Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and constructions-have been extensively studied, the performance of LRCs under random erasures and errors has remained largely unexplored. In this work, we study the error- and erasure-correction performance of binary linear LRCs under majority-logic decoding (MLD). Focusing on LRCs with fixed locality and varying availability, we derive explicit upper bounds on the probability of decoding failure over the memoryless Binary Erasure Channel (BEC) and Binary Symmetric Channel (BSC). Our analysis characterizes the behavior of the bit-error rate (BER) and block-error rate (BLER) as functions of the locality and availability parameters. We show that, under mild growth conditions on the availability, the block decoding failure probability vanishes asymptotically, and that majority-logic decoding can successfully correct virtually all of error and erasure patterns of weight linear in the blocklength. The results reveal a substantial gap between worst-case guarantees and typical performance under stochastic channel models.

We consider computing systems that partition jobs into tasks, add redundancy through coding, and assign the encoded tasks to different computing nodes for parallel execution. The expected execution time depends on the level of redundancy. The computing nodes execute large jobs in batches of tasks. We show that the expected execution time depends on the batch size as well. The optimal batch size that minimizes the execution time depends on the level of redundancy under a fixed number of parallel servers and other system parameters. Furthermore, we show how to (jointly) optimize the redundancy level and batch size to reduce the expected job completion time for two service-time distributions. The simulation presented helps us appreciate the claims.

Low Earth Orbit (LEO) nano-satellites can provide uplink connectivity for large numbers of distributed Internet of Things (IoT) sensing devices. To achieve a target Quality-of-Service (QoS), devices must send packets multiple times, due to collisions. This paper characterises the achievable set of terminal QoS targets, and determines the optimal uplink packet attempt rates. We show that QoS target feasibility is determined by the solution of a linear program (LP), and that the solution gives the optimal packet attempt rates. We show that the QoS targets can be modified using the shadow prices from the LP, to obtain feasibility. We show that our LP based approach can support greater than 30% more ground sensor terminals, compared to existing schemes.

This paper analyses the data message success rate for Internet of Things (IoT) sensing devices communicating over Low Earth Orbit (LEO) satellite links. We present an analytical framework for optimizing multi-objective multi-packet reception on the uplink. We present an analytical result for the probability of message success for a given ground terminal, and present an analytical result for the overall probability of message success, averaged across all terminals.

This paper presents an efficient practical Zak-OTFS modulation implementation using time and frequency windowing methods. We present two general classes of delay-Doppler (DD) twisted convolution (TC) filters (Type-1 and Type-2), and show that they can be realized by time and frequency windowing functions. We then propose practical methods to generate time domain Zak-OTFS signals, for actual transmission, using the windowing functions. For Type-1, the signals are generated using an interpolation filter. For Type-2, they are generated using a form of precoded OFDM. We show that this allows a wide variety of pulse shapes to be implemented in practice for Zak-OTFS modulation. This was not previously possible. We also show that the Type-2 signals are more spectrally efficient than their Type-1 counterparts. Finally, we compare the channel predictability of the two implementations.

This paper develops a beam direction optimization framework for next-generation GEO satellite networks. The objective is to meet traffic demands at user locations. Given beam-pointing directions, the downlink of the GEO satellite is a vector broadcast channel that consists of a single transmitter and multiple distributed ground users. We characterize the downlink channel matrix for the multibeam satellite network by using an array factor formula for uniform planar arrays. We obtain a necessary and sufficient condition dependent on the downlink channel matrix to provision traffic demands by meeting given SINR targets at user locations. Utilizing the necessary and sufficient conditions, we formulate a joint beam direction and power optimization problem to attain target SINRs which uses minimum total power. Our results demonstrate that analog beamforming with optimized beam shifts can achieve an SINR gain of 8 dB when compared to analog beamforming without beam direction optimization. It also offers a spatial multiplexing advantage of 90 km by enabling simultaneous provisioning of user locations in close proximity within the same frequency band. When compared to hybrid beamforming, our scheme can achieve an SINR gain of 2 dB.

In this paper, we consider a millimeter wave network deployed to cover an urban street. Each base station (BS) employs hybrid beamforming with a limited number of radio frequency (RF) chains. Its link to any user equipment (UE) is prone to being blocked by vehicles and pedestrians moving along the street. We propose a Round Robin (RR) access protocol with proactive cell switching in which each UE switches its connection to the least loaded line of sight BS at the end of its RR transmission frame or any time when its link is blocked. We compare the UE connectivity performance of the proposed protocol to the conventional cellular network association protocols and the RR protocols which switch only when the link is blocked. Our results reveal the impacts of different system parameters (i.e. the number of BSs, the number of RF chains, the length of RR transmission frame) on the performance of the protocol, and the importance of cell switching in dealing with load balancing as well as blockage

This paper presents a new distributed slot reservation frame-work for joint resource allocation and flow control in mmWave IAB networks. We derive the Dynamic Slot Reservation (DSR) algorithm from a novel approach to solve a minimum clearing time linear program in a completely distributed manner. The algorithm to solve this problem, the Static Slot Reservation (SSR) algorithm, is also a contribution of the paper. We compare the delay performance of the DSR algorithm with a well known optimal, centralized algorithm, the joint-MWM algorithm, for a realistic IAB network scenario of multi-hop flows. We show that flows that traverse several links have significantly lower delays under DSR than under the joint-MWM algorithm. This paper also provides an instantaneous rate control policy for IAB networks which changes flow rates based on the number of flows at each node in the network. The flow rates under this policy are the same as the steady-state flow rates achieved by the DSR algorithm. We prove that the proposed flow control policy provides stability for all flow arrival rate vectors that are achievable by any flow control policy. This paper provides distributed admission control policies to provide rate and/or latency guarantees to flows under dynamic scenarios with stochastic flow arrivals and changing access link rates.

We consider a large-scale service system where incoming tasks have to be instantaneously dispatched to one out of many parallel server pools. The user-perceived performance degrades with the number of concurrent tasks and the dispatcher aims at maximizing the overall quality of service by balancing the load through a simple threshold policy. We demonstrate that such a policy is optimal on the fluid and diffusion scales, while only involving a small communication overhead, which is crucial for large-scale deployments. In order to set the threshold optimally, it is important, however, to learn the load of the system, which may be unknown. For that purpose, we design a control rule for tuning the threshold in an online manner. We derive conditions that guarantee that this adaptive threshold settles at the optimal value, along with estimates for the time until this happens. In addition, we provide numerical experiments that support the theoretical results and further indicate that our policy copes effectively with time-varying demand patterns. Summary of Contribution: Data centers and cloud computing platforms are the digital factories of the world, and managing resources and workloads in these systems involves operations research challenges of an unprecedented scale. Due to the massive size, complex dynamics, and wide range of time scales, the design and implementation of optimal resource-allocation strategies is prohibitively demanding from a computation and communication perspective. These resource-allocation strategies are essential for certain interactive applications, for which the available computing resources need to be distributed optimally among users in order to provide the best overall experienced performance. This is the subject of the present article, which considers the problem of distributing tasks among the various server pools of a large-scale service system, with the objective of optimizing the overall quality of service provided to users. A solution to this load-balancing problem cannot rely on maintaining complete state information at the gateway of the system, since this is computationally unfeasible, due to the magnitude and complexity of modern data centers and cloud computing platforms. Therefore, we examine a computationally light load-balancing algorithm that is yet asymptotically optimal in a regime where the size of the system approaches infinity. The analysis is based on a Markovian stochastic model, which is studied through fluid and diffusion limits in the aforementioned large-scale regime. The article analyzes the load-balancing algorithm theoretically and provides numerical experiments that support and extend the theoretical results.

Distributed computing enablesparallelexecution of smaller tasks that make up a large computing job. Its purpose is to reduce the job completion time. However, random fluctuations in task service times lead to straggling tasks with long execution times. Redundancy providesdiversitythat allows job completion when only a subset of redundant tasks is executed, thus removing the dependency on the straggling tasks. Under constrained resources (here, a fixed number of parallel servers), increasing redundancy reduces the available resources for parallelism. In this paper, we characterize thediversity vs. parallelismtrade-off and identify the optimal strategy among replication, coding, and splitting, which minimizes the expected job completion time. We consider three common service time distributions and establish three models that describe the scaling of these distributions with the task size. We find that different distributions with different scaling models operate optimally at different redundancy levels, thus requiring very different code rates.

We consider the stability region of a mmWave integrated access and backhaul (IAB) network with stochastic arrivals and time-varying link rates. In the scheduling of links, we consider a limit on the number of RF chains, and the half-duplex constraint which occurs due to the wireless backhaul links. We characterize the stability region, and propose a back-pressure policy for the IAB network under the RF chains and half-duplex constraints. To implement the back-pressure policy, it is required to compute the maximum weighted schedule, which is a complex problem in general. For the IAB network, we present a distributed message passing scheme to compute the maximum weighted schedule, with almost linear complexity. We also investigate a class of local scheduling policies for the IAB network, which have a smaller stability region in general, but require no message passing. We characterize the stability region for the local class, and show that it is same as the global stability region, if the link rates are un-varying. We provide a bound on the gap between local and global regions when the links are time varying. We propose a local max-weight algorithm which achieves the stability region for the local class, and we present numerical results.

Covert communication prevents legitimate transmission from being detected by a warden while maintaining certain covert rate at the intended user. Prior works have considered the design of covert communication over conventional low-frequency bands, but few works so far have explored the higher-frequency millimeter-wave (mmWave) spectrum. The directional nature of mmWave communication makes it attractive for covert transmission. However, how to establish such directional link in a covert manner in the first place remains as a significant challenge. In this paper, we consider a covert mmWave communication system, where legitimate parties Alice and Bob adopt beam training approach for directional link establishment. Accounting for the training overhead, we develop a new design framework that jointly optimizes beam training duration, training power and data transmission power to maximize the effective throughput of Alice-Bob link while ensuring the covertness constraint at warden Willie is met. We further propose a dual-decomposition successive convex approximation algorithm to solve the problem efficiently. Numerical studies demonstrate interesting tradeoff among the key design parameters considered and also the necessity of joint design of beam training and data transmission for covert mmWave communication.

To facilitate load balancing, distributed systems store data redundantly. We evaluate the load balancing performance of storage schemes in which each object is stored at d different nodes, and each node stores the same number of objects. In our model, the load offered for the objects is sampled uniformly at random from all the load vectors with a fixed cumulative value. We find that the load balance in a system of n nodes improves multiplicatively with d as long as d = o(log(n)), and improves exponentially once d = Θ(log(n)). We show that the load balance improves in the same way with d when the service choices are created with XOR's of r objects rather than object replicas. In such redundancy schemes, storage overhead is reduced multiplicatively by r. However, recovery of an object requires downloading content from r nodes. At the same time, the load balance increases additively by r. We express the system's load balance in terms of the maximal spacing or maximum of d consecutive spacings between the ordered statistics of uniform random variables. Using this connection and the limit results on the maximal d-spacings, we derive our main results.

Millimetre wave (mmWave) beam tracking is a challenging task because tracking algorithms are required to provide consistent high accuracy with low probability of loss of track and minimal overhead. To meet these requirements, we propose in this article a new cost-effective analog beam tracking framework namely Adaptive Tracking with Stochastic Control (ATSC). Under this framework, beam direction updates are made using a novel mechanism based on measurements taken from only two beam directions perturbed from the current data beam. To achieve high tracking accuracy and reliability, we provide a systematic approach to jointly optimise the algorithm parameters. The complete framework includes a method for adapting the tracking rate together with a criterion for realignment (perceived loss of track). ATSC adapts the amount of tracking overhead that matches well to the mobility level, without incurring frequent loss of track, as verified by an extensive set of experiments under both representative statistical channel models as well as realistic urban scenarios simulated by ray-tracing software. In particular, numerical results show that ATSC can track dominant channel directions with high accuracy for vehicles moving at 72 km/hour in complicated urban scenarios, with an overhead of less than 1%.

In this paper, we propose an adaptive beam search algorithm for the initial alignment of millimetre-Wave beams. The proposed algorithm works by gradually deactivating beams that are unlikely the best beam from a pre-synthesised codebook to save overhead, based on a Bayesian probability criterion with a uniform improper prior. The beam deactivations can be implemented with low-complexity operations that require computing a low-degree polynomial or a search through a look-up table. The proposed algorithm does not require prior knowledge of channel statistics or signal to noise ratios (SNRs) to optimise the amount of searching time, and uses a suitable amount of time to achieve satisfactory beam search accuracy in different SNRs and fading scenarios. Numerical results confirm that the proposed algorithm can adapt to a wide range of channels with a fixed algorithm parameter, and can achieve better balance between beam search overhead and accuracy than non-adaptive approaches with fixed overhead.

Distributed computing enables parallel execution of tasks that make up a large computing job. Random fluctuations in service times (inherent to computing environments) often cause a non-negligible number of straggling tasks with long completion time. Redundancy, in the form of task replication and erasure coding, has emerged as a potentially powerful way to curtail the variability in service time, as it provides diversity that allows a job to be completed when only a subset of redundant tasks gets executed. Thus both redundancy and parallelism reduce the execution time, but compete for resources of the system. In situations of constrained resources (here fixed number of parallel servers), increasing redundancy reduces the available level of parallelism. We characterize the diversity vs. parallelism tradeoff for three common models of task size dependent execution times. We find that different models operate optimally at different levels of redundancy, and thus may require very different code rates.

Millimeter wave (mmWave) multiple-input multiple-output (MIMO) communication systems with a large number of antennas are power hungry when using conventional high-resolution analog-to-digital/digital-to-analog converters (A/Ds). To reduce the power consumption of mmWave MIMO systems, existing studies have considered hybrid structures with a reduced number of high-resolution or low-resolution A/Ds at either the transmitter or the receiver side. In this paper, we propose and investigate a multi-user hybrid architecture with low-resolution A/Ds equipped at both the transmitter and the receivers. To mitigate the impact of utilizing low-resolution A/Ds at the transceivers, we propose a novel data transmission scheme, which exploits a weighted phased-array to synthesize the beamforming matrix in the analog domain so as to mitigate inter-user interference. Under the scheme proposed, we derive the achievable rate and the energy efficiency to establish guidelines on the optimal resolution choice of A/Ds for hybrid mmWave systems. For a typical total transmit power at the BS, e.g., 30 dBm, the proposed scheme with 5~6-bit A/Ds can significantly improve the energy efficiency by as much as 100% over that of the conventional hybrid MIMO architecture with high-resolution A/Ds (10-bit A/Ds), without significant degradation in data rate performance.

In this article, we consider joint optimization of user association and resource allocation in three tier HetNets. We formulate the objective of minimizing the resources required to clear a given set of files, as a linear program. We show that the optimal user association is determined by a rate-biasing rule, where a bias value is associated with each BS. We show that each rate-bias value crucially only takes values from a finite set which we characterize. We present a complete analytical solution along with new structural results. Using these results, we present efficient distributed algorithms for optimal control of three tier HetNets. The method involves a 1D search for a resource variable at the macro-level, and 2D search at the pico-level for a resource variable and a bias value. We apply our results to a variety of hierarchical network examples.

Millimeter Wave (mmWave) communications rely on highly directional beams to combat severe propagation loss. In this paper, an adaptive beam search algorithm based on spatial scanning, called Iterative Deactivation and Beam Shifting (IDBS), is proposed for mmWave beam alignment. IDBS does not require advance information such as the Signal-to-Noise Ratio (SNR) and channel statistics, and matches the training overhead to the unknown SNR to achieve satisfactory performance. The algorithm works by gradually deactivating beams using a Bayesian probability criterion based on a uniform improper prior, where beam deactivation can be implemented with low-complexity operations that require computing a low-degree polynomial or a search through a look-up table. Numerical results confirm that IDBS adapts to different propagation scenarios such as line-of-sight and non-line-of-sight and to different SNRs. It can achieve better tradeoffs between training overhead and beam alignment accuracy than existing non-adaptive algorithms that have fixed training overheads.

Swift and accurate alignment of transmitter (Tx) and receiver (Rx) beams is one of the fundamental design challenges to support directional transmission in millimeter-wave cellular communications. In this paper, we propose a new Optimized Two-Stage Search (OTSS) algorithm for Tx-Rx beam alignment via beam training. In contrast to one-shot exhaustive search, OTSS judiciously divides the training energy budget into two stages. In the first stage, OTSS explores and trains all candidate Tx-Rx beam pairs and then discards a set of less favorable pairs learned from the measured received signal. In the second stage, OTSS takes an extra measurement for each of the remaining pairs and combines with the previous measurement to determine the best one. For OTSS, we derive fundamental bounds on its misalignment probability under a single-path channel model with ideal codebooks and establish a guideline on its optimized parameter choices. Numerical results have confirmed the advantage of OTSS over the state-of-the-art baselines.

Swift and accurate alignment of transmitter (Tx) and receiver (Rx) beams is a fundamental design challenge to enable the reliable outdoor millimeter-wave communications. In this paper, we propose a new optimized two-stage search (OTSS) algorithm for Tx–Rx beam alignment via spatial scanning. In contrast to one-shot exhaustive search, the OTSS judiciously divides the training energy budget into two stages. In the first stage, OTSS explores and trains all candidate beam pairs and, then, eliminates a set of less favorable pairs learned from the received signal profile. In the second stage, OTSS takes an extra measurement for the each of the survived pairs and combines with the previous measurement to determine the best one. For the OTSS, we derive an upper bound on its misalignment probability, under a single-path channel model with training codebooks having an ideal beam pattern. We also characterize the decay rate function of the upper bound with respect to the training budget and further derive the optimal design parameters of OTSS that maximize the decay rate. OTSS is proved to asymptotically outperform the state-of-the-art beam alignment algorithms and is numerically shown to achieve better performance with limited training budget and practically synthesized beams.

As the Internet-of-Things (IoT) emerges, connecting immense numbers of sensors and devices, the continual growth in wireless communications increasingly manifests itself in terms of a larger and denser population of nodes with intermittent traffic patterns. A crucial issue that arises in these conditions is how to set the activation rates as a function of the network density and traffic intensity. Depending on the scaling of the activation rates, dense node populations may either result in excessive activations and potential collisions, or long delays that may increase with the number of nodes, even at low load. Motivated by the above issues, we examine optimal activation rate scalings in ultra-dense networks with intermittent traffic sources. We establish stability conditions, and provide closed-form expressions which indicate that the mean delay is roughly inversely proportional to the nominal activation rate. We also discuss a multi-scale mean-field limit, and use the associated fixed point to determine the buffer content and delay distributions. The results provide insight in the scalings that minimize the delay while preventing excessive activation attempts. Extensive simulation experiments demonstrate that the mean-field asymptotics yield highly accurate approximations, even when the number of nodes is moderate.

We formulate a linear programming problem to find the minimum clearing time in HetNets. Although this program is NP hard in general, we consider particular topologies that arise in HetNets, including a two cell HetNet and a linear chain of HetNets, both with wireless backhaul, and we provide an efficient, greedy algorithm that provably solves the minimum clearing time problem for these networks. We show how this algorithm can be applied to jointly optimize the ABS time across multiple macros in a HetNet, and we demonstrate capacity gains of the algorithm, compared to standard approaches to Inter Cell Interference Coordination. This paper provides insight into how to manage interference in presence of more than one macro, and how to efficiently operate wireless backhaul in HetNets.

We propose a beamforming technique for the multicell downlink of a multicarrier code division multiple access (MC-CDMA) system with sparse signatures. We propose a distributed beamforming algorithm using the sum-product algorithm. The distributed beamforming algorithm converges very quickly to the centralized beamforming solution, minimizing the delay associated with computation of the transmit vector. The complexity of distributed beamforming depends on the number of base stations (BSs) that are in range of each user, not on the size of the entire network.

In millimeter wave cellular communication, fast and reliable beam alignment via beam training is crucial to harvest sufficient beamforming gain for the subsequent data transmission. In this paper, we establish fundamental limits in beam-alignment performance under both the exhaustive search and the hierarchical search that adopts multi-resolution beamforming codebooks, accounting for time-domain training overhead. Specifically, we derive lower and upper bounds on the probability of misalignment for an arbitrary level in the hierarchical search, based on a single-path channel model. Using the method of large deviations, we characterize the decay rate functions of both bounds and show that the bounds coincide as the training sequence length goes large. We go on to characterize the asymptotic misalignment probability of both the hierarchical and exhaustive search, and show that the latter asymptotically outperforms the former, subject to the same training overhead and codebook resolution. We show via numerical results that this relative performance behavior holds in the non-asymptotic regime. Moreover, the exhaustive search is shown to achieve significantly higher worst case spectrum efficiency than the hierarchical search, when the pre-beamforming signal-to-noise ratio (SNR) is relatively low. This paper hence implies that the exhaustive search is more effective for users situated further from base stations, as they tend to have low SNR.

In this paper, we develop an analytical framework for the initial access (also known as base station (BS) discovery) in a millimeter-wave communication system and propose an effective strategy for transmitting the reference signals (RSs) used for BS discovery. Specifically, by formulating the problem of BS discovery at user equipments (UEs) as hypothesis tests, we derive a detector based on the generalized likelihood ratio test and characterize the statistical behavior of the detector. The theoretical results obtained allow analysis of the impact of key system parameters on the performance of BS discovery, and show that RS transmission with narrow beams may not be helpful in improving the overall BS discovery performance due to the cost of spatial scanning. Using the method of large deviations, we identify the desirable beam pattern that minimizes the average miss-discovery probability of UEs within a targeted detectable region. We then propose to transmit the RS with sequential scanning, using a pre-designed codebook with narrow and/or wide beams to approximate the desirable patterns. The proposed design allows flexible choices of the codebook sizes and the associated beam widths to better approximate the desirable patterns. Numerical results demonstrate the effectiveness of the proposed method.

Heterogenous wireless networks (Hetnets) provide a powerful approach to meet the massive growth in traffic demands, but also impose a significant challenge on backhaul. Caching at small base stations (BSs) and wireless small cell backhaul have been proposed as attractive solutions to address this new challenge. In this paper, we consider the optimal caching and user association to minimize the total time to satisfy the average demands in cached-enabled Hetnets with wireless backhaul. We formulate this problem as a mixed discrete- continuous optimization for given bandwidth and cache resources. First, we characterize the structure of the optimal solution. Specifically, we show that the optimal caching is to store the most popular files at each pico BS, and the optimal user association has a threshold form. We also obtain the closed-form optimal solution in the homogenous scenario of pico cells. Then, we analyze the impact of bandwidth and cache resources on the minimum total time to satisfy the average demands. Finally, using numerical simulations, we verify the analytical results.

With the rapid advance of the Internet of Everything, both the number of devices and the range of applications that rely on wireless connectivity show huge growth. Driven by these pervasive trends, wireless networks grow in size and complexity, supporting immense numbers of nodes and data volumes, with highly diverse traffic profiles and performance requirements. While well-established methods are available for evaluating the throughput of persistent sessions with saturated buffers, these provide no insight in the delay performance of flows with intermittent packet arrivals. The occurrence of empty buffers in the latter scenario results in a complex interaction between activity states and packet queues, which severely complicates the performance analysis. Motivated by these challenges, we develop a mean-field approach to analyze buffer contents and packet delays in wireless networks in a many-sources regime. The mean-field behavior simplifies the analysis of a large-scale network with packet arrivals and buffer dynamics to a low-dimensional fixed-point calculation for a network with saturated buffers. In particular, the analysis yields explicit expressions for the buffer content and packet delay distribution in terms of the fixed-point solution. Extensive simulation experiments demonstrate that these expressions provide highly accurate approximations, even for a fairly moderate number of sources.

Coordinated scheduling/beamforming (CS/CB) is a cost-effective coordinated multipoint (CoMP) transmission paradigm that has been incorporated in the recent long-term evolution cellular standard. In this paper, we study CS/CB with the aim of developing low-complexity multicell coordinated user scheduling policies. We focus on a class of multicell interfering broadcast networks in which base stations have only local data and local channel state information, but each has sufficient antennas to serve multiple users using zero-forcing beamforming. The coordination problem is formulated as finding scheduling decisions across the cells such that the network sum rate is maximized. Starting from the two-cell model, we uncover the structure for a good scheduling decision, which in turn leads to the definition of two distributed scheduling policies of differing complexity and intercell coordination. Asymptotic theoretical bounds on the average sum rate are derived to predict the performance of the policies proposed. We extend to some example networks containing more than two cells and develop network-wide coordination policies. Numerical results confirm the effectiveness of the proposed policies and shed light on practical coordinated system design.

This work introduces a novel cooperation framework that allows mobile service providers (MSPs) to offload traffic onto each other so that temporarily unused spectrum/resources of cellular bands can be opportunistically harvested. Specifically, through traffic offloading, MSPs aim to maximize their profit while maintaining their QoS commitment. For that purpose, we model the strategic cooperation between MSPs as a stochastic Markov game in which the dynamics of MSPs' resources and user behaviors are captured by an underlying Markov decision process. We prove that the game is irreducible and admits a Nash Equilibrium at which all MSPs benefit from traffic offloading. A practical algorithm that uses only local information to govern traffic offloading at MSPs is then developed. Numerical simulations show that by designing appropriate profit sharing contracts, this algorithm can achieve almost the same performance as that of a socially optimal solution.

Generalized spatial modulation (GSM) is a variant of spatial modulation (SM) which offers enhanced spectral efficiency with a moderate increase in signal processing complexity. This paper proposes a novel compressive sensing (CS) aided detection algorithm which offers better performance than traditional CS based detection algorithms. In contrast to widely considered frequency-flat channel models, we have adopted frequency-selective wireless channel models to account for high data-rate applications. Our proposed algorithm offers superior performance over traditional CS based algorithms even in the presence of channel estimation errors. Numerical experiments are conducted to investigate the mathematical analysis under different suppositions on channel state information. Normalized mean-square error (NMSE) and bit-error rate (BER) versus signal-to-noise (SNR) curves are studied to investigate the performance under different detection algorithms.

The deployment of pico cells to cover traffic hot spots within the footprint of a macro cell provides a powerful approach to meet the massive growth in traffic demands fueled by smartphones and bandwidth-hungry applications. Joint optimization of resource allocation and user association is critical to achieve the maximum capacity benefits and performance gains in such heterogeneous network deployments (HetNets). In order to gain insight in the achievable capacity gains, we examine in the present paper the stability and performance of a HetNet system in the presence of flow-level dynamics. The stability condition reveals that in stationary traffic conditions the maximum capacity can be achieved with a static resource split and traffic association rule, provided that these are suitably selected. This suggests that dynamic adaptation on time scales commensurate with the variations in traffic parameters suffices to extract most of the achievable capacity gains. For the case of static cell boundaries and Proportional Fair scheduling, we also present a method for evaluating the flow-level performance in terms of the distribution of the number of active file transfers and expected transfer delay.

Heterogeneous wireless networks (HetNets) provide a means to increase network capacity by introducing small cells and adopting a layered architecture. HetNets allocate resources flexibly through time sharing and cell range expansion/contraction allowing a wide range of possible schedulers. In this paper, we define the capacity of a HetNet down link in terms of the maximum number of downloads per second, which can be achieved for a given offered traffic density. Given this definition we show that the capacity is determined via the solution to a continuous linear program (LP). If the solution is smaller than 1 then there is a scheduler such that the number of mobiles in the network has ergodic properties with finite mean waiting time. If the solution is greater than 1 then no such scheduler exists. These results have clear implications for network planning. The above results continue to hold if a more general class of schedulers is considered.

We investigate a joint user association and resource allocation problem in a three-tier heterogeneous network. Orthogonal resource allocation among different tiers is assumed. The problem is formulated as minimizing the total resources required to satisfy given user traffic demands. We first examine the structure of the optimal solution for this convex optimization problem and show that the optimal user association and hence resource allocation is determined by a bias value on the data rate offered by each base station. We then develop distributed algorithms based on the dual ascent method in determining the optimal rate bias for each BS. Numerical experiments demonstrate that the developed algorithms converge fast and produce close-to-optimal solutions. It is also shown that under cross-tier orthogonal resource allocation, the three-tier deployment provides significant performance improvement over a two-tier deployment, using the same set of base stations in each case.

A popular way for using radio-frequency (RF) signals (e.g. WiFi) to position people or device indoors is by matching received radio signal strength (RSS) to fingerprints that are spatial signatures of such measures. Traditionally such signal maps are built by manual collection of repeated measurements at predefined locations following a spatial sampling scheme. Recently, such labor intensive processes are being replaced by robot-based automation or crowd-sourced simultaneous localization and mapping (SLAM). These new approaches produce time-stamped trajectories along with time-stamped RSS as the human or robot moves freely about the building. However, they require an additional procedure to segment the continuous RF samples into fingerprint cells to produce a robust signal map. In this paper, we explore several strategies for building optimal signal maps from RSS collected along robotic or pedestrian trajectories. We compare two clustering algorithms with a baseline strategy that divides the trajectories into a hierarchy of fixed-size grids. We study the trade-off between the spatial extent of the fingerprint cells and the differentiability of the RSS distribution in each cell, as well as their impact on localization accuracy and on fingerprint storage. We experimented with traces collected by an autonomous robot exploring a large multi-floor office building.

Stability properties for optimum utility based scheduling algorithms in wireless Heterogeneous Networks (Hetnets) is investigated. Utility based schedulers are modelled as a Markov process which is shown not only to have ergodic properties but also certain finite moments, depending on the algorithm choice. The same properties adhere to periodic versions of these schedulers.

We consider a coordinated multiuser scheduling problem for a multicell mutually interfering broadcast network. In particular, we focus on a two-cell cluster, where both base stations have only local data and local channel state information, but each has sufficient number of antennas to serve multiple homogeneous users under a full zero-forcing beamforming transmission. The scheduling problem is formulated as finding proper scheduled users and hence beamformers across the cells such that the sum rate is maximized. We uncover the structure for a good scheduling decision, which in turn motivates three distributed coordinated scheduling policies of different levels of complexity. For the simplest policy, we derive a lower bound on the expected achievable sum rate. It is shown in the large user population limit, the simplest policy suffices to preserve the best possible multiplexing gain and multiuser diversity gain for the model studied, but it does induce a pairing loss on the sum rate due to the limited coordination between cells.

The deployment of pico cells to cover traffic hot spots within the footprint of a macro cell provides a powerful approach to meet the massive growth in traffic demands fueled by smartphones and bandwidth-hungry applications. Joint optimization of resource allocation and user association is of critical importance to achieve the maximum capacity benefits in such heterogeneous network deployments (HetNets). We first examine the problem of minimizing the amount of resources required to satisfy given traffic demands. We characterize the structure of the optimal solution, and identify a simple optimality condition in terms of the physical transmission rates of the edge users between the macro cell and the various pico cells. We further demonstrate how these structural properties can be leveraged in designing a distributed online algorithm for achieving a max-min fair throughput allocation across all users. Numerical experiments are presented to illustrate the results.

The deployment of pico cells to cover traffic hot spots within the footprint of a macro cell provides a powerful approach to meet the massive growth in traffic demands fueled by smartphones and bandwidth-hungry applications. Joint optimization of resource allocation and user association is of critical importance to achieve the maximal capacity benefits in such heterogeneous network deployments (HetNets). We specifically examine the problem of maximizing the aggregate throughput utility of the various users. We characterize the structure of the optimal solution, and identify a simple optimality condition in terms of the transmission rates of the edge users between the macro cell and the various pico cells. Exploiting the structural properties, we develop distributed online algorithms for the broad class of alpha-fair utility functions, which includes several common fairness notions. Numerical experiments are presented to illustrate the results.

Consider several source nodes communicating across a wireless network to a destination node with the help of several layers of relay nodes. Recent work by Avestimehr has approximated the capacity of this network up to an additive gap. The communication scheme achieving this capacity approximation is based on compress-and-forward, resulting in noise accumulation as the messages traverse the network. As a consequence, the approximation gap increases linearly with the network depth. This paper develops a computation alignment strategy that can approach the capacity of a class of layered, time-varying wireless relay networks up to an approximation gap that is independent of the network depth. This strategy is based on the compute-and-forward framework, which enables relays to decode deterministic functions of the transmitted messages. Alone, compute-and-forward is insufficient to approach the capacity as it incurs a penalty for approximating the wireless channel with complex-valued coefficients by a channel with integer coefficients. Here, this penalty is circumvented by carefully matching channel realizations across time slots to create integer-valued effective channels that are well suited to compute-and-forward. Unlike prior constant gap results, the approximation gap obtained in this paper also depends closely on the fading statistics, which are assumed to be i.i.d. Rayleigh.

In this work we examine the behavior of the minimum singular value of random Vandermonde matrices. In particular, we prove that the minimum singular value s1(N) is at most N exp(-C√N) where N is the dimension of the matrix and C is a constant. Furthermore, the value of the constant C is determined explicitly. The main result is obtained in two different ways. One approach uses techniques from stochastic processes and in particular, a construction related to the Brownian bridge. The other one is a more direct analytical approach involving combinatorics and complex analysis. As a consequence, we obtain a lower bound on the maximum absolute value of a random polynomial on the unit circle, which may be of independent mathematical interest.

We analyze the asymptotic behavior of compute-and-forward relay networks in the regime of high signal-to-noise ratios. We consider a section of such a network consisting of K transmitters and K relays. The aim of the relays is to reliably decode an invertible function of the messages sent by the transmitters. An upper bound on the capacity of this system can be obtained by allowing full cooperation among the transmitters and among the relays, transforming the network into a K × K multiple-input multiple-output (MIMO) channel. The number of degrees of freedom of compute-and-forward is hence at most K. In this paper, we analyze the degrees of freedom achieved by the lattice coding implementation of compute-and-forward proposed recently by Nazer and Gastpar. We show that this lattice implementation achieves at most 2/(1+1/K) ≤ 2 degrees of freedom, thus exhibiting a very different asymptotic behavior than the MIMO upper bound. This raises the question if this gap of the lattice implementation to the MIMO upper bound is inherent to compute-and-forward in general. We answer this question in the negative by proposing a novel compute-and-forward implementation achieving K degrees of freedom.

Various methods have been developed for indoor localization using WLAN signals. Algorithms that fingerprint the Received Signal Strength Indication (RSSI) of WiFi for different locations can achieve tracking accuracies of the order of a few meters. RSSI fingerprinting suffers though from two main limitations: first, as the signal environment changes, so does the fingerprint database, which requires regular updates; second, it has been reported that, in practice, certain devices record more complex (e.g bimodal) distributions of WiFi signals, precluding algorithms based on the mean RSSI. In this article, we propose a simple methodology that takes into account the full distribution for computing similarities among fingerprints using Kullback-Leibler divergence, and that performs localization through kernel regression. Our method provides a natural way of smoothing over time and trajectories. Moreover, we propose unsupervised KL-divergence-based recalibration of the training fingerprints. Finally, we apply our method to work with histograms of WiFi connections to access points, ignoring RSSI distributions, and thus removing the need for recalibration. We demonstrate that our results outperform nearest neighbors or Kalman and Particle Filters, achieving up to 1m accuracy in office environments. We also show that our method generalizes to non-Gaussian RSSI distributions.

This paper considers the scheduling problem for networks with interference constraints and switchover delays, where it takes a nonzero time to reconfigure each service schedule. Switchover delay occurs in many telecommunication applications such as satellite, optical or delay tolerant networks (DTNs). Under zero switchover delay it is well known that the Max-Weight algorithm is throughput-optimal without requiring knowledge of the arrival rates. However, we show that this property of Max-Weight no longer holds when there is a nonzero switchover delay. We propose a class of variable frame based Max-Weight (VFMW) algorithms which employ the Max-Weight schedule corresponding to the beginning of the frame during an interval of duration dependent on the queue sizes. The VFMW algorithms dynamically adapt the frame sizes to the stochastic arrivals and provide throughput-optimality without requiring knowledge of the arrival rates. Numerical results regarding the application of the VFMW algorithms to DTN and optical networks demonstrate a good delay performance.

We analyze the asymptotic behavior of compute-and-forward relay networks in the regime of high signal-to-noise ratios. We consider a section of such a network consisting of K transmitters and K relays. The aim of the relays is to reliably decode an invertible function of the messages sent by the transmitters. An upper bound on the capacity of this system can be obtained by allowing full cooperation among the transmitters and among the relays, transforming the network into a K × K multiple-input multiple-output (MIMO) channel. The number of degrees of freedom of compute-and-forward is hence at most K. In this paper, we analyze the degrees of freedom achieved by the lattice coding implementation of compute-and-forward proposed recently by Nazer and Gastpar. We show that this lattice implementation achieves at most 2=(1+1=K) ≤ 2 degrees of freedom, thus exhibiting a very different asymptotic behavior than the MIMO upper bound. This raises the question if this gap of the lattice implementation to the MIMO upper bound is inherent to compute-and-forward in general. We answer this question to the negative by proposing a novel compute-and-forward implementation achieving K degrees of freedom.

We examine threshold-based transmission strategies for distributed opportunistic medium access in a scenario with fairly general probabilistic interference conditions. Specifically, collisions between concurrent transmissions are governed by arbitrary probabilities, allowing for a form of channel capture and covering binary interference constraints as an important special case. We address the problem of setting the threshold values so as to optimize the aggregate throughput utility of the various users, and particularly focus on a weighted logarithmic throughput utility function (Proportional Fairness). We provide an adaptive algorithm for finding the optimal threshold values in a distributed fashion, and rigorously establish the convergence of the proposed algorithm under mild statistical assumptions. Moreover, we discuss how the algorithm may be adapted to achieve packet-level stability with only limited exchange of queue length information among the various users. We also conduct extensive numerical experiments to corroborate the theoretical convergence results.

This paper centers on the limit eigenvalue distribution for random Vandermonde matrices with unit magnitude complex entries. The phases of the entries are chosen independently and identically distributed from the interval [-π,π] . Various types of distribution for the phase are considered and we establish the existence of the empirical eigenvalue distribution in the large matrix limit on a wide range of cases. The rate of growth of the maximum eigenvalue is examined and shown to be no greater thanO(logN) and no slower thanO(logN/loglogN) whereNis the dimension of the matrix. Additional results include the existence of the capacity of the Vandermonde channel (limit integral for the expected log determinant).

In this paper we investigate the tracking performance of the downstream (DS) crosstalk (XT) channel estimation based on the reported signal to noise ratio (SNR), in particular for digital subscriber line (DSL) systems. Aiming to its simplicity, the SNR-assisted XT estimation, has been recognized in ITU as a backward compatible method that does not require any change in the very high speed digital subscriber line 2 (VDSL2) standard. This low complex algorithm can be used for XT channel estimation in dynamic spectrum management (DSM) techniques today. The algorithm as proposed, relies on sending perturbing signals on the victim lines (VLs) and reporting the SNRs by those lines to acquire the crosstalk channel from some disturber line (DL) to the VLs. We generalize this concept to include full startup, tracking and joining scenarios as well as the impact of different perturbation signal choices. Simulation results reveal that starting from no crosstalk precompensation, and updating a precoder matrix based on the DS crosstalk channel estimates, the far-end crosstalk (FEXT) free SNR can be reached in few iterations (36 SNR measurements for the four lines case).

Rapid acquisition of accurate crosstalk estimates is a core requirement for effective preceding in digital subscriber line (DSL) systems. It is shown that signal-to-noise ratio (SNR) reports provided by customer premises equipment (CPE) can be used to perform this task by "tuning" the precoder, i.e., iterating alternate steps of estimation and precoder adaptation. Such an approach has the advantage that it can be applied to legacy CPEs. Estimation algorithms are designed using techniques from stochastic control.

The downlink transmission in multi-user multiple- input multiple-output (MIMO) systems has been extensively studied from both communication-theoretic and information-theoretic perspectives. Most of these papers assume perfect/imperfect channel knowledge. In general, the problem of channel estimation is studied separately. However, in interference-limited communication systems with high mobility, the problem of channel estimation is tightly coupled with the problem of maximizing throughput of the system. In this paper, scheduling and preconditioning in the presence of reciprocal time-division duplex (TDD) training are considered. In the case of homogeneous users, a scheduling scheme is proposed and an improved lower bound on the sum capacity is derived. The problem of choosing training sequence length to maximize net throughput of the system is also studied. In the case of heterogeneous users, a modified pre-conditioning method is proposed and an optimized pre-conditioning matrix is derived. This method is combined with a scheduling scheme to further improve achievable weighted-sum rate.

We study the problem of efficiently scheduling users in a Gaussian broadcast channel withMtransmit antennas andKindependent receivers, each with a single antenna. We first focus on a scenario with two transmit antennas and statistically identical users, and analyze the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. In particular, we consider a scheme that picks the user with the largest channel gain, and selects a second user from the nextL- 1 strongest ones to form the best pair, taking channel orientations into account as well. We prove that the expected rate gap converges to 1/(L- 1) nats/symbol when the total number of usersKtends to infinity. AllowingLto increase withK, it may be deduced that transmitting to a properly chosen pair of users is asymptotically optimal, while considerably reducing the feedback overhead and scheduling complexity. Next, we tackle the problem of maximizing aweightedsum rate in a scenario with heterogeneous user characteristics. We establish a novel upper bound for the weighted sum capacity, which we then use to show that the maximum expected weighted sum rate can be asymptotically achieved by transmitting to a suitably selected subset of at mostMCusers, whereCdenotes the number of distinct user classes. Numerical experiments indicate that the asymptotic results are remarkably accurate and that the proposed schemes operate close to absolute performance bounds, even for a moderate number of users.

We evaluate the asymptotic normalized average distributions of a class of combinatorial configurations in random, regular and irregular, binary low-density parity-check (LDPC) code ensembles. Among the configurations considered are trapping and stopping sets. These sets represent subsets of variable nodes in the Tanner graph of a code that play an important role in determining the height and point of onset of the error-floor in its performance curve. The techniques used for deriving the spectra include large deviations theory and statistical methods for enumerating binary matrices with prescribed row and column sums. These techniques can also be applied in a setting that involves more general structural entities such as subcodes and/or minimal codewords, that are known to characterize other important properties of soft-decision decoders of linear block codes

Trapping sets represent subgraphs in the Tanner graph of a code that, for certain classes of channels, exhibit a strong influence on the height and point of onset of the error-floor. We compute the asymptotic normalized distributions of trapping sets in random, irregular, binary low-density parity-check (LDPC) code ensembles. Our derivations rely on techniques from large deviation theory and statistical methods for enumeracting random-like matrices. Similar methods can be used for computing the spectra of other combinatorial entities in LDPC code, such as subcodes and/or minimal codewords.

Two incremental redundancy hybrid ARQ (IR-HARQ) schemes are compared: one is based on LDPC code ensembles with random transmission assignments, the other is based on recently introduced Raptor codes. A number of important issues, such as rate and power control, and error rate performance after each transmission on time varying binary-input, symmetric-output channels are addressed by analyzing performance of LDPC and Raptor codes on parallel channels. The theoretical results obtained for random code ensembles are tested on several practical code examples by simulation. Both theoretical and simulation results show that both LDPC and Raptor codes are suitable for HARQ schemes. Which codes would make a better choice depends mainly on the width of the signal-to-noise operating range of the HARQ scheme, prior knowledge of that range, and other design parameters and constraints dictated by standards.

The capacity region of the Gaussian multi-antenna broadcast channel was characterized recently in [19]. It was shown that a scheme based on Dirty Paper Coding [2] achieves the full capacity region when the transmitter has perfect channel state information. However, this scheme potentially involves considerable amounts of feedback and complex algorithms for coding and user selection. This has led to a quest for practical transmission schemes and ways to reduce the amount of channel state information required. In particular, it has been shown that when the total number of users is large, the sum capacity can be closely approached by transmitting to a small subset of near-orthogonal users. In order to further quantify the latter observation, we study a Gaussian broadcast channel with two transmit antennas and K statistically identical, independent users each with a single receive antenna. We obtain an exact asymptotic characterization of the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. Specifically, we consider various simple schemes for user-pair selection that take into account the channel norms as well as the relative orientation of the channel vectors. We conclude that a scheme that picks the strongest user and selects a second user to form the best pair, is asymptotically optimal, while also being attractive in terms of feedback and operational complexity.

We examine communication over slowly varying flat-fading additive white Gaussian noise (AWGN) channels with delayed channel state information (CSI) feedback to the transmitter and finite decoding delay constraints. Under a block-fading channel model, it is shown that a broadcast strategy maximizes the expected reliably received rate when the decoding delay constraint is one block and in certain cases when the delay constraint is two blocks. The latter requires a new analysis of underlying parallel Gaussian broadcast channels (GBCs) which are not degraded in the same direction

An LDPC code based hybrid ARQ scheme with random transmission assignments is analyzed. The spectrum properties of LDPC code ensembles that are necessary for this analysis are derived. Very good estimates of maximum-likelihood decoding error rates after each transmission are provided. The results are tested on practical code examples by simulation

We are concerned with the allocation of the base station transmitter time in time-varying mobile communications with many users who are transmitting data. Time is divided into small scheduling intervals, and the channel rates for the various users are available at the start of the intervals. Since the rates vary randomly, in selecting the current user there is a conflict between full use (by selecting the user with the highest current rate) and fairness (which entails consideration for users with poor throughput to date). The proportional fair scheduler of the Qualcomm High Data Rate system and related algorithms are designed to deal with such conflicts. The aim here is to put such algorithms on a sure mathematical footing and analyze their behavior. The available analysis, while obtaining interesting information, does not address the actual convergence for arbitrarily many users under general conditions. Such algorithms are of the stochastic approximation type and results of stochastic approximation are used to analyze the long-term properties. It is shown that the limiting behavior of the sample paths of the throughputs converges to the solution of an intuitively reasonable ordinary differential equation, which is akin to a mean flow. We show that the ordinary differential equation (ODE) has a unique equilibrium and that it is characterized as optimizing a concave utility function, which shows that PFS is not ad-hoc, but actually corresponds to a reasonable maximization problem. These results may be used to analyze the performance of PFS. The results depend on the fact that the mean ODE has a special form that arises in problems with certain types of competitive behavior. There is a large set of such algorithms, each one corresponding to a concave utility function. This set allows a choice of tradeoffs between the current rate and throughout. Extensions to multiple antenna and frequency systems are given. Finally, the infinite backlog assumption is dropped and the data is allowed to arrive at random. This complicates the analysis, but the same results hold.

Wireless local area networks (WLANS) (1997) allow the transmission of bursty data traffic over fading, wireless links. We formulate and analyze a simple model of controlled ALOHA in a Rayleigh fading environment. We consider the application of a one bit per slot feedback control algorithm, from (Sylvie Ghez, et al., 1989), and propose a new algorithm involving higher rates of feedback per slot. Our algorithm is based on an optimization framework, which enables one to determine the desired rate of feedback, and we demonstrate the effectiveness of our algorithm in improving delay performance as compared to the 1-bit feedback algorithm.

The relative delay tolerance of data applications, together with the bursty traffic characteristics, opens up the possibility for scheduling transmissions so as to optimize throughput. A particularly attractive approach, in fading environments, is to exploit the variations in the channel conditions, and transmit to the user with the currently 'best' channel. We show that the 'best' user may be identified as the maximum-rate user when the feasible rates are weighed with some appropriately determined coefficients. Interpreting the coefficients as shadow prices, or reward values, the optimal strategy may thus be viewed as a revenue-based policy. Calculating the optimal revenue vector directly is a formidable task, requiring detailed information on the channel statistics. Instead, we present adaptive algorithms for determining the optimal revenue vector on-line in an iterative fashion, without the need for explicit knowledge of the channel behavior. Starting from an arbitrary initial vector, the algorithms iteratively adjust the reward values to compensate for observed deviations from the target throughput ratios. The algorithms are validated through extensive numerical experiments. Besides verifying long-run convergence, we also examine the transient performance, in particular the rate of convergence to the optimal revenue vector. The results show that the target throughput ratios are tightly maintained, and that the algorithms are well able to track changes in the channel conditions or throughput targets.

It is shown that the encoding/decoding problem for any asynchronous M-user discrete memoryless multiple-access channel can be reduced to corresponding problems for at most 2M-1 single-user discrete memoryless channels. This result, which extends a similar result for Gaussian channels, reduces the seemingly hard task of finding good multiple-access codes to the much better understood task of finding good codes for single-user channels. As a by-product, some interesting properties of the capacity region of M-user asynchronous discrete memoryless channels are derived.

We study the design and performance of underlay-overlay (U-O) wireless networks, which promise capacity gains over conventional fixed-reuse cellular networks. To address the two principal problems in U-O networks, namely, (a). Where are the underlay boundaries to be placed? (b). How are the channels to be allocated? we propose an optimization procedure and a traffic model respectively. Our objective is to match spectrum allocated to the underlay to absorption (proportion of underlay traffic), subject to statistical interference constraints. Numerical results demonstrate the effectiveness of our design procedure and suggest substantial capacity gains from U-O networks.

We derive bounds for the performance of dynamic channel assignment (DCA) schemes which strengthen the existing Erlang bound. The construction of the bounds is based on a reward paradigm as an intuitively appealing way of characterizing the achievable carried traffic region. In one-dimensional networks, our bounds closely approach the performance of maximum packing (MP), which is an idealized DCA scheme. This suggests not only that the bounds are extremely tight, but also that no DCA scheme, however sophisticated, can be expected to outperform MP in any significant manner, if at all. Our bounds extend to scenarios with varying re-use which may arise in the case of dynamic re-use partitioning or measurement-based DCA schemes. In these cases, the bounds slightly diverge from the performance of MP, which inflicts higher blocking on outer calls than inner calls, but not to the extent required to maximize carried traffic. This reflects the trade-off that arises in the case of varying re-use between efficiency and fairness. Asymptotic analysis confirms that schemes which minimize blocking intrinsically favor inner calls over outer calls, whereas schemes which do not discriminate among calls inevitably produce higher network-average blocking.

Approximate capacity bounds are obtained by estimating the probability that the SNR equations for the received powers in a CDMA network have no solution, using large deviations techniques. The construction of the bounds is illustrated using a single micro cell example and extensions of this are given subsequently. The results suggest that micro cells are an effective method for extending the capacity of a CDMA cellular network.

We examine the behaviour of the information theoretic capacity of jointly detected (multiuser) symbol synchronous DS-SSMA systems, when randomly selected spreading sequences are used. We find upper and lower bounds on capacity for a certain cross-correlation measure, and show that if the number of users is larger than the sequence length, that the lower bound tends to the maximum capacity with increasing sequence length. This implies that for large systems, random spreading sequences are optimal in terms of capacity. We also examine more realistic cases for the number of users and sequence length, and find that in certain cases that the use of random spreading sequences results only in a very small decrease in capacity. I. Introduction In a recent paper by Rupf and Massey [1], it was shown that any sequence multiset that achieves Welch's lower bound on total squared correlation [2] (denoted a WBE set) maximises capacity for the Gaussian direct sequence spread spectrum multiple access ...