The era of operating wireless systems at the millimeter wave spectrum, ranging from 30 GHz to 300 GHz, is coming. With several gigahertz potential spectrum, mmWave will be used for access channels in 5G cellular networks. The Federal Communications Commission (FCC) in the USA has been considering making rules to authorize mobile operations in certain mmWave band with county-size licenses.

MmWave cellular networks will operate in a different manner from conventional cellular systems below 6 GHz: for one thing, measurements reveal different propagation conditions, , e.g. the sensitivity to blockage, at mmWave from those at sub-6 GHz frequencies; for another, mmWave cellular networks will apply different architectures, e.g. analog or hybrid directional beamforming with large arrays, for signal processing. Consequently, new mathematical models are required for analyzing mmWave cellular networks, as previous ones for low frequencies do not directly apply.

Our group has made breakthroughs in building up analytical models for mmWave cellular networks, using stochastic geometry. The proposed model takes account for key mmWave features, including the blockage effects from buildings and human bodies, and the use of directional beamforming. Based on the model, the distributions of the SINR and rate in mmWave cellular systems were derived in analytical expressions. The results showed that given the blockage distributions, the mmWave performance is much sensitive to the base station density: comparable SINR coverage to that in the low frequency system can be achieved with sufficient base station density, which translates into much higher rate due to the larger bandwidth.

Another application of the mmWave system model is to compare the performance of massive MIMO in sub-6 GHz and mmWave bands using a common framework. Our analysis showed that in terms of the throughput per unit area, the optimal carrier frequency to deploy massive MIMO depends on the base station density: mmWave outperforms in dense base station networks, while its performance degrades with sparse base stations due to the coverage holes resulted from blockage effects.

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.

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.

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 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 [4], 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 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.

Massive multiple-input multiple-out (MIMO) is a promising technique for 5G cellular networks. Prior work showed that high throughput can be achieved with a large number of base station antennas through simple signal processing in massive MIMO networks. The carrier frequencies for massive MIMO systems, however, are not clear yet; as the propagation channels and hardware constraints will be much different from sub-6 GHz and millimeter wave (mmWave) band.

To compare the performance of massive MIMO in the UHF and mmWave bands, our group have proposed a stochastic geometry framework to analyze the signal-to-interference-plus-noise ratio (SINR) and the rate of massive MIMO in both sub-6 GHz and mmWave bands. The proposed models incorporate key features of different frequency bands, such as different large-scale path loss and small-scale fading correlations. Based on the proposed models, analytical expressions for the SINR and rate distribution derived for both sub-6 GHz and mmWave systems.

The asymptotic SINR coverage and rate was analyzed in a sub-6 GHz large-scale massive MIMO networks, when the number of base station antennas goes to infinity; the results showed that the asymptotic SINR is limited by pilot contamination, and the SINR coverage increases with a larger path loss exponent.

The framework into the case of finite base station antennas, where we expressed the SINR distribution as a functions of the number of a function of the numbers of base stations and simultaneously served users per cell, in sub-6 GHz uplink networks. Our analyses show that to maintain the same spatial-average SINR distribution at a typical user, the number of base station antennas should scale superlinearly with the number of served users in a cell, which is different from the linear scaling law examined in most prior work.

The performance of mmWave massive MIMO was examined where it is showed that the SINR coverage performance is much sensitive to the base station density. In certain dense base station case, the SINR coverage approaches the asymptotic limit with around 200 antennas, while in the sparse networks, the SINR coverage is poor and limited by noise and coverage holes due to blockages.

The performance comparison between sub-6 GHz and mmWave massive MIMO was present in low BS density, mmWave massive MIMO networks suffer from severe outage due to building blockages; in the case of dense BS networks, mmWave networks are shown to provide comparable SINR to sub-6 GHz systems, which translates into a magnitude order higher cell throughput due to the larger bandwidth.

It is worth noting that communication at mmWave frequencies has non-trivial differences when compared to communication at conventional cellular frequencies (CCF). This leads to possibility of uncoordinated sharing among operators. The independent cellular operators who own licenses for separate frequency bands may agree to share the complete rights of operation in each other’s bands without any explicit coordination. Sharing licenses may allow all networks to use the full spectrum simultaneously without impacting the individual achieved rates and help operators to reduce their expenses by sharing the license costs.

The established the theoretical feasibility of spectrum license sharing among mmWave cellular operators. Here, it is presented a tractable model for a multi-operator system containing multiple independent cellular networks, each owned by an operator. It is computed the performance in terms of the SINR and rate distribution for downlink mobile users of each network. Using the analysis, the comparison systems with fully shared licenses and exclusive licenses for different access rules and explore the trade-offs between system performance and spectrum cost and shown sharing spectrum licenses increases the per-user rate when antennas have narrow beams and is favored when there is a low density of users. We also consider a multi-operator system where BSs of all the networks are co-located to show that the simultaneous sharing of spectrum and infrastructure is also feasible.

THe analyzing secondary licensing for mmWave cellular systems. We consider a two-operator system where the first operator that primarily owns an exclusive-use license of a certain band can sell a restricted secondary license of the same band to the second operator. This secondary network has a restriction on the maximum interference it can cause to the original network. Using stochastic geometry, we derive expressions for the coverage and rate of both networks, and establish the feasibility of secondary licensing in licensed mmWave bands. To explain economic trade-offs, we consider a revenue-pricing model for both operators in the presence of a central licensing authority. The results show that the original operator and central network authority can benefit from secondary licensing when the maximum interference threshold is properly adjusted.

Fig. 1(a) Illustration describing the differences between the considered systems. For a typical user of operator 1, the figure shows all accessible networks this user can connect to, all interfering networks, and the available spectrum after license sharing

Fig. (b) Rate coverage in a two-network mmWave system with Rayleigh fading and BS antenna with 20^o beamwidth. Shared licenses (Systems 3 and 4) perform better than exclusive licenses (System 1).