Multi-Cell MIMO Cooperative Networks: A New Look at Interference

This paper presents an overview of the theory and currently known techniques for multi-cell MIMO (multiple input multiple output) cooperation in wireless networks. In dense networks where interference emerges as the key capacity-limiting factor, multi-cell cooperation can dramatically improve the system performance. Remarkably, such techniques literally exploit inter-cell interference by allowing the user data to be jointly processed by several interfering base stations, thus mimicking the benefits of a large virtual MIMO array. Multi-cell MIMO cooperation concepts are examined from different perspectives, including an examination of the fundamental information-theoretic limits, a review of the coding and signal processing algorithmic developments, and, going beyond that, consideration of very practical issues related to scalability and system-level integration. A few promising and quite fundamental research avenues are also suggested.

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title: Cooperative Communications
abstract: This article reviews progress in cooperative communication networks. Our survey is by no means exhaustive. Instead, we assemble a representative sample of recent results to serve as a roadmap for the area. Our emphasis is on wireless networks, but many of the results apply to cooperation in wireline networks and mixed wireless/wireline networks. We intend our presentation to be a tutorial for the reader who is familiar with information theory concepts but has not actively followed the field. For the active researcher, this contribution should serve as a useful digest of significant results. This article is meant to encourage readers to find new ways to apply the ideas of network cooperation and should make the area sufficiently accessible to network designers to contribute to the advancement of networking practice.

title: From theory to practice: an overview of MIMO space-time coded wireless systems
abstract: This paper presents an overview of progress in the area of multiple input multiple output (MIMO) space-time coded wireless systems. After some background on the research leading to the discovery of the enormous potential of MIMO wireless links, we highlight the different classes of techniques and algorithms proposed which attempt to realize the various benefits of MIMO including spatial multiplexing and space-time coding schemes. These algorithms are often derived and analyzed under ideal independent fading conditions. We present the state of the art in channel modeling and measurements, leading to a better understanding of actual MIMO gains. Finally, the paper addresses current questions regarding the integration of MIMO links in practical wireless systems and standards.

title: Soft handoff extends CDMA cell coverage and increases reverse link capacity
abstract: The effect of handoff techniques on cell coverage and reverse link capacity is investigated for a spread spectrum CDMA system. It is shown that soft handoff increases both parameters significantly relative to conventional hard handoff.

title: CDMA: Principles of Spread Spectrum Communication
abstract: 1.   Basic Limitations of the Conventional Approach. Spread Spectrum Principles. Organization of the Book. 2. Random and Pseudorandom Signal Generation.  Pseudorandom Sequences. Maximal Length Linear Shift Register Sequences. Randomness Properties of MLSR Sequences.  Generating Pseudorandom Signals (Pseudonoise) from Pseudorandom Sequences. First- and Second-Order Statistics of Demodulator Output in Multiple Access Interference.  Bound for Bandlimited Spectrum. Error Probability for BPSK or QPSK with Constant Signals in Additive Gaussian Noise and Interference.  Optimum Receiver Filter for Bandlimited Spectrum. 3. Synchronization of Pseudorandom Signals.  Acquisition of Pseudorandom Signal Timing.  Testing for BPSK Spreading.  Testing for QPSK Spreading. Effect of Frequency Error. Additional Degradation When N is Much Less Than One Period. Detection and False Alarm Probabilities. Fixed Signals in Gaussian Noise (L=1). Fixed Signals in Gaussian Noise with Postdetection Integration (L>1). Rayleigh Fading Signals (L>/=1). The Search Procedure and Acquisition Time. Single-Pass Serial Search (Simplified). Single-Pass Serial Search (Complete). Multiple Dwell Serial Search. Time Tracking of Pseudorandom Signals. Early-Late Gate Measurement Statistics. Time Tracking Loop. Carrier Synchronization.  Likelihood Functions and Probability Expressions. Bayes and Neyman-Pearson Hypothesis Testing. Coherent Reception in Additive White Gaussian Noise. Noncoherent Reception in AWGN for Unfaded Signals. Noncoherent Reception of Multiple Independent Observations of Unfaded Signals in AWGN. Noncoherent Reception of Rayleigh-Faded Signals in AWGN. 4. Modulation and Demodulation of Spread Spectrum Signals in Multipath and Multiple Access Interference.  Chernoff and Battacharyya Bounds. Bounds for Gaussian Noise Channel.  Bound for Time-Synchronous Multiple Access Interference with BPSK Spreading. Chernoff Bound for Time-Synchronous Multiple Access Interference with QPSK Spreading. Improving the Chernoff Bound by a Factor of 2.  Signal Structure and Exploitation. Pilot-Aided Coherent Multipath Demodulation. Chernoff Bounds on Error Probability for Coherent Demodulation with Known Path Parameters. Rayleigh and Rician Fading Multipath Components.  Quasi-optimum Noncoherent Multipath Reception for M-ary Orthogonal Modulation. Performance Bounds. Search Performance for Noncoherent Orthogonal M-ary Demodulators. Power Measurement and Control for Noncoherent Orthogonal M-ary Demodulators. Power Control Loop Performance. Power Control Implications.  Bound with Imperfect Parameter Estimates. 5. Coding and Interleaving.  Interleaving to Achieve Diversity. Forward Error Control Coding - Another Means to Exploit Redundancy. Convolutional Code Structure. Maximum Likelihood Decoder - Viterbi Algorithm. Generalization of the Preceding Example. Convolutional Code Performance Evaluation. Error Probability for Tailed-off Block. Bit Error Probability. Generalizations of Error Probability Computation.  Generalization to Arbitrary Memoryless Channels - Coherent and Noncoherent. Error Bounds for Binary-Input, Output-Symmetric Channels with Integer Metrics. A Near-Optimal Class of Codes for Coherent Spread Spectrum Multiple Access.  Decoder Implementation. Generating Function and Performance. Performance Comparison and Applicability. Orthogonal Convolutional Codes for Noncoherent Demodulation of Rayleigh Fading Signals.  Performance for L-Path Rayleigh Fading.   Improved Bounds for Symmetric Memoryless Channels and the AWGN Channel.  Upper Bound on Free Distance of Rate 1/n Convolutional Codes. 6. Capacity, Coverage, and Control of Spread Spectrum Multiple Access Networks. General.  Propagation Model. Single-Cell Reception - Hard Handoff. Soft Handoff Reception by the Better of the Two Nearest Cells. Soft Handoff Reception by the Best of Multiple Cells. Cell Coverage Issues with Hard and Soft Handoff. Hard Handoff. Soft Handoff. Erlang Capacity of Reverse Links. Erlang Capacity for Conventional Assigned-Slot Multiple Access. Spread Spectrum Multiple Access Outage - Single Cell and Perfect Power Control. Outage with Multiple-Cell Interference. Outage with Imperfect Power Control. An Approximate Explicit Formula for Capacity with Imperfect Power Control. Designing for Minimum Transmitted Power. Capacity Requirements for Initial Accesses. Erlang Capacity of Forward Links. Forward Link Power Allocation. Soft Handoff Impact on Forward Link. Orthogonal Signals for Same-Cell Users.  Reduction with Multisectored and Distributed Antennas.  Epilogue.

title: Capacity and power control in spread spectrum macrodiversity radio networks
abstract: What is the capacity of the uplink of a radio network of receivers? We consider a spread spectrum model in which each user is decoded by all the receivers in the network (macrodiversity). We use a carrier-to-interference performance criterion that we derive from Shannon theory; each user must find the right transmitter power level to satisfy its carrier-to interference constraint. Satisfying this requirement for all users is equivalent to solving a fixed point problem. We use this power control problem to derive the network capacity region and find that the feasibility of a configuration of users is independent of their positions in the network; each user can be assigned a bandwidth that is independent of the user's position in the network. Our capacity region is an upper bound over all schemes that treat the interference of other users as pure noise. To show that the capacity can be realized in practice, we propose a decentralized power adaptation algorithm and prove global convergence to the fixed point via a monotonicity argument.

title: Resource pooling and effective bandwidths in CDMA networks with multiuser receivers and spatial diversity
abstract: Much of the performance analysis on multiuser receivers for direct-sequence code-division multiple-access (CDMA) systems is focused on worst case near-far scenarios. The user capacity of power-controlled networks with multiuser receivers are less well-understood. Tse and Hanly (see ibid., vol.45, p.541-657, 1999) have shown that under some conditions, the user capacity of an uplink power-controlled CDMA cell for several important linear receivers can be very simply characterized via a notion of effective bandwidth. We show that these results extend to the case of antenna arrays. We consider a CDMA system consisting of users transmitting to an antenna array with a multiuser receiver, and obtain the limiting signal-to-interference (SIR) performance in a large system using random spreading sequences. Using this result, we show that the SIR requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own requirement. Our results show that the total number of degrees of freedom of the whole system is the product of the spreading gain and the number of antennas. In the case when the fading distributions to the antennas are identical, we show that a curious phenomenon of "resource pooling" arises: the multiantenna system behaves like a system with only one antenna but with the processing gain the product of the processing gain of the original system and the number of antennas, and the received power of each user the sum of the received powers at the individual antennas.

title: Shannon-theoretic approach to a Gaussian cellular multiple-access channel
abstract: We obtain Shannon-theoretic limits for a very simple cellular multiple-access system. In our model the received signal at a given cell site is the sum of the signals transmitted from within that cell plus a factor /spl alpha/ (0/spl les//spl alpha//spl les/1) times the sum of the signals transmitted from the adjacent cells plus ambient Gaussian noise. Although this simple model is scarcely realistic, it nevertheless has enough meat so that the results yield considerable insight into the workings of real systems. We consider both a one dimensional linear cellular array and the familiar two-dimensional hexagonal cellular pattern. The discrete-time channel is memoryless. We assume that N contiguous cells have active transmitters in the one-dimensional case, and that N/sup 2/ contiguous cells have active transmitters in the two-dimensional case. There are K transmitters per cell. Most of our results are obtained for the limiting case as N/spl rarr//spl infin/. The results include the following. (1) We define C/sub N/,C/spl circ//sub N/ as the largest achievable rate per transmitter in the usual Shannon-theoretic sense in the one- and two-dimensional cases, respectively (assuming that all signals are jointly decoded). We find expressions for limN/spl rarr//spl infin/C/sub N/ and limN/spl rarr//spl infin/C/spl circ//sub N/. (2) As the interference parameter /spl alpha/ increases from 0, C/sub N/ and C/spl circ//sub N/ increase or decrease according to whether the signal-to-noise ratio is less than or greater than unity. (3) Optimal performance is attainable using TDMA within the cell, but using TDMA for adjacent cells is distinctly suboptimal. (4) We suggest a scheme which does not require joint decoding of all the users, and is, in many cases, close to optimal.

title: Enhancing the cellular downlink capacity via co-processing at the transmitting end
abstract: A linear pre-processing plus encoding scheme is proposed, which significantly enhances cellular downlink performance, while putting the complexity burden on the transmitting end. The approach is based on LQ factorization of the channel transfer matrix combined with the "writing on dirty paper" approach (Caire, G. and Shamai, S., Proc. 38th Annual Allerton Conference on Communication, Control and Computing, 2000) for eliminating the effect of uncorrelated interference, which is fully known at the transmitter but unknown at the receiver. The attainable average rates with the proposed scheme approach those of optimum joint processing at the high SNR region.

title: The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel
abstract: The Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) is considered. The dirty-paper coding (DPC) rate region is shown to coincide with the capacity region. To that end, a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality, to show that a superposition of Gaussian codes is optimal for the degraded vector broadcast channel and that DPC is optimal for the nondegraded case. Furthermore, the capacity region is characterized under a wide range of input constraints, accounting, as special cases, for the total power and the per-antenna power constraints

title: Elements of Information Theory
abstract: Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1.  Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality.  Problems.  Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set.  Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate.  Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains.  Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins.  Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English.  Problems.  Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem.  Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information.  Problems.   Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback.  Problems.  Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function.  Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory.   Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms.   Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle.  Problems.  Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks.  Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP).  Problems.  Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants.  Problems. Historical Notes. Bibliography. List of Symbols. Index.

title: An overview of limited feedback in wireless communication systems
abstract: It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finite-rate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, single-user, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.

title: Adaptation, Coordination, and Distributed Resource Allocation in Interference-Limited Wireless Networks
abstract: A sensible design of wireless networks involves striking a good balance between an aggressive reuse of the spectral resource throughout the network and managing the resulting co-channel interference. Traditionally, this problem has been tackled using a ldquodivide and conquerrdquo approach. The latter consists in deploying the network with a static or semidynamic pattern of resource reutilization. The chosen reuse factor, while sacrificing a substantial amount of efficiency, brings the interference to a tolerable level. The resource can then be managed in each cell so as to optimize the per cell capacity using an advanced air interface design. In this paper, we focus our attention on the overall network capacity as a measure of system performance. We consider the problem of resource allocation and adaptive transmission in multicell scenarios. As a key instance, the problem of joint scheduling and power control simultaneously in multiple transmit-receive links, which employ capacity-achieving adaptive codes, is studied. In principle, the solution of such an optimization hinges on tough issues such as the computational complexity and the requirement for heavy receiver-to-transmitter feedback and, for cellular networks, cell-to-cell channel state information (CSI) signaling. We give asymptotic properties pertaining to rate-maximizing power control and scheduling in multicell networks. We then present some promising leads for substantial complexity and signaling reduction via the use of newly developed distributed and game theoretic techniques.

title: Network MIMO: Overcoming Intercell Interference in Indoor Wireless Systems
abstract: Network MIMO is a family of techniques whereby each user in a wireless system is served through all the access points within its range of influence. By tightly coordinating the transmission and reception of signals at multiple access points, network MIMO transcends the limits on spectral efficiency due to intercell interference. Taking prior information- theoretic analyses of Network MIMO to the next level, this paper quantifies the spectral efficiency gains obtainable under realistic propagation and operational conditions. Our study relies on detailed simulations and, for specificity, is conducted within the framework of the IEEE 802.16e Mobile WiMAX system. All the relevant physical-layer functionalities of Mobile WiMAX are accurately replicated. Furthermore, to facilitate the coordination between access points, we postulate an indoor deployment organized around a gigabit-ethernet backhaul. The results confirm that Network MIMO stands to provide a multiple-fold increase in spectral efficiency under such conditions.

title: Multiuser MIMO downlink with limited inter-cell cooperation: Approximate interference alignment in time, frequency and space
abstract: We consider a realistic albeit simplified scenario for wireless cellular systems of the next generation (4G and beyond), where MIMO-OFDM, opportunistic scheduling, channel state information at the transmitter and limited base-station cooperation are envisaged. We propose two strategies with limited base-station cooperation that can be easily implemented with today's technology and achieve an approximate form of inter-cell interference alignment. The first strategy consists of imposing a ldquopower maskrdquo in frequency such that adjacent cooperative clusters of base stations generate different interference levels in different frequency subchannels. The second strategy consists of switching between different cooperative clusters such that no user is in a permanently disadvantaged location.We compare single-user and multiuser MIMO systems in terms of average throughput as a function of the user location.

title: The capacity region of the symbol-asynchronous Gaussian multiple-access channel
abstract: An equivalent discrete-time Gaussian channel parametrized by the signal cross-correlations is derived to obtain an equivalent channel model with discrete-time outputs. The main feature introduced by the lack of symbol synchronism is that the channel has memory. This is due to the overlap of each symbol transmitted by a user with two consecutive symbols transmitted by the other user. It is shown that if the transmitters are assigned the same waveform, symbol asynchronism has no effect on the two-user capacity region of the white Gaussian channel which is equal to the Cover-Syner pentagon, whereas if the assigned waveforms are different (e.g., code division multiple access), the symbol-asynchronous capacity region is no longer a pentagon. An alternative representation of the capacity region which results in a particularly compact characterization of the fundamental limits of the multiple-access channel in the region of signal-to-noise ratios is also considered.

title: On information rates of the fading Wyner cellular model via the thouless formula for the strip
abstract: We apply the theory of random Schrodinger operators to the analysis of multi-users communication channels similar to the Wyner model, which are characterized by short-range inter-cell broadcasting. With H the channel transfer matrix, HH? is a narrow-band matrix and in many aspects is similar to a random Schrodinger operator. We relate the per-cell sum-rate capacity of the channel to the integrated density of states of a random Schrodinger operator; the latter is related to the top Lyapunov exponent of a random sequence of matrices via a version of the Thouless formula. Unlike related results in classical random matrix theory, limiting results do depend on the underlying fading distributions. We also derive explicit results in the high-SNR regime for some particular cases.

title: Sum Rate Characterization of Joint Multiple Cell-Site Processing
abstract: The sum-rate capacity of a cellular system model is analyzed, considering the uplink and downlink channels, while addressing both nonfading and flat-fading channels. The focus is on a simple Wyner-like multicell model, where the system cells are arranged on a circle, and the cell sites are located at the boundaries of the cells. For the uplink channel, analytical expressions of the sum-rate capacities are derived for intra-cell time-division multiple-access (TDMA) scheduling, and a "wideband" (WB) scheme (where all users are active simultaneously utilizing all bandwidths for coding). Assuming individual equal per-cell power constraints, and using the Lagrangian uplink-downlink duality principle, an analytical expression for the sum-rate capacity of the downlink channel is derived for nonfading channels, and shown to coincide with the corresponding uplink result. Introducing flat-fading, lower and upper bounds on the average per-cell ergodic sum-rate capacity are derived. The bounds exhibit an O(loge K) multiuser diversity factor for a number of users per cell K Gt 1, in addition to the array diversity gain. Joint multicell processing is shown to eliminate out-of-cell interference, which is traditionally considered to be a limiting factor in high-rate reliable communications.

title: Suboptimality of TDMA in the low-power regime
abstract: We consider multiaccess, broadcast, and interference channels with additive Gaussian noise. Although the set of rate pairs achievable by time-division multiple access (TDMA) is not equal to the capacity region, the TDMA achievable region converges to the capacity region as the power decreases. Furthermore, TDMA achieves the optimum minimum energy per bit. Despite those features, this paper shows that the growth of TDMA-achievable rates with the energy per bit is suboptimal in the low-power regime except in special cases: multiaccess channels where the users' energy per bit are identical and broadcast channels where the receivers have identical signal-to-noise ratios. For the additive Gaussian noise interference channel, we identify a small region of interference parameters outside of which TDMA is also shown to be suboptimal. The effect of fading (known to the receiver) on the suboptimality of TDMA is also explored.

title: Distributed decoding in a cellular multiple-access channel
abstract: Distributed decoding in the uplink of a rectangular planar cellular array with local message passing is considered. Two algorithms are proposed and compared: a BCJR-type algorithm applied to linear subgraphs, and belief propagation applied to the 2D graph of the cellular array.

title: Downlink Macro-Diversity in Cellular Networks
abstract: In this paper, we study the potential benefit of base-station (BS) cooperation for downlink transmission in a modified Wyner-type multicell model. Besides the dirty-paper-coding (DPC) precoder, we also analyze several linear precoding schemes, including co-phasing, zero-forcing (ZF) and MMSE precoders. For the nonfading case, analytical sum rate expression is obtained for each scheme. In networks of a large number N of cells, a high signal-to-noise-ratio (SNR) asymptotic gap is shown between the sum rate performances of DPC and ZF precoders. Moreover, the MMSE precoder sum rate expression in large networks indicates different behaviors of MMSE precoder in different SNR regimes: in the SNR > N<sup>2</sup> regime, it coincides with the ZF precoder, while, in the SNR < N<sup>2</sup> regime, it coincides with the co-phasing precoder. For the Rayleigh fading case, Monte-Carlo simulations demonstrate the effectiveness of linear precoding schemes with the proposed user selection criterion.

title: Uplink Macro Diversity of Limited Backhaul Cellular Network
abstract: 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.

title: Rate region of the quadratic Gaussian CEO problem
abstract: In the so-called CEO problem, a hidden source random process is of interest to a central unit or the "CEO". But this process cannot be observed directly. L sensors or agents observe independently corrupted versions of the source. They encode their observations without cooperating with one another and send through rate constrained noiseless channels to the CEO. The problem was first studied by T. Berger et al. (1996) in the context of discrete memoryless sources. The quadratic Gaussian version of the problem was studied. The best result known to date is the characterization of the sum-rate when all the agents have the same quality of observations. Here we characterize the rate region for any number of agents without assuming that their quality of observations is the same. This is one of the few examples of multiterminal lossy source coding problems in which the rate region can be characterized completely.

title: Structured superposition for backhaul constrained cellular uplink
abstract: In this paper, we demonstrate the advantage of the inherent algebraic structure of lattice codes, for the uplink channel of a cellular deployment. The out-of-cell interference is assumed to be symmetric, as in Wyner's model. We employ a new relaying technique, compute-and-forward, which allows cell-sites to decode equations of the transmitted bits by exploiting the channel interference. However, the standard compute-and-forward technique is penalized whenever the channel coefficients are non-integer. We develop a superposition strategy to mitigate this penalty. By using part of the power towards a private message, we can effectively modify the channel seen by compute-and-forward. We demonstrate that, in certain regimes, this mixed strategy significantly outperforms decode-and-forward, compress-and-forward, and ordinary compute-and-forward.

title: A cognitive network with clustered decoding
abstract: 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.

title: Interference channel with a relay: Models, relaying strategies, bounds
abstract: This paper discusses the impact of relaying in interference-limited networks by studying a two-user Gaussian interference channel with a relay (ICR). Various models for relay reception and transmission are possible: The relay can receive and transmit in the same band as the sources (i.e., in-band relay reception/ transmission), or else relay reception, or both reception and transmission, can take place over orthogonal links of limited capacity (i.e., out-of-band relay reception or/ and transmission). In all scenarios, the selection of either signal relaying, interference forwarding or a combination thereof for the relay operation is identified as a common design choice. While signal relaying enables the destination to obtain a stronger desired signal or additional information, interference forwarding helps removing part of the interference. Important scenarios under which signal relaying and interference forwarding are optimal are identified, including cognitive relaying where the relay is unaware of the source codebooks and out-of band relaying, both under certain modified strong interference conditions and the latter under additional capacity constraints on the orthogonal relay links.

title: Interference Mitigation Through Limited Receiver Cooperation
abstract: Interference is a major issue limiting the performance in wireless networks. Cooperation among receivers can help mitigate interference by forming distributed MIMO systems. The rate at which receivers cooperate, however, is limited in most scenarios. How much interference can one bit of receiver cooperation mitigate? In this paper, we study the two-user Gaussian interference channel with conferencing decoders to answer this question in a simple setting. We identify two regions regarding the gain from receiver cooperation: linear and saturation regions. In the linear region, receiver cooperation is efficient and provides a degrees-of-freedom gain, which is either one cooperation bit buys one over-the-air bit or two cooperation bits buy one over-the-air bit. In the saturation region, receiver cooperation is inefficient and provides a power gain, which is bounded regardless of the rate at which receivers cooperate. The conclusion is drawn from the characterization of capacity region to within two bits/s/Hz, regardless of channel parameters. The proposed strategy consists of two parts: 1) the transmission scheme, where superposition encoding with a simple power split is employed and 2) the cooperative protocol, where one receiver quantize-bin-and-forwards its received signal and the other after receiving the side information decode-bin-and-forwards its received signal.

title: Gaussian Z-Interference Channel With a Relay Link: Achievability Region and Asymptotic Sum Capacity
abstract: This paper studies a Gaussian Z-interference channel with a rate-limited digital relay link from one receiver to another. Achievable rate regions are derived based on a combination of a Han-Kobayashi common-private power-splitting technique and either a compress-and-forward relay strategy or a decode-and-forward strategy for interference subtraction at the other end. For the Gaussian Z-interference channel with a digital link from the interference-free receiver to the interfered receiver, the capacity region is established in the strong interference regime; an achievable rate region is established in the weak interference regime. In the weak interference regime, the decode-and-forward strategy is shown to be asymptotically sum-capacity achieving in the high signal-to-noise ratio and high interference-to-noise ratio limit. In this case, each relay bit asymptotically improves the sum capacity by one bit. For the Gaussian Z-interference channel with a digital link from the interfered receiver to the interference-free receiver, the capacity region is established in the strong interference regime; achievable rate regions are established in the moderately strong and weak interference regimes. In addition, the asymptotic sum capacity is established in the limit of a large relay link rate. In this case, the sum capacity improvement due to the digital link is bounded by half a bit when the interference link is weaker than a certain threshold, but the sum capacity improvement becomes unbounded when the interference link is strong.

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

title: Information theoretic considerations for cellular mobile radio
abstract: We present some information-theoretic considerations used to determine upper bounds on the information rates that can be reliably transmitted over a two-ray propagation path mobile radio channel model, operating in a time division multiplex access (TDMA) regime, under given decoding delay constraints. The sense in which reliability is measured is addressed, and in the interesting eases where the decoding delay constraint plays a significant role, the maximal achievable rate (capacity), is specified in terms of capacity versus outage. In this case, no coding capacity in the strict Shannon sense exists. Simple schemes for time and space diversity are examined, and their potential benefits are illuminated from an information-theoretic stand point. In our presentation, we chose to specialize to the TDMA protocol for the sake of clarity and convenience. Our main arguments and results extend directly to certain variants of other multiple access protocols such as code division multiple access (CDMA) and frequency division multiple access (FDMA), provided that no fast feedback from the receiver to the transmitter is available.

title: Individual Outage Rate Regions for Fading Multiple Access Channels
abstract: In this paper, outage regions are computed for the quasi-static fading multiple access channel (MAC) with constraints on the individual user outage probabilities and no channel state information at the transmitters (CSIT). An outage rate region is defined as the set of rate vectors for which the user outage probability constraints are satisfied simultaneously. Outage probability is typically defined in terms of a common outage event, defined as the event that a target user rate vector lies outside the achievable region of the MAC, conditioned on the fading state. In contrast, rate regions without CSIT are computed in this paper based on individual outage events and individual probability constraints that are satisfied simultaneously. An individual outage event for a given user occurs if the user's message is not correctly decoded, irrespective of the decoding success of the messages for other users. Individual outage rate regions are useful for the MAC with heterogeneous user channels and quality-of-service (QoS) requirements. Explicit outage rate regions and total throughputs are computed for the two-user fading MAC. It is shown that rate regions and throughputs are significantly larger using individual outage probabilities than using the common outage probability.

title: Information Theoretic Aspects of Users' Activity in a Wyner-Like Cellular Model
abstract: 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.

title: Information-theoretic considerations for symmetric, cellular, multiple-access fading channels - Part II
abstract: For pt.I see ibid., vol.43, no.6, p.1877-94 (1997). A simple idealized linear (and planar) uplink, cellular, multiple-access communication model, where only adjacent cell interference is present and all signals may experience fading is considered. Shannon theoretic arguments are invoked to gain insight into the implications on performance of the main system parameters and multiple-access techniques. The model treated in Part I (Shamai, 1997) is extended here to account for cell-site receivers that may process also the received signal at an adjacent cell site, compromising thus between the advantage of incorporating additional information from other cell sites on one hand and the associated excess processing complexity on the other. Various settings which include fading, time-division multiple access (TDMA), wideband (WB), and (optimized) fractional inter-cell time sharing (ICTS) protocols are investigated and compared. In this case and for the WB approach and a large number of users per cell it is found, surprisingly, that fading may enhance performance in terms of Shannon theoretic achievable rates. The linear model is extended to account for general linear and planar configurations. The effect of a random number of users per cell is investigated and it is demonstrated that randomization is beneficial. Certain aspects of diversity as well as some features of TDMA and orthogonal code-division multiple access (CDMA) techniques in the presence of fading are studied in an isolated cell scenario.

title: CTH13-3: Symmetric Rate Capacity of Cellular Systems with Cooperative Base Stations
abstract: Cooperation among base stations has demonstrated substantial capacity gain in cellular systems. The optimal transmission scheme under full base station cooperation requires all users to transmit simultaneously and a central joint receiver for multi-user detection. We consider some sub-optimal but more practical schemes of orthogonal channel access either within a cell (intra-cell TDMA) or among cells (inter-cell time sharing), which correspond to a partitioning of overall channel resources. The effects of various schemes on the uplink capacity of a cellular system are then compared for a modified Wyner model.

title: Shannon-theoretic approach to a Gaussian cellular multiple-access channel with fading
abstract: 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-site's 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.

title: On the spectrum of large random hermitian finite-band matrices
abstract: 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.

title: Capacity of Finite State Channels Based on Lyapunov Exponents of Random Matrices
abstract: The finite-state Markov channel (FSMC) is a time-varying channel having states that are characterized by a finite-state Markov chain. These channels have infinite memory, which complicates their capacity analysis. We develop a new method to characterize the capacity of these channels based on Lyapunov exponents. Specifically, we show that the input, output, and conditional entropies for this channel are equivalent to the largest Lyapunov exponents for a particular class of random matrix products. We then show that the Lyapunov exponents can be expressed as expectations with respect to the stationary distributions of a class of continuous-state space Markov chains. This class of Markov chains, which is closely related to the prediction filter in hidden Markov models, is shown to be nonirreducible. Hence, much of the standard theory for continuous state-space Markov chains cannot be applied to establish the existence and uniqueness of stationary distributions, nor do we have direct access to a central limit theorem (CLT). In order to address these shortcomings, we utilize several results from the theory of random matrix products and Lyapunov exponents. The stationary distributions for this class of Markov chains are shown to be unique and continuous functions of the input symbol probabilities, provided that the input sequence has finite memory. These properties allow us to express mutual information and channel capacity in terms of Lyapunov exponents. We then leverage this connection between entropy and Lyapunov exponents to develop a rigorous theory for computing or approximating entropy and mutual information for finite-state channels with dependent inputs. We develop a method for directly computing entropy of finite-state channels that does not rely on simulation and establish its convergence. We also obtain a new asymptotically tight lower bound for entropy based on norms of random matrix products. In addition, we prove a new functional CLT for sample entropy and apply this theorem to characterize the error in simulated estimates of entropy. Finally, we present numerical examples of mutual information computation for intersymbol interference (ISI) channels and observe the capacity benefits of adding memory to the input sequence for such channels

title: Random Matrix Theory and Wireless Communications
abstract: Random matrix theory has found many applications in physics, statistics and engineering since its inception. Although early developments were motivated by practical experimental problems, random matrices are now used in fields as diverse as Riemann hypothesis, stochastic differential equations, condensed matter physics, statistical physics, chaotic systems, numerical linear algebra, neural networks, multivariate statistics, information theory, signal processing and small-world networks. This article provides a tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained. Furthermore, the application of random matrix theory to the fundamental limits of wireless communication channels is described in depth.

title: On Certain Large Random Hermitian Jacobi Matrices With Applications to Wireless Communications
abstract: 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.

title: High-SNR power offset in multiantenna communication
abstract: The analysis of the multiple-antenna capacity in the high-SNR regime has hitherto focused on the high-SNR slope (or maximum multiplexing gain), which quantifies the multiplicative increase as a function of the number of antennas. This traditional characterization is unable to assess the impact of prominent channel features since, for a majority of channels, the slope equals the minimum of the number of transmit and receive antennas. Furthermore, a characterization based solely on the slope captures only the scaling but it has no notion of the power required for a certain capacity. This paper advocates a more refined characterization whereby, as a function of SNR|/sub dB/, the high-SNR capacity is expanded as an affine function where the impact of channel features such as antenna correlation, unfaded components, etc., resides in the zero-order term or power offset. The power offset, for which we find insightful closed-form expressions, is shown to play a chief role for SNR levels of practical interest.

title: On the Capacity of Cellular Networks with MIMO Links
abstract: We provide scaling results for the sum capacity of the multi-access, uplink channel in a flat fading environment, when there is interference from other cells. We consider a scaling regime where the number of antennas per user remains fixed but the number of antennas at the base station and the number of users in each cell grow large together. We characterize the asymptotic behaviour of the spectral efficiencies in each cell, in three scenarios: 1) single cell processing with full frequency reuse 2) single cell processing, with frequency re-use partitioning of adjacent cells and 3) base station cooperative decoding (macro-diversity). It is shown that base station cooperation provides very significant gains in spectral efficiency over single cell processing.

title: How much training is needed in multiple-antenna wireless links?
abstract: Multiple-antenna wireless communication links promise very high data rates with low error probabilities, especially when the wireless channel response is known at the receiver. In practice, knowledge of the channel is often obtained by sending known training symbols to the receiver. We show how training affects the capacity of a fading channel-too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We compute a lower bound on the capacity of a channel that is learned by training, and maximize the bound as a function of the received signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the number of transmit antennas-this number is also the smallest training interval length that guarantees meaningful estimates of the channel matrix. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger than the number of antennas. We show that training-based schemes can be optimal at high SNR, but suboptimal at low SNR.

title: On the achievable throughput of a multiantenna Gaussian broadcast channel
abstract: A Gaussian broadcast channel (GBC) with r single-antenna receivers and t antennas at the transmitter is considered. Both transmitter and receivers have perfect knowledge of the channel. Despite its apparent simplicity, this model is, in general, a nondegraded broadcast channel (BC), for which the capacity region is not fully known. For the two-user case, we find a special case of Marton's (1979) region that achieves optimal sum-rate (throughput). In brief, the transmitter decomposes the channel into two interference channels, where interference is caused by the other user signal. Users are successively encoded, such that encoding of the second user is based on the noncausal knowledge of the interference caused by the first user. The crosstalk parameters are optimized such that the overall throughput is maximum and, surprisingly, this is shown to be optimal over all possible strategies (not only with respect to Marton's achievable region). For the case of r>2 users, we find a somewhat simpler choice of Marton's region based on ordering and successively encoding the users. For each user i in the given ordering, the interference caused by users j>i is eliminated by zero forcing at the transmitter, while interference caused by users j<i is taken into account by coding for noncausally known interference. Under certain mild conditions, this scheme is found to be throughput-wise asymptotically optimal for both high and low signal-to-noise ratio (SNR). We conclude by providing some numerical results for the ergodic throughput of the simplified zero-forcing scheme in independent Rayleigh fading.

title: Transmitter Optimization for the Multi-Antenna Downlink With Per-Antenna Power Constraints
abstract: This paper considers the transmitter optimization problem for a multiuser downlink channel with multiple transmit antennas at the base-station. In contrast to the conventional sum-power constraint on the transmit antennas, this paper adopts a more realistic per-antenna power constraint, because in practical implementations each antenna is equipped with its own power amplifier and is limited individually by the linearity of the amplifier. Assuming perfect channel knowledge at the transmitter, this paper investigates two different transmission schemes under the per-antenna power constraint: a minimum-power beamforming design for downlink channels with a single antenna at each remote user and a capacity-achieving transmitter design for downlink channels with multiple antennas at each remote user. It is shown that in both cases, the per-antenna downlink transmitter optimization problem may be transformed into a dual uplink problem with an uncertain noise. This generalizes previous uplink-downlink duality results and transforms the per-antenna transmitter optimization problem into an equivalent minimax optimization problem. Further, it is shown that various notions of uplink-downlink duality may be unified under a Lagrangian duality framework. This new interpretation of duality gives rise to efficient numerical optimization techniques for solving the downlink per-antenna transmitter optimization problem

title: Downlink Multicell Processing with Limited-Backhaul Capacity
abstract: 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.

title: Cooperative Multicell Zero-Forcing Beamforming in Cellular Downlink Channels
abstract: 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.

title: Uplink Throughput of TDMA Cellular Systems with Multicell Processing and Amplify-and-Forward Cooperation Between Mobiles
abstract: 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 their'simplicity 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.

title: Throughput of Low-Power Cellular Systems With Collaborative Base Stations and Relaying
abstract: In this correspondence, joint (cooperative) decoding at the base stations combined with collaborative transmission (relaying) is investigated as a means to improve the uplink throughput of current cellular systems over fading channels. Intracell orthogonal medium access control (e.g., TDMA, FDMA, or orthogonal CDMA) and Decode-and-Forward relaying by either a mobile terminal or a fixed relay are assumed. Moreover, the cellular system is modeled according to a simplified framework introduced by Wyner. The per-cell achievable ergodic throughput is calculated for different system configurations and then characterized in the low-power (wideband) regime in terms of minimum energy per bit required for reliable communication and slope of the spectral efficiency. The analysis allows to clearly assess the relative merits of both cooperation among base stations and at the terminal level within the considered model.

title: Cellular Systems with Full-Duplex Amplify-and-Forward Relaying and Cooperative Base-Stations
abstract: 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.

title: Uplink sum-rate analysis of a multicell system with feedback
abstract: The capacity region of a Multiple Access Channel can be increased by feedback to the sources, since feedback enables cooperative transmission. Focusing on a linear cellular system (as for a highway or a corridor), a novel transmission strategy is proposed that exploits feedback from the neighboring mobile stations (MSs). The strategy enables cooperative communications via ldquoanalog network codingrdquo (i.e., broadcasting and interference cancellation via side information) to exchange signalling information among MSs. Numerical results show that the proposed technique provides gains over non-cooperative strategies in the low-signal-to-noise-ratio regime.

title: Cellular systems with full-duplex compress-and-forward relaying and cooperative base stations
abstract: 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.

title: A new achievable rate region for the interference channel
abstract: A new achievable rate region for the general interference channel which extends previous results is presented and evaluated. The technique used is a generalization of superposition coding to the multivariable case. A detailed computation for the Gaussian channel case clarifies to what extent the new region improves previous ones. The capacity of a class of Gaussian interference channels is also established.

title: Throughput of Cellular Systems with Conferencing Mobiles and Cooperative Base Stations
abstract: This paper considers an enhancement to multicell processing for the uplink of a cellular system, whereby the mobile stations are allowed to exchange messages on orthogonal channels of fixed capacity (conferencing). Both conferencing among mobile stations in different cells and in the same cell (inter- and intracell conferencing, resp.) are studied. For both cases, it is shown that a rate-splitting transmission strategy, where part of the message is exchanged on the conferencing channels and then transmitted cooperatively to the base stations, is capacity achieving for sufficiently large conferencing capacity. In case of intercell conferencing, this strategy performs convolutional pre-equalization of the signal encoding the common messages in the spatial domain, where the number of taps of the finite-impulse response equalizer depends on the number of conferencing rounds. Analysis in the low signal-to-noise ratio regime and numerical results validate the advantages of conferencing as a complementary technology to multicell processing.

title: Multiple-access channels with different generalized feedback signals
abstract: This paper is concerned with a communication channel with two senders and one receiver, in which each sender observes a private feedback signal. The two feedback signals are not necessarily equivalent to or derived from the signal observed by the receiver. An achievable rate region is demonstrated for this multiple-access channel by means of a new superposition coding scheme. In particular it is shown that a rate region, previously obtained for the multiple-access channel with "perfect" feedback to both senders, remains achievable when the feedback connection to one of the senders is eliminated.

title: Interference Alignment and Degrees of Freedom of the  $K$-User Interference Channel
abstract: For the fully connected K user wireless interference channel where the channel coefficients are time-varying and are drawn from a continuous distribution, the sum capacity is characterized as C(SNR)=K/2log(SNR)+o(log(SNR)) . Thus, the K user time-varying interference channel almost surely has K/2 degrees of freedom. Achievability is based on the idea of interference alignment. Examples are also provided of fully connected K user interference channels with constant (not time-varying) coefficients where the capacity is exactly achieved by interference alignment at all SNR values.

title: Binary Power Control for Sum Rate Maximization over Multiple Interfering Links
abstract: We consider allocating the transmit powers for a wireless multi-link (N-link) system, in order to maximize the total system throughput under interference and noise impairments, and short term power constraints. Employing dynamic spectral reuse, we allow for centralized control. In the two-link case, the optimal power allocation then has a remarkably simple nature termed binary power control: depending on the noise and channel gains, assign full power to one link and minimum to the other, or full power on both. Binary power control (BPC) has the advantage of leading towards simpler or even distributed power control algorithms. For N>2 we propose a strategy based on checking the corners of the domain resulting from the power constraints to perform BPC. We identify scenarios in which binary power allocation can be proven optimal also for arbitrary N. Furthermore, in the general setting for N>2, simulations demonstrate that a throughput performance with negligible loss, compared to the best non-binary scheme found by geometric programming, can be obtained by BPC. Finally, to reduce the complexity of optimal binary power allocation for large networks, we provide simple algorithms achieving 99% of the capacity promised by exhaustive binary search.

title: Optimal and Distributed Scheduling for Multicell Capacity Maximization
abstract: We address the problem of multicell co-channel scheduling in view of mitigating interference in a wireless data network with full spectrum reuse. The centralized joint multicell scheduling optimization problem, based on the complete co-channel gain information, has so far been justly considered impractical due to complexity and real-time cell-to-cell signaling overhead. However, we expose here the following remarkable result for a large network with a standard power control policy. The capacity maximizing joint multicell scheduling problem admits a simple and fully distributed solution. This result is proved analytically for an idealized network. From the constructive proof, we propose a practical algorithm that is shown to achieve near maximum capacity for realistic cases of simulated networks of even small sizes.

title: Inter-Cell Coordination, Opportunistic Beamforming and Scheduling
abstract: In high speed downlink packet access systems (HS-DPA), opportunistic beamforming has been proposed as a viable technique for improving the system capacity by taking advantage of the multiuser diversity due to the time varying fluctuations of the mobile users channels. In opportunistic beamforming with proportional fair scheduling, mobile users who have the largest rates when compared with their averaged throughputs, are scheduled over preferred spatial beams, thereby yielding improved throughput-delay tradeoffs. In this paper, we consider cellular architectures where base stations coordinate to service users. These base stations are assumed equipped with smart antenna systems which generate pilot beams according to a predefined algorithm, collect only an SINR report from the users, and provide opportunistic scheduling. We propose schemes where the base stations coordinate to generate beams that reduce the inter-cell interference to the users considered for service. Through computer simulations we show that the proposed base station coordination technique provides significant performance gains in downlink packet access cellular systems. Furthermore this is achieved with the use of only modest feedback (SINR) from the users i.e. without the need for excessive channel state information feedback.

title: Self-Organizing Dynamic Fractional Frequency Reuse in OFDMA Systems
abstract: We describe an algorithm for sub-carrier and power allocation that achieves out-of-cell interference avoidance through dynamic fractional frequency reuse (FFR) in downlink of cellular systems based on orthogonal frequency division multiple access (OFDMA). The focus in on the constant-bit-rate (CBR) traffic type flows (e.g., VoIP). Our approach is based on the continuous "selfish" optimization of resource allocation by each sector. No a priori frequency planning and/or inter-cell coordination is required. We show, both analytically (on a simple illustrative example) and by simulations (of a more realistic system), that the algorithm leads the system to "self-organize" into efficient frequency reuse patterns.

title: Self-Organizing Dynamic Fractional Frequency Reuse for Best-Effort Traffic through Distributed Inter-Cell Coordination
abstract: Self-optimization of the network, for the purposes of improving overall capacity and/or cell edge data rates, is an important objective for next generation cellular systems. We propose algorithms that automatically create efficient, soft fractional frequency reuse (FFR) patterns for enhancing performance of orthogonal frequency division multiple access (OFDMA) based cellular systems for forward link best effort traffic. The Multi- sector Gradient (MGR) algorithm adjusts the transmit powers of the different sub-bands by systematically pursuing maximization of the overall network utility. We show that the maximization can be done by sectors operating in a semi-autonomous way, with only some gradient information exchanged periodically by neighboring sectors. The Sector Autonomous (SA) algorithm adjusts its transmit powers in each sub-band independently in each sector using a non-trivial heuristic to achieve out- of-cell interference mitigation. This algorithm is completely autonomous and requires no exchange of information between sectors. Through extensive simulations, we demonstrate that both algorithms provide substantial performance improvements. In particular, they can improve the cell edge data throughputs significantly, by up to 66% in some cases for the MGR, while maintaining the overall sector throughput at the same level as that achieved by the traditional approach. The simulations also show that both algorithms lead the system to "self-organize" into efficient, soft FFR patterns with no a priori frequency planning.

title: Introducing power-shaped advanced resource assignment ( PSARA ) in fixed broadband wireless access systems
abstract: In thispaperweproposeanew techniquefor assigning radiochannelsin TDMA-basedfixedbroadbandwireless accesssystems(FBWA) with full frequencyreuse. The proposedtechnique, namedPower-ShapedAdvancedResource Assignement (PSARA),has the aim of partially organizing the intercell and intersector interferencein a cellular systemwhere basestationsassignradio resources in an uncoordinatedfashion. This is doneby usingan appropriatesetof powerprofilesthat limit (or shape)the power transmittedin each slot of the frame. Theallocation algorithm assignstime slots to users on the basis of the power required to fulfill a predefined carrier-to-interferenceratio,which is suitablyestimated. Simulationresultsfor a typical cellular FBWA system showthat this techniquesignificantly improvesthe capacity with respectto a systemthat assignsresources withoutpowershaping, evenwith powercontrol.

title: Dynamic Spectrum Management: Complexity and Duality
abstract: Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectral densities dynamically in response to physical channel conditions. Due to co-channel interference, the achievable data rate of each user depends on not only the power spectral density of its own, but also those of others in the system. Given any channel condition and assuming Gaussian signaling, we consider the problem to jointly determine all users' power spectral densities so as to maximize a system-wide utility function (e.g., weighted sum-rate of all users), subject to individual power constraints. For the discretized version of this nonconvex problem, we characterize its computational complexity by establishing the NP-hardness under various practical settings, and identify subclasses of the problem that are solvable in polynomial time. Moreover, we consider the Lagrangian dual relaxation of this nonconvex problem. Using the Lyapunov theorem in functional analysis, we rigorously prove a result first discovered by Yu and Lui (2006) that there is a zero duality gap for the continuous (Lebesgue integral) formulation. Moreover, we show that the duality gap for the discrete formulation vanishes asymptotically as the size of discretization decreases to zero.

title: Coordinated Scheduling and Power Allocation in Downlink Multicell OFDMA Networks
abstract: We consider a multicell orthogonal frequency-division multiple-access (OFDMA) wireless network with universal frequency reuse and treat the problem of cochannel interference mitigation via base station coordination in the downlink. Assuming that coordinated access points only share channel quality measurements but not user data symbols, we propose to select the set of cochannel users and the power allocation across tones to maximize the weighted system sum rate subject to per-base-station power constraints. Since this is a nonconvex combinatorial problem, efficient suboptimal algorithms are presented and discussed, each requiring a different level of coordination among base stations and a different feedback signaling overhead. Simulation results are provided to assess the performances of the proposed strategies.

title: Joint scheduling and dynamic power spectrum optimization for wireless multicell networks
abstract: This paper proposes a joint proportionally fair scheduling and dynamic power spectrum adaptation algorithm for wireless multicell networks. The proposed system allows multiple base-stations in a multicell network to be coordinated by exchanging interference pricing messages among each other. The messages summarize the effect of intercell interference, and they are functions of transmit power spectra, signal-to-noise ratios, direct and interfering channel gains, and the proportional fairness variables for each user. The use of interference pricing allows the transmit power spectra and user schedule within each base-station to be optimized jointly, while taking into consideration both the intercell interference and the fairness among the users in multiple cells. This paper proposes two power spectrum optimization methods, one based on the Karush-Kuhn-Tucker (KKT) condition of the optimization problem, and another based on the Newton's method. The proposed methods can achieve a throughput improvement of 40%–55% for users at the cell edge as compared to a conventional per-cell optimized system, while maintaining proportional fairness.

title: Non-cooperative resource competition game by virtual referee in multi-cell OFDMA networks
abstract: In this paper, a distributive non-cooperative game is proposed to perform sub-channel assignment, adaptive modulation, and power control for multi-cell multi-user orthogonal frequency division multiplexing access (OFDMA) networks. Each individual user's goal is to minimize his/her own transmitted power in a distributed manner under the constraints that the desirable rate is achieved and the transmitted power is bounded. The pure non-cooperative game may result in non-convergence or some undesirable Nash Equilibriums with low system and individual performances. To enhance the performances, a virtual referee is introduced to the networks and is in charge of monitoring and improving the outcome of non-cooperative competition for resources among the distributed users. If the game outcome is not desirable, either the required transmission rates should be reduced or some users should be prevented from using some radio resources such as sub-channels, so that the rest of users can share the limited resources more efficiently. Moreover, it can be shown that the introduction of the virtual referee does not increase the complexity of the networks. From the simulation results in a two-cell case, the proposed scheme reduces the transmitted power by 80% and 25% compared with the fixed channel assignment algorithm and the iterative water-filling algorithm in the literature, respectively. The achievable rate can be improved by 10%. In a multi-cell case, the proposed scheme can have up to 40% power reduction compared with the iterative water-filling algorithm when the co-channel interferences are severe.

title: A power control game based on outage probabilities for multicell wireless data networks
abstract: We present a game-theoretic treatment of distributed power control in CDMA wireless systems using outage probabilities. We first prove that the noncooperative power control game considered admits a unique Nash equilibrium (NE) for uniformly strictly convex pricing functions and under some technical assumptions on the SIR threshold levels. We then analyze global convergence of continuous-time as well as discrete-time synchronous and asynchronous iterative power update algorithms to the unique NE of the game. Furthermore, we show that a stochastic version of the discrete-time update scheme, which models the uncertainty due to quantization and estimation errors, converges almost surely to the unique NE point. We finally investigate and demonstrate the convergence and robustness properties of these update schemes through simulation studies.

title: Cooperative Game Theory and the Gaussian Interference Channel
abstract: In this paper we discuss the use of cooperative game theory for analyzing interference channels. We extend our previous work, to games with N players as well as frequency selective channels and joint TDM/FDM strategies. We show that the Nash bargaining solution can be computed using convex optimization techniques. We also show that the same results are applicable to interference channels where only statistical knowledge of the channel is available. Moreover, for the special case of two player 2 times K frequency selective channel (with K frequency bins) we provide an O(K log2 K) complexity algorithm for computing the Nash bargaining solution under mask constraint and using joint FDM/TDM strategies. Simulation results are also provided.

title: Distributed interference compensation for wireless networks
abstract: We consider a distributed power control scheme for wireless ad hoc networks, in which each user announces a price that reflects compensation paid by other users for their interference. We present an asynchronous distributed algorithm for updating power levels and prices. By relating this algorithm to myopic best response updates in a fictitious game, we are able to characterize convergence using supermodular game theory. Extensions of this algorithm to a multichannel network are also presented, in which users can allocate their power across multiple frequency bands.

title: WSN11-1: Distributed Cross-Layer Optimization of Wireless Sensor Networks: A Game Theoretic Approach
abstract: This paper proposes a distributed optimization framework for wireless multihop sensor networks base on a game theoretic approach. We show that the cross-layer optimization problem can be decomposed into two subproblems corresponding to two separate layers (the physical and the application layers) of the overall system. By modelling each subproblem as a noncooperative game, we aim to solve the nonconvex application-layer rate- allocation and physical-layer power-allocation subproblems in a distributed manner. Further, we prove the existence, uniqueness, and stability of the Nash equilibria for both games under certain sufficient conditions. Finally, we show that by using a set of dual variables as the market prices to coordinate the physical layer supply and the application layer demand, the overall optimization process strikes a right balance between the two layers in an overall cross-layer design.

title: Distributed interference pricing for OFDM wireless networks with non-separable utilities
abstract: We present a distributed algorithm for allocating power among multiple interfering transmitters in a wireless network using orthogonal frequency division multiplexing (OFDM). The algorithm attempts to maximize the sum over user utilities, where each user's utility is a function of his total transmission rate. Users exchange interference prices reflecting the marginal cost of interference on each sub-channel, and then update their power allocations given the interference prices and their own channel conditions. A similar algorithm was studied earlier assuming that each user's utility function is a separable function of the user's rate per sub-channel. Here, we do not assume this separability. We give a different algorithm for updating each user's power allocation and show that this algorithm converges monotonically. Numerical results comparing this algorithm to several others are also presented.

title: Price-Based Spectrum Management in Cognitive Radio Networks
abstract: Cognitive radios (CRs) have a great potential to improve spectrum utilization by enabling users to access the spectrum dynamically without disturbing licensed primary radios (PRs). A key challenge in operating these radios as a network is how to implement an efficient medium access control (MAC) mechanism that can adaptively and efficiently allocate transmission powers and spectrum among CRs according to the surrounding environment. Most existing works address this issue via suboptimal heuristic approaches or centralized solutions. In this paper, we propose a novel joint power/channel allocation scheme that improves the performance through a distributed pricing approach. In this scheme, the spectrum allocation problem is modeled as a noncooperative game, with each CR pair acting as a player. A price-based iterative water-filling (PIWF) algorithm is proposed, which enables CR users to reach a good Nash equilibrium (NE). This PIWF algorithm can be implemented distributively with CRs repeatedly negotiating their best transmission powers and spectrum. Simulation results show that the social optimality of the NE solution is dramatically improved through pricing. Depending on the different orders according to which CRs take actions, we study sequential and parallel versions of the PIWF algorithm. We show that the parallel version converges faster than the sequential version. We then propose a corresponding MAC protocol to implement our resource management schemes. The proposed MAC allows multiple CR pairs to be first involved in an admission phase, then iteratively negotiate their transmission powers and spectrum via control-packet exchanges. Following the negotiation phase, CRs proceed concurrently with their data transmissions. Simulations are used to study the performance of our protocol and demonstrate its effectiveness in terms of improving the overall network throughput and reducing the average power consumption.

title: Multiuser Water-filling in the Presence of Crosstalk
abstract: Spectrum optimization is an important part of the design of interference-limited multiuser communication systems. While traditional water-filling provides a closed-form solution to the transmit optimization problem in a single-user system, the multiuser version of the problem often leads to nonconvex problem formulations which are difficult to solve. Motivated by high-speed parallel-link and digital subscriber line applications, this paper investigates two practical multiuser settings in which global or local optimal solutions to the multiuser spectrum optimization problems can be found efficiently. The first part of this paper considers a high-speed transmission system in which practical (but suboptimal) minimum-mean-squared-error linear equalizers (MMSE-LEs) are used at the receiver. The optimal single-user transmit spectrum in this case involves a modified water-filling solution. Surprisingly, such a modified water-filling spectrum can be shown to be near-optimal in a multiuser setting as well, if the direct-link and the crosstalk characteristics are symmetric and if crosstalk is reasonably small. Thus, for practical parallel-link systems using MMSE linear equalizers, the optimal single-user and multiuser spectra are nearly identical. The second part of this paper considers numerical techniques for solving a nonconvex multiuser rate maximization problem for digital subscriber line applications. A new ingredient in the proposed approach is a taxation scheme that takes into account the effect of interference between neighboring lines. This leads to a modified iterative water-filling algorithm which is capable of finding local optimum solutions to the multiuser spectrum optimization problem efficiently.

title: Distributed dynamic resource allocation for multicell SDMA packet access net
abstract: This paper addresses the issues of distributed dynamic resource allocation (DRA) in the downlink of a SDMA broadband wireless packet network with multiple access points and adaptive antennas. Packet access and downlink beamforming make the intercell interference hard to predict, and how to handle it in order to efficiently perform slot and power allocation is still an open issue. We propose here new DRA strategies for efficient allocation in a distributed environment, which jointly consider spatial compatibility of users and an intercell interference estimation based on a fraction of the worst case interference measurements. The latter is independent of the actual allocation. We consider a low mobility TDD system with synchronized base stations and we assume perfect channel knowledge. The algorithms which are introduced and compared are the distributed max-min fit (DMMF) and the distributed reverse fit (DRF), which are based on the max-min fit criterion, the DMMF combined with the novel concept of nulls preallocation, where each AP reserves some beamforming nulls for the most interfered users of neighboring cells, and the power shaping technique (PS-DRA for SDMA), which efficiently exploits static power preallocation on time slots. The numerical results show that our techniques are able to significantly reduce the gap between a greedy centralized strategy that fully coordinates all the access ports and the baseline case of random distributed allocation, previously proposed for packet access. However, distributed power control in a packet switched environment with downlink beamforming still remains a hard task: nevertheless, PS-DRA is an efficient solution for joint slot-power allocation

title: Coordinated beamforming for the multicell multi-antenna wireless system
abstract: In a conventional wireless cellular system, signal processing is performed on a per-cell basis; out-of-cell interference is treated as background noise. This paper considers the benefit of coordinating base-stations across multiple cells in a multi-antenna beamforming system, where multiple base-stations may jointly optimize their respective beamformers to improve the overall system performance. Consider a multicell downlink scenario where base-stations are equipped with multiple transmit antennas employing either linear beamforming or nonlinear dirty-paper coding, and where remote users are equipped with a single antenna each, but where multiple remote users may be active simultaneously in each cell. This paper focuses on the design criteria of minimizing either the total weighted transmitted power or the maximum per-antenna power across the base-stations subject to signal-to-interference-and-noise-ratio (SINR) constraints at the remote users. The main contribution of the paper is an efficient algorithm for finding the joint globally optimal beamformers across all base-stations. The proposed algorithm is based on a generalization of uplink-downlink duality to the multicell setting using the Lagrangian duality theory. An important feature is that it naturally leads to a distributed implementation in time-division duplex (TDD) systems. Simulation results suggest that coordinating the beamforming vectors alone already provide appreciable performance improvements as compared to the conventional per-cell optimized network.

title: Distributed Beamforming Coordination in Multicell MIMO Channels
abstract: Coordination in a multi-cell/link environment has been attracting a lot of attention in the research community recently. In this paper, we consider the problem of coordinated beamforming where base stations (BS) equipped with multiple antennas attempt to serve a separate user each despite the interference generated by the other bases. We propose a framework for a distributed optimization of the beamformers at each base, where distributed is defined as using "local CSIT" only. We present and compare two distributed approaches (one iterative and another direct approach) which have in common the optimization of the beamformers as a combination of so-called egoistic and altruistic solutions for this problem. We provide the intuitions behind these approaches and some theoretical grounds for optimality in certain cases. Performance is finally illustrated through numerical simulations.

title: Transmit beamforming and power control for cellular wireless systems
abstract: Joint power control and beamforming schemes are proposed for cellular systems where adaptive arrays are used only at base stations. In the uplink, mobile power and receiver diversity combining vectors at the base stations are calculated jointly. The mobile transmitted power is minimized, while the signal-to-interference-and-noise ratio (SINR) at each link is maintained above a threshold. A transmit diversity scheme for the downlink is also proposed where the transmit weight vectors and downlink power allocations are jointly calculated such that the SINR at each mobile is above a target value. The proposed algorithm achieves a feasible solution for the downlink if there is one and minimizes the total transmitted power in the network. In a reciprocal network it can be implemented in a decentralized system, and it does not require global channel response measurements. In a nonreciprocal network, where the uplink and downlink channel responses are different, the proposed transmit beamforming algorithm needs to be implemented in a centralized system, and it requires a knowledge of the downlink channel responses. The performances of these algorithms are compared with previously proposed algorithms through numerical studies.

title: Solution of the multiuser downlink beamforming problem with individual SINR constraints
abstract: We address the problem of joint downlink beamforming in a power-controlled network, where independent data streams are to be transmitted from a multiantenna base station to several decentralized single-antenna terminals. The total transmit power is limited and channel information (possibly statistical) is available at the transmitter. The design goal: jointly adjust the beamformers and transmission powers according to individual SINR requirements. In this context, there are two closely related optimization problems. P1: maximize the jointly achievable SINR margin under a total power constraint. P2: minimize the total transmission power while satisfying a set of SINR constraints. In this paper, both problems are solved within a unified analytical framework. Problem P1 is solved by minimizing the maximal eigenvalue of an extended crosstalk matrix. The solution provides a necessary and sufficient condition for the feasibility of the SINR requirements. Problem P2 is a variation of problem P1. An important step in our analysis is to show that the global optimum of the downlink beamforming problem is equivalently obtained from solving a dual uplink problem, which has an easier-to-handle analytical structure. Then, we make use of the special structure of the extended crosstalk matrix to develop a rapidly converging iterative algorithm. The optimality and global convergence of the algorithm is proven and stopping criteria are given.

title: Iterative multiuser uplink and downlink beamforming under SINR constraints
abstract: We study the problem of power efficient multiuser beamforming transmission for both uplink and downlink. The base station is equipped with multiple antennas, whereas the mobile units have single antennas. In the uplink, interference is canceled by successive decoding. In the downlink, ideal "dirty paper" precoding is assumed. The design goal is to minimize the total transmit power while maintaining individual SINR constraints. In the uplink, the optimization problem is solved by a recursive formula with low computational complexity. The downlink problem is solved by exploiting the duality between uplink and downlink; thus, the uplink solution carries over to the downlink. In the second part of the paper, we show how the solution can be applied to the problem of rate balancing in Gaussian multiuser channels. We propose a strategy for throughput-wise optimal transmission for broadcast and multiple access channels under a sum power constraint. Finally, we show that single-user transmission achieves the sum capacity in the low-SNR regime. We completely characterize the SNR-range where single-user transmission is optimal.

title: Linear precoding via conic optimization for fixed MIMO receivers
abstract: In this paper, the problem of designing linear precoders for fixed multiple-input-multiple-output (MIMO) receivers is considered. Two different design criteria are considered. In the first, the transmitted power is minimized subject to signal-to-interference-plus-noise-ratio (SINR) constraints. In the second, the worst case SINR is maximized subject to a power constraint. It is shown that both problems can be solved using standard conic optimization packages. In addition, conditions are developed for the optimal precoder for both of these problems, and two simple fixed-point iterations are proposed to find the solutions that satisfy these conditions. The relation to the well-known uplink-downlink duality in the context of joint transmit beamforming and power control is also explored. The proposed precoder design is general, and as a special case, it solves the transmit rank-one beamforming problem. Simulation results in a multiuser system show that the resulting precoders can significantly outperform existing linear precoders.

title: System evaluation of optimal downlink beamforming with congestion control in wireless communication
abstract: We investigate the use of congestion control and joint optimal downlink beamforming, power control, and access point allocation, in a multi-cell wireless communication system. The access points of the system employ smart antennas and single antennas are used at the terminals. The possibility to send messages to multiple terminals at the same frequency in the same time slot is exploited. We show how previously proposed algorithms for optimal downlink beamforming easily can be extended to determine also the optimal access point for each mobile terminal. In order to assign resources, optimal beamforming requires a feasible set of mobiles, i.e. that all admitted users can be offered the required signal-to-interference-and-noise ratio. Therefore, an algorithm for deciding which mobile terminals to admit or reject from a congested system is proposed and evaluated. Using the proposed congestion algorithm, joint optimal downlink beamforming is evaluated and the throughput increase as compared to decentralized beamforming algorithms and other congestion control strategies is assessed from a system point of view. The results show that the proposed strategy can almost double the throughput compared to decentralized beamforming algorithms and give a fivefold increase in throughput compared to conventional beamforming without any interference suppression.

title: Network Duality for Multiuser MIMO Beamforming Networks and Applications
abstract: For any multiple-input multiple-output (MIMO) network with linear beamformers, it is shown that there exists a dual network that attains the same signal-to-interference-plus-noise ratio (SINR) performance. This network duality concept is a generalization of the virtual uplink concept investigated by Rashid-Farrokhi . We first develop the dual relation using a generic duality theory in linear programming. This approach naturally leads to the construction of a dual network, and provides machinery for handling a generalized cost function. We then consider the joint MIMO beamforming and power control problem with individual SINR constraints. We apply the network duality to this problem and propose a high-performance iterative algorithm which, compared with past centralized approaches, has improved convergence behavior. Finally, we propose a simpler distributed version of the algorithm tailored for a cellular downlink. This algorithm can be readily implemented in a distributed fashion, since it does not require information exchange between base stations. The algorithm achieves performance close to that of centralized ones, and outperforms other decentralized approaches available in the literature

title: Multi-cell uplink-downlink beamforming throughput duality based on Lagrangian duality with per-base station power constraints
abstract: Despite significant research efforts in beamforming, the maximum achievable downlink throughput with beamforming in a multi-cell environment is not available due to difficulty in finding optimal downlink beamforming. Thus, to reformulate the problem into a more solvable form, we derive dual uplink throughput optimization problem to multi-cell downlink beam- forming throughput maximization with per-base station (BS) power constraints based on Lagrangian duality. The optimal downlink beamforming is shown to be a minimum mean squared error (MMSE) beamforming in the dual uplink. It is also shown that the dual uplink problem achieves the same optimal throughput as the primal downlink problem.

title: On Downlink Network MIMO under a Constrained Backhaul and Imperfect Channel Knowledge
abstract: Next generation mobile communications systems will most likely employ network MIMO in order to mitigate inter-cell interference and improve system fairness and spectral efficiency. Critical issues of such schemes are, however, the large extent of backhaul infrastructure required for the information exchange between cooperating base stations, and the availability of channel knowledge at transmitter and receiver. In this paper, we consider a cooperative downlink transmission under a constrained backhaul, limited channel knowledge at base station and terminal side, and a per-antenna power constraint. We derive inner capacity bounds for different cooperation schemes through uplink/downlink duality and provide numerical results showing the superiority of certain cooperation schemes in terms of rate/backhaul tradeoff for different interference scenarios.

title: Coordinated linear beamforming in downlink multi-cell wireless networks
abstract: We consider a multi-cell wireless network with universal frequency reuse and treat the problem of co-channel interference mitigation in the downlink channel. Assuming that each base station serves multiple single-antenna mobiles via space-division multiple-access, we jointly optimize the linear beam-vectors across a set of coordinated cells and resource slots: the objective function to be maximized is the instantaneous weighted sum-rate subject to per-base-station power constraints. After deriving the general structure of the optimal beam-vectors, a novel iterative algorithm is presented which attempts to solve the Karush-Kuhn-Tucker conditions of the non-convex problem at hand. The proposed algorithm admits a distributed implementation which we illustrate. Also, various approaches to choose the initial beam-vectors are considered, one of which maximizes the signal-to-leakage-plus-noise ratio. Finally, simulation results are provided to assess the performance of the proposed algorithm.

title: Cooperative Interference Management With MISO Beamforming
abstract: In this correspondence, we study the downlink transmission in a multi-cell system, where multiple base stations (BSs) each with multiple antennas cooperatively design their respective transmit beamforming vectors to optimize the overall system performance. For simplicity, it is assumed that all mobile stations (MSs) are equipped with a single antenna each, and there is one active MS in each cell at one time. Accordingly, the system of interests can be modeled by a multiple-input single-output (MISO) Gaussian interference channel (IC), termed as MISO-IC, with interference treated as noise. We propose a new method to characterize different rate-tuples for active MSs on the Pareto boundary of the achievable rate region for the MISO-IC, by exploring the relationship between the MISO-IC and the cognitive radio (CR) MISO channel. We show that each Pareto-boundary rate-tuple of the MISO-IC can be achieved in a decentralized manner when each of the BSs attains its own channel capacity subject to a certain set of interference-power constraints (also known as interference-temperature constraints in the CR system) at the other MS receivers. Furthermore, we show that this result leads to a new decentralized algorithm for implementing the multi-cell cooperative downlink beamforming.

title: Competitive Design of Multiuser MIMO Systems Based on Game Theory: A Unified View
abstract: This paper considers the noncooperative maximization of mutual information in the Gaussian interference channel in a fully distributed fashion via game theory. This problem has been studied in a number of papers during the past decade for the case of frequency-selective channels. A variety of conditions guaranteeing the uniqueness of the Nash Equilibrium (NE) and convergence of many different distributed algorithms have been derived. In this paper we provide a unified view of the state-of- the-art results, showing that most of the techniques proposed in the literature to study the game, even though apparently different, can be unified using our recent interpretation of the waterfilling operator as a projection onto a proper polyhedral set. Based on this interpretation, we then provide a mathematical framework, useful to derive a unified set of sufficient conditions guaranteeing the uniqueness of the NE and the global convergence of waterfilling based asynchronous distributed algorithms. The proposed mathematical framework is also instrumental to study the extension of the game to the more general MIMO case, for which only few results are available in the current literature. The resulting algorithm is, similarly to the frequency-selective case, an iterative asynchronous MIMO waterfilling algorithm. The proof of convergence hinges again on the interpretation of the MIMO waterfilling as a matrix projection, which is the natural generalization of our results obtained for the waterfilling mapping in the frequency-selective case.

title: Competition Versus Cooperation on the MISO Interference Channel
abstract: We consider the problem of coordinating two competing multiple-antenna wireless systems (operators) that operate in the same spectral band. We formulate a rate region which is achievable by scalar coding followed by power allocation and beamforming. We show that all interesting points on the Pareto boundary correspond to transmit strategies where both systems use the maximum available power. We then argue that there is a fundamental need for base station cooperation when performing spectrum sharing with multiple transmit antennas. More precisely, we show that if the systems do not cooperate, there is a unique Nash equilibrium which is inefficient in the sense that the achievable rate is bounded by a constant, regardless of the available transmit power. An extension of this result to the case where the receivers use successive interference cancellation (SIC) is also provided. Next we model the problem of agreeing on beamforming vectors as a non-transferable utility (NTU) cooperative gametheoretic problem, with the two operators as players. Specifically we compute numerically the Nash bargaining solution, which is a likely resolution of the resource conflict assuming that the players are rational. Numerical experiments indicate that selfish but cooperating operators may achieve a performance which is close to the maximum-sum-rate bound.

title: Balancing Egoism and Altruism on Interference Channel: The MIMO Case
abstract: Abstract- This paper considers the so-called Multiple-Input- Multiple-Output interference channel (MIMO-IC) which has relevance in applications such as multi-cell coordination in cellular networks as well as spectrum sharing in cognitive radio networks among others. We address the design of pre- coding (i.e. beamforming) vectors at each sender with the aim of striking a compromise between beamforming gain at the intended receiver (Egoism) and the mitigation of interference created towards other receivers (Altruism). Combining egoistic and altruistic beamforming has been shown previously to be instrumental to optimizing the rates in a Multiple-Input-Single- Output (MISO) interference channel (i.e. where receivers have no interference canceling capability). Here we explore these game-theoretic concepts in the more general context of MIMO channels and use the framework of Bayesian games which allows us to derive (semi-)distributed precoding techniques. We draw parallels with important existing work on the MIMO-IC, including rate-optimizing and interference-alignment precoding techniques, and show how such techniques may be re-interpreted through a common prism based on balancing egoistic and altruistic beamforming. Our analysis and simulations attest the improvements in terms of complexity and performance.

title: Gaussian Interference Channel Capacity to Within One Bit
abstract: The capacity of the two-user Gaussian interference channel has been open for 30 years. The understanding on this problem has been limited. The best known achievable region is due to Han and Kobayashi but its characterization is very complicated. It is also not known how tight the existing outer bounds are. In this work, we show that the existing outer bounds can in fact be arbitrarily loose in some parameter ranges, and by deriving new outer bounds, we show that a very simple and explicit Han-Kobayashi type scheme can achieve to within a single bit per second per hertz (bit/s/Hz) of the capacity for all values of the channel parameters. We also show that the scheme is asymptotically optimal at certain high signal-to-noise ratio (SNR) regimes. Using our results, we provide a natural generalization of the point-to-point classical notion of degrees of freedom to interference-limited scenarios.

title: Cochannel Interference Mitigation and Cooperative Processing in Downlink Multicell Multiuser MIMO Networks
abstract: Recently, the remarkable capacity potential of multiple-input multiple-output (MIMO) wireless communication systems was unveiled. The predicted enormous capacity gain of MIMO is nonetheless significantly limited by cochannel interference (CCI) in realistic cellular environments. The previously proposed advanced receiver technique improves the system performance at the cost of increased receiver complexity, and the achieved system capacity is still significantly away from the interference-free capacity upper bound, especially in environments with strong CCI. In this paper, base station cooperative processing is explored to address the CCI mitigation problem in downlink multicell multiuser MIMO networks, and is shown to dramatically increase the capacity with strong CCI. Both information-theoretic dirty paper coding approach and several more practical joint transmission schemes are studied with pooled and practical per-base power constraints, respectively. Besides the CCI mitigation potential, other advantages of cooperative processing including the power gain, channel rank/conditioning advantage, and macrodiversity protection are also addressed. The potential of our proposed joint transmission schemes is verified with both heuristic and realistic cellular MIMO settings.

title: Base Station Cooperation for Multiuser MIMO: Joint Transmission and BS Selection
abstract: The predicted enormous capacity gain of multiple-input multiple-output (MIMO) systems is significantly limited by co-channel interference (CCI), or by realistic outdoor propagation environments. In this paper, a common framework is proposed for the study of cooperative base stations (BS), to address those problems encountered on downlink of multicell multiuser MIMO systems. Specifically, both joint transmission (JT) and BS selection among cooperative base stations are analyzed and compared with each other. Some other advantages of BS cooperation are also explored including the power gain, channel rank/conditioning advantage, and macro-diversity.

title: Throughput of Cellular Systems with Conferencing Mobiles and Cooperative Base Stations
abstract: This paper considers an enhancement to multicell processing for the uplink of a cellular system, whereby the mobile stations are allowed to exchange messages on orthogonal channels of fixed capacity (conferencing). Both conferencing among mobile stations in different cells and in the same cell (inter- and intracell conferencing, resp.) are studied. For both cases, it is shown that a rate-splitting transmission strategy, where part of the message is exchanged on the conferencing channels and then transmitted cooperatively to the base stations, is capacity achieving for sufficiently large conferencing capacity. In case of intercell conferencing, this strategy performs convolutional pre-equalization of the signal encoding the common messages in the spatial domain, where the number of taps of the finite-impulse response equalizer depends on the number of conferencing rounds. Analysis in the low signal-to-noise ratio regime and numerical results validate the advantages of conferencing as a complementary technology to multicell processing.

title: Coordinating multiple antenna cellular networks to achieve enormous spectral efficiency
abstract: Intercell interference limits the capacity of wireless networks. To mitigate this interference we explore coherently coordinated transmission (CCT) from multiple base stations to each user. To treat users fairly, we explore equal rate (ER) networks. We evaluate the downlink network efficiency of CCT as compared to serving each user with single base transmission (SBT) with a separate base uniquely assigned to each user. Efficiency of ER networks is measured as total network throughput relative to the number of network antennas at 10% user outage. Efficiency is compared relative to the baseline of single base transmission with power control, (ER-SBT), where base antenna transmissions are not coordinated and apart from power control and the assignment of 10% of the users to outage, nothing is done to mitigate interference. We control the transmit power of ER systems to maximise the common rate for ER-SBT, ER-CCT based on zero forcing, and ER-CCT employing dirty paper coding. We do so for (no. of transmit antennas per base, no. of receive antennas per user) equal to (1,1), (2,2) and (4,4). We observe that CCT mutes intercell interference enough, so that enormous spectral efficiency improvement associated with using multiple antennas in isolated communication links occurs as well for the base-to-user links in a cellular network.

title: Limited Downlink Network Coordination in Cellular Networks
abstract: We investigate the downlink throughput of cellular systems where groups of M antennas - either co-located or spatially distributed - transmit to a subset of a total population of K > M users in a coherent, coordinated fashion in order to mitigate intercell interference. We consider two types of coordination: the capacity-achieving technique based on dirty paper coding (DPC), and a simpler technique based on zero-forcing (ZF) beamforming with per-antenna power constraints. During a given frame, a scheduler chooses the subset of the K users in order to maximize the weighted sum rate, where the weights are based on the proportional-fair scheduling algorithm. We consider the weighted average sum throughput among K users per cell in a multi-cell network where coordination is limited to a neighborhood of M antennas. Consequently, the performance of both systems is limited by interference from antennas that are outside of the M coordinated antennas. Compared to a 12-sector baseline which uses the same number of antennas per cell site, the throughput of ZF and DPC achieve respective gains of 1.5 and 1.75.

title: Coordinating Base Stations for Greater Uplink Spectral Efficiency in a Cellular Network
abstract: We propose an ambitious approach towards lifting the limits imposed by cochannel interference on the uplink spectral efficiency of a cellular network, viz., coordinating several base stations in the reception of users within their coverage area, and suppressing interference between users by means of coherent linear beamforming across the base stations. We evaluate by simulation the potential gain in spectral efficiency from such coordination, when there is 1 user per base station antenna in the network, and all users (but for a small fraction in outage) must be served at a constant and common data rate. We highlight the dependence of the spectral efficiency gain on the number of rings of neighbors with which each base station is coordinated, as well as the underlying signal-to-noise ratio (SNR) distribution in the network. Results from this study point to the possibility of doubling the uplink spectral efficiency with 1-ring coordination and nearly quadrupling it with 4-ring coordination, under high-SNR conditions.

title: Coordinated Multi-cell MIMO Systems with Cellular Block Diagonalization
abstract: A clustered base transceiver station (BTS) coordination strategy is proposed to realize the gains of multiuser MIMO communication in interference-limited cellular systems. In the proposed coordination strategy, users are divided into two groups: a full intra-cluster coordination group to enhance the sum rate gain and a limited inter-cluster coordination group to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. Because of the per-BTS power constraints, three combined precoder and power allocation algorithms are considered in this paper with different performance complexity tradeoffs. Simulations show that the proposed coordination strategy improves the sum rate over conventional systems and reduces the impact of interference for the cluster-edge users.

title: Coordination in a Multi-Cell Multi-Antenna Multi-User W-CDMA System: A Beamforming Approach
abstract: The problem of designing joint power control and optimal beamforming (JPCOB) algorithms for the downlink of a coordinated multi-cell WCDMA system is considered throughout this paper. In this case, the JPCOB design is formulated as the problem of minimizing the total transmitted power in the coordinated multi-cell system, subject to a certain quality of service requirement for each user. In this paper, the performance of two JPCOB algorithms based on different beamforming approaches is compared over the coordinated multi-cell system. The first one, obtains local beamformers by means of the well-known virtual uplink-downlink duality. In contrast, the second algorithm implements multi-base beamformers, taking into account match filter equalizers at the receivers. Moreover, realistic system parameters, such as per-base station power constraints or the asynchronous nature of the signals arriving at the receivers, are taken into account. Simulation results show that the algorithm based on multi-base beamforming presents attractive properties, such as an inherent multi-base scheduling technique or a decreasing total transmitted power as the degree of coordination between base stations is increased.

title: Performance of multiuser MIMO and network coordination in downlink cellular networks
abstract: We consider a wireless network with multiple cells where base stations with multiple antennas transmit to multiple users, each with multiple antennas. Using single-user (SU) MIMO as a baseline, we evaluate the system throughput performance of multiuser (MU) MIMO with generalized zero-forcing beamforming under a multiuser proportional fair scheduling metric. We consider network MIMO extensions of this technique by coordinating transmission among clusters of spatially distributed bases. By significantly mitigating intercell interference, network MIMO provides a tradeoff between improved performance and increased backhaul complexity that depends on the coordination cluster size. We describe a general technique for simulating cellular networks that is applicable to next-generation packet-based cellular standards, and we evaluate the performance of MU and network MIMO in heavily loaded networks. Compared to the SU MIMO baseline, median system throughput can be doubled by coordinating MU MIMO transmission among clusters of 3 adjacent cells.

title: Writing on dirty paper
abstract: A channel with output Y = X + S + Z is examined, The state S \sim N(0, QI) and the noise Z \sim N(0, NI) are multivariate Gaussian random variables ( I is the identity matrix.). The input X \in R^{n} satisfies the power constraint (l/n) \sum_{i=1}^{n}X_{i}^{2} \leq P . If S is unknown to both transmitter and receiver then the capacity is \frac{1}{2} \ln (1 + P/( N + Q)) nats per channel use. However, if the state S is known to the encoder, the capacity is shown to be C^{\ast} =\frac{1}{2} \ln (1 + P/N) , independent of Q . This is also the capacity of a standard Gaussian channel with signal-to-noise power ratio P/N . Therefore, the state S does not affect the capacity of the channel, even though S is unknown to the receiver. It is shown that the optimal transmitter adapts its signal to the state S rather than attempting to cancel it.

title: Capacity and lattice strategies for canceling known interference
abstract: We consider the generalized dirty-paper channel Y=X+S+N,E{X/sup 2/}/spl les/P/sub X/, where N is not necessarily Gaussian, and the interference S is known causally or noncausally to the transmitter. We derive worst case capacity formulas and strategies for "strong" or arbitrarily varying interference. In the causal side information (SI) case, we develop a capacity formula based on minimum noise entropy strategies. We then show that strategies associated with entropy-constrained quantizers provide lower and upper bounds on the capacity. At high signal-to-noise ratio (SNR) conditions, i.e., if N is weak relative to the power constraint P/sub X/, these bounds coincide, the optimum strategies take the form of scalar lattice quantizers, and the capacity loss due to not having S at the receiver is shown to be exactly the "shaping gain" 1/2log(2/spl pi/e/12)/spl ap/ 0.254 bit. We extend the schemes to obtain achievable rates at any SNR and to noncausal SI, by incorporating minimum mean-squared error (MMSE) scaling, and by using k-dimensional lattices. For Gaussian N, the capacity loss of this scheme is upper-bounded by 1/2log2/spl pi/eG(/spl Lambda/), where G(/spl Lambda/) is the normalized second moment of the lattice. With a proper choice of lattice, the loss goes to zero as the dimension k goes to infinity, in agreement with the results of Costa. These results provide an information-theoretic framework for the study of common communication problems such as precoding for intersymbol interference (ISI) channels and broadcast channels.

title: Trellis and convolutional precoding for transmitter-based interference presubtraction
abstract: This paper studies the combination of practical trellis and convolution codes with Tomlinson-Harashima precoding (THP) for the presubtraction of multiuser interference that is known at the transmitter but not known at the receiver. It is well known that a straightforward application of THP suffers power, modulo, and shaping losses. This paper proposes generalizations of THP that recover some of these losses. At a high signal-to-noise ratio (SNR), the precoding loss is dominated by the shaping loss, which is about 1.53 dB. To recover shaping loss, a trellis-shaping technique is developed that takes into account the knowledge of a noncausal interfering sequence, rather than just the instantaneous interference. At rates of 2 and 3 bits per transmission, trellis shaping is shown to be able to recover almost all of the 1.53-dB shaping loss. At a low SNR, the precoding loss is dominated by power and modulo losses, which can be as large as 3-4 dB. To recover these losses, a technique that incorporates partial interference presubtraction (PIP) within convolutional decoding is developed. At rates of 0.5 and 0.25 bits per transmission, PIP is able to recover 1-1.5 dB of the power loss. For intermediate SNR channels, a combination of the two schemes is shown to recover both power and shaping losses.

title: Multiaccess Fading Channels-Part I: Polymatroid Structure, Optimal Resource Allocation and Throughput Capacities
abstract: In multiaccess wireless systems, dynamic allocation of resources such as transmit power, bandwidths, and rates is an important means to deal with the time-varying nature of the environment. We consider the problem of optimal resource allocation from an information-theoretic point of view. We focus on the multiaccess fading channel with Gaussian noise, and define two notions of capacity depending on whether the traffic is delay-sensitive or not. We characterize the throughput capacity region which contains the long-term achievable rates through the time-varying channel. We show that each point on the boundary of the region can be achieved by successive decoding. Moreover, the optimal rate and power allocations in each fading state can be explicitly obtained in a greedy manner. The solution can be viewed as the generalization of the water-filling construction for single-user channels to multiaccess channels with arbitrary number of users, and exploits the underlying polymatroid structure of the capacity region.

title: On the duality of Gaussian multiple-access and broadcast channels
abstract: We define a duality between Gaussian multiple-access channels (MACs) and Gaussian broadcast channels (BCs). The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of the BC (both constant and fading) can be written in terms of the capacity region of the dual MAC, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the BC is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different capacity definitions for fading channels such as outage capacity and minimum-rate capacity. Using duality, many results known for only one of the two channels can be extended to the dual channel as well.

title: Precoding for the Multiantenna Downlink: Multiuser SNR Gap and Optimal User Ordering
abstract: This paper develops a practical design method for implementing Tomlinson-Harashima precoding (THP) in a downlink channel with multiple antennas at the transmitter and a single antenna at each receiver. A two-step design process is proposed for minimizing the total transmit power while satisfying every user's minimum data rate and maximum bit-error rate (BER) requirements. First, the BER and rate requirements are converted to "virtual rate" requirements, which account for the gap-to-capacity introduced by practical quadrature amplitude modulation (QAM) and THP. The second step is to determine the transmit covariance matrices (which specify the entire THP system) that will provide these virtual rates at the minimum total transmit power. As one of the main features in the proposed scheme, an algorithm for finding the optimal user encoding (or presubtraction) order in polynomial time is proposed. In addition, we also propose an algorithm that finds a near-optimal order, but which is much less complex. The proposed method outperforms existing zero-forcing-based THP systems in term of power efficiency

title: Achievable Rates for the Gaussian Interference Relay Channel
abstract: In this paper, an interference relay channel where two independent sources communicate with two destinations by the help of a relay is studied. The relay is full-duplex and employs decode-forward type strategy. Using Carleial's rate splitting where each source transmits common messages to be decoded at both destinations and private messages for the desired destination, an achievable rate region is obtained. The relay decodes both common and private messages and transmits them cooperatively with the sources to the destinations. For the symmetric Gaussian interference relay channel, the results show that the maximum rate sum is achieved when the relay helps the sources in the transmission of common messages only. Moreover, unlike the regular interference channel, when the relay is present, the sources continue to transmit common information even when the interfering links can support much less rate than the direct links.

title: On Achievable Rates for Interference Relay Channel with Interference Cancelation
abstract: We consider two interfering source-destination pairs that are assisted by a common relay. The relay simultaneously helps both sources to improve communication rates. We provide coding strategies that combine dirty paper coding, beamforming and interference reduction techniques at the relay and give an achievable rate region for Gaussian interference relay channel. The region shows significant rate gain can be obtained by performing generalized dirty-paper coding at the relay.

title: On the capacity of the interference channel with a relay
abstract: Capacity gains due to relaying in wireless networks with multiple source-destination pairs are analyzed. A two- source, two-receiver network with the relay is considered. The focus is on the scenario in which, due to channel conditions, the relay can observe the signal from only one source. The relay can thus help the intended receiver of this message, via message forwarding, to decode it. In addition, the relay can simultaneously help the unintended receiver subtract the interference associated with this message. We call the latter strategy interference forwarding. An achievable rate region employing decode-and-forward (that simultaneously does message and interference forwarding) at the relay is derived and analyzed. This strategy is shown to achieve the capacity region under certain conditions. Our results demonstrate that the relay can help both receivers, despite the fact that it forwards only the message intended for one of them. This applies in general to communications in the presence of an interferer transmitting at any arbitrary rate. Interference forwarding improves reception of interfering signals at the receivers. This facilitates decoding of the unwanted messages and eliminating the resulting interference. Therefore, in networks with multiple source-destination pairs, in addition to relaying messages, interference forwarding may also be employed to help in combating interference.

title: Relay strategies for interference-forwarding
abstract: We consider relaying strategies in networks with multiple source-destination pairs and possibly additional outside sources of interference. We study these networks in the discrete, memoryless setup, and focus on relaying strategies based on forwarding the interference. In particular, the relay encodes the interference signal so as to make it easier for the receiver to remove it. The objective is to help receivers with weak interference by making the interference strong enough so that these receivers are able to cancel it completely. Our proposed approach is a combination of ideas from decode-and-forward (DF) and/or estimate-and-forward (EF) but applied to the interfering signal rather than the desired signal. When based only on DF, the relay first decodes (part of) the interfering signal it wants to enhance. It then encodes the interference in such a way as to increase the interference at the assisted receiver. The rate of the relayed interference is not limited by the rate from the relay to the original destination of the forwarded message, thus, interference cancellation is not a by-product of enhancing the desired information at its intended destination, but a goal in itself. We call this method interference-forwarding (IF). IF can also be based on EF where, instead of forwarding the exact interfering signal, the relay simply sends a compressed version of it to the assisted receiver. Rate increase can thus be obtained even if the signal received at the relay is independent of the desired message and consists only of interference and noise.

title: Capacity of a Class of Deterministic Relay Channels
abstract: The capacity of a class of deterministic relay channels with the transmitter input X, the receiver output Y, the relay output Y1 = f(X,Y), and a separate communication link from the relay to the receiver with capacity R0, is shown to be C(R0) =max min{I(X;Y) + R0, I(X;Y,Y1)}.  Thus every bit from the relay is worth exactly one bit to the receiver. Two alternative coding schemes are presented that achieve this capacity. The first scheme, "hash-and-forward", is based on a variation of the usual random binning on the relay outputs, while the second scheme uses the usual "compress-and- forward". In fact, these two schemes can be combined to give a class of optimal coding schemes. As a corollary, this relay capacity result confirms a conjecture by Ahlswede and Han on the capacity of a channel with rate-limited state information at the decoder in the special case when the channel state is recoverable from the channel input and output.

title: Capacity of a Class of Deterministic Relay Channels
abstract: The capacity of a class of deterministic relay channels with the transmitter input X, the receiver output Y, the relay output Y1 = f(X,Y), and a separate communication link from the relay to the receiver with capacity R0, is shown to be C(R0) =max min{I(X;Y) + R0, I(X;Y,Y1)}.  Thus every bit from the relay is worth exactly one bit to the receiver. Two alternative coding schemes are presented that achieve this capacity. The first scheme, "hash-and-forward", is based on a variation of the usual random binning on the relay outputs, while the second scheme uses the usual "compress-and- forward". In fact, these two schemes can be combined to give a class of optimal coding schemes. As a corollary, this relay capacity result confirms a conjecture by Ahlswede and Han on the capacity of a channel with rate-limited state information at the decoder in the special case when the channel state is recoverable from the channel input and output.

title: Coding Techniques for Primitive Relay Channels
abstract: We give a comprehensive discussion on coding techniques for the primitive relay channel, in which the channel input X is transmitted to the relay Y1 and the ultimate receiver Y over a channel p(y, y1|x) and the relay can facilitate the communication between the transmitter and the receiver by sending some information to the receiver over a separate noiseless link of capacity R0. In particular, we compare three known coding schemes, “decode-and-forward,” “compress-andforward,” and “hash-and-forward,” clarify their limitations, and explore further extensions. Possible unification of these coding schemes is also discussed, as well as a few open problems reflecting major difficulties in proving optimality.

title: Universal relaying for the interference channel
abstract: This paper considers a Gaussian relay-interference channel and introduces a generalized hash-and-forward relay strategy, where the relay sends out a bin index of its quantized observation, and the receivers first decode the relay quantization codeword to a list, then use the list to help decode the respective messages from the transmitters. The main advantage of the proposed approach is in a scenario where the relay observes a linear combination of the transmitted signals and broadcasts a common relay message through a digital relay link of fixed rate to help both receivers of the interference channel. We show that when compared to the achievable rates with interference treated as noise, generalized hash-and-forward can provide one bit of rate improvement for every relay bit for both users at the same time in an asymptotic regime where the background noises go down to zero. The proposed approach is universal, in contrast to the compress-and-forward or amplify-and-forward strategies which are not asymptotically optimal for multiple users simultaneously, if at all.

title: Interference Management Using Nonlinear Relaying
abstract: We consider the three-node Gaussian relay channel where the relay observes a noisy version of the interference present in the source--destination link. We investigate three fundamental relaying approaches: linear relaying, memoryless nonlinear relaying, and compress-and-forward (CF). For interference-limited cases, we illustrate that optimized memoryless nonlinear relaying almost achieves the capacity.

title: Capacity of Interference Channels With Partial Transmitter Cooperation
abstract: Capacity regions are established for several two-sender, two-receiver channels with partial transmitter cooperation. First, the capacity regions are determined for compound multiple-access channels (MACs) with common information and compound MACs with conferencing. Next, two interference channel models are considered: an interference channel with common information (ICCI) and an interference channel with unidirectional cooperation (ICUC) in which the message sent by one of the encoders is known to the other encoder. The capacity regions of both of these channels are determined when there is strong interference, i.e., the interference is such that both receivers can decode all messages with no rate penalty. The resulting capacity regions coincide with the capacity region of the compound MAC with common information.

title: Zero-forcing for the symmetric Interference Channel with conferencing encoders
abstract: A two-user Gaussian Interference Channel (GIC) is considered in which encoders are connected through noiseless links with finite capacities. New genie-aided upper bounds on the sum-capacity are developed which incorporate the capacities of the cooperative links. When the GIC is symmetric, with possibly different cooperation link capacities, the sum-capacity is characterized within 2.13 bits gap for all values of the channel parameters. In the achievable scheme, each transmitter sends a private and a common message, and zero-forces the part of the other transmitter's private message, communicated over the conference between the encoders.

title: On Base Station Cooperation Schemes for Downlink Network MIMO under a Constrained Backhaul
abstract: Next generation mobile communications systems will most likely employ multi-cell cooperative signal processing schemes, often referred to as network MIMO, as these are known to effectively combat inter-cell interference and improve system fairness and spectral efficiency. A major downside of such schemes is, however, the large extent of backhaul infrastructure required for the information exchange between cooperating base stations. In this paper, we observe a cooperative downlink transmission from two base stations to two terminals under different extents of available backhaul capacity. We adapt some well-known concepts from the Gaussian interference channel and observe a variety of possible cooperation schemes. We observe that it is beneficial to use an adaptive cooperation concept, where the base stations exchange either the data to be jointly transmitted itself or partially preceded and compressed signals, depending on the instantaneous channel realization.

title: Partial zero-forcing precoding for the interference channel with partially cooperating transmitters
abstract: A communication model is considered in which the classic two-user Gaussian interference channel is augmented by noiseless rate-limited digital conferencing links between the transmitters. We propose a partial zero-forcing precoding strategy based on a shared-private rate splitting scheme at the transmitter, in which each transmitter communicates part of its message to the other transmitter, and subsequently partially pre-subtracts the interfering signal using a zero-forcing precoder. We prove an outer bound and show that the proposed strategy is asymptotically sum-capacity achieving in a very weak interference regime, where both the signal-to-noise ratio (SNR) and the interference-to-noise ratio (INR) go to infinity while their ratio in dB scale is kept fixed. In this case, every cooperation bit results in one-bit gain in sum capacity. We also consider a different asymptotic regime where the transmit power constraints and the channel gains are fixed while the noise powers go down to zero. In this case, if one compares with the achievable sum rate with interference treated as noise, one cooperation bit can in fact result in more than one-bit gain in achievable sum rate.

title: On the Optimal Number of Cooperative Base Stations in Network MIMO Systems
abstract: We consider a multi-cell, frequency-selective fading, uplink channel (network MIMO) where K user terminals (UTs) communicate simultaneously with B cooperative base stations (BSs). Although the potential benefit of multi-cell cooperation grows with B, the overhead related to the acquisition of channel state information (CSI) will rapidly dominate the uplink resource. Thus, there exists a non-trivial tradeoff between the performance gains of network MIMO and the related overhead in channel estimation for a finite coherence time. Using a close approximation of the net ergodic achievable rate based on recent results from random matrix theory, we study this tradeoff by taking some realistic aspects into account such as unreliable backhaul links and different path losses between the UTs and BSs. We determine the optimal training length, the optimal number of cooperative BSs and the optimal number of sub-carriers to be used for an extended version of the circular Wyner model where each UT can communicate with B BSs. Our results provide some insight into practical limitations as well as realistic dimensions of network MIMO systems.

title: Team decision for the cooperative MIMO channel with imperfect CSIT sharing
abstract: We consider the problem of joint MIMO precoding across multiple distant cooperating transmitters. The transmitters are assumed to be sharing user data and aim at serving a group of users in a distributed MIMO broadcast-like fashion. Among application scenarios, we find the so-called network MIMO setup. The novelty of our setup resides in the fact that each of the transmitters obtains imperfect and importantly, different, estimates of the same global multi-user channel. Despite not sharing the same vision over the CSIT, the transmitters seek to jointly act in a consistent manner in designing the precoders. This problem in facts falls in the class of so-called Team Decision Theory problems. We present some solutions to the problem of beamforming design in this case and illustrate the benefits in practical network scenarios.

title: Iterative multiuser detection, macrodiversity combining, and decoding for the TDMA cellular uplink
abstract: A soft-input soft-output (SISO) multiuser detector (MUD) suitable for inclusion in iterative processing architectures is presented and applied to the detection of the coded time division multiple access (TDMA) cellular uplink. A SISO-MUD processor is located at each base station in the network, and adjacent base stations share information concerning the mobiles they serve. Because the MUD outputs are soft, they are suitable for postdetection macrodiversity combining. The combined signals are then passed to a SISO forward error correction (FEC) decoder, and the soft outputs are fed back to the multiuser detectors. Processing continues in an iterative fashion in accordance with the turbo principle. Simulation results are presented that indicate that use of such a scheme enables cellular systems to be overloaded with more than just one cochannel user per cell at the price of a minimal loss in signal-to-noise ratio (SNR). The proposed implementation assumes the availability of both perfect channel state information and a high capacity backhaul.

title: Turbo Base-Station Cooperation for Intercell Interference Cancellation
abstract: Interference cancellation is an important issue since the coverage and capacity in the uplink are mainly interference limited. The interference from the own cell can be mitigated by multiuser detection. However, there does not exist a powerful interference cancellation technique for the interference from neighboring cells, the intercell interference. This work proposes a technique for combating the intercell interference. Since base-stations in wireless systems are connected through a backbone network, we propose the exchange of information through the network between the base-stations, in order to help each other in the detection of the signals. We present several strategies how this could be performed. Especially, we propose an iterative way for reducing the intercell interference: The Turbo Base-Station Cooperation. Simulation results show remarkable gains, especially in the presence of a strong interferer.

title: A computational paradigm for space-time multiuser detection
abstract: In a general wireless system, cells are loosely defined and user signals appear at multiple antennas with various powers and delays. Despite the enormous performance benefits of system-wide maximum-likelihood multiuser detection (ML MUD), its application to such systems is hampered by the lack of a regular structure. Prior work usually dismisses the possibility on computational grounds as exponential in the total number of users, at least. This paper is the first to address efficient computation of system-wide ML MUD. We present a computational organization that achieves dramatic reduction in complexity through exploitation of the partial overlap of user sets at different antennas. This algorithm, which applies to code-division multiple access or narrowband systems, can be viewed as a spatio-temporal extension of the well-known Viterbi algorithm (VA), and, like the VA, it is derived from dynamic programming principles.

title: Distributed Decoding for Wyner Cellular Systems
abstract: This paper investigates a one-dimensional model of a cellular Gaussian multiple-access channel based on the model in- troduced by Wyner. A closed form expression is given for the sum- rate constraint with a finite number of cells. It is demonstrated that optimal joint decoding can be accomplished using a variation of the forward-backward algorithm that operates on the posterior codeword probabilities.

title: Information capacity of wyner's cellular network with LMMSE receivers
abstract: We derive the Linear Minimum Mean Square Error (LMMSE) receiver for Wyner's model of a linear cellular array. By exploiting the special structure of the channel model, we obtain explicit Mean Square Error (MSE) expressions and information capacity formulae for both finite-sized as well as infinite-sized linear cellular arrays. We show that the performance of an individual user becomes insensitive to the array size for large array sizes and that the proportion of users achieving almost the same performance converges to one, as the array size tends to infinity. The effects of intercell interference and noise on the performance of each user are also investigated.

title: Distributed linear multiuser detection in cellular networks based on Kalman smoothing
abstract: We consider the problem of multiuser detection in cellular networks. In particular, we present a distributed forward-backward algorithm with local message passing for efficient implementation of the linear minimum mean square error (LMMSE) receiver, for a simple model of a 1D cellular system. The distributed algorithm is based on the well-known interpretation of Kalman smoothing as a linear combination of the forward and backward filtered estimates. We also show that near-optimal performance can be achieved by only relying on information from a local linear segment of the entire array. This results in a limited extent distributed algorithm that greatly reduces processing delay, especially for large networks, yet with little loss in performance.

title: Distributed Downlink Beamforming in Cellular Networks
abstract: We consider a cellular network where base stations can cooperate to determine the signals to be transmitted on the downlink. Using a particular downlink beamformer structure, we recast our downlink beamforming problem as a virtual linear minimum mean square error (LMMSE) estimation problem. Based on this virtual set up, we remodel the network as a factor graph with loops and present a simple distributed cooperative scheme for base stations based on the sum-product algorithm. We study the condition for convergence for the distributed algorithm and demonstrate its performance via simulations.

title: Distributed Downlink Beamforming With Cooperative Base Stations
abstract: In this paper, we consider multicell processing on the downlink of a cellular network to accomplish ldquomacrodiversityrdquo transmit beamforming. The particular downlink beamformer structure we consider allows a recasting of the downlink beamforming problem as a virtual linear mean square error (LMMSE) estimation problem. We exploit the structure of the channel and develop distributed beamforming algorithms using local message passing between neighboring base stations. For 1-D networks, we use the Kalman smoothing framework to obtain a forward-backward beamforming algorithm. We also propose a limited extent version of this algorithm that shows that the delay need not grow with the size of the network in practice. For 2-D cellular networks, we remodel the network as a factor graph and present a distributed beamforming algorithm based on the sum-product algorithm. Despite the presence of loops in the factor graph, the algorithm produces optimal results if convergence occurs.

title: Reduced-Complexity Belief Propagation for System-Wide MUD in the Uplink of Cellular Networks
abstract: System-wide multiuser detection (MUD), in which all base stations (BSs) of a cellular system cooperate to detect the data of all mobile stations (MSs), has much promise. However, little is known at present about practical techniques or their performance. An attractive method is belief propagation (BP), with message exchange between nearby cooperating BSs over a backbone landline network, but its performance is known only for a greatly simplified network model and its computation load grows exponentially with the number of interfering MS symbols at each BS. In this paper, we present a reduced complexity variation of BP (RCBP) and show that its performance is close to or identical to that of BP in the simplified network. We also observe excellent performance by iterative multiuser detection and decoding of low-density parity check codes (LDPC). Furthermore, we examine RCBP performance in a realistic wireless network model, with path loss, shadowing, fading and power control. These results, though poorer than those of the simplified network, show that system-wide MUD with cooperating BSs provides great improvement compared with conventional systems.

title: Linear Multiuser Receivers: Effective Interference, Effective Bandwidth and User Capacity
abstract: Multiuser receivers improve the performance of spread-spectrum and antenna-array systems by exploiting the structure of the multiaccess interference when demodulating the signal of a user. Much of the previous work on the performance analysis of multiuser receivers has focused on their ability to reject worst case interference. Their performance in a power-controlled network and the resulting user capacity are less well-understood. We show that in a large system with each user using random spreading sequences, the limiting interference effects under several linear multiuser receivers can be decoupled, such that each interferer can be ascribed a level of effective interference that it provides to the user to be demodulated. Applying these results to the uplink of a single power-controlled cell, we derive an effective bandwidth characterization of the user capacity: the signal-to-interference requirements of all the users can be met if and only if the sum of the effective bandwidths of the users is less than the total number of degrees of freedom in the system. The effective bandwidth of a user depends only on its own SIR requirement, and simple expressions are derived for three linear receivers: the conventional matched filter, the decorrelator, and the MMSE receiver. The effective bandwidths under the three receivers serve as a basis for performance comparison.

title: Clustered local decoding for Wyner-type cellular models
abstract: 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.

title: On the Capacity of MIMO Cellular Networks with Macrodiversity
abstract: We consider the information theoretic limits of the uplink in a MIMO cellular network with two types of macrodiversity. In the first case, the whole network acts as a multi-access channel where every base station antenna array is part of a central receiver (global macrodiversity). In the second case, we partition the network into clusters of cooperating base stations (local macrodiversity) thereby eliminating the growth in complexity at the receiver with network size. Macrodiversity is shown to provide very significant gains in sum capacity over single cell processing schemes where co-channel interference is the dominant impairment. We also explore the rate at which the sum capacity of the local macrodiversity scheme approaches that of global macrodiversity as the cluster size increases.

title: Multiuser MIMO downlink with limited inter-cell cooperation: Approximate interference alignment in time, frequency and space
abstract: We consider a realistic albeit simplified scenario for wireless cellular systems of the next generation (4G and beyond), where MIMO-OFDM, opportunistic scheduling, channel state information at the transmitter and limited base-station cooperation are envisaged. We propose two strategies with limited base-station cooperation that can be easily implemented with today's technology and achieve an approximate form of inter-cell interference alignment. The first strategy consists of imposing a ldquopower maskrdquo in frequency such that adjacent cooperative clusters of base stations generate different interference levels in different frequency subchannels. The second strategy consists of switching between different cooperative clusters such that no user is in a permanently disadvantaged location.We compare single-user and multiuser MIMO systems in terms of average throughput as a function of the user location.

title: Sum Rate of Linear Cellular Systems with Clustered Joint Processing
abstract: In this paper we derive the sum rate of the uplink of a linear network of cells when clustered coordinated processing is adopted among the base stations in a generalised fading environment. Various cluster isolation schemes along with an interference allowance scheme are analysed and compared in terms of achievable sum rate with each other and to the optimum case of a system with central processor. Numerical results are produced for a real-world scenario.

title: A Framework for Optimizing the Uplink Performance of Distributed Antenna Systems under a Constrained Backhaul
abstract: It has recently been shown that multi-cell cooperations in cellular networks, enabling distributed antenna systems and joint transmission or joint detection across cell boundaries, can significantly increase capacity, especially that of users at cell borders. Such concepts, typically implicitly assuming unlimited information exchange between base stations, can also be used to increase the network fairness. In practical implementations, however, the large amounts of received signals that need to be quantized and transmitted via an additional backhaul between the involved cells to central processing points, will be a non-negligible issue. In this paper, we thus introduce an analytical framework to observe the uplink performance of cellular networks in which joint detection is only applied to a subset of selected users, aiming at achieving best possible capacity and fairness improvements under a strongly constrained backhaul between sites. This reveals a multi-dimensional optimization problem, where we propose a simple, heuristic algorithm that strongly narrows down and serializes the problem while still yielding a significant performance improvement.

title: A Dynamic Clustering Approach in Wireless Networks with Multi-Cell Cooperative Processing
abstract: Multi-cell cooperative processing (MCP) has recently attracted a lot of attention because of its potential for co-channel interference (CCI) mitigation and spectral efficiency increase. MCP inevitably requires increased signaling overhead and inter-base communication. Therefore in practice, only a limited number of base stations (BSs) can cooperate in order for the overhead to be affordable. The intrinsic problem of which BSs shall cooperate in a realistic scenario has been only partially investigated. In this contribution linear beamforming has been considered for the sum-rate maximisation of the uplink. A novel dynamic greedy algorithm for the formation of the clusters of cooperating BSs is presented for a cellular network incorporating MCP. This approach is chosen to be evaluated under a fair MS scheduling scenario (round-robin). The objective of the clustering algorithm is sum-rate maximisation of the already selected MSs. The proposed cooperation scheme is compared with some fixed cooperation clustering schemes. It is shown that a dynamic clustering approach with a cluster consisting of 2 cells outperforms static coordination schemes with much larger cluster sizes.

title: Networked MIMO with clustered linear precoding
abstract: A clustered base transceiver station (BTS) coordination strategy is proposed for a large cellular MIMO network, which includes full intra-cluster coordination-to enhance the sum rate-and limited inter-cluster coordination-to reduce interference for the cluster edge users. Multi-cell block diagonalization is used to coordinate the transmissions across multiple BTSs in the same cluster. To satisfy per-BTS power constraints, three combined precoder and power allocation algorithms are proposed with different performance and complexity tradeoffs. For inter-cluster coordination, the coordination area is chosen to balance fairness for edge users and the achievable sum rate. It is shown that a small cluster size (about 7 cells) is sufficient to obtain most of the sum rate benefits from clustered coordination while greatly relieving channel feedback requirement. Simulations show that the proposed coordination strategy efficiently reduces interference and provides a considerable sum rate gain for cellular MIMO networks.

title: Multiple Frequency Offset Estimation for the Downlink of Coordinated MIMO Systems
abstract: We consider downlink MIMO beamforming from several coordinated basestations (BSs), and the associated problem of in dependent carrier frequency offsets (CFOs) at the BSs which cause accumulated phase errors to compromise beamforming accuracy. Correction of the CFOs requires estimation of their values, so our topic is multiple CFO estimation, a little-explored area. We present a robust and easily generalized estimator that accounts for the training sequence (TS) correlations caused by the CFOs, and show that it meets the Cramer-Rao lower bound (CRLB) at moderate signal-to-noise ratios (SNRs). The performance of the estimator is contingent upon TSs short enough to ensure convexity of the log-likelihood over the allowable CFO ranges. For combinations of TS length and CFO range that violate this constraint, we present two suboptimal estimators based on segmentation of the TS, both of which also meet the CRLB at moderate to high SNRs.

title: Joint Detection and CFO Compensation in Asynchronous Multi-User MIMO OFDM Systems
abstract: It is well known that carrier frequency offsets caused by inaccuracies of local oscillators between transmitter and receiver stations destroy the orthogonality among OFDM subcarriers and induce additional intercarrier interference. In conjunction with MIMO transmission where different users interfere with each other, this effect strongly degrades the signal detection performance if it is not compensated beforehand. In the uplink of multi-user systems different CFOs between all mobile terminals occur whereas its correction is more difficult. In this paper we consider the uplink of a fully asynchronous system with different transmitter and receiver CFOs which appears in distributed MIMO systems with separate users and base stations. We describe a combined scheme for joint CFO correction and spatial layer detection in frequency domain. The detection performance is shown for some selected equaliser concepts. In this way we present interference cancellation algorithms with low and scalable complexity. Finally, numerical simulation results are provided to compare the detection performance.

title: On Uplink Network MIMO under a Constrained Backhaul and Imperfect Channel Knowledge
abstract: It is known that next generation mobile communications systems will most likely employ multi-cell signal processing - often referred to as network MIMO - in order to improve spectral efficiency and fairness. Many publications exist that predict strong achievable rate improvements, but usually neglecting various practical issues connected to network MIMO. In this paper, we analyse the impact of a constrained backhaul infrastructure and imperfect channel knowledge on uplink network MIMO from an information theoretical point of view. Especially the latter aspect leads to the fact that the channel conditions for which network MIMO is reasonably beneficial are strongly constrained. We observe different base station cooperation schemes in scenarios of maximal 3 base stations and 3 terminals, provide simulation results, and discuss the practicability of the discussed schemes and the implications of our results.

title: Determining backhaul bandwidth requirements for network MIMO
abstract: In systems employing coordinated base station transmission and reception (also known as network MIMO), information needs to be shared among clusters of coordinated bases. This information includes coherent channel state information, user data, and baseband received signals. The cost of leasing and maintaining a reliable backhaul to share this information will be the dominant operational expense for cellular systems with network MIMO. In this paper we analyze the bandwidth requirements for sharing information among coordinated bases for network MIMO as a function of the coordination cluster size and channel characteristics. We find that for moderate Doppler speeds, the channel state information is a negligible fraction of the overall backhaul bandwidth. We also show that sending linearly quantized baseband signals over the backhaul achieves a significant fraction of ideal unquantized sum rate performance for uplink network MIMO based on zero-forcing.

title: A WiMAX-Based Implementation of Network MIMO for Indoor Wireless Systems
abstract: It is well known that multiple-input multiple-output (MIMO) techniques can bring numerous benefits, such as higher spectral efficiency, to point-to-point wireless links. More recently, there has been interest in extending MIMO concepts to multiuser wireless systems. Our focus in this paper is on network MIMO, a family of techniques whereby each end user in a wireless access network is served through several access points within its range of influence. By tightly coordinating the transmission and reception of signals at multiple access points, network MIMO can transcend the limits on spectral efficiency imposed by cochannel interference. Taking prior information-theoretic analyses of network MIMO to the next level, we quantify the spectral efficiency gains obtainable under realistic propagation and operational conditions in a typical indoor deployment. Our study relies on detailed simulations and, for specificity, is conducted largely within the physical-layer framework of the IEEE 802.16e Mobile WiMAX system. Furthermore, to facilitate the coordination between access points, we assume that a high-capacity local area network, such as Gigabit Ethernet, connects all the access points. Our results confirm that network MIMO stands to provide a multiple-fold increase in spectral efficiency under these conditions.

title: Multisite field trial for LTE and advanced concepts
abstract: The 3GPP LTE standard is stable now in its first release (Release 8), and the question is how good its performance is in real-world scenarios. LTE is also a good base for further innovations, but it must be proven that they offer performance advantages for the price of their complexity. This article evaluates the performance of LTE Release 8 as a baseline and advanced concepts currently in discussion such as cooperative MIMO based on system-level simulations, and measurements in the laboratory and a multisite field testbed within the EASY-C project.

title: Field trials using coordinated multi-point transmission in the downlink
abstract: We report on field trials using CoMP transmission in the downlink of a mobile radio network. Two new features enable over-the-air CoMP transmission from physically separated base stations and terminals. These are distributed synchronization and a fast virtual local area network. Using VLAN tags, terminals feed back the multi-cell channel state information to their serving bases where it is multiplexed with shared data. Both are multicast to other cooperative base stations over the backhaul. In our trials, two terminals are served in two overlapping cells and placed in specific indoor, outdoor-to-indoor and outdoor scenarios. We have realized both intra-site as well as inter-site CoMP. While outage is indeed a big problem at the cell edge with full frequency reuse, with CoMP it is not observed anymore. Average throughput gains by factors 4 to 22 are observed when using CoMP compared to interference-limited transmission while between 27 and 78% of the isolated cell throughput is measured in both cells simultaneously.