Multiuser Wireless Sytems and Networks
(Project Proposal)
1 Introduction

MIMO communication and cognitive radios have both been two of the most productive areas of research thelast decade in the wireless communication community. Generally speaking, a cognitive radio automatically adapts its transmission and/or reception parameters in a way that it is bene_cial to him and/or to the entirewireless communication network. A typical paradigm (and the one that this project will assume) is onewhere secondary users (SUs) communicate (radios that do not \own" the wireless resources that are usingfor their communication) and coexist with the primary users (PUs) without harming their communication.MIMO technology provides a means for the SUs to adapt their transmission in a way that the PUs are not severely a_ected.
In this project, my starting point will be a recent work from Yair Noam and Andrea Goldsmith [1],where the authors propose a Null-Space Learning algorithm for Spatial coexistence. In few words, the SUTransmitter learns the null-space of the PU receiver and then transmits only in this subspace so as to causeminimal interference. The goal of this project is to extend this work for time-varying channels and to proposetracking algorithms that could mitigate the e_ects of a changing wireless environment.In section 2 we are going to present the framework in which we are going to work on, and in section 3we are going to provide a detailed description of the goals and plans of this project.

2 Starting Point

The starting point of this project is the work in [1]. In the latter, the authors assume a static scenario, where all the channels are time-invariant. As shown in Figure 1, H1;2 denotes the channel matrix between the secondary transmitter (SU-Tx) and the primary receiver (PU-Rx), H2;1 denotes the channel matrix between the primary transmitter (PU-Tx) and the SU-Tx and H1;1 denotes the channel matrix between the
PU-Tx and the PU-Rx. Note that the secondary receiver is not depicted in the _gure, since it is irrelevant in our current discussion. Using the Figure we get that: y1(t) = H11x1(t) +H12x2(t) + v1(t) 8t 2 N
The main idea of the current framework is the following: The SU-Tx needs to learn the null space of the matrix H12 through an algorithm without any actual cooperation with the PU-Rx or the PU-Tx. In this work, the authors propose an iterative technique that is based on the Jacobi eigenvalue method, assuming that the primary network has a power control mechanism that \reacts" to the change of interference of the PU-Rx. The SU-Tx senses this reaction through the H2;1 channel and thus is able to make intelligent decisions. In another work from the same authors, the PU-Rx sends a beacon with the interference it senses.
In that case, the power control mechanism is not needed and actually the PU-Tx does not take any part in the learning process.
More speci_cally, the SU-Tx sends a sequence of messages fx(n)g (that are explicitly de_ned in [1]) and through the feedback that it gets (with either two mechanisms described above), it manages to _nd the null-space of the matrix H12. More details on the algorithm is out of scope of this proposal and are omitted.