Spectral Efficiency Scaling Laws in Dense Random Wireless Networks with Multiple Receive Antennas

This paper considers large random wireless networks where transmit-and-receive node pairs communicate within a certain range while sharing a common spectrum. By modeling the spatial locations of nodes based on stochastic geometry, analytical expressions for the ergodic spectral efficiency of a typical node pair are derived as a function of the channel state information available at a receiver (CSIR) in terms of relevant system parameters: the density of communication links, the number of receive antennas, the path loss exponent, and the operating signal-to-noise ratio. One key finding is that when the receiver only exploits CSIR for the direct link, the sum of spectral efficiencies linearly improves as the density increases, when the number of receive antennas increases as a certain super-linear function of the density. When each receiver exploits CSIR for a set of dominant interfering links in addition to the direct link, the sum of spectral efficiencies linearly increases with both the density and the path loss exponent if the number of antennas is a linear function of the density. This observation demonstrates that having CSIR for dominant interfering links provides a multiplicative gain in the scaling law. It is also shown that this linear scaling holds for direct CSIR when incorporating the effect of the receive antenna correlation, provided that the rank of the spatial correlation matrix scales super-linearly with the density. Simulation results back scaling laws derived from stochastic geometry.Comment: Submitte

Deploying Dense Networks for Maximal Energy Efficiency: Small Cells Meet Massive MIMO

How would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, tools from stochastic geometry are used in this paper to model future cellular networks and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable uplink energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closed-form expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is achieved by also equipping the BSs with multiple antennas and operate in a "massive MIMO" fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user.Comment: To appear in IEEE Journal on Selected Areas in Communications, 15 pages, 7 figures, 1 tabl

Modeling and analyzing wireless networks using stochastic geometry

Over the past decade, stochastic geometric models, and most notably the planar Poisson point process (PPP) model, have become popular for the analysis of spectral efficiency in wireless networks, in both the D2D and the cellular contexts [1]. By modeling base station (BS) and user locations as spatial point processes, stochastic geometry has recently been recognized as a tractable and efficient analytical tool to quantify key performance metrics. This tool provides a natural way of defining and computing macroscopic properties of multiuser information theory. These properties are obtained by averaging over all node patterns found in a large random network of the Euclidean plane. For example, some key performance metrics such as signal to interference and noise ratio and data rate depend on the network geometric configurations. This tool has thus been widely adopted for analyzing the network performance and broadening network design. This thesis proposes new models to represent several new scenarios. Three main scenarios are considered: 3-D inbuilding networks, MIMO adhoc networks, and multihop communication under mmWave networks. To do so, mathematical tools such as Poisson point processes, Poisson line processes, Boolean models and Poisson bipolar models are used. Each model is 1) generative in that it has a clear physical interpretation, 2) leads to explicit analytical representations of important wireless performance metrics, and 3) highly parametric, with parameters expressing the geometric characteristic of the elements of networks. Physical interpretations from these models are quite different from previous results. The core of this thesis is focused on the effects of correlated shadowing. Shadowing is the effect that the received signal power fluctuates due to objects obstructing the propagation path. By introducing an independent shadowing term over links, it is possible to model the effect of shadow fading. Most previous papers analyzing urban networks assume that shadowing fields are independent over links. With this assumption, it is possible to derive simple closed-form expressions of important network performance metrics. However, this assumption cannot capture that shadowing fields are spatially correlated. This thesis goes beyond the independent shadowing approximation and analyzes the effects of correlated shadowing on various performance metricsElectrical and Computer Engineerin

Dynamic Spectrum Sharing in Cognitive Radio and Device-to-Device Systems

abstract: Cognitive radio (CR) and device-to-device (D2D) systems are two promising dynamic spectrum access schemes in wireless communication systems to provide improved quality-of-service, and efficient spectrum utilization. This dissertation shows that both CR and D2D systems benefit from properly designed cooperation scheme. In underlay CR systems, where secondary users (SUs) transmit simultaneously with primary users (PUs), reliable communication is by all means guaranteed for PUs, which likely deteriorates SUs’ performance. To overcome this issue, cooperation exclusively among SUs is achieved through multi-user diversity (MUD), where each SU is subject to an instantaneous interference constraint at the primary receiver. Therefore, the active number of SUs satisfying this constraint is random. Under different user distributions with the same mean number of SUs, the stochastic ordering of SU performance metrics including bit error rate (BER), outage probability, and ergodic capacity are made possible even without observing closed form expressions. Furthermore, a cooperation is assumed between primary and secondary networks, where those SUs exceeding the interference constraint facilitate PU’s transmission by relaying its signal. A fundamental performance trade-off between primary and secondary networks is observed, and it is illustrated that the proposed scheme outperforms non-cooperative underlay CR systems in the sense of system overall BER and sum achievable rate. Similar to conventional cellular networks, CR systems suffer from an overloaded receiver having to manage signals from a large number of users. To address this issue, D2D communications has been proposed, where direct transmission links are established between users in close proximity to offload the system traffic. Several new cooperative spectrum access policies are proposed allowing coexistence of multiple D2D pairs in order to improve the spectral efficiency. Despite the additional interference, it is shown that both the cellular user’s (CU) and the individual D2D user's achievable rates can be improved simultaneously when the number of D2D pairs is below a certain threshold, resulting in a significant multiplexing gain in the sense of D2D sum rate. This threshold is quantified for different policies using second order approximations for the average achievable rates for both the CU and the individual D2D user.Dissertation/ThesisDoctoral Dissertation Electrical Engineering 201

Deploying Dense Networks for Maximal Energy Efficiency: Small Cells Meet Massive MIMO

How would a cellular network designed for maximal energy efficiency look like? To answer this fundamental question, we model future cellular networks using stochastic geometry and obtain a new lower bound on the average uplink spectral efficiency. This enables us to formulate a tractable energy efficiency (EE) maximization problem and solve it analytically with respect to the density of base stations (BSs), the transmit power levels, the number of BS antennas and users per cell, and the pilot reuse factor. The closed-form expressions obtained from this general EE maximization framework provide valuable insights on the interplay between the optimization variables, hardware characteristics, and propagation environment. Small cells are proved to give high EE, but the EE improvement saturates quickly with the BS density. Interestingly, the maximal EE is obtained by also equipping the BSs with multiple antennas and operate in a "massive MIMO" fashion, where the array gain from coherent detection mitigates interference and the multiplexing of many users reduces the energy cost per user

Analysis of millimeter wave ad hoc networks

Over the coming few years, the next-generation of wireless networks will be standardized and defined. Ad hoc networks, which operate without expensive infrastructure, are desirable for use cases such as military networks or disaster relief. Millimeter wave (mmWave) technology may enable high speed ad hoc networks. Directional antennas and building blockage limit the received interference power while the huge bandwidth enables high data rates. For this reason, understanding the interference and network performance of mmWave ad hoc networks is crucial for next-generation network design. In my first contribution, I derive the SINR complementary cumulative distribution function (CCDF) for a random single-hop mmWave ad hoc network. These base results are used to further give insights in mmWave ad hoc networks. The SINR distribution is used to compute the transmission capacity of a mmWave ad hoc network using a Taylor bound. The CDF of the interference to noise ratio (INR) is also derived which shows that mmWave ad hoc networks are line-of-sight interference limited. I extend my work in the second contribution to include general clustered Poisson point processes to derive insights in the effect of different spatial interference patterns. Using the developed framework, I derive the ergodic rate of both spatially uniform and cluster mmWave ad hoc networks. I develop scaling trends for the antenna array size to keep the ergodic rate constant. The impact of beam alignment is computed in the final part of the contribution. Finally, I account for the overhead of beam alignment in mmWave ad hoc networks. The final contribution leverages the first two contributions to derive the expected training time a mmWave ad hoc network must perform before data transmission occurs. The results show that the optimal conditions for minimizing the training time are different than the optimal conditions for maximizing rate.Electrical and Computer Engineerin