Oren Somekh

Shannon-theoretic approach to a Gaussian cellular multiple-access channel with fading

Shannon-theoretic limits on the achievable throughput for a simple infinite cellular multiple-access channel (MAC) model (Wyner 1994) in the presence of fading are presented. In this model, which is modified to account for flat fading, the received signal, at a given cell-sites antenna, is the sum of the faded signals transmitted from all users within that cell plus an attenuation factor /spl alpha//spl isin/[0,1] times the sum of the faded signals received from the adjacent cells, accompanied by Gaussian additive noise. This model serves as a tractable model providing considerable insight into complex and analytically intractable real-world cellular communications. Both linear and planar cellular arrays are considered with exactly K active users in each cell. We assume a hyper-receiver, jointly decoding all of the users, incorporating the received signals from all of the active cell-sites. The hyper-receiver is assumed to be aware of the codebooks and realizations of the fading processes of all the users in the system. In this work we consider the intracell time-division multiple-access (TDMA) and the wideband (WB) protocols. We focus on the maximum reliably transmitted equal rate. Bounds to this rate are found for the intracell TDMA protocol by incorporating information-theoretic inequalities and the Chebyshev-Markov moment theory as applied to the limiting distribution of the eigenvalues of a quadratic form of tridiagonal random matrices. We demonstrate our results for the special case where the amplitudes of the fading coefficients are drawn from a Rayleigh distribution, i.e., Rayleigh fading. For this special case, we observe the rather surprising result that fading may increase the maximum equal rate, for a certain range of /spl alpha/ as compared to the nonfaded case. In this setting, the WB strategy, which achieves the maximum reliable equal rate of the model, is proved to be superior to the TDMA scheme. An upper bound to the maximum equal rate of the WB scheme is also obtained. This bound is asymptotically tight when the number of users is large (K/spl Gt/1). The asymptotic bound shows that the maximum equal rate of the WB scheme in the presence of fading is higher than the rate which corresponds to the nonfaded case for any intercell interference factor /spl alpha//spl isin/[0,1] signal-to-noise ratio (SNR) values. This result is found to be independent of the statistics of the fading coefficients.

Uplink Macro Diversity of Limited Backhaul Cellular Network

In this work, new achievable rates are derived for the uplink channel of a cellular network with joint multicell processing (MCP), where unlike previous results, the ideal backhaul network has finite capacity per cell. Namely, the cell sites are linked to the central joint processor via lossless links with finite capacity. The new rates are based on compress-and-forward schemes combined with local decoding. Further, the cellular network is abstracted by symmetric models, which render analytical treatment plausible. For this family of idealistic models, achievable rates are presented for both Gaussian and fading channels. The rates are given in closed form for the classical Wyner model and the soft-handover model. These rates are then demonstrated to be rather close to the optimal unlimited backhaul joint processing rates, even for modest backhaul capacities, supporting the potential gain offered by the joint MCP approach. Particular attention is also given to the low-signal-to-noise ratio (SNR) characterization of these rates through which the effect of the limited backhaul network is explicitly revealed. In addition, the rate at which the backhaul capacity should scale in order to maintain the original high-SNR characterization of an unlimited backhaul capacity system is found.

Downlink multicell processing with limited-backhaul capacity

Multicell processing in the form of joint encoding for the downlink of a cellular system is studied under the assumption that the base stations (BSs) are connected to a central processor (CP) via finitecapacity links (finite-capacity backhaul). To obtain analytical insight into the impact of finite-capacity backhaul on the downlink throughput, the investigation focuses on a simple linear cellular system (as for a highway or a long avenue) based on theWyner model. Several transmission schemes are proposed that require varying degrees of knowledge regarding the system codebooks at the BSs. Achievable rates are derived in closed-form and compared with an upper bound. Performance is also evaluated in asymptotic regimes of interest (high backhaul capacity and extreme signal-to-noise ratio, SNR) and further corroborated by numerical results. The major finding of this work is that even in the presence of oblivious BSs (that is, BSs with no information about the codebooks) multicell processing is able to provide ideal performance with relatively small backhaul capacities, unless the application of interest requires high data rate (i.e., high SNR) and the backhaul capacity is not allowed to increase with the SNR. In these latter cases, some form of codebook information at the BSs becomes necessary.

Local Base Station Cooperation Via Finite-Capacity Links for the Uplink of Linear Cellular Networks

Cooperative decoding at the base stations (or access points) of an infrastructure wireless network is currently well recognized as a promising approach for intercell interference mitigation, thus enabling high frequency reuse. Deployment of cooperative multicell decoding depends critically on the tolopology and quality of the available backhaul links connecting the base stations. This work studies a scenario where base stations are connected only if in adjacent cells, and via finite-capacity links. Relying on a linear Wyner-type cellular model with no fading, achievable rates are derived for the two scenarios where base stations are endowed only with the codebooks of local (in-cell) mobile stations, or also with the codebooks used in adjacent cells. Moreover, both uni- and bidirectional backhaul links are considered. The analysis sheds light on the impact of codebook information, decoding delay, and network planning (frequency reuse) on the performance of multicell decoding as enabled by local and finite-capacity backhaul links. Analysis in the high-signal-to-noise ratio (SNR) regime and numerical results validate the main conclusions.

Cooperative Multicell Zero-Forcing Beamforming in Cellular Downlink Channels

In this work, a multicell cooperative zero-forcing beamforming (ZFBF) scheme combined with a simple user selection procedure is considered for the Wyner cellular downlink channel. The approach is to transmit to the user with the ldquobestrdquo local channel in each cell. The performance of this suboptimal scheme is investigated in terms of the conventional sum-rate scaling law and the sum-rate offset for an increasing number of users per cell. We term this characterization of the sum-rate for large number of users as high-load regime characterization, and point out the similarity of this approach to the standard affine approximation used in the high-signal-to-noise ratio (SNR) regime. It is shown that, under an overall power constraint, the suboptimal cooperative multicell ZFBF scheme achieves the same sum-rate growth rate and slightly degraded offset law, when compared to an optimal scheme deploying joint multicell dirty-paper coding (DPC), asymptotically with the number of users per cell. Moreover, the overall power constraint is shown to ensure in probability, equal per-cell power constraints when the number of users per-cell increases.

An information theoretic view of distributed antenna processing in cellular systems

This chapter presents a survey of information theoretic results available on DAS in cellular systems. The treatment focuses on the derivation of the sum-rate of different inter-cell and intra-cell communications strategies for both uplink and downlink. A simple symmetric family of cellular models in which the inter-cell interferences are emerging from a the adjacent cells only is considered. Although hardly realistic, this family of models accounts for essential parameters of cellular systems such as inter-cell interference and fading. Whenever computation of the sum-rate is intractable or yields little insight into the problem, asymptotic performance criteria (e.g. extreme-SNR parameters) are evaluated. Emphasis is placed on the assessment of benefits of cooperation among APs (i.e. joint detection/precoding).The rapid growth in mobile communications has led to an increasing demand for wideband high data rate communications services. In recent years, the Distributed Antenna System (DAS) has emerged as a promising candidate beyond 3G and 4G mobile communications. Distributed Antenna Systems: Open Architecture for Future Wireless Communications is a comprehensive technical guide that covers the fundamental concepts, recent advances and open issues of the DAS. The topic is explored with various key challenges in diverse scenarios, including architecture, capacity, connectivity, scalability, medium access control, scheduling, dynamic channel assignment and cross-layer optimization. The primary focus of this book is the introduction of concepts, effective protocols, system integration, performance analysis techniques, simulations and experiments, and more importantly, future research directions in the DAS. The first part of the book introduces DAS fundamentals, including channel models and theoretical issues, examining the capacity of the DAS with different structures. Concentrating on the MAC and protocols for the DAS, the second part of the book includes information on distributed signal processing, optimal resource allocation, cooperative MAC protocols, cross layer design, and distributed organization. The third part presents case studies and applications of the DAS, including experiment, RF engineering, and applications.

Estimating Sizes of Social Networks via Biased Sampling

Abstract This article presents algorithms for estimating the number of users in online social networks. Although such networks sometimes publish such statistics, there are good reasons to validate their reports. The proposed schemes can also estimate the cardinality of network subpopulations. Because this information is seldom voluntarily divulged, such algorithms must operate only by interacting with the social networks’ public Applications Programming Interfaces (APIs). No other external information can be assumed. Due to obvious traffic and privacy concerns, the number of such interactions is severely limited. We therefore focus on minimizing the number of API interactions needed for producing good-sized estimates. We adopt the standard abstraction of social networks as undirected graphs and perform random walk-based node sampling. By counting the number of collisions or nonunique nodes in the sample, we produce a size estimate. Then we show analytically that the estimate error vanishes with high probability for fewer samples than those required by prior-art algorithms. Moreover, although provably correct for any graph, our algorithms excel when applied to social network-like graphs. The proposed algorithms were evaluated on synthetic and real social networks such as Facebook, IMDB, and DBLP. Our experiments corroborate the theoretical results and demonstrate the effectiveness of the algorithms.

Uplink Macro Diversity with Limited Backhaul Capacity

In this contribution we present new achievable rates, for the non-fading uplink channel of a cellular network, with joint cell-site processing, where unlike previous results, the error-free backhaul network has finite capacity per-cell. Namely, the cell-sites are linked to the central joint processor via lossless links with finite capacity. The cellular network is modeled by the circular Wyner model, which yields closed form expressions for the achievable rates. For this idealistic model, we present achievable rates for cell-sites that use compress-and forward scheme, combined with local decoding, and inter-cell time-sharing. These rates are then demonstrated to be rather close to the optimal unlimited backhaul joint processing rates, already for modest backhaul capacities, supporting the potential gain offered by the joint cell-site processing approach.

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 and 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 that alleviates these limitations, without sacrificing the system throughput scaling in the regime of large n. The scheme entails a two-hop communication protocol, in which sources communicate with destinations only through half-duplex relays. All nodes operate in a completely distributed fashion, with no cooperation. The key idea is to schedule at each hop only a subset of nodes that can benefit from multiuser diversity. To select the source and destination nodes for each hop, CSI is required at receivers (relays for the first hop, and destination nodes for the second hop), and an index-valued CSI feedback at 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 log 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. Simulation results indicate a rather fast convergence to the asymptotic limits with the systems size, demonstrating the practical importance of the scaling results.

Uplink Throughput of TDMA Cellular Systems with Multicell Processing and Amplify-and-Forward Cooperation Between Mobiles

Cooperation between base stations and collaborative transmission between mobile terminals are two technologies currently under study as promising paradigms for next generation communications systems. In this paper, we provide a first look to the interplay between these two approaches by studying the per-cell achievable sum-rate (throughput) of different cooperative protocols under a simplified model for the uplink of a TDMA cellular system. The analysis is limited to non-regenerative (amplify-and-forward) cooperation schemes between terminals for theirsimplicity and appeal to a practical implementation. A closed form expression for the (asymptotic) achievable rate of multicell processing combined with amplify-and-forward collaboration at the terminals is derived for an AWGN (i.e., no fading) scenario. Moreover, the impact of fading is investigated numerically, allowing to draw some conclusions on the impact of multicell diversity (or macrodiversity) on the performance of collaborative schemes among the terminals. In particular, we show that while AF cooperation is generally advantageous for single cell processing (i.e., with no collaboration between base stations), its benefits when combined with multicell processing are limited to the regime of low to moderate transmission rates.