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When mmWave Communications Meet Network Densification: A Scalable Interference Coordination Perspective
Wei Feng, Yanmin Wang, Dengsheng Lin, Ning Ge, Jianhua Lu, Shaoqian Li
TL;DR
MmWave links are challenged by high path loss and blockages, while ultra-dense deployments bring co-channel interference. The paper proposes large-scale-CSI-based coordinated FRB allocation; simulations report substantial gains over existing methods, although the scheme is guaranteed only to reach a local optimum.
Problem
High path loss and blockages make it challenging for mmWave communications to achieve sufficient link margin.
Source: §I · pp. 1–2Method
The paper proposes dense, amorphous mmWave BS deployment and a polynomial-time greedy coordinated FRB allocation scheme using large-scale CSI.
Source: §I · p. 2, §VI · p. 8Results
The proposed scheme provides substantial gains over existing methods and performs well in user fairness and system efficiency, though only local-optimum convergence is guaranteed.
Source: §I · p. 2Takeaways & Limitations
Dense deployment reduces access distance and expands serving-BS choice, while coordination addresses the resulting co-channel interference using low-cost, location-dependent large-scale CSI.
Source: §VI · p. 8The model requires more BS sites and adds costs such as synchronization among multiple BSs.
Source: §VI · p. 8
Abstract
from arXiv · showhide
The millimeter-wave (mmWave) communication is envisioned to provide orders of magnitude capacity improvement. However, it is challenging to realize a sufficient link margin due to high path loss and blockages. To address this difficulty, in this paper, we explore the potential gain of ultra-densification for enhancing mmWave communications from a network-level perspective. By deploying the mmWave base stations (BSs) in an extremely dense and amorphous fashion, the access distance is reduced and the choice of serving BSs is enriched for each user, which are intuitively effective for mitigating the propagation loss and blockages. Nevertheless, co-channel interference under this model will become a performance-limiting factor. To solve this problem, we propose a large-scale channel state information (CSI) based interference coordination approach. Note that the large-scale CSI is highly location-dependent, and can be obtained with a quite low cost. Thus, the scalability of the proposed coordination framework can be guaranteed. Particularly, using only the large-scale CSI of interference links, a coordinated frequency resource block allocation problem is formulated for maximizing the minimum achievable rate of the users, which is uncovered to be a NP-hard integer programming problem. To circumvent this difficulty, a greedy scheme with polynomial-time complexity is proposed by adopting the bisection method and linear integer programming tools. Simulation results demonstrate that the proposed coordination scheme based on large-scale CSI only can still offer substantial gains over the existing methods. Moreover, although the proposed scheme is only guaranteed to converge to a local optimum, it performs well in terms of both user fairness and system efficiency.
I. INTRODUCTION
MmWave links face severe attenuation from path loss, shadowing, blockages, and limited transmit power. The paper studies dense, amorphous deployments and large-scale-CSI coordination to address those challenges while managing interference.
I. INTRODUCTION
- High path loss, shadowing, blockages, and limited transmit power make sufficient mmWave link margin difficult to achieve.Link-level beamforming also faces sparse multipath, beam-training costs, and blockage-related outages.Source: §I · pp. 1–2
- Dense, amorphous mmWave BS deployment reduces access distance and increases serving-BS choice, providing ways to mitigate propagation loss and blockages.The model reflects deployments shaped by limited sites, blockages, and potentially subscriber-deployed BSs.Source: §I · p. 2
- Co-channel interference limits performance in the amorphous network, motivating scalable coordination using slowly varying, location-dependent large-scale CSI instead of costly full CSI.The passage identifies pilot, estimation-processor, and feedback overhead as costs of acquiring full CSI.Source: §I · p. 2
- The proposed large-scale-CSI coordinated FRB allocation maximizes the users’ minimum achievable rate and offers substantial gains, with good fairness and system efficiency despite only local-optimum convergence being guaranteed.The problem is NP-hard in general, and the proposed greedy solution has polynomial-time complexity.Source: §I · p. 2
II. SYSTEM MODEL
The system uses a microwave BS for global control and densely deployed, amorphous mmWave BSs for high-capacity transmission. It assumes reused FRBs across frequency division clusters and coordination based on large-scale CSI.
II. SYSTEM MODEL
- A microwave BS provides global control while amorphous, densely deployed mmWave BSs support high-capacity transmission; clusters reuse FRBs, creating co-channel interference.Each frequency division cluster contains K BS–user pairs assigned orthogonal FRBs to mitigate strong within-cluster interference.Source: §II · p. 2
- The choice of K depends on BS density, user requirements, and available FRBs; optimizing K and forming clusters optimally remain open issues.The model also leaves the effects of limited backhaul capability outside its scope.Source: §II · p. 2
- Each BS uses a uniform linear array, one RF chain, and analog beamforming, while each mobile terminal has one omnidirectional antenna.The analog beamforming assumption avoids requiring multiple RF chains at the BS.Source: §II · p. 3
- Only large-scale CSI is assumed available for interference links, limiting the coordination input to that channel-information category.The model categorizes channel parameters as large-scale or small-scale to control CSI acquisition cost.Source: §II · p. 3
A. Problem Formulation
The formulation selects frequency resource blocks to maximize the minimum achievable user rate. It uses statistical interference-link gains based on large-scale CSI and assumes equal BS transmit-power allocation across the front antenna elements.
A. Problem Formulation
- Each BS’s transmit power is equally allocated across its front Na antenna elements, and analog beamforming aligns element signals to focus energy on the corresponding user.The prose identifies the phase-shifting vector as the analog-beamforming mechanism.Source: A. Problem Formulation · pp. 3–4
- The interference-link channel gain is obtained by taking an expectation over the unknown small-scale CSI.This provides a statistical channel-gain basis for the interference-link calculation.Source: A. Problem Formulation · p. 4
- The FRB allocation objective maximizes the minimum achievable rate across users, a criterion noted as significant when users require similar QoS.The allocation strategy is the decision variable in the optimization.Source: A. Problem Formulation · p. 4
B. Problem Analysis
The coordinated FRB allocation problem is polynomial-time solvable for two frequency division clusters but NP-hard for any fixed number of at least three. The analysis establishes this boundary using assignment-problem transformations and reductions.
B. Problem Analysis
- The FRB allocation problem is polynomial-time solvable when N = 2 but NP-hard with respect to K for every fixed N ≥3.The nonlinear integer-programming objective makes the general problem difficult to solve.Source: B. Problem Analysis · p. 4
- For N = 2, bisection transforms the problem into linear bottleneck assignment problems, which are polynomial-time solvable.The proof uses the polynomial-time solvability of LBAPs.Source: B. Problem Analysis · p. 4
- For fixed N ≥3, a polynomial reduction from three-dimensional axial bottleneck assignment establishes NP-hardness.The analysis relies on 3BAP being NP-hard.Source: B. Problem Analysis · p. 4
IV. A GREEDY COORDINATED FRB ALLOCATION SCHEME
The coordinated FRB allocation problem is NP-hard in general, making optimal solutions computationally difficult for dense networks. This section introduces a low-complexity greedy approach and a degraded case that informs it.
IV. A Greedy Coordinated FRB Allocation Scheme
- For more than three FDCs and many users per FDC, finding an optimal coordinated FRB allocation can be computation-consuming.The section presents a degraded case to offer insight into the original problem before introducing the greedy scheme.Source: §IV · p. 4
- The proposed approach uses a greedy scheme with polynomial-time complexity to solve the allocation problem.It builds on the degraded case and is presented as a low-complexity alternative to solving the original problem directly.Source: §IV · p. 4
- The original coordinated FRB allocation problem is NP-hard in general.The section motivates the greedy approach by noting the computational difficulty of finding an optimal solution.Source: §IV · p. 4
A. A Degraded Case
The degraded case fixes the FRB allocations of the first U −1 FDCs and optimizes the remaining FDC. Its allocation problem can be solved in polynomial time using bisection and feasibility subproblems.
A. A Degraded Case
- With the first U −1 FDCs’ FRB allocations fixed, the degraded case optimizes the allocation for FDC U.The other system parameters remain the same as in the original case; only the optimization variables are reduced.Source: A. A Degraded Case · p. 4
- Exhaustive search for the degraded nonlinear integer program has complexity factorial in the users per FDC, K!.The passage motivates a polynomial-time algorithm instead.Source: A. A Degraded Case · p. 5
- The degraded allocation problem can be solved in polynomial time by bisection over a series of feasibility problems.Each feasibility problem is transformed equivalently into a linear bottleneck assignment problem.Source: A. A Degraded Case · pp. 5–6
- The bisection search takes around 10 iterations to converge for both K = 3 and K = 10 in the sampled scenarios.The figure reports iteration counts for 10 randomly selected scenarios out of 1000.Source: A. A Degraded Case · p. 6, Figure 2 · p. 6
B. A Greedy Solution
The greedy scheme adds FDCs sequentially, then repeatedly optimizes each FDC’s FRB allocation while fixing the others. It converges in fewer than five iterations in the reported simulations, but is only a pathway to a local optimum.
B. A Greedy Solution
- Optimizing one FDC at a time while fixing the others may fail to find the global optimum, but can provide a pathway to a local optimum.The scheme is presented as a greedy approach based on this observation.Source: B. A Greedy Solution · p. 6
- The scheme first adds FDCs to a subsystem one by one, then iteratively optimizes each FDC’s allocation with the others fixed.The final step solves N subproblems, each using the allocation formulation with U = N.Source: B. A Greedy Solution · p. 6
- FDCs with greater total interference power are optimized earlier to give more severely affected FDCs higher priority.The ordering is described as consistent with the fairness-oriented optimization target.Source: B. A Greedy Solution · p. 6
- For both K = 3 and K = 10, the proposed scheme converges in fewer than 5 iterations in the reported simulations.The figure shows the convergence speed under the Section V simulation setting.Source: B. A Greedy Solution · p. 7, Figure 3 · p. 7
- The scheme can run periodically or be triggered when total co-channel interference exceeds a threshold.Threshold-triggered operation requires a real-time interference estimator.Source: B. A Greedy Solution · p. 7
V. SIMULATION RESULTS
The simulations show that the proposed scheme improves minimum achievable rates over the compared methods for both K=3 and K=10. For K=3, it performs near the exhaustive-search optimum, while its system-efficiency gains are not proportional to its minimum-rate gains.
V. SIMULATION RESULTS
- Simulations use N=10 mmWave BSs, K=3 or 10 users, and a 28 GHz carrier, averaging results over 1,000 scenarios.The scenarios combine 10 large-scale CSI conditions with 100 small-scale Rayleigh fading realizations each.Source: §V · p. 7
- For K=3, the proposed local-optimum scheme stays near the exhaustive-search global optimum and beats and single-FDC, with larger gains at higher transmit power.The reported increase in gain is attributed to more severe co-channel interference at higher transmit power.Source: §V · pp. 7–8, Figure 4 · p. 7
- For K=10, the proposed scheme significantly outperforms the other methods; exhaustive search is omitted because it is too time-consuming.Fig. 5 reports minimum normalized achievable rate for K=10.Source: §V · p. 8, Figure 5 · p. 8
- At the same BS density, minimum achievable rate is slightly better for K=3 than K=10 because the worst-user channel worsens as the user count increases.The K=3 and K=10 comparison is made under the same conditions.Source: §V · p. 8
- For K=3, frequency reuse improves total spectral efficiency and the proposed scheme gains system efficiency, but sum-rate gains are not proportional to minimum-rate gains.The scheme focuses on improving the poorest user's rate, which can damage rates for some related users.Source: §V · p. 8, Figure 6 · p. 8
VI. CONCLUSIONS
The paper proposes dense, amorphous mmWave deployments to reduce access distance and expand serving-BS choice, then coordinates frequency blocks using large-scale CSI to address resulting co-channel interference. The scheme improves system performance, but the model entails added deployment costs and leaves practical BS-density optimization for future work.
VI. CONCLUSIONS
- Large-scale-CSI coordinated FRB allocation maximizes the minimum user rate and significantly improves system performance, with good fairness and efficiency despite only local-optimum convergence being guaranteed.The paper reports performance not far from the global optimum.Source: §VI · p. 8
- The dense, amorphous deployment reduces access distance and expands each user's serving-BS choice to help mitigate propagation loss and blockages.The conclusion identifies co-channel interference as a performance-limiting factor under this model.Source: §VI · p. 8
- The model requires more BS sites and adds costs such as synchronization among multiple BSs.Source: §VI · p. 8
- Practical BS-site limits and comprehensive costs remain for future study, including investigation of the practically optimal mmWave BS density.Source: §VI · pp. 8–9
APPENDIX A PROOF OF THEOREM 1
The appendix establishes that the coordinated allocation problem is NP-hard for three or more FDCs, while the two-FDC case can be solved in polynomial time. It also relates the proof formulations to assignment problems and reductions used to establish these complexity results.
APPENDIX A PROOF OF THEOREM 1
- When N = 2, the allocation problem can be transformed into linear bottleneck assignment problems and solved in polynomial time.The proof matches users across the two FDCs and optimizes the scheduling order.Source: Appendix A · p. 9
- For N = 3, the allocation problem is NP-hard, and the proof extends this result to every fixed N > 3 by embedding the three-FDC case as a special case.Source: Appendix A · p. 10
APPENDIX B PROOF OF LEMMA 1
- Appendix B transforms the problem into a linear bottleneck assignment problem with a K×K cost matrix.Source: Appendix B · p. 10
APPENDIX C LEMMA 2
- The cited arguments show that (38) is a special case of (45), making (38) polynomially reducible to (45); they also establish that (45) is polynomially reducible to (37).Source: Appendix C · p. 11