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Ergodic Capacity Analysis of Remote Radio Head Associations in Cloud Radio Access Networks

Mugen Peng, Shi Yan, H. Vincent Poor

arXiv:1410.5890v1cs.ITmath.IT

TL;DR

The paper studies how single-nearest and N-nearest RRH associations affect ergodic capacity in C-RANs. It derives closed-form expressions and evaluates them through simulation. The reported results show nonlinear capacity gains and support limiting association to no more than 4 RRHs to balance gain and implementation cost.

  • Problem

    The letter examines how RRH association strategies affect C-RAN capacity, extending prior analysis to multiple RRH antennas, varying path-loss exponents, and ergodic capacity.

    Source: §I · p. 1

  • Method

    The authors characterize outage probability and derive closed-form ergodic-capacity expressions for single-nearest and N-nearest RRH association.

    Source: §I · p. 1

  • Results

    RRH association number should not exceed 4 to balance performance gain and implementation cost, while RRH density has a greater impact on performance gain than antennas per RRH.

    Source: A. Single nearest RRH association · p. 2, §V · p. 4

  • Takeaways & Limitations

    When RRH density is fixed, more antennas are preferred because they provide higher gains than increasing RRH association.

    Source: §V · p. 4

    The reported closed-form ergodic-capacity expressions are for path-loss exponent 4.

    Source: §V · p. 4

Abstract

from arXiv · show

Characterizing user to Remote Radio Head (RRH) association strategies in cloud radio access networks (C-RANs) is critical for performance optimization. In this letter, the single nearest and N--nearest RRH association strategies are presented, and the corresponding impact on the ergodic capacity of C-RANs is analyzed, where RRHs are distributed according to a stationary point process. Closed-form expressions for the ergodic capacity of the proposed RRH association strategies are derived. Simulation results demonstrate that the derived uplink closed-form capacity expressions are accurate. Furthermore, the analysis and simulation results show that the ergodic capacity gain is not linear with either the RRH density or the number of antenna per RRH. The ergodic capacity gain from the RRH density is larger than that from the number of antennas per RRH,which indicates that the association number of the RRH should not be bigger than 4 to balance the performance gain and the implementation cost.

I. INTRODUCTION

The letter examines RRH association and capacity in multi-antenna C-RANs, extending prior work to broader channel and performance settings. It derives closed-form capacity expressions and reports how association choices and network parameters affect performance.

  • Prior C-RAN studies addressed outage for single-antenna nodes with path-loss exponent 2, while separate work found large-scale fading exponent affects capacity.The letter frames its analysis around multiple antennas, varying path-loss exponents, and ergodic capacity.Source: §I · p. 1
  • The letter characterizes outage probability and closed-form ergodic capacity for single-nearest and N-nearest association with multiple RRH antennas and path-loss exponent 4.It also analyzes how antenna count and RRH density affect performance.Source: §I · p. 1
  • The authors conclude that associating no more than 4 RRHs balances performance gains and implementation complexity.The stated aim also includes constraints on radio-resource consumption.Source: §I · p. 1

II. SYSTEM MODEL

The system model places a single-antenna uplink user at the origin of a disc containing Poisson-distributed RRHs. It models fading across RRH antennas and introduces nearest-RRH association.

  • RRH locations are modeled as a two-dimensional Poisson point process of intensity λ in a disc of radius R, with the user at its origin.The number of RRHs in the disc is random, with mean πR²λ.Source: §II · p. 1
  • With maximal ratio combining for full-diversity gains, the channel gain across L antennas is modeled as Γ(L, 1) for a large number of antennas.Individual antenna fading gains are modeled as zero-mean, unit-variance complex Gaussian variables.Source: §II · p. 1
  • Under single-nearest association, the user connects to the nearest RRH, which has maximum received power when shadow fading remains constant.Source: §II · p. 2

2) N-nearest RRH association:

N-nearest association selects a practicable set of nearby RRHs, avoiding the instantaneous-CSI and signaling demands of choosing the N best instantaneous links.

  • The user associates with the N nearest RRHs among the total RRHs, with N no greater than the number available.Source: 2) N-nearest RRH association · p. 2
  • When transmit powers are equal, the selected N RRHs can be those with maximum average received power over the observed interval.Source: 2) N-nearest RRH association · p. 2
  • Selecting the N best instantaneous links requires instantaneous CSI and backhaul signaling overhead that increases with the total RRH count.The proposed practicable strategy instead selects the N RRHs with the largest received power at the BBU.Source: 2) N-nearest RRH association · p. 2

III. PERFORMANCE ANALYSIS

The analysis expresses the received SNR for a user at distance r_i from an RRH and identifies thermal noise power as a model parameter.

  • The received SNR is specified for a user at distance r_i from the i-th RRH.Source: §III · p. 2
  • The additive thermal noise power is denoted by σ².Source: §III · p. 2

A. Single nearest RRH association

The single-nearest strategy associates the user with its nearest RRH and characterizes its outage probability and high-SNR ergodic capacity. Capacity increases nonlinearly with antenna count, RRH density, and transmit power, with RRH density having the larger impact than antenna count.

A. Single nearest RRH association

  • The outage probability for single-nearest association is characterized for a received-SNR threshold T at the serving RRH.The derivation uses the serving-RRH distance distribution and a lower incomplete gamma function.Source: A. Single nearest RRH association · p. 2
  • The high-SNR capacity approximation follows from the SNR density and the approximation log2(1 + γ) ≈ log2(γ).The paper presents the result as the uplink ergodic capacity for single-nearest association.Source: A. Single nearest RRH association · p. 2
  • Ergodic capacity increases nonlinearly with antenna count L, RRH intensity λ, and transmit power P_U, with λ having a larger impact than L.The high-SNR capacity expression is for single-nearest RRH association.Source: A. Single nearest RRH association · p. 2

B. N-nearest RRH association

The section develops outage and ergodic-capacity analyses for N-nearest RRH association, including a two-RRH case and an extension to larger N. It uses stochastic-geometry methods and gives a capacity upper bound whose dependence on RRH density is especially strong.

B. N-nearest RRH association

  • The N-nearest strategy combines received signals using MRC, and its two-RRH SNR pdf is approximated before deriving ergodic capacity.Source: B. N-nearest RRH association · pp. 2–3
  • For N = 2, the outage probability uses the joint distribution of the two nearest RRH distances, and taking the expectation of H_i reduces a double integral to a single integral.Source: B. N-nearest RRH association · p. 3
  • For N > 2, deriving an exact pdf for P_N^i is difficult; the analysis uses the mapping from a two-dimensional PPP to a one-dimensional PPP.Source: B. N-nearest RRH association · p. 3
  • For N > 2 and α = 4, the section simplifies the expression in (18) and derives ergodic capacity for the N-nearest association strategy.Source: B. N-nearest RRH association · p. 3
  • The upper capacity bound depends on L, PU, and λ, with λ entering quadratically and identified as the primary capacity factor relative to L and PU.This is the bound described for the large-N case.Source: B. N-nearest RRH association · p. 3

IV. NUMERICAL RESULTS

The numerical results compare capacity across transmit power, antenna count, and association number, and report that simulations match the closed-form expressions. Gains from adding RRHs diminish at higher association numbers, while antenna increases also raise capacity.

IV. NUMERICAL RESULTS

  • Monte Carlo results match the closed-form expressions, and capacity gaps among N = 4, 8, and infinite association are not large for L = 4 and λ = 10^-4.Source: §IV · p. 3, Figure 1 · p. 4
  • With L = 4, increasing N from 1 to 2 and from 4 to infinite improves capacity by about 0.58 bps/Hz and 0.28 bps/Hz, respectively.Source: §IV · p. 4, Figure 1 · p. 4
  • Capacity rises with antenna count; L = 8, N = 2 yields about 9.21 bps/Hz, versus 8.06 bps/Hz for L = 2, N = 8.Source: §IV · pp. 3–4, Figure 2 · p. 4

V. CONCLUSION

The conclusion presents closed-form capacity expressions for single-nearest and N-nearest association at path-loss exponent 4. It recommends balancing association gains against implementation cost and notes the relative capacity gains of density and antennas.

V. CONCLUSION

  • The paper presents closed-form ergodic-capacity expressions for single-nearest and N-nearest RRH association when the path-loss exponent is 4.Source: §V · p. 4
  • The RRH association number should not exceed 4 to balance performance gain and implementation cost.Source: §V · p. 4
  • RRH density has a greater impact on capacity gain than antennas per RRH, but at fixed density more antennas are preferred over increasing association number.Source: §V · p. 4

VI. APPENDIX A

Appendix A sets up a joint-probability calculation for RRH locations by defining a circle and surrounding ring around the origin. The two-dimensional Poisson process supplies the basis for writing that probability.

VI. APPENDIX A

  • The calculation concerns the joint probability that no more than one RRH lies in the ring from radius r1 to r2.Source: §VI · p. 4
  • The circle ⊙r1 is centered at the origin with radius r1, and the ring φr1r2 extends from radius r1 to r2.Source: §VI · p. 4
  • Because RRHs follow a two-dimensional Poisson process, the appendix writes the joint probability for the circle-and-ring regions using that process.Source: §VI · p. 4
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