On the Capacity of the Finite Field Counterparts of Wireless Interference Networks

This work explores how degrees of freedom (DoF) results from wireless networks can be translated into capacity results for their finite field counterparts that arise in network coding applications. The main insight is that scalar (SISO) finite field channels over $\mathbb{F}_{p^n}$ are analogous to n x n vector (MIMO) channels in the wireless setting, but with an important distinction -- there is additional structure due to finite field arithmetic which enforces commutativity of matrix multiplication and limits the channel diversity to n, making these channels similar to diagonal channels in the wireless setting. Within the limits imposed by the channel structure, the DoF optimal precoding solutions for wireless networks can be translated into capacity optimal solutions for their finite field counterparts. This is shown through the study of the 2-user X channel and the 3-user interference channel. Besides bringing the insights from wireless networks into network coding applications, the study of finite field networks over $\mathbb{F}_{p^n}$ also touches upon important open problems in wireless networks (finite SNR, finite diversity scenarios) through interesting parallels between p and SNR, and n and diversity.Comment: Full version of paper accepted for presentation at ISIT 201

Information theoretic limits of MIMO wireless networks with bounded input and imperfect CSIT

In this thesis, we investigate some information theoretic limits of two specific types of MIMO wireless networks. In the first one, the effect of channel uncertainty at the transmitter (due to estimation error, feedback latency, and so on) in MIMO broadcast channels is investigated. In this setting, we capture this imperfectness in the bounds for the DoF region of the channel. The second one is the point to point deterministic MIMO channel with input amplitude constraint. For certain settings, the capacity of this channel is derived, while for the general problem, upper and lower bounds for the capacity are obtained.Open Acces

Fundamental Limits in MIMO Broadcast Channels

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system paramaters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling

Performance analysis of spatially distributed MIMO systems

With the growing popularity of ad-hoc sensor networks, spatially distributed multiple-input multiple-output (MIMO) systems have drawn a lot of attention. This work considers a spatially distributed MIMO system with randomly distributed transmit and receive antennas over spatial regions. The authors use the modal decomposition of wave propagation to analyse the performance limits of such system, since the sampling of the spatial regions populated with antennas is a form of mode excitation. Specifically, they decompose signals into orthogonal spatial modes and apply concepts of MIMO communications to quantify the instantaneous capacity and the outage probability. The authors’ analysis shows that analogous to conventional point-to-point MIMO system, the instantaneous capacity of spatially distributed MIMO system over Rayleigh fading channel is equivalent to a Gaussian random variable. Afterwards, they derive an accurate closed-form expression for the outage probability of proposed system utilising the definition of instantaneous capacity. Besides, in rich scattering environment, the spatially distributed MIMO system provides best performance when the spatial regions are of same size, and each region is equipped with equal number of antennas. Furthermore, to facilitate the total transmit power allocation among the channels, they propose an algorithm which indicates a significant performance improvement over conventional equal transmit power allocation scheme, even at low signal-to-noise ratio