#### Date of Award

Spring 1-1-2012

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Electrical, Computer & Energy Engineering

#### First Advisor

Mahesh K. Varanasi

#### Second Advisor

Youjian Liu

#### Third Advisor

Shannon Hughes

#### Fourth Advisor

Peter Mathys

#### Fifth Advisor

Brian Rider

#### Abstract

A multiple-input multiple-output (MIMO) communication network consists of a set of multi-antenna transmitters and receivers that communicate over a common noisy medium. Each transmitter has access to a set of messages, each of which it needs to deliver to one of the receivers. Since the transmitter(s) transmit multiple messages over such networks, each receiver encounters interference due to undesired transmissions. This interference seen by the receivers is, in fact, the main factor that limits the capacity regions of such networks. Hence, to attain high data-rates, efficient interference management is crucial, and for the same reason, these networks are also known as interference networks. A common and by far the most important MIMO interference network is a wireless cellular network.

A wireless signal after its transmission undergoes attenuation or fading. The set of all channel fading coefficients between different pairs of transmit-receive antennas is called the channel state. If this channel state is known to all terminals of the network, sophisticated interference management schemes can be implemented to achieve high data-rates. While, in practice, channel state information (CSI) can be obtained at the receivers via pilot transmissions, there is no natural way for acquiring CSI at transmitters (CSIT). Unfortunately, the lack of CSIT severely affects the capacity regions of almost all MIMO networks. To avoid this capacity loss, the next-generation cellular standards are making a provision for having feedback links from the receivers to the transmitters over which the latter can be informed about the channel state. However, due to the dynamic nature of the wireless environment, the channel state is time-varying, which makes it difficult for the transmitters to obtain feedback in a timely manner. Specifically, by the time feedback is available to the transmitters, the channel state may have already changed to a significantly different value. This motivates the study of MIMO interference networks with strictly delayed feedback, which is the main topic of this thesis.

We analyze various feedback models depending upon whether the channel state or the channel outputs (i.e., the received signals) or both or a function of the two is fed back. We further consider the worst-case scenario, where the channel state changes independently across time and feedback is available with some delay. Under such a setting, feedback is rather outdated because the information obtained via feedback is completely irrelevant as far as the current channel state is concerned. It may seem here that outdated feedback can not be of much use, which is indeed true for the simplest MIMO network with a single transmitter-receiver pair.

Surprisingly, we prove here for the MIMO broadcast channel (BC, a one-to-two, generally, one-to-many system) and for the MIMO interference channel (IC, a system with two transmit-receive pairs) that outdated feedback can significantly improve their capacity regions, relative to the no-feedback case. To obtain such a result, we develop new interference management schemes, wherein each transmitter, using (delayed) feedback, determines and transmits the interference experienced in the past by the receivers. This technique allows a transmitter to deliver useful information to one receiver without creating any additional interference at the others. This point manifests interference alignment, and hence, feedback-based schemes developed in this work are called retrospective interference alignment (RIA) schemes. We then go a step ahead to derive information-theoretic converse arguments, which prove that our RIA schemes are optimal in the degrees-of-freedom (DoF) region sense, which provides a first-degree of approximation to the capacity region.

Specifically, we characterize here the DoF regions of MIMO broadcast and interference channels under two important settings of (i) delayed CSIT, which involves delayed feedback of the channel state, and (ii) Shannon feedback, which incorporates delayed CSIT as well as channel-output feedback. It is shown that delayed CSIT holds even a DoF benefit over no CSIT. Moreover, for a class of MIMO ICs, characterized by certain relationships on numbers of antennas at different terminals, the entire instantaneous-CSIT DoF region can be achieved with just delayed CSIT, and thus, for these ICs, delays involved in getting CSIT do not result in any loss of DoF. Further, it observed that over the MIMO BC, Shannon feedback is as good as delayed CSIT in the DoF-region sense, which however is not true for the IC. That is, for a class of MIMO ICs, Shannon feedback leads to a DoF improvement, even relative to delayed CSIT. This result is explained intuitively by pointing out that partial transmitter cooperation, induced by Shannon feedback, enables a more efficient form of interference alignment than what is feasible with just delayed CSIT. In addition, these results on delayed CSIT and Shannon feedback are strengthened by identifying scenarios of limited feedback, wherein not all channel fading coefficients and received signals are fed back, but still, the DoF region remains unaltered. As a case in point, for all MIMO BCs and for a large class of MIMO ICs, the DoF region with Shannon feedback is shown to be achievable with just the channel-output feedback.

Subsequently, we study a more general class of interference networks which consist of one or more full-duplex terminals that have simultaneous transmission and reception capabilities. These special terminals can aid communication between other transmitters and receivers, and hence, networks with such terminals are called cooperative interference networks. We study two important cooperative networks. The first one, called the layered multi-hop IC, is an IC wherein the transmitters can communicate with the receivers only through the intermediate layers of relays. The second network is termed as the MIMO IC (analogously, BC) with receiver cooperation, where the receivers are assumed to have full-duplex capability so that each of them can also transmit a signal over the same shared medium which is the heard by other receivers. We show, quite contrary to the conclusions available for interference networks, that over both of these cooperative networks, efficient interference alignment schemes can be worked out using the full-duplex terminals, even though the transmitters have no feedback whatsoever. Moreover, these schemes yield an improvement in the DoF region.

In particular, it is shown for the layered multi-hop network that having Shannon feedback to the relays obviates the need for having any feedback to the transmitters. This result is proved by developing a DoF-region-optimal retro-cooperative interference alignment (RCIA) scheme, which makes use of partial relay cooperation induced by Shannon feedback. In fact, a complementary conclusion is also derived, where delayed CSIT is proved to render feedback to the relays unnecessary. This result thus shows that even feedback-independent relaying strategies can yield a DoF improvement.

Next, on the front of our second cooperative network, it is proved for an important subclass that having receiver cooperation without feedback is as good as having Shannon feedback without receiver cooperation. In fact, a stronger conclusion is also derived, where any form of feedback is shown to be useless, in the presence of receiver cooperation. These results are obtained by proposing RCIA schemes, in which the receivers exchange useful information over cooperative links without creating any additional interference at each other.

#### Recommended Citation

Vaze, Chinmay Shankar, "Degrees of Freedom of Single-hop and Multi-hop MIMO Interference Networks with Feedback and Cooperation" (2012). *Electrical, Computer & Energy Engineering Graduate Theses & Dissertations*. 49.

https://scholar.colorado.edu/ecen_gradetds/49