text: Millimeter wave (mmWave) signals are much more sensitive to blockage, which results in a significant increase of the outage probability, especially for the users at the edge of the cells. In this paper, we exploit the technique of base station (BS) cooperation to improve the performance of the cell-edge users in the downlink transmission of mmWave cellular networks. We design two cooperative schemes, which are referred to as fixed-number BS cooperation (FNC) scheme and fixed-region BS cooperation (FRC) scheme, respectively. In FNC scheme, the cooperative BSs consist of the M nearest BSs around the served cell-edge users, and in FRC scheme, the cooperative BSs include all the BSs located within a given region. We derive the expressions for the average rate and outage probability of a typical cell-edge user located at the origin based on the stochastic geometry framework. To reduce the computational complexity of our analytical results for the outage probability, we further propose a Gamma approximation based method to provide approximations with satisfying accuracy. Our analytical results incorporate the critical characteristics of mmWave channels, i.e., the blockage effects, the different path loss of LOS and NLOS links and the highly directional antenna arrays. Simulation results show that the performance of the cell-edge users is greatly improved when mmWave networks are combined with the technique of BS cooperation.
  @cite_14: In this paper, a new mathematical framework to the analysis of millimeter wave cellular networks is introduced. Its peculiarity lies in considering realistic path-loss and blockage models, which are derived from recently reported experimental data. The path-loss model accounts for different distributions of line-of-sight and non-line-of-sight propagation conditions and the blockage model includes an outage state that provides a better representation of the outage possibilities of millimeter wave communications. By modeling the locations of the base stations as points of a Poisson point process and by relying on a noise-limited approximation for typical millimeter wave network deployments, simple and exact integral as well as approximated and closed-form formulas for computing the coverage probability and the average rate are obtained. With the aid of Monte Carlo simulations, the noise-limited approximation is shown to be sufficiently accurate for typical network densities. The noise-limited approximation, however, may not be sufficiently accurate for ultra-dense network deployments and for sub-gigahertz transmission bandwidths. For these case studies, the analytical approach is generalized to take the other-cell interference into account at the cost of increasing its computational complexity. The proposed mathematical framework is applicable to cell association criteria based on the smallest path-loss and on the highest received power. It accounts for beamforming alignment errors and for multi-tier cellular network deployments. Numerical results confirm that sufficiently dense millimeter wave cellular networks are capable of outperforming micro wave cellular networks, in terms of coverage probability and average rate.
  @cite_7: Millimeter wave (mmWave) cellular systems will require high-gain directional antennas and dense base station (BS) deployments to overcome a high near-field path loss and poor diffraction. As a desirable side effect, high-gain antennas offer interference isolation, providing an opportunity to incorporate self-backhauling , i.e., BSs backhauling among themselves in a mesh architecture without significant loss in the throughput, to enable the requisite large BS densities. The use of directional antennas and resource sharing between access and backhaul links leads to coverage and rate trends that significantly differ from conventional UHF cellular systems. In this paper, we propose a general and tractable mmWave cellular model capturing these key trends and characterize the associated rate distribution. The developed model and analysis are validated using actual building locations from dense urban settings and empirically derived path loss models. The analysis shows that, in sharp contrast to the interference-limited nature of UHF cellular networks, the spectral efficiency of mmWave networks (besides the total rate) also increases with the BS density, particularly at the cell edge. Increasing the system bandwidth does not significantly influence the cell edge rate, although it boosts the median and peak rates. With self-backhauling, different combinations of the wired backhaul fraction (i.e., the fraction of BSs with a wired connection) and the BS density are shown to guarantee the same median rate (QoS).
  @cite_28: Millimeter wave (mmWave) holds promise as a carrier frequency for fifth generation cellular networks. Because mmWave signals are sensitive to blockage, prior models for cellular networks operated in the ultra high frequency (UHF) band do not apply to analyze mmWave cellular networks directly. Leveraging concepts from stochastic geometry, this paper proposes a general framework to evaluate the coverage and rate performance in mmWave cellular networks. Using a distance-dependent line-of-site (LOS) probability function, the locations of the LOS and non-LOS base stations are modeled as two independent non-homogeneous Poisson point processes, to which different path loss laws are applied. Based on the proposed framework, expressions for the signal-to-noise-and-interference ratio (SINR) and rate coverage probability are derived. The mmWave coverage and rate performance are examined as a function of the antenna geometry and base station density. The case of dense networks is further analyzed by applying a simplified system model, in which the LOS region of a user is approximated as a fixed LOS ball. The results show that dense mmWave networks can achieve comparable coverage and much higher data rates than conventional UHF cellular systems, despite the presence of blockages. The results suggest that the cell size to achieve the optimal SINR scales with the average size of the area that is LOS to a user.
  @cite_6: In this paper, we provide an analytical framework to analyze heterogeneous downlink millimeter-wave (mm-wave) cellular networks consisting of @math tiers of randomly located base stations (BSs), where each tier operates in an mm-wave frequency band. Signal-to-interference-plus-noise ratio (SINR) coverage probability is derived for the entire network using tools from stochastic geometry. The distinguishing features of mm-wave communications, such as directional beamforming, and having different path loss laws for line-of-sight and non-line-of-sight links are incorporated into the coverage analysis by assuming averaged biased-received power association and Nakagami fading. By using the noise-limited assumption for mm-wave networks, a simpler expression requiring the computation of only one numerical integral for coverage probability is obtained. Also, the effect of beamforming alignment errors on the coverage probability analysis is investigated to get insight on the performance in practical scenarios. Downlink rate coverage probability is derived as well to get more insights on the performance of the network. Moreover, the effect of deploying low-power smaller cells and the impact of biasing factor on energy efficiency is analyzed. Finally, a hybrid cellular network operating in both mm-wave and @math -wave frequency bands is addressed.
  @cite_39: Ad hoc networks provide an on-demand, infrastructure-free means to communicate between soldiers in war zones, aid workers in disaster areas, or consumers in device-to-device (D2D) applications. Unfortunately, ad hoc networks are limited by interference due to nearby transmissions. Millimeter-wave (mmWave) devices offer several potential advantages for ad hoc networks, including reduced interference due to directional antennas and building blockages, not to mention huge bandwidth channels for large data rates. This paper uses a stochastic geometry approach to characterize the one-way and two-way signal-to-interference ratio distribution of a mmWave ad hoc network with directional antennas, random blockages, and ALOHA channel access. The interference-to-noise ratio shows that a fundamental limitation of an ad hoc network, interference, may still be an issue. The performance of mmWave ad hoc networks is bounded by the transmission capacity and area spectral efficiency. The results show that mmWave networks can support much higher densities and larger spectral efficiencies, even in the presence of blockage, compared with lower frequency communication for certain link distances. Due to the increased bandwidth, the rate coverage of mmWave can be much greater than lower frequency devices.
  @cite_24: The millimeter-wave (mmWave) band offers the potential for high-bandwidth communication channels in cellular networks. It is not clear, however, whether both high data rates and coverage in terms of signal-to-noise-plus-interference ratio can be achieved in interference-limited mmWave cellular networks due to the differences in propagation conditions and antenna topologies. This article shows that dense mmWave networks can achieve both higher data rates and comparable coverage relative to conventional microwave networks. Sum rate gains can be achieved using more advanced beamforming techniques that allow multiuser transmission. The insights are derived using a new theoretical network model that incorporates key characteristics of mmWave networks.
  @cite_0: Recent studies show that millimeter wave (mmWave) communications can offer orders of magnitude, which increases in the cellular capacity. However, the secrecy performance of an mmWave cellular network has not been investigated so far. Leveraging the new path-loss and blockage models for mmWave channels, which are significantly different from the conventional microwave channel, this paper comprehensively studies the network-wide physical layer security performance of the downlink transmission in an mmWave cellular network under a stochastic geometry framework. We first study the secure connectivity probability and the average number of perfect communication links per unit area in a noise-limited mmWave network for both non-colluding and colluding eavesdroppers scenarios, respectively. Then, we evaluate the effect of the artificial noise (AN) on the secrecy performance, and derive the analysis result of average number of perfect communication links per unit area in an interference-limited mmWave network. Numerical results demonstrate the network-wide secrecy performance, and provide interesting insights into how the secrecy performance is influenced by various network parameters: antenna array pattern, base station intensity, and AN power allocation.
summary: To analyze the performance of the mmWave networks, theoretical channel models have been proposed to describe the new propagation characteristics in mmWave bands @cite_24 @cite_28 @cite_14 @cite_7 @cite_39 @cite_6 . In @cite_24 @cite_28 , the authors proposed a LOS ball model to approximate the irregular LOS region, which was shown to be flexible yet accurate enough to capture the features of the blockage effects in mmWave bands by the field measurements @cite_7 . The LOS ball model was further extended to the two-ball-based blockage model in @cite_14 and the multiple-ball-based blockage model in @cite_6 to account for the three different states of each link, i.e., LOS, NLOS and outage. Based on the established theoretical channel models, the network-wide system performance of the mmWave networks was investigated, e.g., in @cite_7 @cite_39 @cite_0 .