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Open vs Closed Access Femtocells in the Uplink
Ping Xia, Vikram Chandrasekhar, Jeffrey G. Andrews
TL;DR
The paper examines which access mode better serves femtocell owners and the network operator, including interference issues such as the “Dead Zone” or “Loud Neighbor” problem. It derives lower bounds and analyzes interference and user-density effects, finding that open access is strictly better for the home user in non-orthogonal CDMA, while operator benefits in orthogonal access can remain limited.
Problem
The paper asks which access mode meets femtocell owners’ and network operators’ interests, in the context of interference problems such as the “Dead Zone” or “Loud Neighbor” problem.
Method
The paper derives lower bounds on open-access performance and analyzes interference distributions, density effects, and cutoff user loading.
Results
In non-orthogonal multiple access, namely CDMA, open access is a strictly better choice for the home user, while the macrocell base station can remain overloaded after serving cellular users through the femtocell.
Takeaways & Limitations
The results support choosing open access for the home user in CDMA while accounting for user-density-dependent cutoff loading in orthogonal access.
Abstract
from arXiv · showhide
Femtocells are assuming an increasingly important role in the coverage and capacity of cellular networks. In contrast to existing cellular systems, femtocells are end-user deployed and controlled, randomly located, and rely on third party backhaul (e.g. DSL or cable modem). Femtocells can be configured to be either open access or closed access. Open access allows an arbitrary nearby cellular user to use the femtocell, whereas closed access restricts the use of the femtocell to users explicitly approved by the owner. Seemingly, the network operator would prefer an open access deployment since this provides an inexpensive way to expand their network capabilities, whereas the femtocell owner would prefer closed access, in order to keep the femtocell's capacity and backhaul to himself. We show mathematically and through simulations that the reality is more complicated for both parties, and that the best approach depends heavily on whether the multiple access scheme is orthogonal (TDMA or OFDMA, per subband) or non-orthogonal (CDMA). In a TDMA/OFDMA network, closed-access is typically preferable at high user densities, whereas in CDMA, open access can provide gains of more than 200% for the home user by reducing the near-far problem experienced by the femtocell. The results of this paper suggest that the interests of the femtocell owner and the network operator are more compatible than typically believed, and that CDMA femtocells should be configured for open access whereas OFDMA or TDMA femtocells should adapt to the cellular user density.
I. INTRODUCTION
The paper examines open versus closed femtocell access amid interference, backhaul, and capacity trade-offs affecting both femtocell owners and network operators. It asks how the preferred access mode changes with multiple-access protocol and cellular-user density.
- Motivation: Femtocells are low-power, low-cost, end-user-controlled base stations using third-party backhaul to improve indoor coverage and offload cellular traffic.They extend coverage without additional cellular towers and can improve network capacity.
- Access modes: Closed access protects the owner’s femtocell capacity, backhaul, privacy, and security but can create severe cross-tier interference.Only specified subscribers are served in closed access.
- Access modes: Open access lets nearby cellular users use the femtocell and can reduce macro-to-femto interference by admitting strong interferers.However, handed-off users may transmit at higher power, increasing femto-to-macro interference and potentially degrading remaining macrocell users’ QoS.
- Research questions: The paper evaluates whether owner and operator interests align and how access control depends on multiple-access protocol, user density, scheduling, and backhaul constraints.The analysis focuses on uplink interference and resource-sharing trade-offs.
- Related work: Prior work generally found adaptive or user-limited open access preferable because it mitigates interference while constraining femtocell backhaul sharing.This paper extends the analysis to the uplink and emphasizes that conclusions depend on orthogonal versus non-orthogonal access.
- Implementation considerations: Open-access implementation may incur increased handover frequency and overhead signaling.Hybrid access and power-control techniques were proposed to reduce these handovers while mitigating cross-tier interference.
C. Contributions
The paper combines analytical bounds and simulations to compare uplink open and closed access from both femtocell-owner and network-operator perspectives. Its conclusions differ sharply between CDMA and TDMA/OFDMA and vary with cellular-user density.
- Contributions: The paper evaluates uplink open and closed access using the femtocell owner’s achieved rate and cellular users’ performance as viewpoints.It derives capacity-related results and uses numerical results to illustrate the main takeaways.
- Orthogonal access: For TDMA or OFDMA, owner and operator preferences depend strongly on cellular-user density: incompatible, open access, and closed access are preferred at low, medium, and high density, respectively.The paper therefore suggests adaptive access control for LTE and WiMAX.
- Non-orthogonal access: In CDMA, open access is strictly better for the home user and provides more than a factor of 3 rate gain in typical propagation scenarios.The reported gain comes from lowering interference.
- Non-orthogonal access: Open access is preferred for CDMA femtocells from both femtocell-owner and network-operator viewpoints.For operators, open access performs almost like closed access at low cellular-user density and significantly better at high density.
- System scope: The system model considers a macrocell with a single femtocell, random cellular-user positions, and cellular users served by either the macrocell or an open-access FAP.The single-femtocell scope focuses on cross-tier interference mitigation when femtocell density is not very high.
A. Channel Model and Interference
The channel model represents uplink path loss and cross-tier interference without short-term fading or coordination between base stations. The paper derives interference-factor distributions for orthogonal access and summed-interference distributions for CDMA.
- Channel assumptions: The model includes path loss only, ignores short-term fading, and uses different outdoor and indoor path-loss exponents to represent wall penetration loss.The exponents satisfy α > β in the stated model.
- Interference model: Uplink power control expresses macrocell-to-femtocell and femtocell-to-macrocell interference through received powers and channel gains.Macrocell user Uj contributes Pchj/gj at the FAP, while femtocell user Ui contributes Pfgi/hi at the macrocell base station.
- Interference model: Each cellular user’s interference factor is defined as hj/gj, and the users are reordered by their interference factors’ ordered statistics.This ordering identifies the strongest interferers for access decisions.
- Orthogonal access: For TDMA/OFDMA, the paper derives the interference-factor CDF used to calculate outage probability.The derivation includes geometric quantities such as r, L(i), and ϕ.
- Non-orthogonal access: For CDMA, additive interference is modeled through the CDF of sums of independently distributed interference factors.An upper bound is obtained using a dominant-interferer argument.
- Analytical framework: The derived individual and summed interference CDFs support outage-probability calculations for orthogonal and non-orthogonal multiple access, respectively.The model assumes no power-control or resource-scheduling coordination among FAPs and macrocell base stations.
B. Hand off Metric and Procedure
The open-access handoff metric serves cellular users when they both cause home-user outage and can be accommodated by the FAP. The procedure admits the strongest interferers first, up to a resource limit K.
- Handoff metric: A cellular user is eligible for open-access service when it causes outage to the home user and the FAP has available resources.This metric allows cellular users to share femtocell resources when they can increase owner capacity by reducing co-channel interference.
- Handoff metric: The FAP can serve at most K additional cellular users under the access-control procedure.K bounds the number of cellular users handed off from the macrocell.
- Handoff procedure: When cellular users cause home-user outage, the FAP hands off the noisiest macrocell interferer first and continues while outage persists and the limit K is not exceeded.This procedure prioritizes the users that most reduce macro-to-femto interference.
- Handoff procedure: Serving the strongest interferers maximally reduces interference and makes the paper’s open-access admission control optimal under its assumption.The admitted users then create the smallest possible interference at the macrocell among the selected users.
C. Resource Allocation and Ergodic Rate
The analysis allocates time and limited femtocell backhaul among the home user and supported cellular users, then evaluates access policies using ergodic rates and cellular sum throughput.
- Backhaul Allocation: The FAP’s modest, shared backhaul capacity Cb is divided between the home user and supported cellular users through λL and µL.Backhaul allocation is included because femtocells commonly rely on DSL or cable modem capacity that may be shared.
- Time Allocation: Time allocation in orthogonal access fairly divides macrocell resources among cellular users, while the FAP assigns fractions λL and µL to the home and supported users.The macrocell user fraction is 1/M when M users are served; at the FAP, the home user and each supported cellular user receive λL and µL, respectively.
- Ergodic Rate: Each user’s required rate is limited by its allocated resources and backhaul, and succeeds only when its received SIR reaches the corresponding target.Otherwise, the user is in outage and its rate is zero.
- Ergodic Rate: The analysis models service events by the number L of additional cellular users served at the FAP and tracks their SIR targets and success probabilities.The resulting ergodic rate is each user’s rate requirement multiplied by its success probability.
- Evaluation Metrics: Open and closed access are evaluated by the home user’s ergodic rate C0 and cellular users’ aggregate throughput Csum.Csum is defined as the sum of all cellular users’ ergodic rates.
- Scope: Handover signaling can affect mobile and femtocell rates, but its impact is excluded because it is difficult to quantify and varies across protocols.The analysis therefore does not include handover-signaling overhead.
III. CAPACITY CONTOURS IN ORTHOGONAL MULTIPLE ACCESS SCHEMES
For TDMA or OFDMA, the paper derives capacity behavior under open and closed access and identifies how cellular-user density and interference shape the preferred policy.
- Capacity Analysis: In TDMA or OFDMA, the paper derives the home-user ergodic rate and cellular-user sum throughput for open access, including the special case where K = 1.The analysis treats TDMA as representative of orthogonal allocation on a per-subband basis.
- Closed Access: The home user’s rate in TDMA is independent of the number of cellular users, because interference is time shared rather than scaled by N.This is the principal closed-access outcome highlighted by the analysis.
- Closed Access: Closed access has a cutoff user loading N*c: cellular users achieve maximum sum throughput Csum = NC below the cutoff, but Csum = 0 above it.The cutoff is governed by whether the cellular users’ SIR target constraint remains feasible.
- Open Access: Open-access cellular sum throughput lies strictly between 0 and NC because macro-to-femto and femto-to-macro interference are random.Thus, the operator’s access choice depends on the user-loading regime relative to the cutoff.
- Open Access: Open access reduces sum throughput when N ≤ N*c because handed-off cellular users increase femto-to-macro interference.The additional interference bottlenecks open-access performance in this regime.
- High-Density Regime: At very high cellular-user density, open access is inferior to closed access for the home-user rate because lost femtocell backhaul and time resources dominate.The handoff metric should therefore consider interferer activity time, not only distance.
IV. CAPACITY CONTOURS IN NON-ORTHOGONAL MULTIPLE ACCESS SCHEME
In CDMA, open access improves the home user’s rate by reducing macro-to-femto interference, while its effect on cellular sum throughput depends on cellular user loading. The analysis derives success probabilities, ergodic rates, and throughput expressions for closed and open access.
- Closed Access: Theorem 3 gives the closed-access CDMA ergodic rate of the home user and sum throughput of cellular users.Closed access serves no cellular user through the FAP, so L=0 in the analysis.
- Open Access: Theorem 4 derives a lower bound for the home user’s ergodic rate under open access.Open-access success probabilities differ for the home user, supported cellular users, and remaining macrocell users.
- Home-User Performance: Open access has strictly better home-user performance than closed access in CDMA, regardless of femtocell resource allocation after handoff.The improvement follows because CDMA interference is additive and handing off strong interferers reduces macro-to-femto interference.
- Cellular Throughput: For K=1, Theorem 5 provides the open-access CDMA sum-throughput expression and corresponding lower bounds.The theorem specializes the analysis to a FAP serving at most one cellular user.
- Cellular Throughput: Open access improves cellular users’ sum throughput for large N but can deteriorate it for small N.With open access, femto-to-macro interference can exceed a threshold and cause outage for macrocell users remaining outside the femtocell.
- Implications: In CDMA, open access is preferred by both the femtocell owner and network operator, with performance almost as good as closed access for small N and strictly better for large N.The analysis therefore identifies compatible interests between the two parties in the non-orthogonal setting.
V. NUMERICAL RESULTS & CONCLUSION
The numerical results normalize both the home user’s ergodic rate and cellular users’ sum throughput by C, using the system parameters listed in Table I.
- Numerical Setup: The plots normalize the home user’s ergodic rate and cellular users’ sum throughput by C.The numerical setup uses the notations and system parameters in Table I.
A. TDMA or OFDMA Access
In TDMA/OFDMA, open-access effects depend strongly on cellular user density and femtocell resource allocation. Both parties prefer open access at medium density and closed access at high density, while their preferences diverge at low density.
- Cellular User Density: For K=3 and N=20, open access yields about a 15% home-user rate gain and almost a 20% cellular-user rate loss.The reported gain and loss are approximately comparable in percentage terms.
- Cellular User Density: Open access has a cutoff loading N∗o for cellular throughput, separating low- and high-density regimes.The analysis identifies distinct throughput behavior below and above this loading.
- Cellular User Density: At high cellular user density, open access provides little home-user rate gain and does not significantly relieve macrocell overload.The resulting sum throughput is attributed to the K cellular users served at the FAP, while privacy and security risks remain.
- Femtocell Resource Allocation: The minimum resource-allocation value λ∗ that benefits the home user increases with cellular user density.The home user’s ergodic rate is sensitive to λ, so poorly chosen allocation can sharply degrade open-access performance.
- Summary for TDMA/OFDMA Access: TDMA/OFDMA resource allocation should adapt to N, but no coordination between the FAP and macrocell BS makes this potentially difficult.The paper notes that future inter-BS coordination could be especially important for open access at high user densities.
- Femtocell Resource Allocation: When Cb/C ≥3, λ∗ is mainly determined by the home user’s time-resource needs rather than backhaul capacity.This explains why λ∗ depends on N and why open access is sensitive to FAP resource allocation in TDMA/OFDMA.
- Summary for TDMA/OFDMA Access: In orthogonal access, both parties prefer open access at medium density, closed access at high density, and disagree at low density.The paper therefore recommends access control adaptive to estimated cellular user density.
B. CDMA Access
In CDMA, open access benefits both the femtocell owner and network operator across almost the whole cellular-user-density range. The home-user gain can exceed 200%, while cellular sum-throughput losses are negligible at low density and open access improves throughput at high density.
- Cellular User Density: Open access in CDMA provides a home-user rate gain exceeding 200% (5 dB) across a broad cellular user-density range.This result is reported in the numerical evaluation of the home user’s ergodic rate.
- Cellular User Density: At low density, open access causes only a negligible loss in cellular users’ sum throughput.The low-density regime is N ≤N∗o.
- Cellular User Density: At high density, open access strictly improves cellular users’ sum throughput.The improvement occurs when N ≥N∗o.
- Femtocell Resource Allocation: Open access improves the home user’s rate regardless of how femtocell backhaul is shared or what cellular user density is used.The reported home-user benefit does not require adaptive resource allocation.
- Summary for CDMA Access: Open access benefits both parties across almost the whole density range and does not require adaptive FAP resource allocation.The paper concludes that open access is preferred in 3G CDMA networks.
APPENDIX
The appendix derives the interference-factor distribution by partitioning geometric cases according to circle–macrocell overlap, then applies success-probability calculations to femtocell and cellular users.
- Interference-factor distribution: The interference-factor CDF is divided into five segments according to the range of the interference factor i.For i < 1, S is the area inside the circle; for i > 1, S is the area outside it.
- Geometric cases: The area S is computed differently when the circle lies inside the macrocell, intersects its boundary, or extends outside it.The appendix gives corresponding expressions for contained, intersecting, and exterior cases.
- Success probabilities: For K = 1, the analysis has two events, A0 and A1, and calculates pf,1, ph,1, and pc,1 to obtain success probabilities.The handoff-user success probability is derived using the same technique as the other success probabilities.
- Resource allocation: Time fractions λ1 and µ1 determine the probabilities that a macrocell cellular user experiences interference from the home user and handed-off user.The resulting success probability combines these interference events.
C. The Proof of Theorem 4
The proof and associated results relate access choices, resource allocation, and user-density regimes across TDMA and CDMA femtocell systems. They show that access preferences depend on cellular density and multiple-access behavior.
- The Proof of Theorem 4: For 1 ≤ L ≤ K, pf,L retains the same form and is lower bounded as stated in the proof.
- The Proof of Theorem 4: In CDMA, Γf,L is non-decreasing in λL and non-increasing in L because λL does not increase as L grows.