Nathan Levy

Cooperative Wireless Cellular Systems: An Information-Theoretic View

In this monograph, the impact of cooperation on the performance of wireless cellular systems is studied from an information-theoretic standpoint, focusing on simple formulations typically referred to as Wynertype models. Following ongoing research and standardization efforts, the text covers two main classes of cooperation strategies. The first class is cooperation at the base station (BS) level, which is also known as Multi-Cell Processing (MCP), network Multiple-Input MultipleOutput (MIMO), or Coordinated Multi-Point transmission/reception (CoMP). With MCP, cooperative decoding, for the uplink, or encoding, for the downlink, is enabled at the BSs. MCP is made possible by the presence of an architecture of, typically wired, backhaul links connecting individual BSs to a central processor (CP) or to one another. The second class of cooperative strategies allows cooperation in the form of relaying for conveying data between Mobile Stations (MSs) and BSs in either the uplink or the downlink. Relaying can be enabled by two possible architectures. A first option is to deploy dedicated Relay Stations (RSs) that are tasked with forwarding uplink or downlink traffic. The second option is for the MSs to act as RSs for other MSs. MCP is first studied under ideal conditions on the backhaul links, namely by assuming that all BSs are connected to a CP with unlimitedcapacity links. Both Gaussian (nonfading) and flat-fading channels are analyzed, for the uplink and the downlink, and analytical insights are drawn into the performance advantages of MCP in different relevant operating regimes. Performance comparison is performed with standard Single-Cell Processing (SCP) techniques, whereby each BS decodes, in the uplink, or encodes, in the downlink, independently, as implemented with different spatial reuse factors. Then, practical constraints on the backhaul architecture enabling MCP are introduced. Specifically, three common settings are studied. In the first, all the BSs are connected to a CP via finite-capacity links. In the second, only BSs in adjacent cells are connected via (finite-capacity) backhaul links. In the third, only a subset of BSs is connected to a CP for joint encoding/decoding (clustered cooperation). Achievable rates for the three settings are studied and compared for both the uplink and the downlink. The performance advantages of relaying are analyzed for cellular systems with dedicated RSs and with cooperative MSs. Different techniques are reviewed that require varying degrees of information about system parameters at the MSs, RSs, and BSs. Performance is investigated with both MCP and SCP, revealing a profound interplay between cooperation at the BS level and relaying. Finally, various open problems are pointed out.

A cognitive network with clustered decoding

We study the uplink of a linear cellular model featuring short range inter-cell interference. Specifically, we consider a K-transmitter/K-receiver interference network where the signal transmitted by a given transmitter is interfered by the signal sent by the transmitter to its left. We assume that each transmitter has side-information consisting of the messages of the Jl users to its left and the Jr users to its right, and that each receiver can decode its message using the signals received at its own antenna, at the il antennas to its left, and at the ir antennas to its right. For this setting, we characterize the multiplexing gain, i.e., the asymptotic logarithmic growth of the sum-rate capacity at high SNR, and point out interesting duality aspects. We also present results on the multiplexing gain of a symmetric version of this network where the signal sent by a given transmitter is interfered by the signals sent by the transmitter to its left and the transmitter to its right.

Information Theoretic Aspects of Users' Activity in a Wyner-Like Cellular Model

We address an application of multiuser information theory to the study of the uplink of a communication system with randomly activated users. We first assume that all the messages are jointly decoded by a multicell processor. Then, we relax this hypothesis and study the network under the assumption that the decoding of the message of a given user is only based on the messages received within a given distance of this user. Our results show that for a general class of models, under adequate hypothesis, local decoding performs almost as well as global decoding and that the difference converges to 0 exponentially fast as the size of the decoding window goes to infinity.

Clustered Local Decoding for Wyner-Type Cellular Models

We study the uplink of Wyner-type cellular models featuring short range inter-cell interference. We assume that the decoding of the message sent by a given transmitter is done locally, that is using only the signals received at the antennas in its vicinity.

Cognitive Wyner Networks With Clustered Decoding

We study an interference network where equally numbered transmitters and receivers lie on two parallel lines, with each transmitter opposite its intended receiver. We consider two short-range interference models: the asymmetric network, where the signal sent by each transmitter is interfered only by the signal sent by its left neighbor (if present), and a symmetric network, where it is interfered by both its left and its right neighbors. Each transmitter is cognizant of its own message, the messages of the t_ℓ transmitters to its left, and the messages of the t_r transmitters to its right. Each receiver decodes its message based on the signals received at its own antenna, at the r_r receive antennas to its left, and at the r_r receive antennas to its right. For such networks, we provide upper and lower bounds on the multiplexing gain, i.e., on the high signal-to-noise ratio asymptotic logarithmic growth of the sum-rate capacity. In some cases, our bounds coincide, e.g., for the asymmetric network. Our results exhibit an equivalence between the transmitter sideinformation parameters t_ℓ, tr and the receiver side-information parameters r_ℓ, r_r in the sense that increasing/decreasing t_ℓ or t_r by a positive integer δ has the same effect on the multiplexing gain as increasing/decreasing r_ℓ or r_r by δ. Moreover-even in asymmetric networks-there is an equivalence between the left side-information parameters (t_ℓ, r_ℓ) and the right sideinformation parameters (t_r, r_r).

On Certain Large Random Hermitian Jacobi Matrices With Applications to Wireless Communications

In this paper we study the spectrum of certain large random Hermitian Jacobi matrices. These matrices are known to describe certain communication setups. In particular, we are interested in an uplink cellular channel which models mobile users experiencing a soft-handoff situation under joint multicell decoding. Considering rather general fading statistics we provide a closed-form expression for the per-cell sum-rate of this channel in high signal-to-noise ratio (SNR), when an intra-cell time-division multiple-access (TDMA) protocol is employed. Since the matrices of interest are tridiagonal, their eigenvectors can be considered as sequences with second-order linear recurrence. Therefore, the problem is reduced to the study of the exponential growth of products of two-by-two matrices. For the case where K users are simultaneously active in each cell, we obtain a series of lower and upper bound on the high-SNR power offset of the per-cell sum-rate, which are considerably tighter than previously known bounds.

On Information Rates of the Fading Wyner Cellular Model via the Thouless Formula for the Strip

In this paper, we apply the theory of random Schrödinger operators to the analysis of multiusers communication channels similar to the Wyner model, which are characterized by short-range intercell interference. With H the channel transfer matrix, HHf is a narrow band matrix, a fact that does not permit the use of classical random matrices theory. On the other hand, HHf is in many aspects similar to a random Schrödinger operator. We relate the per-cell sum-rate capacity of the channel to the integrated density of states of a random Schrödinger operator; the latter is then related to the top Lyapunov exponent of a random sequence of matrices via a version of the Thouless formula. We also derive several bounds on the limiting per-cell sum-rate capacity, some based on the theory of random Schrödinger operators, and some derived from information theoretical considerations. Finally, we get explicit results in the high-signal-to-noise ratio (SNR) regime for some particular cases.

Central limit theorem and large deviations of the fading Wyner cellular model via product of random matrices theory

AbstractWe apply the theory of products of random matrices to the analysis of multi-user communication channels similar to the Wyner model, which are characterized by short-range intra-cell broadcasting. We study fluctuations of the per-cell sum-rate capacity in the non-ergodic regime and provide results of the type of the central limit theorem (CLT) and large deviations (LD). Our results show that CLT fluctuations of the per-cell sum-rate Cm are of order

On certain large random Hermitian Jacobi matrices with applications to wireless communications

1/\sqrt m