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-SNR, when an intra-cell 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

Cellular Systems with Full-Duplex Compress-and-Forward Relaying and Cooperative Base Stations

In this paper the advantages provided by multicell processing of signals transmitted by mobile terminals (MTs) which are received via dedicated relay terminals (RTs) are studied. It is assumed that each RT is capable of full-duplex operation and receives the transmission of adjacent relay terminals. Focusing on intra-cell TDMA and non-fading channels, a simplified relay-aided uplink cellular model based on a model introduced by Wyner is considered. Assuming a nomadic application in which the RTs are oblivious to the MTs' codebooks, a form of distributed compress-and-forward (CF) scheme with decoder side information is employed. The per-cell sum-rate of the CF scheme is derived and is given as a solution of a simple fixed point equation. This achievable rate reveals that the CF scheme is able to completely eliminate the inter-relay interference, and it approaches a ``cut-set-like'' upper bound for strong RTs transmission power. The CF rate is also shown to surpass the rate of an amplify-and-forward scheme via numerical calculations for a wide range of the system parameters.Comment: Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 6 - 11, 200

Distributed MIMO Systems with Oblivious Antennas

A scenario in which a single source communicates with a single destination via a distributed MIMO transceiver is considered. The source operates each of the transmit antennas via finite-capacity links, and likewise the destination is connected to the receiving antennas through capacity-constrained channels. Targeting a nomadic communication scenario, in which the distributed MIMO transceiver is designed to serve different standards or services, transmitters and receivers are assumed to be oblivious to the encoding functions shared by source and destination. Adopting a Gaussian symmetric interference network as the channel model (as for regularly placed transmitters and receivers), achievable rates are investigated and compared with an upper bound. It is concluded that in certain asymptotic and non-asymptotic regimes obliviousness of transmitters and receivers does not cause any loss of optimality.Comment: In Proc. of the 2008 IEEE International Symposium on Information Theory (ISIT 2008), Toronto, Ontario, Canad

Cellular Systems with Full-Duplex Amplify-and-Forward Relaying and Cooperative Base-Stations

In this paper the benefits provided by multi-cell processing of signals transmitted by mobile terminals which are received via dedicated relay terminals (RTs) are assessed. Unlike previous works, each RT is assumed here to be capable of full-duplex operation and receives the transmission of adjacent relay terminals. Focusing on intra-cell TDMA and non-fading channels, a simplified uplink cellular model introduced by Wyner is considered. This framework facilitates analytical derivation of the per-cell sum-rate of multi-cell and conventional single-cell receivers. In particular, the analysis is based on the observation that the signal received at the base stations can be interpreted as the outcome of a two-dimensional linear time invariant system. Numerical results are provided as well in order to provide further insight into the performance benefits of multi-cell processing with relaying.Comment: To appear in the Proc. of the 2007 IEEE International Symposium on Information Theor

Budget-Constrained Item Cold-Start Handling in Collaborative Filtering Recommenders via Optimal Design

It is well known that collaborative filtering (CF) based recommender systems provide better modeling of users and items associated with considerable rating history. The lack of historical ratings results in the user and the item cold-start problems. The latter is the main focus of this work. Most of the current literature addresses this problem by integrating content-based recommendation techniques to model the new item. However, in many cases such content is not available, and the question arises is whether this problem can be mitigated using CF techniques only. We formalize this problem as an optimization problem: given a new item, a pool of available users, and a budget constraint, select which users to assign with the task of rating the new item in order to minimize the prediction error of our model. We show that the objective function is monotone-supermodular, and propose efficient optimal design based algorithms that attain an approximation to its optimum. Our findings are verified by an empirical study using the Netflix dataset, where the proposed algorithms outperform several baselines for the problem at hand.Comment: 11 pages, 2 figure

Opportunistic Relaying in Wireless Networks

Relay networks having $n$ source-to-destination pairs and $m$ half-duplex relays, all operating in the same frequency band in the presence of block fading, are analyzed. This setup has attracted significant attention and several relaying protocols have been reported in the literature. However, most of the proposed solutions require either centrally coordinated scheduling or detailed channel state information (CSI) at the transmitter side. Here, an opportunistic relaying scheme is proposed, which alleviates these limitations. The scheme entails a two-hop communication protocol, in which sources communicate with destinations only through half-duplex relays. The key idea is to schedule at each hop only a subset of nodes that can benefit from \emph{multiuser diversity}. To select the source and destination nodes for each hop, it requires only CSI at receivers (relays for the first hop, and destination nodes for the second hop) and an integer-value CSI feedback to the transmitters. For the case when $n$ is large and $m$ is fixed, it is shown that the proposed scheme achieves a system throughput of $m/2$ bits/s/Hz. In contrast, the information-theoretic upper bound of $(m/2)\log \log n$ bits/s/Hz is achievable only with more demanding CSI assumptions and cooperation between the relays. Furthermore, it is shown that, under the condition that the product of block duration and system bandwidth scales faster than $\log n$, the achievable throughput of the proposed scheme scales as $\Theta ({\log n})$. Notably, this is proven to be the optimal throughput scaling even if centralized scheduling is allowed, thus proving the optimality of the proposed scheme in the scaling law sense.Comment: 17 pages, 8 figures, To appear in IEEE Transactions on Information Theor

Distributed Exploration in Multi-Armed Bandits

We study exploration in Multi-Armed Bandits in a setting where $k$ players collaborate in order to identify an $\epsilon$-optimal arm. Our motivation comes from recent employment of bandit algorithms in computationally intensive, large-scale applications. Our results demonstrate a non-trivial tradeoff between the number of arm pulls required by each of the players, and the amount of communication between them. In particular, our main result shows that by allowing the $k$ players to communicate only once, they are able to learn $\sqrt{k}$ times faster than a single player. That is, distributing learning to $k$ players gives rise to a factor $\sqrt{k}$ parallel speed-up. We complement this result with a lower bound showing this is in general the best possible. On the other extreme, we present an algorithm that achieves the ideal factor $k$ speed-up in learning performance, with communication only logarithmic in $1/\epsilon$