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Communication-Sensing Region for Cell-Free Massive MIMO ISAC Systems
Weihao Mao, Yang Lu, Chong-Yung Chi, Bo Ai, Zhangdui Zhong, Zhiguo Ding
TL;DR
The paper addresses modeling and beamforming for Cell-Free massive MIMO ISAC, where target-location uncertainty affects signal propagation and channel estimation. It derives channel-estimation-error statistics and defines a C-S region with three beamforming cases; numerical results characterize the trade-off and compare the system and proposed scheme with cellular, ZF, and MRT baselines.
Problem
The paper addresses how to model uplink training and downlink transmission jointly in Cell-Free massive MIMO ISAC, where target-location uncertainty affects signal propagation and prior designs used perfect CSI without uplink pilot training.
Source: C. Main Contributions · p. 4, §VI · p. 27Method
The paper derives channel-estimation-error statistics and defines a C-S region through sensing-only, communication-only, and ISAC beamforming cases.
Source: §VI · p. 27Results
Numerical results demonstrate the C-S region and communication-sensing trade-off, compare it with the traditional cellular system, and report the proposed scheme’s advantage over ZF and MRT.
Source: §VI · p. 27Takeaways & Limitations
The three-case C-S region provides a framework for studying communication and radar-sensing trade-offs in Cell-Free massive MIMO ISAC.
Source: §VI · p. 27
Abstract
from arXiv · showhide
This paper investigates the system model and the transmit beamforming design for the Cell-Free massive multi-input multi-output (MIMO) integrated sensing and communication (ISAC) system. The impact of the uncertainty of the target locations on the propagation of wireless signals is considered during both uplink and downlink phases, and especially, the main statistics of the MIMO channel estimation error are theoretically derived in the closed-form fashion. A fundamental performance metric, termed communication-sensing (C-S) region, is defined for the considered system via three cases, i.e., the sensing-only case, the communication-only case and the ISAC case. The transmit beamforming design problems for the three cases are respectively carried out through different reformulations, e.g., the Lagrangian dual transform and the quadratic fractional transform, and some combinations of the block coordinate descent method and the successive convex approximation method. Numerical results present a 3-dimensional C-S region with a dynamic number of access points to illustrate the trade-off between communication and radar sensing. The advantage for radar sensing of the Cell-Free massive MIMO system is also studied via a comparison with the traditional cellular system. Finally, the efficacy of the proposed beamforming scheme is validated in comparison with zero-forcing and maximum ratio transmission schemes.
I. INTRODUCTION
ISAC combines communication and radar sensing over shared resources, creating a performance trade-off. The introduction motivates Cell-Free massive MIMO ISAC and identifies gaps in characterizing that trade-off and modeling target-reflected pilot signals.
A. Background
- Shared spectrum, power, and transmit antennas create a trade-off between communication and radar sensing in ISAC.Cell-Free massive MIMO distributes antennas across APs connected to a central processing unit, and is presented as attractive for combining ISAC with coverage and sensing capabilities.Source: A. Background · p. 2
- Prior works generally concentrated on communication or radar-sensing performance under respective design requirements, and few existing works focused on studying the entire communication-sensing operating region.[17] defined and derived the C-S region for a single-target DFRC system; obtained the C-S region for a rate-splitting multiple access-assisted DFRC system.Source: A. Background · p. 3, B. Related Works · p. 3
B. Related Works
- In Cell-Free massive MIMO, pilot training is challenging, and training becomes even more challenging in the presence of location-unknown targets.Source: B. Related Works · p. 4
C. Main Contributions
The paper models Cell-Free massive MIMO ISAC with target-location uncertainty and derives channel-estimation-error statistics. It defines a C-S region, develops beamforming designs for its three cases, and reports trade-off results and gains over ZF and MRT.
System model
- The system model accounts for target-reflected signals during uplink pilot training and downlink transmission, with closed-form first- and second-order statistics of channel-estimation error.The paper states that this joint treatment of the phases had not previously been reported in the open literature, to the authors’ knowledge.Source: C. Main Contributions · pp. 4–5
C-S region
- The C-S region characterizes communication-sensing trade-offs through sensing-only, communication-only, and joint ISAC beamforming cases.The respective designs minimize sensing beampattern-matching MSE, maximize sum rate, and maximize sum rate subject to sensing-MSE requirements.Source: C. Main Contributions · p. 5
Beamforming design
- The sensing-only problem is convex; the communication-only and ISAC designs use BCD-based methods with Lagrangian dual and quadratic fractional transforms, and SCA, respectively.The ISAC design is reformulated similarly to the communication-only case before applying SCA in a BCD manner.Source: C. Main Contributions · p. 5
Numerical results
- The proposed joint C-S beamforming scheme outperforms the ZF and MRT schemes in the reported numerical results.The results also compare the C-S region with the traditional cellular system and examine system-parameter impacts.Source: C. Main Contributions · p. 5
II. SYSTEM MODEL
The system coordinates distributed APs to serve information users and sense targets over shared time-frequency resources. Its channel model includes target-location uncertainty and target-reflected signals in both uplink and downlink phases.
II. SYSTEM MODEL
- A CPU coordinates M APs to serve K single-antenna information users and detect T point-like targets on the same time-frequency resource.The system uses time-division duplexing, with each coherence interval divided into uplink pilot training and downlink information transmission and target sensing.Source: §II · p. 6
- Each target is assigned to one AP for sensing, while each AP senses at most one target; target reflections affect signals in both transmission phases.The channels are modeled as quasi-static and frequency-flat within each coherence interval.Source: §II · p. 6, A. Channel Model · p. 6
A. Channel Model
- Target coordinates may be uncertain, and APs use prior coordinate knowledge from pre-detection technology when modeling target-to-AP sensing channels.The target-to-AP sensing channel assumes line of sight; target-to-user channels include Rayleigh fading.Source: A. Channel Model · p. 7
B. Uplink Pilot Training
Uplink training reuses pilots when the pilot sequence is shorter than the number of information users, then estimates aggregated channels and derives their statistics. Downlink APs jointly transmit information and sensing signals, using estimated target directions to shape sensing beampatterns.
B. Uplink Pilot Training
- When τp < K, pilot sequences must be reused; the channel estimate is formed for the aggregated IU–AP channel rather than its individual propagation links.The aggregated-channel estimate is obtained by linear MMSE, with its mean and auto-correlation matrix and the estimation-error mean and cross-correlation matrix derived in closed form.Source: B. Uplink Pilot Training · p. 8, where Φmk and Φmm′k are given as… · p. 9
C. Downlink Information Transmission and Target Sensing
- In downlink, APs transmit information and sensing signals in dual-function mode, while random channel-estimation errors make joint beamforming design almost prohibitive.The IU ergodic rate is handled using a computationally tractable lower bound based on Jensen’s inequality.Source: C. Downlink Information Transmission… · pp. 10–11
- Each sensing AP uses the estimated target direction to design a practical beampattern by minimizing its MSE from an ideal pattern over sampled directions.Targets are assigned to sensing APs, each AP senses at most one target, and the exact target–AP distance is unknown.Source: C. Downlink Information Transmission… · pp. 10–12
D. Communication-sensing Region
The communication-sensing region describes the trade-off between communication and sensing in the considered system. It is determined from sensing-only, communication-only, and joint ISAC designs.
D. Communication-sensing Region
- More power in communication sidelobes results in a smaller sensing probing range, motivating the study of the communication-sensing region.Figure 2 illustrates the communication–sensing trade-off.Source: D. Communication-sensing Region · p. 12, Figure 2 · p. 13
- The communication-sensing region is obtained by solving transmit-design problems for sensing-only, communication-only, and coexisting-user-and-target ISAC cases.The sensing-only case removes information users, the communication-only case removes targets, and the ISAC case determines the coupled boundary.Source: D. Communication-sensing Region · pp. 13–14
- The ISAC design determines the coupling boundary for R between 0 and Rmax and S above Smin, subject to a sensing-beampattern matching MSE requirement δ.The joint case includes both information users and targets.Source: D. Communication-sensing Region · p. 14
instead of Problem P3
The communication-sensing region boundary is traced between two critical points by varying a sensing or communication requirement. Pilot allocation and target–AP pairing are presented as prerequisites for determining the region.
instead of Problem P3
- The boundary’s critical points are (Smin, RT) and (SI, Rmax); intermediate points follow by solving P3 or P4 under assigned sensing or rate requirements.The other boundary portions hold communication at Rmax or sensing at Smin.Source: instead of Problem P3 · p. 14
III. PILOT ALLOCATION SCHEME AND TARGET-AP PAIRING SCHEME
- Pilot allocation and target–AP pairing are presented separately because uplink pilot training depends on pilot assignments, while downlink transmission and sensing depend on target–AP assignments.The schemes are used before solving the transmit-design problems to determine the communication-sensing region.Source: instead of Problem P3 · pp. 14–15, §III · p. 15
A. Pilot Allocation Scheme
The paper presents HAC pilot allocation and distance-based target–AP pairing, then solves the transmit-design problems used to determine the communication-sensing region. The communication-only design uses reformulations and block coordinate descent, while the sensing-only design decomposes into parallel convex subproblems.
A. Pilot Allocation Scheme
- HAC addresses unavoidable pilot contamination when K > τp by merging the most distant IU clusters until τp remain, assigning a distinct orthogonal pilot to each cluster.IUs in the same cluster reuse a pilot sequence.Source: A. Pilot Allocation Scheme · p. 15
B. Target-AP Pairing Scheme
- Target–AP pairing minimizes the sum of prior target–AP distances by solving an equivalent weighted bipartite-graph matching problem with the Kuhn–Munkres algorithm [34].The method uses prior target–AP distance knowledge because exact target coordinates are unknown.Source: B. Target-AP Pairing Scheme · p. 16
IV. PROPOSED C-S REGION DETERMINATION
- After pilot allocation and target–AP pairing, solving P1, P2, and P3 yields the communication-sensing region.These problems correspond to sensing-only, communication-only, and joint ISAC design, respectively.Source: §IV · p. 16
A. Sensing-only Case
- The sensing-only problem separates into MT convex subproblems because the sensing-signal variables are uncoupled across APs, allowing parallel solution with CVX solvers.The objective is also convex.Source: A. Sensing-only Case · p. 16
B. Communication-only Case
- The communication-only design uses a Lagrangian dual transform and quadratic fractional transform, then optimizes decoupled variables by block coordinate descent.The Lagrangian dual transform yields an inner problem with a closed-form solution and a reformulated outer problem; the approach also permits parallel rather than sequential AP subproblems.Source: B. Communication-only Case · pp. 16, 17, 19
C. ISAC Case
The ISAC beamforming problem is reformulated to address its non-concave objective and non-convex constraints. Auxiliary variables, block coordinate descent, and successive convex approximation yield a BCD-SCA algorithm for a good sub-optimal solution.
C. ISAC Case
- The non-concave objective is reformulated using the Lagrangian dual and quadratic fractional transforms, then expressed with auxiliary variables to obtain a concave objective in the beamformers.The formulation introduces auxiliary variables for terms in the objective, including u_k = C_k({w_mk}).Source: C. ISAC Case · pp. 19–21
- A BCD-SCA algorithm alternates optimization over uncoupled variables and uses SCA to obtain a good sub-optimal solution to Problem P3.The auxiliary variables ι and κ have closed-form updates when the beamformers and Z_m are fixed.Source: C. ISAC Case · pp. 19, 23
- First-order approximations of convex functions restrict the remaining non-convex constraints to form a convex approximation of the problem.The approximation is applied to constraints that remain non-convex after introducing auxiliary variables and a penalty term.Source: C. ISAC Case · pp. 22–23
V. NUMERICAL RESULTS
The numerical section presents the Cell-Free massive MIMO ISAC C-S region and examines its characteristics and parameter impacts.
V. NUMERICAL RESULTS
- The numerical results present the considered system’s C-S region, defined as R_C-S in (21).The section frames the results around the region and its C-S performance trade-off.Source: §V · p. 23
- The section examines characteristics and insights about the communication-sensing performance trade-off.The supplied passage introduces the section’s numerical investigations.Source: §V · p. 23
- The numerical results also consider the impacts of system parameters on C-S performance.The passage identifies parameter impacts as part of the section’s scope.Source: §V · p. 23
INSTANCE SYSTEM PARAMETERS
The numerical results characterize the C-S trade-off as the number of APs and system parameters vary, and compare sensing and beamforming performance across systems and schemes. They report lower normalized MSE for the Cell-Free system than for the traditional cellular system, and higher sum rate for the proposed beamforming scheme than for ZF and MRT.
INSTANCE SYSTEM PARAMETERS
- With 48 antennas fixed and evenly distributed among APs, sum rate increases with AP count, while sensing MSE also increases as each target receives fewer antennas.The figure’s axes represent AP count, sensing MSE, and sum rate.Source: INSTANCE SYSTEM PARAMETERS · p. 24, Figure 3 · p. 24
- For sensing-only comparison under 3 targets, average normalized MSE is 0.0159 in the centralized traditional cellular system and 0.0080 in the Cell-Free system, about half.Source: Figure 4 · p. 25, INSTANCE SYSTEM PARAMETERS · p. 25
- The C-S trade-off occurs on the region boundary between the maximum-sum-rate and minimum-MSE critical points; the stated problems are infeasible when δ < S_min or ζ > R_max.The two critical points are (S_I, R_max) and (S_min, R_T).Source: INSTANCE SYSTEM PARAMETERS · p. 25
- Cell-Free sensing performance is reported as robust to target distribution, whereas traditional-system beampattern matching and sensing performance are sensitive to target dispersiveness.The Cell-Free setup assigns each AP to one target in the described comparison.Source: INSTANCE SYSTEM PARAMETERS · pp. 25–26
- Transmit data first increases with pilot length, peaks at τ_p = 4, then decreases as shorter downlink time outweighs improved channel estimation.The amount of transmit data is given as (τ_c − τ_p)P; the section also reports that larger δ yields more downlink power and transmitted data.Source: Figure 5 · p. 26, INSTANCE SYSTEM PARAMETERS · p. 26
- The proposed beamforming scheme outperforms ZF and MRT across service-area sizes, while ZF performs better than MRT for smaller areas and worse for larger areas.All three schemes perform worse in larger service areas because of greater average path loss.Source: Figure 6 · p. 26, INSTANCE SYSTEM PARAMETERS · pp. 26–27
- Larger δ, corresponding to a lower sensing beampattern-matching MSE requirement, yields more power allocated to downlink transmission and more data transmitted.This is the reported parameter trend for the amount of transmitted data.Source: INSTANCE SYSTEM PARAMETERS · p. 26
VI. CONCLUSION
The paper presents a Cell-Free massive MIMO ISAC system model and downlink beamforming design, alongside a communication-sensing region defined under finite resources. Numerical results characterize the communication–sensing trade-off and report advantages of the proposed beamformer over state-of-the-art ISAC designs.
VI. CONCLUSION
- The channel estimation error's first- and second-order statistics are derived in closed form for the proposed Cell-Free massive MIMO ISAC system.The derivation uses the uplink pilot training model.Source: §VI · p. 27
- The achievable C-S region is defined under finite-resource constraints through sensing-only, communication-only, and ISAC beamforming cases.Numerical results demonstrate the region and its boundary trade-off between communication and radar sensing.Source: §VI · p. 27
- Numerical results characterize system-parameter impacts on beamforming performance and report advantages over state-of-the-art ISAC beamformers.The supplied conclusion identifies parameter sensitivity and beamformer advantages as findings.Source: §VI · p. 27
- The conclusion identifies sensitivity to system parameters, per-AP sensing of multiple targets, and target-detection performance as topics for further study.These studies are left for future work.Source: §VI · p. 27
APPENDIX A. Proof of Proposition 1
The appendix derives channel correlation and estimation-error statistics using the stated channel independence assumptions and LMMSE orthogonality. It also gives a closed-form expression for Cmk.
APPENDIX A. Proof of Proposition 1
- Independent direct and cascade links, including reflections from different targets, are used to derive channel auto- and cross-correlation properties.The proof invokes the channel models' zero-mean and independence properties.Source: Appendix A · pp. 27–28
B. Proof of Proposition 2
- The proof reduces the derivation of the estimation-related matrix to computing Cmk and then gives its closed-form expression.The supplied passage identifies Cmk as the quantity computed in the derivation.Source: B. Proof of Proposition 2 · p. 28
C. Proof of Proposition 3
- LMMSE orthogonality between the channel estimate and estimation error yields the error auto-correlation and cross-correlation matrices.The cross-correlation concerns errors for different access points.Source: C. Proof of Proposition 3 · pp. 28–29