arXiv subjects

Elza Erkip

Publications and source records attributed to Elza Erkip.

At least 73 records · Page 4Linked to original sources

arXiv2020

On the Rates of Convergence in Learning of Optimal Temporally Fair Schedulers

Multi-user schedulers are designed to achieve optimal average system utility (e.g. throughput) subject to a set of fairness criteria. In this work, scheduling under temporal fairness constraints is considered. Prior works have shown that a class of scheduling strategies called threshold based strategies (TBSs) achieve optimal system utility under temporal fairness constraints. The optimal TBS thresholds are determined as a function of the channel statistics. In order to provide performance guarantees for TBSs in practical scenarios --- where the scheduler learns the optimal thresholds based on the empirical observations of the channel realizations --- it is necessary to evaluate the rates of convergence of TBS thresholds to the optimal value. In this work, these rates of convergence and the effect on the resulting system utility are investigated. It is shown that the best estimate of the threshold vector is at least $ω(\frac{1}{\sqrt{t}})$ away from the optimal value, where $t$ is the number of observations of the independent and identically distributed channel realizations. Furthermore, it is shown that under long-term fairness constraints, the scheduler may achieve an average utility that is higher than the optimal long-term utility by violating the fairness criteria for a long initial period. Consequently, the resulting system utility may converge to its optimal long-term value from above. The results are verified by providing simulations of practical scheduling scenarios.

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arXiv2020

On the Joint Typicality of Permutations of Sequences of Random Variables

Permutations of correlated sequences of random variables appear naturally in a variety of applications such as graph matching and asynchronous communications. In this paper, the asymptotic statistical behavior of such permuted sequences is studied. It is assumed that a collection of random vectors is produced based on an arbitrary joint distribution, and the vectors undergo a permutation operation. The joint typicality of the resulting permuted vectors with respect to the original distribution is investigated. As an initial step, permutations of pairs of correlated random vectors are considered. It is shown that the probability of joint typicality of the permuted vectors depends only on the number and length of the disjoint cycles of the permutation. Consequently, it suffices to study typicality for a class of permutations called 'standard permutations', for which, upper-bounds on the probability of joint typicality are derived. The notion of standard permutations is extended to a class of permutation vectors called 'Bell permutation vectors'. By investigating Bell permutation vectors, upper-bounds on the probability of joint typicality of permutations of arbitrary collections of random sequences are derived.

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arXiv2019

Optimizing Pilots and Analog Processing for Channel Estimation in Cell-Free Massive MIMO With One-Bit ADCs

In a cell-free cloud radio access network (C-RAN) architecture, uplink channel estimation is carried out by a centralized baseband processing unit (BBU) connected to distributed remote radio heads (RRHs). When the RRHs have multiple antennas and limited radio front-end resources, the design of uplink channel estimation is faced with the challenges posed by reduced radio frequency (RF) chains and one-bit analog-to-digital converters (ADCs) at the RRHs. This work tackles the problem of jointly optimizing the pilot sequences and the pre-RF chains analog combiners with the goal of minimizing the sum of mean squared errors (MSEs) of the estimated channel vectors at the BBU. The problem formulation models the impact of the ADC operation by leveraging Bussgang's theorem. An efficient solution is developed by means of an iterative alternating optimization algorithm. Numerical results validate the advantages of the proposed joint design compared to baseline schemes that randomly choose either pilots or analog combiners.

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arXiv2019

Rate-Distortion-Memory Trade-offs in Heterogeneous Caching Networks

Caching at the wireless edge can be used to keep up with the increasing demand for high-definition wireless video streaming. By prefetching popular content into memory at wireless access points or end-user devices, requests can be served locally, relieving strain on expensive backhaul. In addition, using network coding allows the simultaneous serving of distinct cache misses via common coded multicast transmissions, resulting in significantly larger load reductions compared to those achieved with traditional delivery schemes. Most prior works simply treat video content as fixed-size files that users would like to fully download. This work is motivated by the fact that video can be coded in a scalable fashion and that the decoded video quality depends on the number of layers a user receives in sequence. Using a Gaussian source model, caching and coded delivery methods are designed to minimize the squared error distortion at end-user devices in a rate-limited caching network. The framework is very general and accounts for heterogeneous cache sizes, video popularities and user-file play-back qualities. As part of the solution, a new decentralized scheme for lossy cache-aided delivery subject to preset user distortion targets is proposed, which further generalizes prior literature to a setting with file heterogeneity.

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arXiv2019

Age of Information with Finite Horizon and Partial Updates

A resource-constrained system monitors a source of information by requesting a finite number of updates subject to random transmission delays. An a priori fixed update request policy is shown to minimize a polynomial penalty function of the age of information over arbitrary time horizons. Partial updates, compressed updates with reduced transmission and information content, in the presented model are shown to incur an age penalty independent of the compression. Finite horizons are shown to have better performance in terms of second order statistic relative to infinite horizons.

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arXiv2019

Centralized Caching and Delivery of Correlated Contents over Gaussian Broadcast Channels

Content delivery in a multi-user cache-aided broadcast network is studied, where a server holding a database of correlated contents communicates with the users over a Gaussian broadcast channel (BC). The minimum transmission power required to satisfy all possible demand combinations is studied, when the users are equipped with caches of equal size. Assuming uncoded cache placement, a lower bound on the required transmit power as a function of the cache capacity is derived. An achievable centralized caching scheme is proposed, which not only utilizes the user's local caches, but also exploits the correlation among the contents in the database. The performance of the scheme, which provides an upper bound on the required transmit power for a given cache capacity, is characterized. Our results indicate that exploiting the correlations among the contents in a cache-aided Gaussain BC can provide significant energy savings.

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arXiv2019

Opportunistic Temporal Fair Mode Selection and User Scheduling for Full-duplex Systems

In-band full-duplex (FD) communications - enabled by recent advances in antenna and RF circuit design - has emerged as one of the promising techniques to improve data rates in wireless systems. One of the major roadblocks in enabling high data rates in FD systems is the inter-user interference (IUI) due to activating pairs of uplink and downlink users at the same time-frequency resource block. Opportunistic user scheduling has been proposed as a means to manage IUI and fully exploit the multiplexing gains in FD systems. In this paper, scheduling under long-term and short-term temporal fairness for single-cell FD wireless networks is considered. Temporal fair scheduling is of interest in delay-sensitive applications, and leads to predictable latency and power consumption. The feasible region of user temporal demand vectors is derived, and a scheduling strategy maximizing the system utility while satisfying long-term temporal fairness is proposed. Furthermore, a short-term temporal fair scheduling strategy is devised which satisfies user temporal demands over a finite window-length. It is shown that the strategy achieves optimal average system utility as the window-length is increased asymptotically. Subsequently, practical construction algorithms for long-term and short-term temporal fair scheduling are introduced. Simulations are provided to verify the derivations and investigate the multiplexing gains. It is observed that using successive interference cancellation at downlink users improves FD gains significantly in the presence of strong IUI.

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arXiv2019

A Concentration of Measure Approach to Database De-anonymization

In this paper, matching of correlated high-dimensional databases is investigated. A stochastic database model is considered where the correlation among the database entries is governed by an arbitrary joint distribution. Concentration of measure theorems such as typicality and laws of large numbers are used to develop a database matching scheme and derive necessary conditions for successful matching. Furthermore, it is shown that these conditions are tight through a converse result which characterizes a set of distributions on the database entries for which reliable matching is not possible. The necessary and sufficient conditions for reliable matching are evaluated in the cases when the database entries are independent and identically distributed as well as under Markovian database models.

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arXiv2019

On Multiterminal Communication over MIMO Channels with One-bit ADCs at the Receivers

The fundamental limits of communication over multiple-input multiple-output (MIMO) networks are considered when a limited number of one-bit analog to digital converters (ADC) are used at the receiver terminals. Prior works have mainly focused on point-to-point communications, where receiver architectures consisting of a concatenation of an analog processing module, a limited number of one-bit ADCs with non-adaptive thresholds, and a digital processing module are considered. In this work, a new receiver architecture is proposed which utilizes adaptive threshold one-bit ADCs - where the ADC thresholds at each channel-use are dependent on the channel outputs in the previous channel-uses - to mitigate the quantization rate-loss. Coding schemes are proposed for communication over the point-to-point and broadcast channels, and achievable rate regions are derived. In the high SNR regime, it is shown that using the proposed architectures and coding schemes leads to the largest achievable rate regions among all receiver architectures with the same number of one-bit ADCs.

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arXiv2019

Tradeoff Between Delay and High SNR Capacity in Quantized MIMO Systems

Analog-to-digital converters (ADCs) are a major contributor to the power consumption of multiple-input multiple-output (MIMO) communication systems with large number of antennas. Use of low resolution ADCs has been proposed as a means to decrease power consumption in MIMO receivers. However, reducing the ADC resolution leads to performance loss in terms of achievable transmission rates. In order to mitigate the rate-loss, the receiver can perform analog processing of the received signals before quantization. Prior works consider one-shot analog processing where at each channel-use, analog linear combinations of the received signals are fed to a set of one-bit threshold ADCs. In this paper, a receiver architecture is proposed which uses a sequence of delay elements to allow for blockwise linear combining of the received analog signals. In the high signal to noise ratio regime, it is shown that the proposed architecture achieves the maximum achievable transmission rate given a fixed number of one-bit ADCs. Furthermore, a tradeoff between transmission rate and the number of delay elements is identified which quantifies the increase in maximum achievable rate as the number of delay elements is increased.

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arXiv2019

On the Fundamental Limits of Multi-user Scheduling under Short-term Fairness Constraints

In the conventional information theoretic analysis of multiterminal communication scenarios, it is often assumed that all of the distributed terminals use the communication channel simultaneously. However, in practical wireless communication systems - due to restricted computation complexity at network terminals - a limited number of users can be activated either in uplink or downlink simultaneously. This necessitates the design of a scheduler which determines the set of active users at each time-slot. A well designed scheduler maximizes the average system utility subject to a set of fairness criteria, which must be met in a limited window-length to avoid long starvation periods. In this work, scheduling under short-term temporal fairness constraints is considered. The objective is to maximize the average system utility such that the fraction of the time-slots that each user is activated is within desired upper and lower bounds in the fairness window-length. The set of feasible window-lengths is characterized as a function of system parameters. It is shown that the optimal system utility is non-monotonic and super-additive in window-length. Furthermore, a scheduling strategy is proposed which satisfies short-term fairness constraints for arbitrary window-lengths, and achieves optimal average system utility as the window-length is increased asymptotically. Numerical simulations are provided to verify the results.

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arXiv2018

A General Framework for Temporal Fair User Scheduling in NOMA Systems

Non-orthogonal multiple access (NOMA) is one of the promising radio access techniques for next generation wireless networks. Opportunistic multi-user scheduling is necessary to fully exploit multiplexing gains in NOMA systems, but compared with traditional scheduling, interrelations between users' throughputs induced by multi-user interference poses new challenges in the design of NOMA schedulers. A successful NOMA scheduler has to carefully balance the following three objectives: maximizing average system utility, satisfying desired fairness constraints among the users and enabling real-time, and low computational cost implementations. In this paper, scheduling for NOMA systems under temporal fairness constraints is considered. Temporal fair scheduling leads to communication systems with predictable latency as opposed to utilitarian fair schedulers for which latency can be highly variable. It is shown that optimal system utility is achieved using a class of opportunistic scheduling schemes called threshold based strategies (TBS). One of the challenges in temporal fair scheduling for heterogeneous NOMA scenarios - where only specific users may be activated simultaneously - is to determine the set of feasible temporal shares. In this work, a variable elimination algorithm is proposed to accomplish this task. Furthermore, an (online) iterative algorithm based on the Robbins-Monro method is proposed to construct a TBS by finding the optimal thresholds for a given system utility metric. Various numerical simulations of practical scenarios are provided to illustrate the effectiveness of the proposed NOMA scheduling in static and mobile scenarios.

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arXiv2018

Rate-Memory Trade-Off for Caching and Delivery of Correlated Sources

This paper studies the fundamental limits of content delivery in a cache-aided broadcast network for correlated content generated by a discrete memoryless source with arbitrary joint distribution. Each receiver is equipped with a cache of equal capacity, and the requested files are delivered over a shared error-free broadcast link. A class of achievable correlation-aware schemes based on a two-step source coding approach is proposed. Library files are first compressed, and then cached and delivered using a combination of correlation-unaware multiple-request cache-aided coded multicast schemes. The first step uses Gray-Wyner source coding to represent the library via private descriptions and descriptions that are common to more than one file. The second step then becomes a multiple-request caching problem, where the demand structure is dictated by the configuration of the compressed library, and it is interesting in its own right. The performance of the proposed two-step scheme is evaluated by comparing its achievable rate with a lower bound on the optimal peak and average rate-memory tradeoffs in a two-file multiple-receiver network, and in a three-file two-receiver network. Specifically, in a network with two files and two receivers, the achievable rate matches the lower bound for a significant memory regime and it is within half of the conditional entropy of files for all other memory values. In the three-file two-receiver network, the two-step strategy achieves the lower bound for large cache capacities, and it is within half of the joint entropy of two of the sources conditioned on the third one for all other cache sizes.

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arXiv2018

On Coding for Cache-Aided Delivery of Dynamic Correlated Content

Cache-aided coded multicast leverages side information at wireless edge caches to efficiently serve multiple unicast demands via common multicast transmissions, leading to load reductions that are proportional to the aggregate cache size. However, the increasingly dynamic, unpredictable, and personalized nature of the content that users consume challenges the efficiency of existing caching-based solutions in which only exact content reuse is explored. This paper generalizes the cache-aided coded multicast problem to specifically account for the correlation among content files, such as, for example, the one between updated versions of dynamic data. It is shown that (i) caching content pieces based on their correlation with the rest of the library, and (ii) jointly compressing requested files using cached information as references during delivery, can provide load reductions that go beyond those achieved with existing schemes. This is accomplished via the design of a class of correlation-aware achievable schemes, shown to significantly outperform state-of-the-art correlation-unaware solutions. Our results show that as we move towards real-time and/or personalized media dominated services, where exact cache hits are almost non-existent but updates can exhibit high levels of correlation, network cached information can still be useful as references for network compression.

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arXiv2018

On MIMO Channel Capacity with Output Quantization Constraints

The capacity of a Multiple-Input Multiple-Output (MIMO) channel in which the antenna outputs are processed by an analog linear combining network and quantized by a set of threshold quantizers is studied. The linear combining weights and quantization thresholds are selected from a set of possible configurations as a function of the channel matrix. The possible configurations of the combining network model specific analog receiver architectures, such as single antenna selection, sign quantization of the antenna outputs or linear processing of the outputs. An interesting connection between the capacity of this channel and a constrained sphere packing problem in which unit spheres are packed in a hyperplane arrangement is shown. From a high-level perspective, this follows from the fact that each threshold quantizer can be viewed as a hyperplane partitioning the transmitter signal space. Accordingly, the output of the set of quantizers corresponds to the possible regions induced by the hyperplane arrangement corresponding to the channel realization and receiver configuration. This connection provides a number of important insights into the design of quantization architectures for MIMO receivers; for instance, it shows that for a given number of quantizers, choosing configurations which induce a larger number of partitions can lead to higher rates.

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arXiv2018

Capturing Capacity and Profit Gains with Base Station Sharing in mmWave Cellular Networks

Due to the greater path loss, shadowing, and increased effect of blockage in millimeter wave cellular networks, base station sharing among network service providers has the potential to significantly improve overall network capacity. However, a service provider may find that despite the technical gains, sharing actually reduces its profits because it makes price competition between service providers tougher. In this work, a weighted scheduling algorithm is described, which gives greater control over how the airtime resource is allocated within a shared cell. It is shown that, under certain market conditions, there exist scheduling weights such that base station sharing is more profitable than not sharing for both service providers in a duopoly market, while still achieving almost as much network capacity as in a conventional base station sharing scenario. Thus, both technical and economic benefits of base station sharing may be realized simultaneously.

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arXiv2018

Centralized Caching and Delivery of Correlated Contents over a Gaussian Broadcast Channel

Content delivery in a multi-user cache-aided broadcast network is studied, where a server holding a database of correlated contents communicates with the users over a Gaussian broadcast channel (BC). The minimum transmission power required to satisfy all possible demand combinations is studied, when the users are equipped with caches of equal size. A lower bound on the required transmit power is derived, assuming uncoded cache placement, as a function of the cache capacity. A centralized joint cache and channel coding scheme is proposed, which not only utilizes the user's local caches, but also exploits the correlation among the contents in the database. This scheme provides an upper bound on the minimum required transmit power for a given cache capacity. Our results indicate that exploiting the correlations among the contents in a cache-aided Gaussian BC can provide significant energy savings.

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arXiv2018

Adaptive Hybrid Beamforming with Massive Phased Arrays in Macro-Cellular Networks

Hybrid beamforming via large antenna arrays has shown a great potential for increasing data rate in cellular networks by delivering multiple data streams simultaneously. In this paper, several beamforming design algorithms are proposed based on the long-term channel information for macro-cellular environments where the base station is equipped with a massive phased array under per-antenna power constraint. Using an adaptive scheme, beamforming vectors are updated whenever the long-term channel information changes. First, the problem is studied when the base station has a single RF chain (single-beam scenario). Semi-definite relaxation (SDR) with randomization is used to solve the problem. As a second approach, a low-complexity heuristic beam composition algorithm is proposed which performs very close to the upper-bound obtained by SDR. Next, the problem is studied for a generic number of RF chains (multi-beam scenario) where the Gradient Projection method is used to obtain local solutions. Numerical results reveal that using massive antenna arrays with optimized beamforming vectors can lead to 5X network throughput improvement over systems with conventional antennas.

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