Downlink SDMA with Limited Feedback in Interference-Limited Wireless Networks

The tremendous capacity gains promised by space division multiple access (SDMA) depend critically on the accuracy of the transmit channel state information. In the broadcast channel, even without any network interference, it is known that such gains collapse due to interstream interference if the feedback is delayed or low rate. In this paper, we investigate SDMA in the presence of interference from many other simultaneously active transmitters distributed randomly over the network. In particular we consider zero-forcing beamforming in a decentralized (ad hoc) network where each receiver provides feedback to its respective transmitter. We derive closed-form expressions for the outage probability, network throughput, transmission capacity, and average achievable rate and go on to quantify the degradation in network performance due to residual self-interference as a function of key system parameters. One particular finding is that as in the classical broadcast channel, the per-user feedback rate must increase linearly with the number of transmit antennas and SINR (in dB) for the full multiplexing gains to be preserved with limited feedback. We derive the throughput-maximizing number of streams, establishing that single-stream transmission is optimal in most practically relevant settings. In short, SDMA does not appear to be a prudent design choice for interference-limited wireless networks.Comment: Submitted to IEEE Transactions on Wireless Communication

A Tractable Approach to Coverage and Rate in Cellular Networks

Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage/outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.Comment: Submitted to IEEE Transactions on Communication

Analysis and Ad-hoc Networking Solutions for Cooperative Relaying Systems

Users of mobile networks are increasingly demanding higher data rates from their service providers. To cater to this demand, various signal processing and networking algorithms have been proposed. Amongst them the multiple input multiple output (MIMO) scheme of wireless communications is one of the most promising options. However, due to certain physical restrictions, e.g., size, it is not possible for many devices to have multiple antennas on them. Also, most of the devices currently in use are single-antenna devices. Such devices can make use of the MIMO scheme by employing cooperative MIMO methods. This involves nearby nodes utilizing the antennas of each other to form virtual antenna arrays (VAAs). Nodes with limited communication ranges can further employ multi-hopping to be able to communicate with far away nodes. However, an ad-hoc communications scheme with cooperative MIMO multi-hopping can be challenging to implement because of its de-centralized nature and lack of a centralized controling entity such as a base-station. This thesis looks at methods to alleviate the problems faced by such networks.In the first part of this thesis, we look, analytically, at the relaying scheme under consideration and derive closed form expressions for certain performance measures (signal to noise ratio (SNR), symbol error rate (SER), bit error rate (BER), and capacity) for the co-located and cooperative multiple antenna schemes in different relaying configurations (amplify-and-forward and decode-and-forward) and different antenna configurations (single input single output (SISO), single input multiple output (SIMO) and MIMO). These expressions show the importance of reducing the number of hops in multi-hop communications to achieve a better performance. We can also see the impact of different antenna configurations and different transmit powers on the number of hops through these simplified expressions.We also look at the impact of synchronization errors on the cooperative MIMO communications scheme and derive a lower bound of the SINR and an expression for the BER in the high SNR regime. These expressions can help the network designers to ensure that the quality of service (QoS) is satisfied even in the worst-case scenarios. In the second part of the thesis we present some algorithms developed by us to help the set-up and functioning of cluster-based ad-hoc networks that employ cooperative relaying. We present a clustering algorithm that takes into account the battery status of nodes in order to ensure a longer network life-time. We also present a routing mechanism that is tailored for use in cooperative MIMO multi-hop relaying. The benefits of both schemes are shown through simulations.A method to handle data in ad-hoc networks using distributed hash tables (DHTs) is also presented. Moreover, we also present a physical layer security mechanism for multi-hop relaying. We also analyze the physical layer security mechanism for the cooperative MIMO scheme. This analysis shows that the cooperative MIMO scheme is more beneficial than co-located MIMO in terms of the information theoretic limits of the physical layer security.Nutzer mobiler Netzwerke fordern zunehmend höhere Datenraten von ihren Dienstleistern. Um diesem Bedarf gerecht zu werden, wurden verschiedene Signalverarbeitungsalgorithmen entwickelt. Dabei ist das "Multiple input multiple output" (MIMO)-Verfahren für die drahtlose Kommunikation eine der vielversprechendsten Techniken. Jedoch ist aufgrund bestimmter physikalischer Beschränkungen, wie zum Beispiel die Baugröße, die Verwendung von mehreren Antennen für viele Endgeräte nicht möglich. Dennoch können solche Ein-Antennen-Geräte durch den Einsatz kooperativer MIMO-Verfahren von den Vorteilen des MIMO-Prinzips profitieren. Dabei schließen sich naheliegende Knoten zusammen um ein sogenanntes virtuelles Antennen-Array zu bilden. Weiterhin können Knoten mit beschränktem Kommunikationsbereich durch mehrere Hops mit weiter entfernten Knoten kommunizieren. Allerdings stellt der Aufbau eines solchen Ad-hoc-Netzwerks mit kooperativen MIMO-Fähigkeiten aufgrund der dezentralen Natur und das Fehlen einer zentral-steuernden Einheit, wie einer Basisstation, eine große Herausforderung dar. Diese Arbeit befasst sich mit den Problemstellungen dieser Netzwerke und bietet verschiedene Lösungsansätze.Im ersten Teil dieser Arbeit werden analytisch in sich geschlossene Ausdrücke für ein kooperatives Relaying-System bezüglicher verschiedener Metriken, wie das Signal-Rausch-Verhältnis, die Symbolfehlerrate, die Bitfehlerrate und die Kapazität, hergeleitet. Dabei werden die "Amplify-and forward" und "Decode-and-forward" Relaying-Protokolle, sowie unterschiedliche Mehrantennen-Konfigurationen, wie "Single input single output" (SISO), "Single input multiple output" (SIMO) und MIMO betrachtet. Diese Ausdrücke zeigen die Bedeutung der Reduzierung der Hop-Anzahl in Mehr-Hop-Systemen, um eine höhere Leistung zu erzielen. Zudem werden die Auswirkungen verschiedener Antennen-Konfigurationen und Sendeleistungen auf die Anzahl der Hops analysiert.  Weiterhin wird der Einfluss von Synchronisationsfehlern auf das kooperative MIMO-Verfahren herausgestellt und daraus eine untere Grenze für das Signal-zu-Interferenz-und-Rausch-Verhältnis, sowie ein Ausdruck für die Bitfehlerrate bei hohem Signal-Rausch-Verhältnis entwickelt. Diese Zusammenhänge sollen Netzwerk-Designern helfen die Qualität des Services auch in den Worst-Case-Szenarien sicherzustellen. Im zweiten Teil der Arbeit werden einige innovative Algorithmen vorgestellt, die die Einrichtung und die Funktionsweise von Cluster-basierten Ad-hoc-Netzwerken, die kooperative Relays verwenden, erleichtern und verbessern. Darunter befinden sich ein Clustering-Algorithmus, der den Batteriestatus der Knoten berücksichtigt, um eine längere Lebensdauer des Netzwerks zu gewährleisten und ein Routing-Mechanismus, der auf den Einsatz in kooperativen MIMO Mehr-Hop-Systemen zugeschnitten ist. Die Vorteile beider Algorithmen werden durch Simulationen veranschaulicht. Eine Methode, die Daten in Ad-hoc-Netzwerken mit verteilten Hash-Tabellen behandelt wird ebenfalls vorgestellt. Darüber hinaus wird auch ein Sicherheitsmechanismus für die physikalische Schicht in Multi-Hop-Systemen und kooperativen MIMO-Systemen präsentiert. Eine Analyse zeigt, dass das kooperative MIMO-Verfahren deutliche Vorteile gegenüber dem konventionellen MIMO-Verfahren hinsichtlich der informationstheoretischen Grenzen der Sicherheit auf der physikalischen Schicht aufweist

Restricted Mobility Improves Delay-Throughput Trade-offs in Mobile Ad-Hoc Networks

In this paper we revisit two classes of mobility models which are widely used to repre-sent users ’ mobility in wireless networks: Random Waypoint (RWP) and Random Direction (RD). For both models we obtain systems of partial differential equations which describe the evolution of the users ’ distribution. For the RD model, we show how the equations can be solved analytically both in the stationary and transient regime adopting standard mathematical techniques. Our main contributions are i) simple expressions which relate the transient dura-tion to the model parameters; ii) the definition of a generalized random direction model whose stationary distribution of mobiles in the physical space corresponds to an assigned distribution

Secure Communications in Millimeter Wave Ad Hoc Networks

Wireless networks with directional antennas, like millimeter wave (mmWave) networks, have enhanced security. For a large-scale mmWave ad hoc network in which eavesdroppers are randomly located, however, eavesdroppers can still intercept the confidential messages, since they may reside in the signal beam. This paper explores the potential of physical layer security in mmWave ad hoc networks. Specifically, we characterize the impact of mmWave channel characteristics, random blockages, and antenna gains on the secrecy performance. For the special case of uniform linear array (ULA), a tractable approach is proposed to evaluate the average achievable secrecy rate. We also characterize the impact of artificial noise in such networks. Our results reveal that in the low transmit powerregime, the use of low mmWave frequency achieves better secrecy performance, and when increasing transmit power, a transition from low mmWave frequency to high mmWave frequency is demanded for obtaining a higher secrecy rate. More antennas at the transmitting nodes are needed to decrease the antenna gain obtained by the eavesdroppers when using ULA. Eavesdroppers can intercept more information by using a wide beam pattern. Furthermore, the use of artificial noise may be ineffective for enhancing the secrecy rate.Comment: Accepted by IEEE Transactions on Wireless Communication