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.

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.

On the Spectrum of Large Random Hermitian Finite-Band Matrices

The open problem of calculating the limiting spectrum (or its Shannon transform) of increasingly large random Hermitian finite-band matrices is described. In general, these matrices include a finite number of non-zero diagonals around their main diagonal regardless of their size. Two different communication setups which may be modeled using such matrices are presented: a simple cellular uplink channel, and a time varying inter-symbol interference channel. Selected recent information-theoretic works dealing directly with such channels are reviewed. Finally, several characteristics of the still unknown limiting spectrum of such matrices are listed, and some reflections are touched upon.

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.

Cooperative Multi-Cell Networks: Impact of Limited-Capacity Backhaul and Inter-Users Links

Cooperative technology is expected to have a great impact on the performance of cellular or, more generally, infrastructure networks. Both multicell processing (cooperation among base stations) and relaying (cooperation at the user level) are currently being investigated. In this presentation, recent results regarding the performance of multicell processing and user cooperation under the assumption of limited-capacity interbase station and inter-user links, respectively, are reviewed. The survey focuses on related results derived for non-fading uplink and downlink channels of simple cellular system models. The analytical treatment, facilitated by these simple setups, enhances the insight into the limitations imposed by limited-capacity constraints on the gains achievable by cooperative techniques.

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.