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Uplink CoMP under a Constrained Backhaul and Imperfect Channel Knowledge

Patrick Marsch, Gerhard Fettweis

arXiv:1002.3356v1cs.IT

TL;DR

Uplink CoMP must balance interference-management gains against additional backhaul and sensitivity to imperfect CSI. This paper builds a framework that analyzes theoretical and practical cooperation concepts under those constraints, finding that CoMP gains and attractive schemes depend strongly on interference conditions, location, CSI, and cooperation design.

  • Problem

    Uplink CoMP faces a trade-off between overcoming inter-cell interference and limiting additional backhaul under imperfect channel knowledge.

  • Method

    The paper jointly analyzes theoretical uplink CoMP concepts and practical algorithms under constrained backhaul and imperfect CSI.

  • Results

    The strongest CoMP gains occur at the cell edge and increase with diminishing CSI, while gains quickly vanish toward the cell center; DAS-C and DIS remain attractive in specified interference regimes.

  • Takeaways & Limitations

    The analysis reduces the attractive set of CoMP concepts to schemes matched to interference conditions and backhaul constraints, with adaptation beneficial for DIS.

Abstract

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Coordinated Multi-Point (CoMP) is known to be a key technology for next generation mobile communications systems, as it allows to overcome the burden of inter-cell interference. Especially in the uplink, it is likely that interference exploitation schemes will be used in the near future, as they can be used with legacy terminals and require no or little changes in standardization. Major drawbacks, however, are the extent of additional backhaul infrastructure needed, and the sensitivity to imperfect channel knowledge. This paper jointly addresses both issues in a new framework incorporating a multitude of proposed theoretical uplink CoMP concepts, which are then put into perspective with practical CoMP algorithms. This comprehensive analysis provides new insight into the potential usage of uplink CoMP in next generation wireless communications systems.

I. INTRODUCTION

The introduction frames uplink CoMP as a response to inter-cell interference, while emphasizing backhaul demand and imperfect CSI as central challenges. The paper addresses these issues by comparing theoretical concepts with practical algorithms in models intended to reflect cellular interference scenarios.

  • A. Motivation: Uplink CoMP can exploit inter-cell interference through multi-cell joint signal processing, promising gains in spectral efficiency and fairness.
  • A. Motivation: Additional backhaul infrastructure and imperfect CSI are identified as major concerns for uplink CoMP.
  • I. INTRODUCTION: The paper develops a framework combining information-theoretic concepts with proposed signal-processing schemes and evaluates both theoretical bounds and practical constraints.
  • B. Related Work: Prior work considers centralized decoding, decentralized exchange of decoded bits, quantized transmit sequences, and adaptation among cooperation strategies.
  • I. INTRODUCTION: Its models represent interference scenarios considered likely in practical cellular systems, yielding conclusions intended to be more relevant than those from overly simplified models.

D. Terminology

The paper defines CoMP as BS cooperation that exchanges received signals or data-bit information to improve rates, distinguishing it from coordination-only schemes. It then specifies the uplink model, including UEs, BSs, channels, signals, noise, power constraints, and backhaul connectivity.

  • D. Terminology: CoMP and BS cooperation exchange received signals or information connected to selected UEs’ data bits to improve data rates.
  • D. Terminology: Joint scheduling and IRC are classified as non-cooperative because they coordinate BSs without exchanging received signals or data-bit information.
  • D. Terminology: Backhaul quantity denotes the additional capacity required by a cooperative scheme beyond a non-cooperative system.
  • A. Transmission Model: The transmission model contains K UEs and M BSs with block-fading, frequency-flat channels, synchronized entities, and Gaussian transmit sequences.
  • A. Transmission Model: Each UE has an individual transmit-power constraint, and a UE decoded by any involved BS can have its decoded bits forwarded to the network.

B. Modeling of Imperfect Channel Knowledge

The imperfect-CSI model replaces the original channel with a power-reduced effective channel and adds Gaussian noise representing channel-estimation uncertainty. The resulting capacity analysis averages over estimation errors under a pilot-based estimation model.

  • B. Modeling of Imperfect Channel Knowledge: The channel estimate and estimation error have multiple independent realizations within each symbol block because of multiple pilots.
  • B. Modeling of Imperfect Channel Knowledge: The estimation error variance is tied to pilot number and power under Gaussian receiver noise, with unit-power pilots and Np = 2 assumed subsequently.
  • B. Modeling of Imperfect Channel Knowledge: Imperfect CSI is modeled using a power-reduced effective channel and an additional Gaussian noise term with diagonal covariance.
  • B. Modeling of Imperfect Channel Knowledge: The model yields an inner bound on the capacity region by considering average rates over many estimation errors.
  • B. Modeling of Imperfect Channel Knowledge: The resulting model makes the differing impact of channel-estimation noise on weak and strong links explicit.

C. Capacity Region Under Infinite BS Cooperation

Under infinite BS cooperation, the uplink is treated as a multiple access channel whose capacity region admits an inner bound based on joint decoding across BSs. The section contrasts this benchmark with non-cooperative decoding and notes the effects of imperfect CSI and alternative schemes.

  • C. Capacity Region Under Infinite BS Cooperation: Theorem 2 gives an inner bound for the uplink capacity region when infinite backhaul enables full cooperation between all BSs.
  • C. Capacity Region Under Infinite BS Cooperation: The bound constrains each user’s rate by its connected-message rate and constrains every message subset by a corresponding sum-capacity expression.
  • C. Capacity Region Under Infinite BS Cooperation: The sum-rate constraint assumes that signals from already decoded UEs have been subtracted from the system.
  • C. Capacity Region Under Infinite BS Cooperation: Under imperfect CSI, residual noise covariance remains and detrimentally affects cooperation strategies.
  • C. Capacity Region Under Infinite BS Cooperation: Superposition-coded common messages are restricted because their benefits are limited by interference scenarios, imperfect CSI, coding gaps, and UE-side modifications.
  • C. Capacity Region Under Infinite BS Cooperation: Without BS cooperation, the model uses BS-UE assignments and an inner bound that allows each BS to decode assigned messages while accounting for other messages.

1) Distributed Interference Subtraction (DIS) [21]:

DIS forwards decoded information between base stations so the receiving base station can reduce interference. Its achievable rates are constrained jointly by interference, decoding conditions, and the available backhaul.

  • Operation: DIS has one base station decode part of a user’s transmission and forward the decoded data to the other for partial interference cancellation.The forwarded information can be source-coded using correlated received signals as side-information.
  • Operation: Both messages from UE 1 are decoded by BS 1, after which the cooperative message is forwarded to BS 2 for interference-reduced decoding.BS 2 reconstructs the forwarded message using its received signal as side-information.
  • Achievable region: The DIS inner bound requires nonnegative rates and imposes rate constraints for each user under a specified assignment, cooperation direction, and backhaul.The theorem parameterizes the region as Rdis(β, a, b, P).
  • Achievable region: The forwarded message must be decoded first at the forwarding base station, and its rate must be low relative to the interference it creates.This decoding-order condition is required for the forwarding operation to work.
  • Relation to CIF: CIF differs from DIS by exchanging quantized transmit sequences, with quantization noise and backhaul determining the achievable rate constraints.The quantization level can be selected through practical quantization or rate-distortion operation, optionally with source coding.

3) Distributed Antenna System - Decentralized Decoding (DAS-D) [50]:

DAS-D uses decentralized decoding in which base stations exchange quantized received signals rather than decoded bits or transmit sequences. Its achievable rates are limited by interference, quantization noise, and the sum backhaul.

  • Operation: DAS-D exchanges quantized receive signals between base stations, optionally using source coding, and each base station then decodes its messages using local and exchanged information.The exchanged signals are reconstructed before decoding.
  • Achievable region: The DAS-D inner bound applies under a sum-backhaul constraint for arbitrary base-station-to-user assignments.The achievable region is denoted Rdasd(β, a, P).
  • Achievable region: DAS-D rate constraints account for interference and quantization noise on the antennas of the corresponding remote base station.Quantization-noise covariances are bounded using practical quantization, rate-distortion operation, or rate-distortion operation with source coding.
  • Backhaul trade-off: Different allocations of backhaul between the two cooperation directions trade the rate of one user equipment against the other.The associated quantization-noise covariances can be optimized for weighted sum-rate objectives.

4) Distributed Antenna System - Centralized Decoding (DAS-C):

DAS-C jointly decodes selected messages at one base station while the other base station contributes quantized received information. The resulting inner bound includes message-rate, interference, quantization, and backhaul constraints.

  • Operation: DAS-C combines non-cooperative decoding, jointly decoded common messages, and quantized information exchanged between base stations.One base station can decode common messages, subtract their transmitted sequences, and forward a quantized residual signal.
  • Operation: The second base station uses its received signal and the information from the first base station to decode its remaining messages.It subtracts the impact of messages decoded locally before using the exchanged information.
  • Achievable region: The DAS-C inner bound is defined for arbitrary assignments and cooperation directions under a backhaul constraint.The rate tuple includes nonnegative user rates and bounds associated with message superposition and joint decoding.
  • Achievable region: DAS-C constraints include residual interference and quantization noise at the base station receiving exchanged information.The backhaul constraint is based on the covariance of the residual or conditioned received signals.
  • FDM variant: Orthogonal-resource FDM schemes can also exchange received signals, but the paper reports that they play a minor role and omits their equations.

F. Performance Regions

Performance regions jointly represent achievable user-rate pairs and the backhaul required by a cooperation scheme. In the example channel, the preferred scheme changes with the available backhaul and channel-estimation conditions.

  • Performance regions: A performance region uses the two user rates on the x- and y-axes and required backhaul on the z-axis.Its top surface represents the non-cooperative capacity region, while the x-y-plane intersection gives the infinite-cooperation inner bound.
  • Imperfect CSI: The infinite-cooperation region deviates from a pentagon because of imperfect channel-state information.
  • Scheme comparison: For the example channel, FDM is beneficial with no or very limited backhaul, DIS is interesting with moderate backhaul, and DAS-C approaches MAC performance with large backhaul.
  • Scheme comparison: DAS-D and CIF are inferior across all backhaul levels in the reported example and are therefore not visible in the performance-region comparison.
  • Overall CoMP gain: CoMP gains are largest at the cell edge and diminish toward the cell center, while multi-cell power control makes performance more homogeneous across scenarios.The relative gain can increase at the cell edge as CSI decreases, attributed to array gain from channel estimation.
  • Overall CoMP gain: With three users and two antennas per base station, CoMP gains are larger because an individual base station cannot spatially separate all three users.

C. Performance of CoMP Schemes for Specific Channels

CoMP performance depends strongly on channel geometry, interference strength, backhaul, and implementation choices. DAS-C dominates strong-interference regimes, while DIS and adaptation become attractive under weaker or asymmetric interference.

  • DAS-C is superior across all backhaul levels in the symmetric cell-edge case, where source coding is highly beneficial because received signals are correlated.
  • DIS and CIF provide no gain in the symmetric cell-edge case because each base station can decode both user equipments without cooperation.
  • DAS-C outperforms DAS-D because centralized decoding enables interference cancellation, whereas DAS-D provides only array gain.
  • In asymmetric weaker-interference regimes, DIS and CIF are superior at low backhaul, while DIS with SPC outperforms compressed interference forwarding.
  • At β = 4 bits per channel use, DAS-C is best under strong interference, DIS under weaker asymmetric interference, CIF under even weaker interference, and DAS-D only under very weak symmetric interference.
  • Adapting between DAS-C and DIS can provide more than 10% sum-rate benefit in the indicated channel regimes and about 50% of CoMP gain with about 1.5 bits of backhaul per bit of sum-rate.
  • SPC and partial local decoding offer only marginal rate or quantization-efficiency improvements, whereas strong-interference covariance assumptions impose practical constraints.
  • For three-base-station simulations, IRC and instantaneous base-station–user assignment improve non-cooperative performance, while pure DAS-C is best among cooperative strategies and FDM is strongly inferior.

IV. PRACTICAL CONSIDERATIONS

Practical uplink CoMP must balance backhaul efficiency against achievable CoMP gain, CSI distribution, complexity, and latency. The analysis favors DAS-C and DIS in different interference regimes while questioning iterative cooperation and highlighting source-coding implementation costs.

  • Code-aware schemes use backhaul efficiently but fail to achieve MAC performance at large backhaul, whereas code-oblivious DAS-C asymptotically obtains the complete CoMP gain.
  • Iterative DIS improves the asymptotic sum-rate but only marginally improves the rate/backhaul trade-off over one-shot cooperation, while adding redundancy and latency.
  • DIS and CIF require only local CSI, whereas DAS-C requires compound-channel knowledge at the decoding base station and CSI distribution over the backhaul.
  • CIF avoids re-modulation during partial interference subtraction, but practical algorithms commonly combine code-aware and code-oblivious strategies.
  • The strongest CoMP gains occur at the cell edge, increase with diminishing CSI, and quickly vanish toward the cell center.
  • The most attractive concepts are DAS-C for strong interference and DIS for local decoding with decoded-bit exchange, with adaptation between them proving beneficial.
  • SPC-based concepts are of minor interest, while source coding is attractive but faces major implementation challenges and sharply increased complexity.

APPENDIX

The appendix develops the imperfect-CSI analysis and compares uplink CoMP schemes across cooperation mechanisms, backhaul requirements, CSI accuracy, and channel scenarios. The results characterize when cooperation provides gains and how those gains vary with network conditions.

  • Imperfect channel knowledge: The imperfect-CSI analysis models an unbiased channel estimate with an uncorrelated estimation error and examines rates for a fixed channel averaged over estimation realizations.The analysis uses Jensen’s inequality to relate the averaged-rate expression to a reference expression; numerical effects are reported as negligible unless noise and channel powers are of similar order.
  • CoMP schemes: The analyzed uplink CoMP schemes include decoded-message exchange, quantized transmit-sequence exchange, simultaneous quantized receive-signal exchange, and quantized receive-signal forwarding for joint decoding.These mechanisms correspond to DIS, CIF, DAS-D, and DAS-C, respectively.
  • Performance evaluation: The performance region represents achievable rates and required backhaul for different BS cooperation schemes and assignments.The appendix also compares schemes under practical aspects and considers theoretical and practical cooperation perspectives.
  • Scenario comparisons: For moderate, asymmetric interference, DIS and CIF are superior in the evaluated scenario, while the figures examine sum-rate as a function of backhaul and cooperation choice.The evaluated scenarios include symmetric cell-edge channels, asymmetric interference, UE-location-dependent scheme selection, and gains from source or superposition coding.
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