Analyzing performance of millimeter wave cellular networks
The era of operating cellular networks in millimeter wave (mmWave) bands is coming, as it offers large bandwidths to solve the spectrum gridlock in 5G networks. MmWave cellular networks, however, will be different from the conventional cellular networks, due to different propagation conditions and hardware constraints, which motivates new mathematical models for mmWave performance analyses. Leveraging concepts from stochastic geometry and random shape theory, we have proposed analytical network models that incorporate key features of mmWave cellular systems, such as blockage (LOS/ NLOS) effects and directional beamforming.
In , we analyzed the blockage effects (a.k.a. LOS/ NLOS effects) by buildings in urban areas: as shown in Fig. (a), the buildings are modeled as a random rectangular process, and the LOS probability is derived to be a exponential decaying function of the link length; the analysis showed that blockages can help improve SINR coverage by blocking more interference.
In [2,3], a general framework to analyze the performance of (single-user) mmWave networks was proposed. In the model, the LOS probability was applied to determine the LOS/ NLOS status of a link, and a sectoring antenna pattern was used to incorporate directional beamforming. Based on the paper, they derived expressions for SINR and rate distributions as functions of the base station density, parameters of blockages (e.g. buildings in urban areas), and geometries of beamforming. It has been found that mmWave networks will move from a power-limited regime to interference-limited regime when increasing base station density; over-densification of base stations, however, will eventually results in a decrease of SINR coverage. More importantly, they showed that mmWave cellular networks can achieve comparable SINR coverage and significantly higher achievable rates than conventional sub-6 GHz networks when the base station density is sufficiently high. Their results indicate that in dense mmWave networks, the SINR and rate performance is mostly determined by the ratio of base station density to the blockage density.
The work in [2,3] focused mainly on the case when base stations and mobile users beamfomring vectors are perfectly designed for maximum beamforming gains. Designing beamforming/combining vectors, though, requires training which may impact both the SINR coverage and rate of mmWave cellular systems. In , we characterize and evaluate the performance of mmWave cellular networks while accounting for the beam training/association overhead. Using stochastic geometry, the effective reliable rate of mmWave cellular networks is derived for two special cases: with near-orthogonal control pilots and with full pilot reuse. Analytical and simulation results provide insights into the answers of three important questions: (i) What is the impact of beam association on mmWave network performance? (ii) Should orthogonal or reused control pilots be employed in the initial beam association phase? (iii) Should exhaustive or hierarchical search be adopted for the beam training phase?
More recent work in  considered the blocking from users’ self-body, as measurements show that mmWave signals suffers from 20-40 dB penetration loss from human body. In Fig. (b), the user’s self-body is modeled as a blocking cone in the angular space, where all the signals and interference come inside the cone are attenuated by certain losses. The analysis showed that self-body blockage will increase SINR outage and around 10% decrease in the achievable rate in mmWave cellular systems.
1. T. Bai, R. Vaze, and R. W. Heath, Jr., “Analysis of blockage effects on urban cellular networks“, IEEE Trans. Wireless Commun., vol. 13, no. 9, pp. 5070-5083, Sep. 2014. (Arxiv)
2. T. Bai and R. W. Heath, Jr., “ Coverage and rate analysis for millimeter wave cellular networks“, IEEE Trans. Wireless Commun., vol.14, no. 2, pp. 1100-1114, Feb. 2015. (Arxiv| Codes)
3. T. Bai, A. Alkhateeb, and R. W. Heath, Jr., “Coverage and capacity of millimeter wave cellular networks“, IEEE Commun. Mag., vol. 52, no. 9, pp. 70-77, Sep. 2015. (Presentation video)
4.A. Alkhateeb, Y.H. Nam, M. Saifur Rahman, J. (Charlie) Zhang, and R. W. Heath Jr., “Initial Beam Association in Millimeter Wave Cellular Systems: Analysis and Design Insights,” submitted to IEEE Transactions on Wireless Communications, Feb., 2016
5. Bai and R. W. Heath, Jr., “Analysis of self-body blocking effects in millimeter wave cellular networks” (invited), in Proc. of Asilomar Conf. on Signal, Systems, and Computers, Pacific Grove, CA, Nov.2014.
This research funded by the National Science Foundation under Grant No. 1218338 and 1319556, and a gift from Huawei.