Benjamin M. Zaidel

Cooperative Wireless Cellular Systems: An Information-Theoretic View

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

Spectral Efficiency of Joint Multiple Cell-Site Processors for Randomly Spread DS-CDMA Systems

A chip-interleaved randomly spread direct-sequence code-division multiple-access (DS-CDMA) scheme is considered, employed in two variants of Wyners infinite linear cell-array model with flat fading. Focusing on the asymptotic setup in which both the number of users per cell and the processing gain go to infinity, while their ratio (the ldquocell loadrdquo) goes to some finite constant, the spectral efficiencies of the optimum and linear minimum mean-squared error (MMSE) joint multicell receivers are investigated. A dramatic performance enhancement as compared to single-cell-site processing is demonstrated. The asymptotic behavior of the two receivers in extreme signal-to-noise ratio (SNR) regimes and in a high cell-load regime are analyzed as well. The impact of chip interleaving versus symbol interleaving is also investigated. Chip-level interleaving is found beneficial in several cases of interests, and is conjectured to be beneficial in general.

Vector Precoding for Gaussian MIMO Broadcast Channels: Impact of Replica Symmetry Breaking

The “replica method” of statistical physics is employed for the large-system analysis of vector precoding for the Gaussian multiple-input multiple-output broadcast channel. The transmitter comprises a linear front-end combined with nonlinear precoding, minimizing transmit energy by means of input alphabet relaxation. For the common discrete lattice-based relaxation, the problem violates replica symmetry and a replica symmetry breaking (RSB) ansatz is taken. The limiting empirical distribution of the precoders output and the limiting transmit energy are derived for one-step RSB. Particularizing to a “zero-forcing” (ZF) linear front-end, a decoupling result is derived. For discrete lattice-based relaxations, the impact of RSB is demonstrated for the transmit energy. The spectral efficiencies of the aforementioned precoding methods are compared to linear ZF and Tomlinson-Harashima precoding (THP). Focusing on quaternary phase shift-keying (QPSK), significant performance gains of both lattice and convex relaxations are revealed for medium to high signal-to-noise ratios (SNRs) when compared to linear ZF precoding. THP is shown to be outperformed as well. Comparing certain lattice-based relaxations for QPSK against a convex counterpart, the latter is found to be superior for low and high SNRs but slightly inferior for medium SNRs in terms of spectral efficiency.

Spectral efficiency of joint multiple cell-site processors for randomly spread DS-CDMA systems

We consider a chip-interleaved randomly spread DS-CDMA scheme employed in Wyners infinite linear cell-array model with flat fading. Focusing on the asymptotic setup, the per-cell spectral efficiencies of the optimum and linear MMSE joint multicell receivers are considered. Performance enhancement as compared to single-cell-site processing is demonstrated. The asymptotic behavior of the two receivers in extreme SNR regimes and in a high cell-load setup is analyzed as well. The impact of chip interleaving vs. symbol interleaving is also considered.

Information-theoretic implications of constrained cooperation in simple cellular models

Recent information theoretic results on cooperation in cellular systems are reviewed, addressing both multicell processing (cooperation among base stations) and relaying (cooperation at the user level). Two central issues are addressed, namely, first multicell processing is studied with either limited-capacity backhaul links to a central processor or only local (and finite-capacity) cooperation among neighboring cells. The role of codebook information, decoding delay and network planning (frequency reuse) are specifically highlighted along with the impact of different transmission/ reception strategies. Next, multicell processing is considered in the presence of cooperation at the user level, focusing on both out-of-band relaying via conferencing users and in-band relaying by means of dedicated relays. Non-fading and fading uplink and downlink channels adhering to simple Wyner-type, cellular system models are targeted.

On the impact of limited-capacity backhaul and inter-users links in cooperative multicell networks

Cooperation based technologies are expected to play a major role in future cellular or, more generally, infrastructure networks. Both multicell processing (cooperation at the base station level) and relaying (cooperation at the user level) are currently being studied. Here, recent works dealing with the performance of multicell processing and user cooperation under the assumption of error-free but limited-capacity inter-base station and inter-user links, respectively, are considered. The survey focuses on related results derived for non-fading uplink and downlink channels of simple cellular setups. The analytical treatment, facilitated by these simple models, enhances the insight into the limitations imposed by capacity constraints on the performance gains provided by cooperative techniques.

On the dirty paper channel with fading dirt

We consider a generalization of Costas “writing on dirty paper” channel. In this generalization, the interference is multiplied by a fading coefficient, which changes in an i.i.d. manner between time instances, according to a general distribution. The value of this fading coefficient is unknown at the transmitter, representing a realistic scenario of imperfect channel state information at the transmitter. For this model, we characterize the achievable rates under Gaussian signaling, and present some illustrative examples in an effort to enhance the insight into this setting.

On replica symmetry breaking in vector precoding for the Gaussian MIMO broadcast channel

The so-called ldquoreplica methodrdquo of statistical physics is employed for the large system analysis of vector precoding for the Gaussian multiple-input multiple-output (MIMO) broadcast channel. Focusing on discrete complex input alphabets, the transmitter is assumed to comprise a linear front-end combined with nonlinear precoding, that minimizes the front-end imposed transmit energy penalty. The energy penalty is minimized by relaxing the input alphabet to a larger alphabet set prior to precoding. The limiting empirical distribution of the precoders output, as well as the limiting energy penalty, are derived while harnessing what is referred to as the first order replica symmetry breaking (1RSB) ansatz. Particularizing to a ldquozero-forcingrdquo (ZF) linear front-end, and non-cooperative users, a decoupling result is derived according to which the channel observed by each of the individual receivers can be effectively characterized by the Markov chain u-x-y, where u is the channel input, x is the equivalent precoder output, and y is the channel output. An illustrative example is considered, based on discrete-lattice alphabet relaxation, for which the impact of replica symmetry breaking is demonstrated. A comparative spectral efficiency analysis reveals significant performance gains compared to linear ZF precoding in the medium to high Eb/N0 region. The performance vs. complexity tradeoff of the nonlinear precoding scheme is also shortly discussed.

The Finite State MAC With Cooperative Encoders and Delayed CSI

In this paper, we consider the finite-state multiple access channel (MAC) with partially cooperative encoders and delayed channel state information (CSI). Here, partial cooperation refers to the communication between the encoders via finite-capacity links. The channel states are assumed to be governed by a Markov process. Full CSI is assumed at the receiver, while at the transmitters, only delayed CSI is available. The capacity region of this channel model is derived by first solving the case of the finite-state MAC with a common message. Achievability for the latter case is established using the notion of strategies, however, we show that optimal codes can be constructed directly over the input alphabet. This results in a single codebook construction that is then leveraged to apply simultaneous joint decoding. Simultaneous decoding is crucial here because it circumvents the need to rely on the capacity regions corner points, a task that becomes increasingly cumbersome with the growth in the number of messages to be sent. The common message result is then used to derive the capacity region for the case with partially cooperating encoders. Next, we apply this general result to the special case of the Gaussian vector MAC with diagonal channel transfer matrices, which is suitable for modeling, e.g., orthogonal frequency division multiplexing-based communication systems. The capacity region of the Gaussian channel is presented in terms of a convex optimization problem that can be solved efficiently using numerical tools. The region is derived by first presenting an outer bound on the general capacity region and then suggesting a specific input distribution that achieves this bound. Finally, numerical results are provided that give valuable insight into the practical implications of optimally using conferencing to maximize the transmission rates.

On the spectrum of large random hermitian finite-band matrices

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