Abhishek K. Gupta

Modeling and Analyzing Millimeter Wave Cellular Systems

We provide a comprehensive overview of mathematical models and analytical techniques for millimeter wave (mmWave) cellular systems. The two fundamental physical differences from conventional sub-6-GHz cellular systems are: 1) vulnerability to blocking and 2) the need for significant directionality at the transmitter and/or receiver, which is achieved through the use of large antenna arrays of small individual elements. We overview and compare models for both of these factors, and present a baseline analytical approach based on stochastic geometry that allows the computation of the statistical distributions of the downlink signal-to-interference-plus-noise ratio (SINR) and also the per link data rate, which depends on the SINR as well as the average load. There are many implications of the models and analysis: 1) mmWave systems are significantly more noise-limited than at sub-6 GHz for most parameter configurations; 2) initial access is much more difficult in mmWave; 3) self-backhauling is more viable than in sub-6-GHz systems, which makes ultra-dense deployments more viable, but this leads to increasingly interference-limited behavior; and 4) in sharp contrast to sub-6-GHz systems cellular operators can mutually benefit by sharing their spectrum licenses despite the uncontrolled interference that results from doing so. We conclude by outlining several important extensions of the baseline model, many of which are promising avenues for future research.

Downlink Multi-Antenna Heterogeneous Cellular Network With Load Balancing

We model and analyze heterogeneous cellular networks with multiple antenna BSs (multi-antenna HetNets) with K classes or tiers of base stations (BSs), which may differ in terms of transmit power, deployment density, number of transmit antennas, number of users served, transmission scheme, and path loss exponent. We show that the cell selection rules in multi-antenna HetNets may differ significantly from the single-antenna HetNets due to the possible differences in multi-antenna transmission schemes across tiers. While it is challenging to derive exact cell selection rules even for maximizing signal-to-interference-plus-noise-ratio (SINR) at the receiver, we show that adding an appropriately chosen tier-dependent cell selection bias in the received power yields a close approximation. Assuming arbitrary selection bias for each tier, simple expressions for downlink coverage and rate are derived. For coverage maximization, the required selection bias for each tier is given in closed form. Due to this connection with biasing, multi-antenna HetNets may balance load more naturally across tiers in certain regimes compared to single-antenna HetNets, where a large cell selection bias is often needed to offload traffic to small cells.

On the Feasibility of Sharing Spectrum Licenses in mmWave Cellular Systems

The highly directional and adaptive antennas used in mmWave communication open up the possibility of uncoordinated sharing of spectrum licenses between commercial cellular operators. There are several advantages to sharing including a reduction in license costs and an increase in spectrum utilization. In this paper, we establish the theoretical feasibility of spectrum license sharing among mmWave cellular operators. We consider a heterogeneous multi-operator system containing multiple independent cellular networks, each owned by an operator. We then compute the signal-to-interference-and-noise ratio and rate distribution for downlink mobile users of each network. Using the analysis, we compare the systems with fully shared licenses and exclusive licenses for different access rules and explore the trade-offs between system performance and spectrum cost. We show that sharing spectrum licenses increases the per-user rate when antennas have narrow beams and is also 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. We show that all networks can share licenses with less bandwidth and still achieve the same per-user median rate as if they each had an exclusive license to spectrum with more bandwidth.

Are we approaching the fundamental limits of wireless network densification

The single most important factor enabling the data rate increases in wireless networks over the past few decades has been densification, namely adding more base stations and access points and thus getting more spatial reuse of the spectrum. This trend is set to continue into 5G and beyond. However, at some point further densification will no longer be able to provide exponentially increasing data rates. Like the end of Moores Law, this will have extensive implications for the entire technology landscape, which depends ever more heavily on wireless connectivity. When and why will this happen? How might we delay this from occurring for as long as possible? These are the questions explored in this article.

Rapid MIMO-OFDM software defined radio system prototyping

Combining MIMO with OFDM, it is possible to significantly reduce receiver complexity as OFDM greatly simplifies equalization at the receiver. MIMO-OFDM is currently being considered for a number of developing wireless standards; consequently, the study of MIMO-OFDM in realistic environments is of great importance. This paper describes an approach for prototyping a MIMO-OFDM systems using a flexible software defined radio (SDR) system architecture in conjunction with commercially available hardware. An emphasis on software permits a focus on algorithm and system design issues rather than implementation and hardware configuration. The penalty of this flexibility, however, is that the ease of use comes at the expense of overall throughput. To illustrate the benefits of the proposed architecture, applications to MIMO-OFDM system prototyping and preliminary MIMO channel measurements are presented. A detailed description of the hardware is provided along with downloadable software to reproduce the system.

SINR and Throughput Scaling in Ultradense Urban Cellular Networks

We consider a dense urban cellular network where the base stations (BSs) are stacked vertically as well as extending infinitely in the horizontal plane, resulting in a greater than two dimensional (2D) deployment. We use a dual-slope path loss model that is well supported empirically, wherein a “close-in” pathloss exponent α₀ is used for distances less than a corner distance R_c, and then changes to α₁ > α₀ outside R_c. We extend recent 2D coverage probability and potential throughput results to d dimensions, and prove that if the close-in path loss exponent α₀ <; d, then the SINR eventually decays to zero. For example, α₀ ≤ 3 results in an eventual SINR of 0 for all users in a 3D network, which is a troubling fact. We also show that the potential (i.e. best case) aggregate throughput decays to zero for α₀ <; d/2. Both of these scaling results also hold for the more realistic case that we term 3D⁺, where there are no BSs below the user, as in a dense urban network with the user on or near the ground.

Downlink coverage probability in MIMO HetNets with flexible cell selection

In this paper, we study the coverage probability of a K-tier multiple-input multiple-output heterogeneous cellular network (MIMO HetNet) assuming (i) zero-forcing precoding at all the base stations (BSs), (ii) Rayleigh fading, (iii) independent Poisson Point Process (PPP) model for the locations of BSs of each tier, and (iv) general cell selection rule that maximizes average received signal-to-interference-plus-noise ratio (SINR) at the users. Our analysis highlights key differences between MIMO HetNets and the more familiar single antenna HetNets in terms of cell selection. While it is challenging to derive exact cell selection rule to maximize average downlink SINR in MIMO HetNets, we show that adding an appropriately chosen per-tier selection bias yields a close approximation. The bias value for each tier is given in closed form. One interpretation of this result is that MIMO HetNets may balance load more naturally across different tiers in certain special cases compared to single antenna HetNets where an artificial selection bias is often needed for load balancing.

Gains of Restricted Secondary Licensing in Millimeter Wave Cellular Systems

Sharing the spectrum among multiple operators seems promising in millimeter wave (mmWave) systems. One explanation is the highly directional transmission in mmWave, which reduces the interference caused by one network on the other networks sharing the same resources. In this paper, we model a mmWave cellular system, where an operator that primarily owns an exclusive-use license of a certain band can sell a restricted secondary license of the same band to another 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 the rate of both networks, and establish the feasibility of secondary licensing in licensed mmWave bands. To explain economic tradeoffs, we consider a revenue-pricing model for both operators in the presence of a central licensing authority. Our results show that the original operator and central network authority can benefit from secondary licensing when the maximum interference threshold is properly adjusted. This means that the original operator and central licensing authority have an incentive to permit a secondary network to restrictively share the spectrum. Our results also illustrate that the spectrum sharing gains increase with narrow beams and when the network densifies.

SNR wall for generalized energy detection under noise uncertainty in cognitive radio

Energy detection (ED) is a popular spectrum sensing technique in cognitive radio to detect the primary user. But the detection performance of ED deteriorates in the presence of noise uncertainty and exhibits associated SNR wall phenomenon. In this paper, the generalized energy detector (GED) is investigated, where the squaring operation of amplitude of received samples in conventional energy detector (CED) is replaced by an arbitrary positive operation p. Our aim is to study the effect of noise uncertainty on the detection performance of GED. We consider different distributions of noise uncertainty. Initially, uniform distribution of noise uncertainty is considered and an expression of the SNR wall for the same is derived. It is shown that the SNR wall for uniformly distributed noise uncertainty is independent of p. The study of the detection performance of GED is further extended for log-normally distributed noise uncertainty, where the SNR wall is calculated numerically.

Rate analysis and feasibility of dynamic TDD in 5G cellular systems

In conventional applications of time division duplex (TDD) in cellular systems, the time resource split between uplink (UL) and downlink (DL) is fixed across all base stations (BSs) in the network. This leads to under utilization of BS resources when there is a mismatch between the expected and experienced UL/DL traffic in a given cell. A dynamic split that varies in each cell is desirable, but is challenging due to the high interference experienced by UL receivers in one cell from DL transmissions in adjacent cells. This paper analyzes the performance of UL users in dynamic TDD enabled next generation cellular networks using a stochastic geometry framework. The analysis highlights the trade-off between spectral efficiency and resource utilization for dynamic TDD. With appropriate interference mitigation, dynamic TDD offers a significant gain in data rates as compared to static TDD, which is higher when the BSs are lightly loaded and/or the fraction of UL users is low.