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Optimized data sharing in multicell MIMO with finite backhaul capacity
Randa Zakhour, David Gesbert
TL;DR
Finite backhaul makes multicell data sharing a trade-off: sharing enables MIMO cooperation but consumes capacity that could carry user data. The paper splits traffic into private and shared messages and characterizes the achievable rate region. Its simulations show that the worthwhile share grows with backhaul capacity, and the rate-splitting approach normally outperforms quantization-based cooperation.
Problem
With finite backhaul, the capacity overhead of sharing user data must be weighed against the gains of network MIMO over the interference channel.
Source: §I · pp. 2–3Method
The paper splits each user’s data into private messages sent by one base station and shared messages jointly transmitted, then characterizes the rate region and beamforming design.
Source: §I · p. 3, C. Over-the-air transmission · p. 6Results
The portion of traffic worth sharing grows with backhaul capacity, and the rate-splitting approach normally outperforms the quantization-based approach.
Source: §VI · pp. 14–15Takeaways & Limitations
The backhaul capacity helps determine how much user data to share; at relatively low capacity, foregoing network MIMO may be preferable, while its appeal rises as capacity increases.
Source: §V · p. 12The rate regions for the rate-splitting schemes are not always smooth or convex because the study does not convexify them through time-sharing between transmit strategies.
Source: §V · p. 12
Abstract
from arXiv · showhide
This paper addresses cooperation in a multicell environment where base stations (BSs) wish to jointly serve multiple users, under a constrained-capacity backhaul. We point out that for finite backhaul capacity a trade-off between sharing user data, which allows for full MIMO cooperation, and not doing so, which reduces the setup to an interference channel but also requires less overhead, emerges. We optimize this trade-off by formulating a rate splitting approach in which non-shared data (private to each transmitter) and shared data are superposed. We derive the corresponding achievable rate region and obtain the optimal beamforming design for both shared and private symbols. We show how the capacity of the backhaul can be used to determine how much of the user data is worth sharing across multiple BSs, particularly depending on how strong the interference is.
I. INTRODUCTION
The paper asks how to balance user-data sharing against finite backhaul capacity in multicell cooperation. It proposes a two-cell rate-splitting scheme that combines private and shared messages, characterizes achievable rates, and optimizes beamforming.
I. INTRODUCTION
- Finite backhaul makes full data sharing costly: its overhead must be offset by the capacity gain over the interference-channel approach.The paper asks whether there is a backhaul-capacity threshold below which sharing is not worthwhile.Source: §I · pp. 2–3
- The paper studies a two-cell setup where each user’s data is split into private messages sent by one base station and shared messages jointly transmitted by multiple base stations.For nontrivial private/shared traffic ratios, this forms a hybrid between the interference and MIMO broadcast channels.Source: §I · p. 3
- The paper characterizes the resulting rate region and reduces boundary-finding to convex optimization problems, also optimizing beamforming for the hybrid channel.It compares rate splitting with network MIMO, the interference channel, and a quantized-signal backhaul approach.Source: §I · p. 3
II. SYSTEM MODEL AND PROPOSED TRANSMISSION SCHEME
- The scheme seeks to use limited backhaul to serve users while bridging the interference-channel and multicell-MIMO settings.The central processor routes private traffic to one transmitter and shared traffic to both.Source: §I · p. 3, §II · p. 4
- The study focuses on data sharing rather than channel-state-information sharing, assuming full global CSIT at each transmitter.Receivers use single-user detection and treat interference as noise.Source: §II · p. 4
A. Particular Cases
The proposed transmission scheme includes the interference and network-MIMO cases as endpoints. Finite backhaul and transmit power constrain its shared and private messages, while the over-the-air segment has a corresponding achievable rate region.
A. Particular Cases
- The scheme reduces to an interference channel when all user data is private, and to network MIMO when all data is shared.These cases arise by forcing the private-message rates to the stated endpoint values.Source: A. Particular Cases · p. 5
B. Backhaul usage
- Each finite-capacity backhaul link carries private messages for its transmitter and shared messages for both users, and total user rate cannot exceed aggregate backhaul capacity.Transmit beamforming vectors are also subject to power constraints.Source: B. Backhaul usage · pp. 5–6, C. Over-the-air transmission · p. 6
C. Over-the-air transmission
- Proposition 1 specifies an achievable rate region for the over-the-air channel using the proposed beamformed transmit signals.The beamforming vectors are subject to power constraints.Source: C. Over-the-air transmission · p. 6
III. RATE REGION
The rate-region boundary is found by fixing the users’ rate proportions and testing which total rates are feasible under the over-the-air and backhaul constraints.
III. RATE REGION
- The boundary is obtained by discretizing the share of total sum rate assigned to user 1 and solving the resulting optimization problem.The feasible region combines the over-the-air rate constraints with backhaul and power constraints; bisection over total rate can test feasibility.Source: §III · p. 7
A. Establishing feasibility of a given rate pair (r1, r2)
For a target user-rate pair, the paper checks whether private-message rates can satisfy backhaul constraints while the rates are supported over the air. It formulates feasibility as power minimization and uses convex optimization once rates are fixed.
A. Establishing feasibility of a given rate pair (r1, r2)
- Backhaul constraints impose a minimum amount of private traffic for a fixed total rate, while that traffic trades off against sharing over the air.The paper describes more sharing as enlarging the over-the-air achievable region, but finite backhaul limits shared data.Source: A. Establishing feasibility of a given… · p. 8
- Feasibility of a target rate pair is checked through a power-minimization problem subject to rate, power, and backhaul constraints.With rates fixed, the remaining power minimization is a convex optimization that can be solved efficiently.Source: A. Establishing feasibility of a given… · p. 8
- For fixed sum rate and user-rate split, the paper conjectures that checking the corner points of the private-rate polytope suffices for feasibility.If both backhaul-derived private-rate lower bounds are zero, only shared messages are needed, as in network MIMO.Source: A. Establishing feasibility of a given… · pp. 7–9
- Dirty-paper coding of shared messages could further expand the achievable rate region by reducing interference at one user.The stated example encodes user 1’s shared message first and applies dirty-paper coding to the other messages at user 2.Source: A. Establishing feasibility of a given… · p. 9
IV. QUANTIZED BACKHAUL (OBLIVIOUS BASE STATIONS)
The paper considers an oblivious-base-station configuration in which the central processor designs transmission and sends each transmitter a quantized version of its signal.
IV. QUANTIZED BACKHAUL (OBLIVIOUS BASE STATIONS)
- The central processor designs transmission, while the backhaul carries quantized versions of the signals each transmitter should send.The base stations are assumed not to know the encoding scheme.Source: §IV · p. 9
A. Oblivious BS with Linear Beamforming
With finite-capacity backhaul, the oblivious-base-station scheme quantizes centrally designed transmit signals. The design treats single-antenna and multi-antenna base stations separately, but the multi-antenna quantization-noise covariance lacks a simple characterization and only local optimality is guaranteed.
A. Oblivious BS with Linear Beamforming
- Finite-capacity backhaul is modeled by quantizing each centrally designed transmit signal before it reaches its base station.The transmitted signal is the designed signal plus independent quantization noise.Source: A. Oblivious BS with Linear Beamforming · p. 9
- The design separates the cases Nt = 1 and Nt ≥ 2 because their quantization-noise covariance problems differ.For Nt = 1, the covariance reduces to a scalar parameter; for Nt ≥ 2, the transmit-signal covariance is rank 2.Source: A. Oblivious BS with Linear Beamforming · pp. 10–11
- For Nt ≥ 2, the power and backhaul constraints do not yield a simple quantization-noise covariance characterization, and attempted solutions guarantee only a local optimum.Source: A. Oblivious BS with Linear Beamforming · p. 11
V. NUMERICAL RESULTS
The numerical results compare rate-splitting, interference-channel, network-MIMO, and quantized network-MIMO schemes under finite backhaul. They show that rate splitting can reach the backhaul-limited sum-rate ceiling, while the advantage of network MIMO grows with backhaul capacity.
V. NUMERICAL RESULTS
- The compared schemes are FRS, ARS, interference-channel beamforming, network-MIMO beamforming, and quantized network MIMO.The single-channel rate-region comparisons use 10 dB SNR and different backhaul constraints.Source: §V · pp. 11–12
- For C = 1 bits/sec/Hz, FRS can reach the maximum possible total sum rate of 2C; as C rises, FRS and ARS outperform NM until their rate regions coincide.At coincidence, the system is limited by the over-the-air rate region rather than backhaul.Source: §V · p. 12, Figure 2 · p. 12
- FRS and ARS rate regions can be nonconvex because the results do not convexify them by time-sharing between transmit strategies.Source: §V · p. 12
- For low C, the maximum sum rate of 2C is achievable at quite low SNR, while increasing C moves that saturation to higher SNR.The results average FRS maximum sum rates over 100 channel samples with Nt = 2.Source: §V · pp. 12, 14
- At low C, most data is carried in private messages, whereas increasing C requires private messages only at higher SNR.For C = 10, below 10 dB, network MIMO almost always maximizes the sum rate.Source: §V · p. 14
VI. CONCLUSION
The paper proposes splitting traffic into private and shared messages, characterizes the two-cell achievable rate region, and reports that the portion worth sharing grows with backhaul capacity. Its rate-splitting approach normally outperforms a quantization-based approach, while dirty-paper coding is not considered.
VI. CONCLUSION
- The study characterizes a two-cell achievable rate region and shows that the traffic portion worth sharing grows with backhaul capacity.The scheme uses private messages sent by one base station and shared messages jointly sent by several base stations.Source: §VI · p. 14
- Figure 6 plots average maximum sum rate versus SNR for backhaul capacities C = 1, 5, and 10 bits/sec/Hz, and also shows the private-message share.The figure concerns symmetric channels; the supplied caption is truncated after mentioning the cross-channel condition.Source: Figure 6 · p. 15, §VI · p. 15
- The rate-splitting approach normally outperforms an approach relying on quantization, but dirty-paper coding is not considered.The authors note that better rates may be attained with dirty-paper coding.Source: §VI · p. 15
APPENDIX A MAC WITH A COMMON MESSAGE
Appendix A presents the MAC with a common message and applies its achievable rates to the proposed transmission scheme under perfect channel state information at the receiver.
APPENDIX A MAC WITH A COMMON MESSAGE
- The common-message MAC has independent messages: one common message known to both encoders and private messages available only to their respective encoders.The theorem describes encoders mapping their available messages to channel input sequences.Source: Appendix A · p. 15
- For a distribution factoring through the common message, encoder inputs, and channel output, the theorem gives individual, sum-rate, and total-rate bounds for an achievable region.The bounds include R1 < I(X1; Y | X2, U), R2 < I(X2; Y | X1, U), R1 + R2 < I(X1, X2; Y | U), and R0 + R1 + R2 < I(X1, X2; Y).Source: Appendix A · pp. 15–16
- For the proposed scheme, the common-message variable corresponds to si,c, and the stated rates are achievable under perfect receiver channel-state information.The passage says the mutual-information expressions match those in equation (9).Source: Appendix A · p. 16
APPENDIX B
Appendix B develops the beamforming optimization through a semidefinite relaxation and KKT conditions, establishing convexity and rank-one optimal matrices.
APPENDIX B
- For fixed rates, the problem is equivalent to a convex optimization, and its dual is also considered for the semidefinite relaxation.The passage introduces the dual problem for both the original problem and its relaxation.Source: Appendix B · pp. 16, 18
- Replacing each beamforming vector outer product with a positive semidefinite matrix yields a convex relaxation with zero duality gap and rank-one optimal matrices.The rank-one result is supported by maximizing useful signal terms subject to power and interference constraints.Source: Appendix B · p. 17
- The KKT conditions imply equality for the constraints associated with Γi, Γi,p, and Γij,max,p.The text identifies these equalities as expected from known MAC-channel properties.Source: Appendix B · pp. 18–19