes interference from BSs declining requests and from BSs outside the requested cluster.Source: A. Expression of Communication Rate · p. 7
• The average data rate increases with BS density and the number of resource blocks.Source: A. Expression of Communication Rate · p. 7
• For L = 1, the interference term I1 can be ignored and the achievable rate simplifies; without cooperation, rate is independent of BS density because signal and interference both increase with density.In the no-cooperation case, the SIR remains constant.Source: A. Expression of Communication Rate · p. 7

• To maximize communication performance, the paper formulates an optimization over cooperative cluster size and simplifies expected data rate to optimize expected SIR.Source: B. Optimal Cooperative Cluster Size · pp. 7–8
• The optimal cluster size is independent of transmission power allocation and is obtained by optimizing the distance ratio η before selecting L.The optimal η is uniquely found for a given distance to the closest BS.Source: B. Optimal Cooperative Cluster Size · p. 8
• The approximated optimal cluster size closely aligns with the burst-search result based on Monte Carlo simulations.Source: B. Optimal Cooperative Cluster Size · p. 8

V. TRADEOFF BETWEEN SENSING AND COMMUNICATION

• Increasing either cooperative cluster improves its corresponding performance, but limited backhaul creates a tradeoff represented by the achievable rate-CRLB region.Fig. 2 illustrates the network-level performance region.Source: §V · p. 8, Figure 2 · p. 8
• Exhaustively searching all feasible cluster sizes and transmit powers is computationally costly, especially when the backhaul capacity region is large.Source: §V · p. 8
• Searching only L and p_c reduces the search space because optimal N and p_s can be derived for each choice, with monotonic rate and CRLB relationships guiding power bounds.For given L, the optimal N is also bounded by the sensing-only optimum and backhaul capacity.Source: §V · p. 8
• Transmit-power search can skip ranges whose candidate rate-CRLB pair is dominated by a pair already on the updated boundary.The proposition uses the monotonic relationship between rate and CRLB with transmit power.Source: §V · p. 8
• A weighted sum with ρ balances sensing and communication performance, and the convex performance boundary can be searched optimally with the Polyblock algorithm.The rate-CRLB region contains achievable pairs under transmit-power and backhaul constraints.Source: §V · p. 8

A. Sensing Performance

• For N ≥ 10, adding cooperative BSs yields only incremental sensing-accuracy gains as distant BSs contribute less because of signal attenuation.The tractable CRLB expression closely approximates simulation results, particularly for larger N.Source: Figure 4 · p. 9, A. Sensing Performance · p. 9
• With the acceptance probability derived in (23), CRLB reaches its minimum at ψ = 15 and increases for N ≥ 15 as loaded BSs decline nearby requests.The resulting clusters draw BSs from farther away as service requests rise.Source: Figure 5 · p. 9, A. Sensing Performance · p. 9
• The expected CRLB decreases more slowly with N than the GDoP, indicating a tradeoff between sensing gains and cooperation costs.The simulation confirms the GDoP scaling; increasing the sensing cluster from N = 3 to N = 6 yields a tenfold geometry-based gain.Source: A. Sensing Performance · p. 9

VI. SIMULATION RESULTS

• The original communication-rate expression agrees with simulation results, supporting the accuracy of the communication analysis.The simulations average across network and small-scale fading realizations, with Mt = 4 transmit antennas, Mr = 5 receive antennas, and Cbackhaul = 8.6 bits/s/Hz.Source: B. Communication Performance · p. 9, §VI · p. 9, Figure 6 · p. 10

B. Communication Performance

• The approximation-search cluster size closely matches Monte Carlo search and the Theorem 2 expression, especially with more than 10 resource blocks.This verifies the proposed low-complexity method for finding the optimal cooperative cluster size.Source: Figure 7 · p. 10, B. Communication Performance · p. 10
• Communication spectral efficiency first rises and then falls with cluster size L; the maximizing L* is consistent across power ratios at a fixed user-BS density.As the user-BS density ratio increases fivefold, the optimal cluster size decreases by approximately the same factor.Source: B. Communication Performance · p. 10

C. Tradeoff between Sensing and Communication

• At backhaul capacities of 8.6 and 4.3 bits/s/Hz, the proposed scheme's user data rate is up to 300% and 85% higher than time-sharing, respectively.The authors attribute the gains to increased backhaul capacity enabling coordination of transmit power and multi-cell resources.Source: C. Tradeoff between Sensing and… · pp. 10–11
• As weighting factor ρ increases, sensing performance decreases while communication performance increases; the cooperative scheme can flexibly enhance both relative to the noncollaborative scheme.The weighted joint metric remains between sensing-only and communication-only performance.Source: Figure 10 · p. 11, C. Tradeoff between Sensing and… · p. 11

VII. CONCLUSION

• The cooperative ISAC scheme combines CoMP joint transmission and distributed radar, with analytically derived S&C performance expressions based on stochastic geometry.The paper formulates profile optimization for network performance and compares it with time-sharing.Source: §VII · p. 11
• The network-wide average cooperative sensing CRLB scales with ln^2 N, less than the N^2 squared geometry gain.The conclusion reports that optimized cooperative clusters and power allocation improve network-level cooperative gain relative to time-sharing.Source: §VII · p. 11

APPENDIX A: PROOF OF PROPOSITION 1

• For Proposition 1, numerator and denominator transformations reduce the expected CRLB calculation to sums of angle-related variables with the same order.The proof uses the zero expectation of cosine differences for distinct BS angles to simplify the expectation.Source: Appendix A · p. 11

APPENDIX B: PROOF OF PROPOSITION 2

• For Proposition 2, the expected transmit beamforming gain is Mt − 1; independence of BS angles and distances supports the subsequent CRLB approximation.The approximation drops lower-order terms and uses independence across BS distances.Source: Appendix B · p. 11

APPENDIX C: PROOF OF THEOREM 1

• For Theorem 1, the harmonic sum HN is approximated by ln(N) + γ + 1/(2N), yielding the logarithmic scaling as N grows.The proof uses lim as N → ∞ of [HN − ln(N)] = γ, where γ = 0.577.Source: Appendix C · p. 12

APPENDIX D: PROOF OF LEMMA 1

• The acceptance probability is tied to whether the number of users in a BS association area is below its maximum load ψ.The average association area is given in terms of N and BS density, and the average user count follows from the user density.Source: Appendix D · p. 12

APPENDIX E: PROOF OF LEMMA 3

• For Lemma 3, the proof models external and intra-cluster interference with Laplace transforms, applying the PPP probability generating functional.The distance ratio ηL normalizes the closest-BS distance by the farthest-BS distance in the cluster.Source: Appendix E · p. 12

APPENDIX F: PROOF OF THEOREM 2

• For Theorem 2, conditional rate and spectral efficiency are averaged over distance and the cluster distance ratio, then combined with the useful-signal and interference Laplace transforms.The proof uses the nearest-BS distance density and the stated distance-ratio distribution.Source: Appendix F · pp. 12–13