In Federated Learning (FL) with over-the-air aggregation, the quality of the signal received at the server critically depends on the receive scaling factors. While a larger scaling factor can reduce the effective noise power and improve training performance, it also compromises the privacy of devices by reducing uncertainty. In this work, we aim to adaptively design the receive scaling factors across training rounds to balance the trade-off between training convergence and privacy in an FL system under dynamic channel conditions. We formulate a stochastic optimization problem that minimizes the overall Rényi differential privacy (RDP) leakage over the entire training process, subject to a long-term constraint that ensures convergence of the global loss function. Our problem depends on unknown future information, and we observe that standard Lyapunov optimization is not applicable. Thus, we develop a new online algorithm, termed AdaScale, based on a sequence of novel per-round problems that can be solved efficiently. We further derive upper bounds on the dynamic regret and constraint violation of AdaSacle, establishing that it achieves diminishing dynamic regret in terms of time-averaged RDP leakage while ensuring convergence of FL training to a stationary point. Numerical experiments on canonical classification tasks show that our approach effectively reduces RDP and DP leakages compared with state-of-the-art benchmarks without compromising learning performance.

This paper studies power-efficient uplink transmission design for federated learning (FL) that employs over-the-air analog aggregation and multi-antenna beamforming at the server. We jointly optimize device transmit weights and receive beamforming at each FL communication round to minimize the total device transmit power while ensuring convergence in FL training. Through our convergence analysis, we establish sufficient conditions on the aggregation error to guarantee FL training convergence. Utilizing these conditions, we reformulate the power minimization problem into a unique bi-convex structure that contains a transmit beamforming optimization subproblem and a receive beamforming feasibility subproblem. Despite this unconventional structure, we propose a novel alternating optimization (AO) approach that guarantees monotonic decrease of the objective value, to allow convergence to a partial optimum. We further consider imperfect channel state information (CSI), which requires accounting for the channel estimation errors in the power minimization problem and FL convergence analysis. We propose a CSI-error-aware joint beamforming algorithm, which can substantially outperform one that does not account for channel estimation errors. Simulation with canonical classification datasets demonstrates that our proposed methods achieve significant power reduction compared to existing benchmarks across a wide range of parameter settings, while attaining the same target accuracy under the same convergence rate.

Federated learning (FL) over wireless networks using analog transmission can efficiently utilize the communication resource but is susceptible to errors caused by noisy wireless links. In this paper, assuming a multi-antenna base station, we jointly design downlink-uplink beamforming to maximize FL training convergence over time-varying wireless channels. We derive the round-trip model updating equation and use it to analyze the FL training convergence to capture the effects of downlink and uplink beamforming and the local model training on the global model update. Aiming to maximize the FL training convergence rate, we propose a low-complexity joint downlink-uplink beamforming (JDUBF) algorithm, which adopts a greedy approach to decompose the multi-round joint optimization and convert it into per-round online joint optimization problems. The per-round problem is further decomposed into three subproblems over a block coordinate descent framework, where we show that each subproblem can be efficiently solved by projected gradient descent with fast closed-form updates. An efficient initialization method that leads to a closed-form initial point is also proposed to accelerate the convergence of JDUBF. Simulation demonstrates that JDUBF substantially outperforms the conventional separate-link beamforming design.

This work addresses the trade-off between convergence and the overall delay in heterogeneous distributed learning systems, where the devices encounter diverse and dynamic communication conditions. We propose to apply adaptive sparsification across the devices and over iterations, formulating an optimization problem to minimize the overall delay while ensuring a specified level of convergence. The resultant stochastic optimization problem cannot be handled by conventional Lyapunov optimization techniques due to the dependency of the per-iteration objective function on the previous iterations. To overcome this challenge, we propose AdaSparse, an online algorithm with a novel per-slot problem that can be solved optimally by searching over a finite discrete space. We further introduce a low-complexity approximation of AdaSparse, termed LC-AdaSparse, which features linear computational complexity and diminishing approximation error. We show that AdaSparse offers strong performance guarantees, simultaneously achieving sub-linear dynamic regret in terms of delay and the optimal rate in terms of convergence. Numerical experiments on classification tasks using standard datasets and various models demonstrate that our approach effectively reduces the communication delay compared with existing benchmarks, to achieve the same levels of learning accuracy.

Differential privacy (DP) limits the impact of individual training data samples by bounding their gradient norms through clipping. Conventional clipping operations assign unequal scaling factors to sample gradients with different norms, leading to a direction mismatch between the true batch gradient and the aggregation of the clipped gradients. Applying a smaller but identical scaling factor to all sample gradients alleviates this direction mismatch; however, it intensifies the magnitude mismatch by excessively reducing the aggregation norm. This work proposes a novel clipping method, termed adaptive sigmoid (AdaSig), which uses a sigmoid function with an adjustable saturation slope to clip the sample gradients. The slope is adaptively adjusted during the training process to balance the trade-off between direction mismatch and magnitude mismatch, as the statistics of sample gradients evolve over the training iterations. Despite AdaSig’s adaptive nature, our convergence analysis demonstrates that differentially private stochastic gradient descent (DP-SGD) with AdaSig clipping retains the best-known convergence rate under non-convex loss functions. Evaluating AdaSig on sentence and image classification tasks across different datasets shows that it consistently improves learning performance compared with established clipping methods.

Federated learning (FL) with over-the-air computation efficiently utilizes the communication resources, but it can still experience significant latency when each device transmits a large number of model parameters to the server. This paper proposes the Segmented Over-The-Air (SegOTA) method for FL, which reduces latency by partitioning devices into groups and letting each group transmit only one segment of the model parameters in each communication round. Considering a multiantenna server, we model the SegOTA transmission and reception process to establish an upper bound on the expected model learning optimality gap. We minimize this upper bound, by formulating the per-round online optimization of device grouping and joint transmit-receive beamforming, for which we derive efficient closed-form solutions. Simulation results show that our proposed SegOTA substantially outperforms the conventional full-model OTA approach and other common alternatives.

The main challenges in designing downlink coordinated multicast beamforming in massive multiple-input multiple output (MIMO) cellular networks are the complex computational solutions and significant fronthaul overhead for centralized coordination. This paper proposes a coordinated multicast beamforming solution that is both computation and communication efficient. For joint BS coordination with individual base station transmit power budgets, we first obtain the optimal structure of coordinated multicast beamforming. It reveals that the beamformer at each BS is naturally distributed and only depends on the local channel state information (CSI) at its serving BS. Moreover, the optimal beamformer is a weighted minimum mean square error (MMSE) beamformer with a low-dimensional structure of unknown weights to be optimized, independent of the number of BS antennas. Utilizing the optimal structural properties, we propose fast algorithms to determine the unknown parameters for the optimal beamformer. The main iterative algorithm decomposes the problem into small subproblems, yielding only closed/semi-closed form updates. Furthermore, we propose a semi-distributed computing approach for the proposed algorithm that allows each BS to compute its beamformer based on the local CSI without the need for global CSI sharing, resulting in the fronthaul overhead independent of the number of BS antennas. We further extend our results to the design under the imperfect CSI and other coordination scenarios. Simulation results demonstrate that our proposed methods can achieve near-optimal performance with significantly lower computational time for massive MIMO systems than the conventional approaches.

This paper studies MapReduce-based heterogeneous coded distributed computing (CDC) where, besides different computing capabilities at workers, input files to be accessed by computing jobs have nonuniform popularity. We propose a file placement strategy that can handle an arbitrary number of input files. Furthermore, we design a nested coded shuffling strategy that can efficiently manage the nonuniformity of file popularity to maximize the coded multicasting opportunity. We then formulate the joint optimization of the proposed file placement and nested shuffling design variables to optimize the proposed CDC scheme. To reduce the high computational complexity in solving the resulting mixed-integer linear programming (MILP) problem, we propose a simple two-file-group-based file placement approach to obtain an approximate solution. Both numerical studies and experimental tests show that the optimized CDC scheme outperforms other alternatives. Also, the proposed two-file-group-based approach achieves nearly the same performance as the conventional branch-and-cut method in solving the MILP problem but with substantially lower computational complexity that is scalable over the number of files and workers. For computing jobs with aggregate target functions that commonly appear in machine learning applications, we propose a heterogeneous compressed CDC (C-CDC) scheme to further improve the shuffling efficiency. The C-CDC scheme uses a local data aggregation technique to compress the data to be shuffled for the shuffling load reduction. We again optimize the proposed C-CDC scheme and explore the two-file-group-based low-complexity approach for an approximate solution. Numerical studies show the proposed C-CDC scheme provides a considerable shuffling load reduction over the CDC scheme, and also, the two-file-group-based file placement approach maintains good performance.

We consider online distributed optimization in a networked system, where multiple devices assisted by a server collaboratively minimize the accumulation of a sequence of global loss functions that can vary over time. To reduce the amount of communication, the devices send quantized and compressed local decisions to the server, resulting in noisy global decisions. Therefore, there exists a tradeoff between the optimization performance and the communication overhead. Existing works separately optimize computation and communication. In contrast, we jointly consider computation and communication over time, by proactively encouraging temporal similarity in the decision sequence to control the communication overhead. We propose an efficient algorithm, termed Online Distributed Optimization with Temporal Similarity (ODOTS), where the local decisions are both computation- and communication-aware. Furthermore, ODOTS uses a novel tunable virtual queue, which removes the commonly assumed Slater’s condition through a modified Lyapunov drift analysis. ODOTS delivers provable performance bounds on both the optimization objective and constraint violation. Furthermore, we consider a variant of ODOTS with multi-step local gradient descent updates, termed ODOTS-MLU, and show that it provides improved performance bounds. As an example application, we apply both ODOTS and ODOTS-MLU to enable communication-efficient federated learning. Our experimental results based on canonical image classification demonstrate that ODOTS and ODOTS-MLU obtain higher classification accuracy and lower communication overhead compared with the current best alternatives for both convex and non-convex loss functions.

We consider online distributed optimization where a server and multiple devices collaborate to minimize a sequence of time-varying global loss functions. To accommodate slow devices that may require multiple time slots to compute their local decisions, the server uses semi-asynchronous aggregation of the local decisions, which complicates device scheduling and performance optimization. In this work, we first analyze the convergence of semi-asynchronous aggregation in the presence of time-varying local update delays and loss-function weights. Our analysis leads to an online scheduling problem to minimize the accumulated age of information on the local decision updates, subject to individual long-term constraints on the total weights of the scheduled devices. We then design an efficient scheduling policy, termed Age-of-Information Minimization with Weight Limits (AIMWeL), through a modified Lyapunov optimization approach that uses the weighted sum of linear age-of-information values and quadratic virtual queues as a new Lyapunov function. We show that AIMWeL has bounded optimality ratio, via a novel double relaxation approach to handle the unique scheduling-dependent communication indicator with time-varying probabilities of completing local decision update caused by semi-asynchronous aggregation. When AIMWeL is applied to semi-asynchronous federated learning, our simulation results based on standard image classification datasets demonstrate that AIMWeL uses significantly less time to reach the same classification accuracy achieved by the current best alternatives for both convex logistic regression and non-convex convolutional neural networks.

This paper studies the design of wireless federated learning (FL) for simultaneously training multiple machine learning models. We consider round robin device-model assignment and downlink beamforming for concurrent multiple model updates. After formulating the joint downlink-uplink transmission process, we derive the per-model global update expression over communication rounds, capturing the effect of beamforming and noisy reception. To maximize the multi-model training convergence rate, we derive an upper bound on the optimality gap of the global model update and use it to formulate a multi-group multicast beamforming problem. We show that this problem can be converted to minimizing the sum of inverse received signal-to-interference-plus-noise ratios, which can be solved efficiently by projected gradient descent. Simulation shows that our proposed multi-model FL solution outperforms other alternatives, including conventional single-model sequential training and multi-model zero-forcing beamforming.

We consider wireless network virtualization (WNV) in an uplink multiple-input multiple-output system, where multiple service providers (SPs) operate in virtually isolated networks managed by an infrastructure provider (InP) that owns the communication equipment. Service isolation is achieved at the physical layer by exploiting a large number of antennas at the base stations. We formulate this WNV as a non-convex optimization problem for the InP, jointly considering the uplink receive beamforming at the BS and the transmit power of the SPs' subscribing user devices. We decompose the problem into two subproblems and derive closed-form solutions to both. We then adopt an alternating optimization approach to combine the closed-form solutions to solve the original problem. Our simulation results show that the proposed method provides strong service isolation among the SPs while retaining efficiency similar to or better than centralized beamforming without virtualization, and it substantially outperforms traditional WNV with strict resource separation.

This paper aims to characterize the memory-rate tradeoff for decentralized caching under nonuniform file popularity and size. We consider a recently proposed decentralized modified coded caching scheme (D-MCCS) and formulate the cache placement optimization problem to minimize the average rate for the D-MCCS. To solve this challenging non-convex optimization problem, we first propose a successive Geometric Programming (GP) approximation algorithm, which guarantees convergence to a stationary point but has high computational complexity. Next, we develop a low-complexity file-group-based approach, where we propose a popularity-first and size-aware (PF-SA) cache placement strategy to partition files into two groups, taking into account the nonuniformity in file popularity and size. Both algorithms do not require the knowledge of active users beforehand for cache placement. Numerical results show that they perform very closely to each other. We further develop a lower bound for decentralized caching under nonuniform file popularity and size as a non-convex optimization problem and solved it using a similar successive GP approximation algorithm. We show that the D-MCCS with the optimized cache placement attains this lower bound when no more than two active users request files at a time. The same is true for files with uniform size but nonuniform popularity and the optimal cache placement being symmetric among files. In these cases, the optimized D-MCCS characterizes the exact memory-rate tradeoff for decentralized caching. For general cases, our numerical results show that the average rate achieved by the optimized D-MCCS is very close to the lower bound.

We consider federated learning in a wireless edge network, where multiple power-limited mobile devices collaboratively train a global model, using their local data with the assistance of an edge server. Exploiting over-the-air computation, the edge server updates the global model via analog aggregation of the local models over noisy wireless fading channels. Unlike existing works that separately optimize computation and communication at each step of the learning algorithm, in this work, we jointly optimize the training of the global model and the analog aggregation of the local models over time. Our objective is to minimize the accumulated training loss at the edge server, subject to individual long-term transmit power constraints at the mobile devices. We propose an efficient algorithm, termed Online Model Updating with Analog Aggregation (OMUAA), to adaptively update the local and global models based on the time-varying communication environment. The trained model of OMUAA is channel-and power-aware, and it is in closed form incurring low computational complexity. We study the mutual impact between model training and analog aggregation over time, to derive performance bounds on the computation and communication performance metrics. Furthermore, we consider a variant of OMUAA with double regularization on both the local and global models, termed OMUAA-DR, and show that it can significantly reduce the convergence time to reach long-term transmit power constraints. In addition, we extend both OMUAA and OMUAA-DR to enable analog gradient aggregation, while preserving their performance bounds. Simulation results based on real-world image classification datasets and typical wireless network settings demonstrate substantial performance gain of OMUAA and OMUAA-DR over the known best alternatives.

We consider cooperative multiple-input multiple-output (MIMO) precoding design with multiple access points (APs) assisted by a central controller (CC) in a fading environment. Even though each AP may have its own local channel state information (CSI), due to the communication delay in the backhaul, neither the APs nor the CC has timely global CSI. Under this hierarchical semi-online setting, our goal is to minimize the accumulated precoding deviation, between the actual local precoders executed by the APs and an ideal cooperative precoder based on timely and perfect global CSI, subject to per-AP transmit power limits. We propose an efficient algorithm, termed Semi-Online Precoding with Information Parsing (SOPIP), which accounts for the network heterogeneity in information timeliness and computational capacity. SOPIP does not require the CC to send the full global CSI to each AP. Instead, it takes advantage of the precoder structure to substantially lower the communication overhead, while allowing each AP to effectively combine its own timely local CSI with the delayed global CSI to enable adaptive precoder updates. We analyze the performance of SOPIP in the presence of multi-slot communication delay, CSI inaccuracy, and gradient estimation error, showing that it has a bounded performance gap from an offline optimal solution. Simulation results under typical cellular system settings further demonstrate the substantial performance gain of SOPIP over other centralized and distributed schemes.

We consider online distributed optimization in a networked system, where multiple devices assisted by a server collaboratively minimize the accumulation of a sequence of global loss functions that can vary over time. To reduce the amount of communication, the devices send quantized and compressed local decisions to the server, resulting in noisy global decisions. Therefore, there exists a tradeoff between the optimization performance and the communication overhead. Existing works separately optimize computation and communication. In contrast, we jointly consider computation and communication over time, by encouraging temporal similarity in the decision sequence to control the communication overhead. We propose an efficient algorithm, termed Online Distributed Optimization with Temporal Similarity (ODOTS), where the local decisions are both computation- and communication-aware. Furthermore, ODOTS uses a novel tunable virtual queue, which completely removes the commonly assumed Slater’s condition through a modified Lyapunov drift analysis. ODOTS delivers provable performance bounds on both the optimization objective and constraint violation. As an example application, we apply ODOTS to enable communication-efficient federated learning. Our experimental results based on real-world image classification demonstrate that ODOTS obtains higher classification accuracy and lower communication overhead compared with the current best alternatives for both convex and non-convex loss functions.

Combining over-the-air uplink transmission and multi-antenna beamforming can improve the efficiency of federated learning (FL). However, to mitigate the significant aggregation error due to communication noise and signal distortion, pre-processing of device signals and post-processing at the server are required. In this paper, we study the optimization of receiver beamforming and device transmit weights in over-the-air FL, to minimize the total transmit power in each communication round while guaranteeing the convergence of FL. We establish sufficient convergence conditions based on the analysis of gradient descent with error and formulate a power minimization problem. An alternating optimization approach is then employed to decompose the problem into tractable subproblems, and efficient solutions are developed for these subproblems. Our proposed method is evaluated through simulation on standard image classification tasks, demonstrating its effectiveness in achieving substantial reductions in transmit power compared with existing alternatives.

We study joint downlink-uplink beamforming design for wireless federated learning (FL) with a multi-antenna base station. Considering analog transmission over noisy channels and uplink over-the-air aggregation, we derive the global model update expression over communication rounds. We then obtain an upper bound on the expected global loss function, capturing the downlink and uplink beamforming and receiver noise effect. We propose a low-complexity joint beamforming algorithm to minimize this upper bound, which employs alternating optimization to breakdown the problem into three subproblems, each solved via closed-form gradient updates. Simulation under practical wireless system setup shows that our proposed joint beamforming design solution substantially outperforms the conventional separate-link design approach and nearly attains the performance of ideal FL with error-free communication links.

In many dynamic systems, decisions on system operation are updated over time, and the decision maker requires an online learning approach to optimize its strategy in response to the changing environment. When the loss and constraint functions are convex, this belongs to the general family of online convex optimization (OCO). In existing OCO works, the environment is assumed to vary in a time-slotted fashion, while the decisions are updated at each time slot. However, many wireless communication systems permit only periodic decision updates,i.e.each decision is fixed over multiple time slots, while the environment changes between the decision epochs. The standard OCO model is inadequate for these systems. Therefore, in this work, we consider periodic decision updates for OCO. We aim to minimize the accumulation of time-varying convex loss functions, subject to both short-term and long-term constraints. Feedback information about the loss functions within the current update period may be delayed and incomplete. We propose an efficient algorithm, termed Periodic Queueing and Gradient Aggregation (PQGA), which employs novel periodic queues together with possibly multi-step aggregated gradient descent to update the decisions over time. We derive upper bounds on the dynamic regret, static regret, and constraint violation of PQGA. As an example application, we study the performance of PQGA for network virtualization in a large-scale multi-antenna system shared by multiple wireless service providers. Simulation results show that PQGA converges fast and substantially outperforms the current best alternative.

We consider online convex optimization (OCO) with multi-slot feedback delay. An agent selects a sequence of online decisions to minimize the accumulation of time-varying convex loss functions, subject to short-term and long-term constraints that may be time-varying. Both the convex loss function and the long-term constraint function may experience multiple time slots of feedback delay to be received by the agent. Existing works on OCO under this general setting has focused on the static regret, which measures the gap of losses between an online decision sequence and a time-invariant static offline benchmark. In this work, besides the static regret, we also consider a more practically meaningful metric, the dynamic regret, where the benchmark is a time-varying online optimal decision sequence. We propose an efficient algorithm, termed Delay-Tolerant Constrained-OCO (DTC-OCO), which uses a novel double regularization together with a new penalty mechanism on the long-term constraint violation, to tackle the asynchrony between information feedback and decision updates. We obtain upper bounds for its static regret, dynamic regret, and constraint violation, proving that they are sublinear under mild conditions. Furthermore, we consider a variation of DTC-OCO with multi-step gradient descent, and show it provides improved dynamic regret and constraint violation bounds for strongly convex loss functions. For numerical demonstration, we apply DTC-OCO to a general network resource allocation problem. Our simulation results suggest substantial performance gain by DTC-OCO over the current best alternative.

This paper studies the heterogeneous coded distributed computing (CDC) where input files required for job access have nonuniform popularity. We propose a file placement strategy that can handle an arbitrary number of input files and a nested coded shuffling strategy to effectively explore coded multicasting opportunities. We then formulate the joint optimization of the proposed file placement strategy and shuffling design variables into a mixed-integer linear programming (MILP) problem. To reduce the computational complexity, we propose a simple two-file-group-based approach to obtain an approximate solution. Numerical results show that the proposed two-file-group-based approach achieves nearly the same performance as solving the MILP problem using the conventional branch-and-cut method but with substantially lower computational complexity.

We consider federated learning in a wireless edge network, where multiple power-limited mobile devices collaboratively train a global model, using their local data with the assistance of an edge server. Exploiting over-the-air computation, the edge server updates the global model via analog aggregation of the local models over noisy wireless fading channels. Unlike existing works that separately optimize computation and communication at each step of the learning algorithm, in this work, we jointly optimize the training of the global model and the analog aggregation of local models over time. Our objective is to minimize the accumulated training loss at the edge server, subject to individual long-term transmit power constraints at the mobile devices. We propose an efficient algorithm, termed Online Model Updating with Analog Aggregation (OMUAA), to adaptively update the local and global models based on the time-varying communication environment. The trained model of OMUAA is channel- and power-aware, and it is in closed form with low computational complexity. We study the mutual impact between model training and analog aggregation over time, to derive performance bounds on the computation and communication performance metrics. Simulation results based on real-world image classification datasets and typical Long-Term Evolution network settings demonstrate substantial performance gain of OMUAA over the known best alternatives.

We consider cooperative multiple-input multiple-output (MIMO) precoding design with multiple access points (APs) assisted by a central controller (CC) in a fading environment. Even though each AP may have its own local channel state information (CSI), due to the communication delay in the backhaul, neither the APs nor the CC has timely global CSI. Under this semi-online setting, our goal is to minimize the accumulated precoding deviation between the actual local precoders executed by the APs and an ideal cooperative precoder based on the global CSI, subject to per-AP transmit power limits. We propose an efficient algorithm, termed Semi-Online Precoding with Information Parsing (SOPIP), which accounts for the network heterogeneity in information timeliness and computational capacity. SOPIP does not require the CC to send the full global CSI to each AP. Instead, it takes advantage of the precoder structure to substantially lower the communication overhead, while allowing each AP to effectively combine its own timely local CSI with the delayed global CSI to enable adaptive precoder updates. We analyze the performance of SOPIP in the presence of both multi-slot communication delay and gradient estimation error, showing that it has a bounded performance gap from an offline optimal solution. Simulation results under typical Long-Term Evolution network settings further demonstrate the substantial performance gain of SOPIP over other centralized and distributed schemes.

We consider device-to-device (D2D) communication underlaid in a cellular network to share the uplink resource of cellular users (CUs). It is a key the emerging Internet of Things to support vehicle-to-everything communication networks. In a multicell scenario, both D2D pairs and CUs may cause significant significant intercell interference (ICI) to the neighboring cells. Furthermore, due to substantial signaling overhead, we assume only partial channel state information (CSI) of D2D links at the base station. We consider joint power control, beamforming, and CU-D2D matching problem, assuming partial CSI from D2D pairs under the general Nakagami fading model. We formulate a joint receive beamforming and robust power control optimization problem for a CU-D2D pair to expected sum rate under the power budget, while meeting the minimum SINR requirements and worst case ICI limits at neighboring cells in a probabilistic sense. We propose an efficient algorithm that combines an iterative D2D feasibility check and a ratio-of-expectation approximation. A performance upper bound is also developed for benchmarking. For multiple CUs and D2D pairs, due to orthogonal channelization within each cell, we first focus on the problem of joint power control and beamforming for a CU-D2D pair and show how our proposed solution can be leveraged to find a solution for this general problem. The complexity analysis of the proposed approach is also provided. Simulation results show that the proposed algorithm gives performance close to the upper bound.

This paper considers the integration of non-orthogonal multiple access (NOMA) into massive multi-input multi-output (MIMO) systems for downlink transmission. We consider the joint design of user clustering, transmit beamforming, and power allocation to minimize the total transmit power while meeting the signal-to-interference-and-noise ratio targets. We decompose this challenging mixed-integer programming problem into three separate subproblems to solve. We propose a low-complexity learning-based user clustering algorithm, which is a modified version of mean shift clustering with a new channel correlation based clustering metric. The proposed clustering algorithm determines the clusters to trade-off between spatial dimension and power dimension offered by respective MIMO and NOMA for user multiplexing. We then design zero-forcing transmit beamformers to eliminate inter-cluster interference and optimize power allocation to minimize the total transmit power. We provide two case studies for both co-located and distributed massive MIMO systems in spatially highly correlated prorogation environments. Simulation results show that our proposed algorithm forms NOMA clusters based on the available degrees of freedom in the system to effectively use both spatial and power dimensions, which results in a substantial performance improvement over MIMO-only methods or other existing clustering methods in such environments.

We use a partially observable Markov decision process (POMDP) framework to design an optimal antenna selection policy for downlink transmit beamforming at a multi-antenna base station (BS) equipped with only a limited number of RF chains. Assuming that the channel state evolves according to a finite-state Markov process and that only the channel coefficients which correspond to previously selected antennas, are available at the BS, we use the POMDP framework for antenna selection with the aim to maximize thelong-term expected downlink data rate. To avoid the high computational complexity of the value iteration algorithm, we focus on the myopic policy and prove thatin the case of positively correlated two-state Markov model for the channel over each antenna, the myopic policy is optimal for antenna selection for any number of RF chains. Based on this finding, for general fading channels, we propose to quantize each channel into two levels and apply the myopic policy for antenna selection. Our simulation results show that using this two-state coarse channel quantization for antenna selection results in only a small loss in performance, as compared to the antenna selection technique which uses full channel state information without quantization.

This paper studies the caching system of multiple cache-enabled users with random demands. Under nonuniform file popularity, we thoroughly characterize the optimal uncoded cache placement structure for the coded caching scheme (CCS). Formulating the cache placement as an optimization problem to minimize the average delivery rate, we identify the file group structure in the optimal solution. We show that, regardless of the file popularity distribution, there areat most three file groupsin the optimal cache placement, where files within a group have the same cache placement. We further characterize the complete structure of the optimal cache placement and obtain the closed-form solution in each of the three file group structures. A simple algorithm is developed to obtain the final optimal cache placement by comparing a set of candidate closed-form solutions computed in parallel. We provide insight into the file groups formed by the optimal cache placement. The optimal placement solution also indicates that coding between file groups may be explored during delivery, in contrast to the existing suboptimal file grouping schemes. Using the file group structure in the optimal cache placement for the CCS, we propose a new information-theoretic converse bound for coded caching that is tighter than the existing best one. Moreover, we characterize the file subpacketization in the CCS with the optimal cache placement solution and show that the maximum subpacketization level in the worst case scales as${\mathcal{ O}}(2^{K}/\sqrt {K})$for$K$users.

This paper considers a caching system of a single server and multiple users. We aim to characterize the memory-rate tradeoff for caching with uncoded cache placement, under nonuniform file popularity. Focusing on the modified coded caching scheme (MCCS) recently proposed by Yu,etal., we formulate the cache placement optimization problem for the MCCS to minimize the average delivery rate under nonuniform file popularity, restricting to a class of popularity-first placements. We then present two information-theoretic lower bounds on the average rate for caching with uncoded placement, one for general cache placements and the other restricted to the popularity-first placements. By comparing the average rate of the optimized MCCS with the lower bounds, we prove that the optimized MCCS attains the general lower bound for the two-user case, providing the exact memory-rate tradeoff. Furthermore, it attains the popularity-first-based lower bound for the case of general$K$users with distinct file requests. In these two cases, our results also reveal that the popularity-first placement is optimal for the MCCS, and zero-padding used in coded delivery incurs no loss of optimality. For the case of$K$users with redundant file requests, our analysis shows that there may exist a gap between the optimized MCCS and the lower bounds due to zero-padding. We next fully characterize the optimal popularity-first cache placement for the MCCS, which is shown to possess a simple file-grouping structure and can be computed via an efficient algorithm using closed-form expressions. Finally, we extend our study to accommodate nonuniformity in both file popularity and size, where we show that the optimized MCCS attains the lower bound for the two-user case, providing the exact memory-rate tradeoff. Numerical results show that, for general settings, the gap between the optimized MCCS and the lower bound only exists in limited cases and is very small.

This paper presents a new virtualization method for the downlink of a multi-cell multiple-input multiple-output (MIMO) network, to achieve service isolation among multiple Service Providers (SPs) that share the base station resources of an Infrastructure Provider (InP). Each SP designs a virtual precoder for its users in each cell, as its service demand to the InP, without the need to be aware of the existence of the other SPs or to know the channel state information (CSI) outside the cell. The InP performs network virtualization to meet the SPs’ service demands while managing both the inter-SP and inter-cell interference. We consider coordinated multi-cell precoding at the InP and formulate an optimization problem to minimize a weighted sum of signal leakage and precoding deviation, with per-cell transmit power constraints. We propose a fully distributed semi-closed-form solution at each cell, without any CSI exchange across cells. We further propose a low-complexity scheme to allocate the virtual transmit power, for the InP to regulate between interference elimination and virtual demand maximization. Simulation results demonstrate that our precoding solution for network virtualization substantially outperforms the traditional spectrum isolation alternative. It can approach the performance of fully cooperative precoding when the number of antennas is large.

We consider online coordinated precoding design for downlink wireless network virtualization (WNV) in a multi-cell multiple-input multiple-output (MIMO) network with imperfect channel state information (CSI). In our WNV framework, an infrastructure provider (InP) owns each base station that is shared by several service providers (SPs) oblivious of each other. The SPs design their precoders as virtualization demands for user services, while the InP designs the actual precoding solution to meet the service demands from the SPs. Our aim is to minimize the long-term time-averaged expected precoding deviation over MIMO fading channels, subject to both per-cell long-term and short-term transmit power limits. We propose an online coordinated precoding algorithm for virtualization, which provides a fully distributed semi-closed-form precoding solution at each cell, based only on the current imperfect CSI without any CSI exchange across cells. Taking into account the two-fold impact of imperfect CSI on both the InP and the SPs, we show that our proposed algorithm is within an$O(\delta)$gap from the optimum over any time horizon, where$\delta $is a CSI inaccuracy indicator. Simulation results validate the performance of our proposed algorithm under two commonly used precoding techniques in a typical urban micro-cell network environment.

We consider robust multi-group multicast beamforming design in massive multiple-input multiple-output (MIMO) large-scale systems. The goal is to minimize the transmit power subject to the minimum signal-to-interference-plus-noise-ratio (SINR) targets under channel uncertainty. Using the exact worst-case SINR constraints, we transform the problem into a non-convex optimization problem. We develop an alternating direction method of multipliers (ADMM)based fast algorithm to solve this problem directly with convergence guarantee. Our two-layer ADMM-based algorithm decomposes the non-convex problem into a sequence of convex subproblems, for which we obtain the semi-closed-form or closed-form solutions. Simulation studies show that our algorithm provides a considerable computational advantage over the conventional interior-point method non-convex solver with nearly identical performance.

We use a partially observable Markov decision process (POMDP) framework to formulate the problem of antenna selection for a base-station, equipped with a large-scale antenna array and a smaller number of RF chains. Assuming that the fading channel evolves according to a finite-state Markov chain and that only partial channel state information (CSI) from the limited selected antennas is available at each time slot, we rely on a POMDP framework for antenna selection to maximize the long-term expected downlink data rate. To avoid the computational complexity associated with the value iteration algorithm, we herein propose to use the simple myopic antenna selection policy based on the fact that for any arbitrary number of antennas and RF chains, under the assumption of positively correlated two-state Markov channel model, the myopic policy is optimal. To apply the optimal myopic policy-based antenna selection for general fading channels, we propose to quantize the channels into two values only for the purpose of antenna selection. Interestingly, our results show that the performance of the myopic antenna selection policy is close to that of the policy which relies on un-quantized full CSI.

We consider multi-group multicast beamforming in large-scale systems to minimize the transmit power subject to the signal-to-interference-plus-noise ratio (SINR) requirements. Based on the optimal multicast beamforming structure, we propose a fast first-order algorithm to obtain the beamforming solution. The algorithm utilizes the successive convex approximation (SCA) method and solves each SCA subproblem by dual reformulation along with the extra-gradient method for fast closed-form updates. Initialization methods are also explored, including an extragradient-based fast initialization approach that is proposed to generate initial feasible points for SCA. Simulations show that the proposed algorithm provides a near-optimal performance with substantially lower computational complexity for large-scale systems than the existing algorithm.

We consider online convex optimization (OCO) with multi-slot feedback delay, where an agent makes a sequence of online decisions to minimize the accumulation of time-varying convex loss functions, subject to short-term and long-term constraints that are possibly time-varying. The current convex loss function and the long-term constraint function are revealed to the agent only after the decision is made, and they may be delayed for multiple time slots. Existing work on OCO under this general setting has focused on the static regret, which measures the gap of losses between the online decision sequence and an offline benchmark that is fixed over time. In this work, we consider both the static regret and the more practically meaningful dynamic regret, where the benchmark is a time-varying sequence of per-slot optimizers. We propose an efficient algorithm, termed Delay-Tolerant Constrained-OCO (DTC-OCO), which uses a novel constraint penalty with double regularization to tackle the asynchrony between information feedback and decision updates. We derive upper bounds on its dynamic regret, static regret, and constraint violation, proving them to be sublinear under mild conditions. We further apply DTC-OCO to a general network resource allocation problem, which arises in many systems such as data networks and cloud computing. Simulation results demonstrate substantial performance gain of DTC-OCO over the known best alternative.

We study the memory-rate tradeoff for decentralized caching under nonuniform file popularity. We formulate the cache placement optimization problem for a recently proposed decentralized modified coded caching scheme (D-MCCS) to minimize the average rate. To solve this non-convex optimization problem, we develop two algorithms: a successive Geometric Programming (GP) approximation algorithm, which guarantees convergence to a stationary point but has a high computational complexity, and a low-complexity approach based on a two-file-group-based placement strategy. We further propose a lower bound on the average rate for decentralized caching under nonuniform file popularity. The lower bound is given as a nonconvex optimization problem, for which we propose a similar successive GP approximation algorithm to compute a stationary point. We show that the optimized MCCS attains the lower bound for the special case of no more than two active users requesting files, or for the general case but satisfying a special condition. Thus, the optimized MCCS characterizes the exact memory-rate tradeoff for decentralized caching in these cases. In general, our numerical result shows that the optimized D-MCCS performs close to the lower bound.

A multicarrier bidirectional filter-and-forward (FF) relay-assisted network in the context of device-to-device communication is investigated. The network consists of two multicarrier-based user devices that can communicate through multiple relay nodes equipped with finite impulse response (FIR) filters to equalize the frequency-selective channels. We jointly design the distributed equalization weight vector and the power allocations at the users to minimize the total transmit power under two quality of service constraints measured by the received sum-rates at the users. We propose a novel semi-closed form sub-optimal solution to this non-convex joint optimization problem. Simulation results show that the proposed design, in conjunction with the FF-based relay nodes, attains substantially better performance than the existing designs associated with amplify-and-forward and multicarrier relay nodes.

We consider online downlink precoding design for multiple-input multiple-output (MIMO) wireless network virtualization (WNV) in a fading environment with imperfect channel state information (CSI). In our WNV framework, a base station owned by an infrastructure provider (InP) is shared by several service providers (SPs) that are oblivious to each other. The SPs design their virtual MIMO transmission demands to serve their own users, while the InP designs the actual downlink precoding to meet the service demands from the SPs. Therefore, the impact of imperfect CSI is two-fold, on both the InP and the SPs. We aim to minimize the long-term time-averaged expected precoding deviation, considering both long-term and short-term transmit power limits. We propose a new online MIMO WNV algorithm to provide a semi-closed-form precoding solution based only on the current imperfect CSI. We derive a performance bound for our proposed algorithm and show that it is within an O(δ) gap from the optimum over any given time horizon, where δ is a normalized measure of CSI inaccuracy. Simulation results with two popular precoding techniques validate the performance of our proposed algorithm under typical urban micro-cell Long-Term Evolution network settings.

We consider downlink multiple-input multiple-output (MIMO) wireless network virtualization (WNV) in a fading environment, via a base station (BS) precoding design. The BS is owned by an infrastructure provider (InP) and is shared by several service providers (SPs) who are oblivious to each other. The SPs realize their virtual-cell transmissions via MIMO precoding provided by the InP. We aim to minimize the time-averaged expected deviation of the precoding provided by the InP from the SPs' virtualization demands, considering both long-term and short-term transmit power limits at the BS. We propose an online MIMO WNV algorithm to provide a precoding solution through Lyapunov optimization. Our online precoding solution only requires the current channel state information, and it has a semi-closed form with low computational complexity. We provide an upper bound on the performance of the proposed algorithm, showing that it can be arbitrarily close to the optimum over any given time horizon. Simulation results validate the performance of our proposed algorithm under typical urban micro-cell settings.

Energy efficiency (EE) is a critical performance measure in the next generation wireless communication systems, especially for battery-constrained Internet of Things (IoT) devices. We investigate the power allocation optimization problem in a multi-channel wireless system for EE maximization, subject to the sum power and the throughput constraints over each group of assigned channels, as well as the total power constraint. Resorting to geometric interpretation on the constraints, we propose the group virtually ceiled and bottomed water-filling (GVC-WF) algorithm to solve this EE maximization problem. Our proposed algorithm computes the exact optimal solution with a quadratic polynomial computational complexity. With the optimality and computational advantages, our proposed algorithm is suitable for power allocation in large-scale wireless systems. Simulation results demonstrate that our proposed power allocation algorithm improves the energy efficiency by more than 40%, as compared to the conventional Dinkelbach's method with the same amount of computations.

Consider a multi-user multi-cluster relay interference network where each cluster contains a source-destination pair communicating through their own dedicated multi-antenna relays. We propose a coordinated relay beamforming design for interference management among relaying clusters, aiming to maximize the minimum signal-to-interference-and-noise ratio (SINR) at destinations, subject to per relay power budgets. We propose a structured relay beam matrix solution based on a weighted sum of two types of beam matrices: zero-forcing (ZF) beamforming and maximum ratio combining (MRC) beamforming, of which we obtain the optimal ZF and MRC beam matrices in closed form. Our proposed beamforming structure allows us to transform the original max-min SINR problem into a low-complexity weight optimization problem, which we solve via the semi-definite relaxation approach. Our solution is highly computationally efficient with the complexity not growing with the number of antennas at each relay. Comparing with the direct approach to obtain relay beam matrices for the original problem, our solution provides a very similar performance but with a significantly lower complexity and thus is scalable and suitable for large-antenna systems. The weights in our relay beamforming solution clearly reveal how the relay power splits and shifts between suppressing inter-cluster interference and maximizing signal beamforming gain as the channel strength or cluster distance changes. The simulation shows that our solution significantly outperforms the MRC-only or ZF-only solution under both the perfect channel-state information (CSI) and imperfect CSI over interference channels.

We utilize the orthogonality and channel hardening properties of massive multiple-input multiple- output (MIMO) systems to propose an efficient uplink transmission scheme for a heterogeneous network (HetNet). Such a network consists of multiple user-equipments (UEs) communicating with a macro-cell base station (MCBS) through a small-cell BS (SCBS) where both BSs have a large number of antennas and deploy zero-forcing (ZF) detection. The SCBS helps relay UEs' information using quantize-forward (QF) relaying with Wyner-Ziv (WZ) binning and multiple-timeslot transmission for the binning indices to the MCBS. The MCBS then deploys separate and sequential decoding for each UE's message. To maximize the rate region, we optimize the quantization levels through geometric programming and further obtain the optimal transmission timeslot durations in terms of the optimal quantization. We show that the proposed scheme has linear codebook size and decoding complexity in the number of UEs, while it achieves the same rate region of other QF schemes that employ joint transmission at the SCBS and/or joint decoding at the MCBS, all of which have exponential complexity. Furthermore, simulation results show that the SCBS should employ finer quantization for UE signals that have strong UE-SCBS links compared with the UE-MCBS links, and the proposed scheme can substantially outperform several existing alternatives under a wide range of parameter settings.

We consider downlink multicast beamforming in a massive MIMO multi-cell network. Aiming at maximizing the minimum SINR among users, for both non-cooperative and cooperative multicasting, we propose a multicast beamforming scheme based on weighted maximum ratio transmission (MRT), and transform the beamforming optimization problem into a weight optimization problem that is solved via the semi-definite relaxation (SDR) approach. The proposed method has a low computational complexity which does not grow with the number of antennas, and thus is suitable for massive MIMO systems. Simulation shows that our proposed multicast beamforming solution yields comparable or better performance than existing approaches but with significantly lower complexity for practical systems with a large but finite number of antennas.

We consider a multi-way relay network with multiple users exchanging information with each other via a multi-antenna relay. The multi-way relaying strategy consists of one multiple access phase and multiple broadcast phases. We jointly design relay beamforming matrices and users' linear processing receivers in the broadcast phases to maximize the minimum signal-to-interference-and-noise ratio (SINR) under the relay power budget. For the non-convex joint optimization problem, we propose to solve it by iteratively optimizing the relay beam matrices and receiver processing matrices in two sub-problems. For the receiver processing, both maximum-ratio-combining (MRC) receiver and zero-forcing (ZF) receiver are designed. We show that our iterative approach with the MRC receiver leads to a local maximum for the original joint optimization problem, while the ZF receiver has the computational advantage with a lower complexity. To further improve the performance, we design the successive interference cancellation at each user's receiver based on the SINR criterion to sequentially decode symbols from other users. Simulation shows that our proposed algorithm for joint design provides substantial improvement in the sum rate than the existing methods that use the sum rate as the design objective. Finally, we investigate the performance of our proposed algorithm under partial channel state informations (CSIs). We show in simulation that using quantized CSIs at each receiver only incurs a small performance loss for the typical range of relay channel quality.

We consider a mobile cloud computing system with multiple users, a remote cloud server, and a computing access point (CAP). The CAP serves both as the network access gateway and a computation service provider to the mobile users. It can either process the received tasks from mobile users or offload them to the cloud. We jointly optimize the offloading decisions of all users, together with the allocation of computation and communication resources, to minimize the overall cost of energy consumption, computation, and maximum delay among users. The joint optimization problem is formulated as a mixed-integer program. We show that the problem can be reformulated and transformed into a non-convex quadratically constrained quadratic program, which is NP-hard in general. We then propose an efficient solution to this problem by semidefinite relaxation and a novel randomization mapping method. Furthermore, when there is a strict delay constraint for processing each user's task, we further propose a three-step algorithm to guarantee the feasibility and local optimality of the obtained solution. Our numerical results show that the proposed solutions give nearly optimal performance under a wide range of parameter settings, and the addition of a CAP can significantly reduce the cost of multi-user task offloading compared with conventional mobile cloud computing where only the remote cloud server is available.

In underlay device-to-device (D2D) communications, a D2D pair reuses the cellular spectrum causing interference to regular cellular users. Maximizing the performance of underlay D2D communications requires joint consideration for the achieved D2D rate and the interference to cellular users. In this paper, we consider the D2D power allocation optimization over multiple resource blocks (RBs), aimed at maximizing either the ergodic D2D rate or the ergodic sum rate of D2D and cellular users, under the long-term sum-power constraint of the D2D users and per-RB probabilistic signal-to-interference-and-noise (SINR) requirements for all cellular users. We formulate stochastic optimization problems for D2D power allocation over time. The proposed optimization framework is applicable to both uplink and downlink cellular spectrum sharing. To solve the proposed stochastic optimization problems, we first convexify the problems by introducing a family of convex constraints as a replacement for the non-convex probabilistic SINR constraints. We then present two dynamic power allocation algorithms: a Lagrange dual-based algorithm that is optimal but with a high computational complexity and a low-complexity heuristic algorithm based on dynamic time averaging. Through simulation, we show that the performance gap between the optimal and heuristic algorithms is small, and the effective long-term stochastic D2D power optimization over the shared RBs can lead to substantial gains in the ergodic D2D rate and the ergodic sum rate.

We consider a general multi-user mobile cloud computing (MCC) system where each mobile user has multiple independent tasks. These mobile users share the computation and communication resources while offloading tasks to the cloud. We study both the conventional MCC where tasks are offloaded to the cloud through a wireless access point, and MCC with a computing access point (CAP), where the CAP serves both as the network access gateway and a computation service provider to the mobile users. We aim to jointly optimize the offloading decisions of all users as well as the allocation of computation and communication resources, to minimize the overall cost of energy, computation, and delay for all users. The optimization problem is formulated as a non-convex quadratically constrained quadratic program, which is NP-hard in general. For the case without a CAP, an efficient approximate solution named MUMTO is proposed by using separable semidefinite relaxation (SDR), followed by recovery of the binary offloading decision and optimal allocation of the communication resource. To solve the more complicated problem with a CAP, we further propose an efficient three-step algorithm named MUMTO-C comprising of generalized MUMTO SDR with CAP, alternating optimization, and sequential tuning, which always computes a locally optimal solution. For performance benchmarking, we further present numerical lower bounds of the minimum system cost with and without the CAP. By comparison with this lower bound, our simulation results show that the proposed solutions for both scenarios give nearly optimal performance under various parameter settings, and the resultant efficient utilization of a CAP can bring substantial cost benefit.

For device-to-device (D2D) underlaid cellular networks, the perfect channel state information (CSI) may not be available at the base station (BS). In this work, under an assumption of partial CSI, we study the problem of maximizing the expected sum rate for a cellular user (CU) and a D2D pair, with receive beamforming at the BS, subject to minimum SINR requirements for both the CU and D2D pair, per-node maximum power, and inter-cell interference constraints in multiple neighboring cells. We solve this non-convex joint optimization problem in two steps. We first consider the D2D admissibility problem to determine whether the D2D pair can reuse the channel resource of the CU. We then propose a robust power control algorithm using a ratio-of-expectation approximation to maximize the expected sum rate. For benchmarking, we further provide an upper bound on the maximum expected sum rate. Simulation results show that our proposed solution gives performance close to the upper bound.

We consider a general multi-user mobile cloud computing system with a computing access point (CAP), where each mobile user has multiple independent tasks that may be processed locally, at the CAP, or at a remote cloud server. The CAP serves both as the network access gateway and a computation service provider to the mobile users. We aim to jointly optimize the offloading decisions of all users' tasks as well as the allocation of computation and communication resources, to minimize the overall cost of energy, computation, and delay for all users. This problem is NP-hard in general. We propose an efficient three-step algorithm comprising of semidefinite relaxation (SDR), alternating optimization (AO), and sequential tuning (ST). It is shown to always compute a locally optimal solution, and give nearly optimal performance under a wide range of parameter settings. Through evaluating the performance of different combinations of the three components of this SDR-AO-ST algorithm, we provide insights into their roles and contributions in the overall solution. We further compare the performance of SDR-AO-ST against a lower bound to the minimum cost, purely local processing, purely cloud processing, and hybrid local-cloud processing without using the CAP. Our numerical results demonstrate the effectiveness of the proposed algorithm in the joint management of computation and communication resources in mobile cloud computing systems with a CAP.

We design distributed relay beamforming in a multiuser peer-to-peer relay network. By exploring Alamouti code at both sources and relays, we propose a rank-two Alamouti-based distributed relay beamforming scheme to minimize per relay power, while meeting the signal-to-interference-and-noise ratio targets. For the nonconvex optimization problem, we propose a rank-constrained separable semidefinite relaxation approach to find an approximate solution, and provide conditions for which it produces an optimal solution and a bound on the gap to the optimal performance. Compared with the traditional rank-one distributed relay beamforming scheme, our proposed Alamouti-based rank-two distributed relay beamforming offers a significantly higher likelihood to produce an optimal solution and a better capability to maintain small performance degradation as the network size increases. As a result, it provides substantially improved relay power efficiency.

For device-to-device (D2D) communication under laid in a cellular network with uplink resource sharing, both cellular and D2D pairs may cause significant inter-cell interference (ICI) at a neighboring base station (BS). In this paper, under optimal BS receive beamforming, we jointly optimize the power of a cellular user (CU) and a D2D pair for their sum rate maximization, while satisfying minimum SINR requirements and worst-case ICI limit in multiple neighboring cells. We solve this non-convex joint optimization problem in two steps. First, the necessary and sufficient condition for the D2D admissibility under given constraints is obtained. Finally, we consider joint power control of the CU and D2D transmitters. We propose a power control algorithm to maximize the sum rate. Depending on the severity of ICI that D2D and CU may cause, we categorize the feasible solution region into five cases, each of which may further include several scenarios based on minimum SINR requirements. The proposed algorithm is optimal when ICI to a single neighboring cell is considered. For multiple neighboring cells, we provide an upper bound on the performance loss by the proposed algorithm and conditions for its optimality. We further extend our consideration to the scenario of multiple CUs and D2D pairs, and formulate the joint power control and CU-D2D matching problem. We show how our proposed solution for one CU and one D2D pair can be utilized to solve this general joint optimization problem. Simulation demonstrates the effectiveness of our power control algorithm and the nearly optimal performance of the proposed approach in the setting of multiple CUs and D2D pairs.

We consider a cellular network where each cell contains multiple source-destination pairs communicating through multiple amplify-and-forward relays using orthogonal channels. We propose an optimal relay beamforming design that minimizes the maximum interference at the neighboring cells subject to per-relay power limits and minimum received signal-to-noise ratio (SNR) requirements. Even though the problem is non-convex, we show that it has zero Lagrange duality gap, and we convert its dual problem to a semi-definite programming problem. Depending on the values of the optimal dual variables, we study three cases to obtain the optimal beam vectors accordingly. This results in an iterative algorithm that provides a semi-closed-form optimal solution. We extend our algorithm to the problem of maximizing the minimum SNR subject to some pre-determined maximum interference constraints at neighboring cells, by the solution to the min-max interference problem along with a bisection search. The solution to this max-min SNR problem gives insight into the worst-case signal-to-interference-and-noise ratio given some maximum interference target. The performance of the proposed algorithm is studied numerically, both for when the knowledge of interference channel is perfect and for when it is imperfect due to either limited feedback or channel estimation error.

In underlay device-to-device (D2D) communication, a D2D pair reuses the cellular spectrum and creates interference to regular cellular users. Optimal operation requires joint consideration for the achieved D2D rate and the added interference to cellular users. Most existing work on D2D rate maximization concerns only the simplified scenario where the D2D pair has access to a single channel or resource block. In this work, we present an optimization solution to allocate the D2D transmission power over multiple channels, to maximize the sum rate between D2D and cellular users, under a sum-power constraint on the D2D transmitter and minimum SINR guarantees at each RB for all cellular users. The proposed optimization is applicable to both uplink and downlink cellular spectrum sharing. Our simulation studies further shed light into how the maximum sum rate is impacted by the available D2D power and the SINR guarantees.

We consider a mobile cloud computing system consisting of multiple users, one computing access point (CAP), and one remote cloud server. The CAP can either process the received tasks from mobile users or offload them to the cloud. We aim to jointly optimize the offloading decisions of all users and the CAP, together with communication and processing resource allocation, to minimize the overall cost of energy, computation, and the maximum delay among all users. It is shown that the problem can be formulated as a non-convex quadratically constrained quadratic program, which is NP-hard in general. We further propose an efficient solution to this problem by semidefinite relaxation and a novel randomization mapping method. Our simulation results show that the proposed algorithm gives nearly optimal performance with only a small number of randomization iterations.

We consider joint design of energy storage management and load scheduling with integrated renewable energy. We aim at optimizing the energy flows and load scheduling simultaneously in order to minimize the overall system cost over a finite time horizon. Our model incorporates battery operational costs and assumes unknown arbitrary dynamics of renewable source, load, and pricing information. Loads are modeled by individual tasks with their own intensities, requested service durations, and maximum and average delay constraints. We use a sequence of problem modification and transformation and employ Lyapunov optimization technique to design the real-time joint control and scheduling policy. Our policy provides an closed-form solution for load scheduling and storage energy management. We show that our proposed algorithm guarantees a bounded performance from an optimal non-causal T-slot look-ahead control policy.

We consider a general multi-user mobile cloud computing system where each mobile user has multiple independent tasks. These mobile users share the communication resource while offloading tasks to the cloud. We aim to jointly optimize the offloading decisions of all users as well as the allocation of communication resource, to minimize the overall cost of energy, computation, and delay for all users. The optimization problem is formulated as a non-convex quadratically constrained quadratic program, which is NP-hard in general. An efficient approximate solution is proposed by using separable semidefinite relaxation, followed by recovery of the binary offloading decision and optimal allocation of the communication resource. For performance benchmark, we further propose a numerical lower bound of the minimum system cost. By comparison with this lower bound, our simulation results show that the proposed algorithm gives nearly optimal performance under various parameter settings.

We consider wireless transmission over fading channel powered by energy harvesting and storage devices. Assuming a finite battery storage capacity, we design an online power control strategy aiming at maximizing the long-term time-averaged transmission rate under battery operational constraints for energy harvesting. We first formulate the stochastic optimization problem, and then develop techniques to transform this problem and employ techniques from Lyapunov optimization to design the online power control solution. In particular, we propose an approach to handle unbounded channel fade which cannot by directly dealt with by Lyapunov framework. Our proposed algorithm determines the transmission power based only on the current energy state of the battery and channel fade conditions, without requiring any knowledge of the statistics of energy arrivals or fading channels. Our online power control solution is a three-stage closed-form solution depending on the battery energy level. It not only provides strategic energy conservation through the battery energy control, but also reveals an opportunistic transmission style based on fading condition, both of which improve the long-term time-averaged transmission rate. We further characterize the performance bound of our proposed algorithm to the optimal solution with a general fading distribution. Simulation results demonstrate a significant performance gain of our proposed online algorithm over alternative online approaches.

We consider amplify-and-forward two-way relaying in a multichannel system with two end nodes and a single relay, with a two-slot multiaccess broadcast (MABC) relaying strategy. We investigate the problem of joint subchannel pairing and power allocation to maximize the achievable sum-rate in the network under the individual power constraints. We propose an iterative approach to solve this challenging mixed-integer programming problem by decomposing it into subchannel pairing optimization and joint power allocation optimization, and solving them iteratively. For subchannel pairing at the relay, we show that, unlike in the one-way relaying case, there exists no explicit SNR-based low-complexity subchannel pairing strategy that is optimal for two-way relaying, and the optimal pairing needs to be performed numerically. Nonetheless, we propose an effective low-complexity suboptimal pairing scheme based on an effective SNR metric. For joint power allocation at all nodes, the optimization problem is nonconvex. We propose an iterative procedure to optimize the power at the two end nodes and at the relay iteratively. Using a problem transformation, we show that each power optimization subproblem turns out to be convex and can be solved efficiently. Our proposed iterative procedure is guaranteed to converge to a locally optimal solution. We then generalize our approach to the weighted sum-rate maximization problem. Simulation results demonstrate the effectiveness of the proposed pairing scheme, as well as the gain of joint optimization approach over other pairing-only or power-allocation-only optimization approaches.

We investigate the optimal relay beamforming problem for multi-user peer-to-peer communication with amplify-and-forward relaying in a multi-channel system. Assuming each source-destination (S-D) pair is assigned an orthogonal channel, we formulate the problem as a min-max per-relay power minimization problem with minimum signal-to-noise (SNR) guarantees. After showing that strong Lagrange duality holds for this nonconvex problem, we transform its Lagrange dual problem to a semi-definite programming problem and obtain the optimal relay beamforming vectors. We identify that the optimal solution can be obtained in three cases, depending on the values of the optimal dual variables. These cases correspond to whether the minimum SNR requirement at each S-D pair is met with equality, and whether the power consumption at a relay is the maximum among relays at optimality. We obtain a semi-closed form solution structure of relay beam vectors, and propose an iterative approach to determine relay beam vector for each S-D pair. We further show that the reverse problem of maximizing the minimum SNR with per-relay power budgets can be solved using our proposed algorithm with an iterative bisection search. Through simulation, we analyze the effect of various system parameters on the performance of the optimal solution. Furthermore, we investigated the effect of imperfect channel side information of the second hop on the performance and quantify the performance loss due to either channel estimation error or limited feedback.

We design distributed online learning and channel access for secondary users in a cognitive radio network. Our goal is to design channel selection and access that can effectively adapt to a wide range of traffic load patterns in the primary network. We propose a distributed adaptive learning and access policy by applying stochastic learning automata (SLA), where each secondary user (SU) probabilistically chooses one of the most available channels to access, with the channel selection probabilities being updated based on the collision events. Our design includes two underlying distributed learning algorithms: learning of primary channel availabilities from each SU's own sensing history, and SLA-based learning of channel selection from each SU's own collision history for collision avoidance. We show that some existing distributed access policies can be viewed as special cases of our proposed adaptive policy, with a set of fixed channel selection probabilities. Next, we formulate the distributed channel selection and access problem as a noncooperative game. We show that it is an exact potential game with at least one pure strategy Nash equilibrium (NE). We prove that, under our proposed adaptive policy, the channel selection probabilities converge toward a pure strategy NE of the game. Simulation demonstrates the effectiveness of our proposed adaptive policy in a wide range of distributions of mean channel availabilities, as compared with other existing policies.

We consider a wireless cellular network with multiple amplify-and-forward (AF) relays in each cell, assisting the communication of multiple source-destination pairs with relay transmission beamforming. Our objective is to minimize the maximum interference power among all active receivers in a neighboring cell subject to per-relay power and minimum received SNR constraints. We propose an efficient algorithm to obtain the optimal relay beamforming vectors. We show that even though the optimization problem is non-convex, it has zero Lagrange duality gap and can be converted to a semi-definite programming problem. The performance of the proposed algorithm is studied numerically, both for the case where the interference channel information is exactly known and for the case of inaccurate channel information due to either limited feedback or channel estimation error. It is demonstrated that the min-max interference approach substantially outperforms the alternative where we simply minimize the maximum relay transmission power.

We consider the design of cost-effective management of energy storage with renewable integration for load supply. We take a finite time horizon approach and formulate the control optimization problem aimed at minimizing the system cost over a fixed time period. Recognizing the unpredictable and nonstationary stochastic nature of system dynamics, we assume unknown arbitrary dynamics of renewable generation, load, and electricity pricing in formulating our problem. Furthermore, we incorporate detailed battery operation cost into the system cost. Different from the infinite time horizon problems in existing works, the coupling of control decisions over time, due to finite battery capacity, is more challenging to manage. We develop a special technique to tackle the technical challenges in solving the problem. Through problem modification and transformation, we are able to apply Lyapunov optimization to design a real-time control algorithm that relies only on the current system dynamics. The proposed control solution has a closed-form expression and thus is simple to implement. Through analysis, the proposed algorithm is shown to have a bounded performance gap to the optimal noncausal T-slot lookahead control policy. Simulation studies show the effectiveness of our proposed algorithm as compared with two alternative real-time and noncausal algorithms.

Considering a bidirectional amplify-and-forward based multi-carrier multi-relay network, we formulate two different joint power allocation and network beamforming problems. In the first formulation, we aim to minimize the total transmit power of the network, subject to two constraints on the transceiver rates. In the second problem, our goal is to maximize the sum-rate of the two transceivers subject to a constraint on the total network transmit power. In both problems, the design parameters include the relay beamforming weights and the transceiver power allocations over all subcarriers. We propose a two-step iterative method to tackle each problem and show that each method leads to (at least) a locally optimum solution. Each iterative method alternates between solving the underlying problem for one set of variables while the other set is fixed and vice versa. Each subproblem is shown to be amenable to a computationally efficient solution. Our simulation results show the efficiency of the proposed techniques.

We consider the design of dynamic spectrum access (DSA) mechanism. Assuming heterogeneous primary channels with distinct availability statistics unknown to each secondary user (SU), we consider the auction-based approaches for spectrum access. We first apply a unit demand (UD) auction by exploring the instantaneous link condition of each SU for its throughput maximization. To address the disadvantages faced in the UD auction, we propose a learning-based unit demand (LBUD) auction. It incorporates a distributed learning of the primary channel availabilities into the auction mechanism to explore both primary channel availability statistics and instantaneous link gains of the SUs for their throughput maximization. The new mechanism not only substantially reduces communication overhead, but also improves the SUs' throughputs when the primary channels have dissimilar availability statistics. We show that the proposed LBUD auction for channel allocation among SUs preserves the strong property of the UD auction. We further propose an adaptive price increment algorithm to improve convergence speed of the iterative procedure used in the auction. Numerical results show the effectiveness of our proposed auction mechanism in terms of the throughput gain.

We herein consider the problem of optimal power allocation in an OFDM two-way relay network with multiple relays. Assuming two-way relaying is performed using analog network coding, we obtain the optimal power allocation across subcarriers and among a relay and two communicating nodes by minimizing the total power consumption in the network subject to two separate rate constraints for each transceiver. We then present an algorithm to solve the proposed optimization problem. Our simulation result shows that the proposed algorithm significantly outperform an equal power allocation scheme, where all subcarriers at all nodes receive the same levels of power and the total power is equal to that consumed in our proposed solution.

We consider a multi-user peer-to-peer relay network with multiple multi-antenna relays for amplify-and-forward relaying. Assuming distributed relay beamforming strategy, we investigate the design of each relay processing matrix to minimize the per-antenna relay power usage for given users' SNR targets. As the problem is NP-hard, we developed an approximate solution through the Lagrange dual domain. Through a sequence of transformations, we obtain a semi-closed form solution which can be determined by solving an efficient semi-definite programming problem. We also considered the semi-definite relaxation (SDR) approach. Compared with the SDR approach, the proposed solution has significantly lower computational complexity. The benefit of such solution is apparent when the optimal solution can be obtained by both approaches. When the solution is suboptimal, simulations show that the SDR approach has better performance. Thus, we proposed a combined method of the two approaches to trade-off performance and complexity. Simulations showed the effectiveness of such combined method.

We consider the design of a distributed online learning and access mechanism for dynamic spectrum access, where channel availability statistics are unknown to each secondary user (SU). Unlike existing distributed access policies, we explore the instantaneous channel gain of SUs' channels for multi-user multi-channel diversity gain. We consider an auction-based approach. For the primary channels with heterogeneous statistics, we apply the unit demand auction [1] to determine each SU's selection of a primary channel based on its instantaneous rate over each channel. We further propose a learning based unit demand (LBUD) auction, where each SU only bids for the M-best channels estimated by itself through distributed learning. The new mechanism not only reduces communication overhead, but also improves the throughput performance when the primary channels have dissimilar availability statistics. In addition, we show that the LBUD auction preserves the strong property of unit demand auction, i.e. it is dominant strategy incentive compatible. To improve the convergence speed of the iterative procedure of channel allocation in the auction, we also propose an adaptive price increment algorithm. Simulations show the effectiveness of our proposed auction mechanism in throughput gain by exploring instantaneous channel fade.

Based on the Gauss-Markov channel model, we investigate the stochastic feedback control for transmit beamforming in multiple-input-single-output systems and design practical implementation algorithms leveraging techniques in dynamic programming and reinforcement learning. We first validate the Markov decision process formulation of the underlying feedback control problem with a 4R-variable (4R-V) state, where R is the number of the transmit antennas. Due to the high complexity of finding an optimal feedback policy under the 4R-V state, we consider a reduced 2-V state. As opposed to a previous study that assumes the feedback problem under such a 2-V state remaining an MDP formulation, our analysis indicates that the underlying problem is no longer an MDP. Nonetheless, the approximation as an MDP is shown to be justifiable and efficient. Based on the quantized 2-V state and the MDP approximation, we propose practical implementation algorithms for feedback control with unknown state transition probabilities. In particular, we provide model-based offline and online learning algorithms, as well as a model-free learning algorithm. We investigate and compare these algorithms through extensive simulations and provide their efficiency analysis. According to these results, the application rule of these algorithms is established under both statistically stable and unstable channels.

In this work, we study the problem of energy storage management with renewable energy integration by designing online control policy to minimize the long-term time-averaged cost. We take into account system input dynamics, and incorporate the batter operation cost for energy storage into the control optimization. Applying Lyapunov optimization technique, we design an on-line control policy that jointly optimizes the decisions for storage from two energy sources and supply to the consumer, which has bounded performance from the optimal scheme. We provide a close-form solution to our control optimization which renders our policy implementation with minimum complexity. Simulations show that introducing renewable energy can effectively reduce the long-term cost and improve the efficiency of energy storage relative to the battery operation cost.

We consider the problem of decentralized online learning and channel access in a cognitive radio network. Based on an existing distributed access policy proposed in [1], named the ρRANDpolicy, we propose an adaptive decentralized access policy in which the distributed coordination among secondary users is adjusted at different stages of learning accuracy of the primary network. Specifically, we exploit a “perceived population” by each secondary user to reduce collision events at different learning stages. We design a metric that measures the level of learning accuracy and use that as an indicator to adjust the “perceived population” by each secondary user. Simulations show that our proposed adaptive policy improves the leading constant of the normalized regret and can provide substantial improvement over the ρRANDpolicy.

The concept of vehicle-to-grid (V2G) has gained recent interest as more and more electric vehicles (EVs) are put to use. In this paper, we consider a dynamic aggregator-EVs system, where an aggregator centrally coordinates a large number of EVs to perform regulation service. We propose a Welfare-Maximizing Regulation Allocation (WMRA) algorithm for the aggregator to fairly allocate the regulation amount among the EVs. The algorithm operates in real time and does not require any prior knowledge on the statistical information of the system. Compared with previous works, WMRA accommodates a wide spectrum of vital system characteristics, including limited EV battery size, EV self charging/discharging, EV battery degradation cost, and the cost of using external energy sources. Furthermore, our simulation results indicate that WMRA can substantially outperform a suboptimal greedy algorithm.

This short correspondence serves as en errata to our paper titled, "Achievable rate region under joint distributed beamforming and power allocation for two-way relay networks," published in IEEE Transactions on Wireless Communications, vol. 11, no. 11, pp. 4026-4037, Nov. 2012. We do not present any novelty in this errata.

We consider amplify-and-forward multi-antenna relaying between a single pair of source and destination under per-antenna power constraints. Our objective is to obtain the optimal relay processing matrix to minimize the maximum individual antenna power for a given received SNR target. The problem is not convex, but it can be shown to satisfy strong Lagrange duality. We reveal a prominent structure of this problem, by establishing its duality with direct point-to-point SIMO beamforming with an uncertain noise. This enables us to derive a semi-closed form expression for the optimal relay processing matrix that depends on a set of dual variables, thus converting the original optimization of a N×N matrix with (N+1) constraints, to a dual problem with (N+1) variables and three constraints. We further show that the dual problem has a semi-definite programming form, so that the proposed solution has polynomial worst-case complexity.

We consider a dual-hop relay network with multiple source-destination (S-D) pairs and multiple relays, where amplify-and-forward relaying strategy is applied and transmission among S-D pairs takes place simultaneously. Network lifetime in this scenario is defined as the time interval over which successful transmission of all S-D pairs through selected relays can be maintained. We aim at designing relay selection to maximize the network lifetime for given data rate requirements of all the S-D pairs. Without knowledge of future channel states, we design relay selection algorithms to maximize perceived network lifetime at the current time. The perceived network lifetime maximization is shown to be a max-min optimization problem. We propose a priority search algorithm which is shown to provide the optimal solution with linear complexity in the number of relays. Furthermore, we propose a suboptimal priority-based selection strategy, the “worst-case” greedy algorithm, with complexity linear in the number of relays and quadratic in the number of S-D pairs. Simulation results show that the performance loss of the “worst-case” greedy algorithm is negligible as compared to the optimal relay selection solution.

We aim to enhance the end-to-end rate of a general dual-hop relay network with multiple channels and finite modulation formats, by jointly optimizing channel pairing, power allocation, and integer bit loading. Such an optimization problem has both a discrete feasible region, due to the combinatoric nature of channel pairing, and a discrete objective, due to the bit loading requirement. For this type of mixed-integer programming problems, the Lagrange dual method generally is inapplicable, due to the non-zero duality gap. However, by exploring the structure of our problem, we are able to bound the gap to within one bit, allowing the extraction of an exact optimal integer solution. We further present complexity reduction techniques, and demonstrate that the proposed solution only requires a computational complexity that is polynomial in the number of channels, realizing efficient implementation in practical systems. Through numerical experiments, we show that the jointly optimal solution can significantly outperform common sub-optimal alternatives.

We consider the problem of jointly optimizing channel pairing, channel-user assignment, and power allocation, to maximize the weighted sum-rate, in a single-relay cooperative system with multiple channels and multiple users. Common relaying strategies are considered, and transmission power constraints are imposed on both individual transmitters and the aggregate over all transmitters. The joint optimization problem naturally leads to a mixed-integer program. Despite the general expectation that such problems are intractable, we construct an efficient algorithm to find an optimal solution, which incurs computational complexity that is polynomial in the number of channels and the number of users. We further demonstrate through numerical experiments that the jointly optimal solution can significantly improve system performance over its suboptimal alternatives.

We obtain the achievable beamforming rate region for a two-way cooperative network consisting of two transceivers and multiple relays, all single-antenna nodes. Assuming that the relay beamforming weights as well as the transceiver transmit powers are the design parameters, this region is characterized under a constraint on the total (network) transmit power consumption. Using the shape of the rate region, we then use a sum-rate maximization approach to obtain the jointly optimal relay beamforming weights and transceiver transmit powers. Interestingly, we show that the sum-rate maximization approach yields the same solution as the max-min fair design approach does. Using this relationship, we further present a semi-closed-form solution to the underlying distributed beamforming problem. We then prove that the transmit power of any of the two transceivers can be obtained as the solution to a one-dimensional optimization problem using a simple bisection method which enjoys a low computational complexity. Furthermore, we extend these results to obtain the relay beamforming weights and transceiver transmit powers corresponding to any point on the boundary of the rate region, through a weighted sum-rate maximization approach.

We consider the problem of jointly optimizing channel pairing, channel-user assignment, and power allocation in a single-relay multiple-access system. The optimization objective is to maximize the weighted sum-rate under total and individual power constraints on the transmitters. By observing the special structure of a three-dimensional assignment problem derived from the original problem, we propose a polynomial-time algorithm based on continuity relaxation and dual minimization. The proposed method is shown to be optimal for all relaying strategies that give a concave rate function in terms of power constraints.

The problem of optimally allocating power for half-duplex two-way relaying in an OFDM system is considered. Assuming two-way relay is performed using analog network coding, and with total network power constraint, we obtain the optimal power allocation across subcarriers and among a relay and two communicating nodes to maximize the achievable sum rate in the network. We show that the resulting solution is a combination of two (usually opposite) power allocation strategies, i.e., water-filling across subcarriers and SNR-balancing between communicating end nodes. Further analysis also shows the optimal power allocation on the relay itself is a water-filling solution.

We study the sum-rate maximization approach when applied to design a decentralized beamformer for two-way relay networks. Considering a constraint on the total transmit power consumed in the whole network, we prove that sum-rate maximization is equivalent to an SNR balancing approach where the smallest of the two receive SNRs is maximized subject to the same total power constraint.

In this paper, we present a semi-closed form solution to the SNR balancing problem, first considered in, in the context of network beamforming design for two-way relay networks. This solution relies on a simple bisection method to obtain the transmit power of one of the two transceivers. Given this transmit power, the relay beamforming weight vector is shown to have a closed-form solution. Simulation results show that the proposed solution has significantly lower computational complexity. We also present a suboptimal solution which does not use the aforementioned bisection algorithm while performs very closely to the optimal beamformer.

We study the effect of relay cluster selection on throughout in multi-hop cooperative communications with one source and one destination. We evaluate the effective relay throughput as a function of the source transmission rate and the network outage probability. Assuming channel side information (CSI) only available at the receivers, we formulate the cluster size optimization to maximize throughput. Furthermore, since the bottleneck of the multi-hop relaying is at the first hop where there is in general a lack of cooperation from the source, for the scenario where CSI is available at the source, we may incorporate opportunistic relay selection at the first hop in the cluster optimization problem. Our results demonstrate how the optimal selection of cluster sizes can significantly increase the relaying throughput.

In this paper, we study power allocation (PA) in a single-relay OFDM system with limited feedback. We propose a PA scheme that uses a codebook of quantized PA vectors designed offline and known to the source, relay, and destination. The destination, which has full knowledge of channel side information (CSI), chooses one of the codebook vectors and conveys back to the source and relay. With the limited amount of available feedback, the design of an appropriate codebook is central to PA, which varies depending on the destination's strategy to choose the optimal PA vector. Assuming high received SNR on either link in the relay path, we first derive the optimal PA solutions as the function of channel realizations with two design criteria, maximizing capacity and minimizing error rate. It is found that when there is high received SNR in either the relay path or the direct path, the optimal solutions for both criteria reduce to simple forms. For maximizing capacity, the available power should be equally allocated to each OFDM subcarrier shared by the source and relay; while for minimum error rate, the available power should be allocated such that the received SNRs for all subcarriers at the destination are the same. The findings lead us to the sub-optimal solutions with great complexity reduction. We then present an adaptation of Lloyd's algorithm to construct a codebook to quantize the optimal PA vectors subject to the amount of feedback. Simulations show that a mild to negligible performance loss can be achieved with only a few bits of feedback at different SNR values.

Orthogonal frequency division multiplexing (OFDM) has become a promising physical layer modulation technology for beyond 3G or 4G wireless communications due to effective inter-symbol interference mitigation for high speed data transmission. However, the timing of the OFDM symbol, i.e., the placement of the DFT collection window in a multi-path time dispersive channel remains an important and challenging issue in OFDM receiver design. An erroneous timing decision creates inter-symbol interference (ISI), inter-carrier interference (ICI), channel attenuation, and channel estimation error, which leads to a penalty on the collected OFDM symbol signal to noise ratio (SNR) resulting in an irreducible error floor. In this paper we quantify such effects and derive an optimal OFDM symbol timing solution in the sense of maximizing the signal to interference ratio (SIR) of the collected OFDM symbol. A practical timing algorithm, referred to as the equilibrium algorithm, is then developed to approximate the optimal timing decision. Compared with existing schemes in the literature, the proposed approach does not rely on explicit detection of individual channel paths or the delay spread boundary and therefore greatly reduces timing complexity. The equilibrium algorithm performs nearly as well as the optimal solution over a variety of channel delay spreads, is simple to implement, and is robust to channel estimation errors.

This paper addresses the problem of optimizing the packet transmission schedule in a multihop wireless network with end-to-end delay constraints. The emphasis is to determine the proper relative weights assigned to the remaining distance and the remaining lifetime in order to rank the urgency of a packet. We consider a general class of cross-layer transmission schemes that represent such relative weights using a single lifetime-distance factor, which includes, as special cases, schedules such as earliest-deadline-first and largest-distance-first. We propose an analytical framework, based on recursive non-homogeneous Markovian analysis, to study the effect of the lifetime-distance factor on packet loss probability in a general multihop environment, with different configurations of peer-node channel contention. Numerical results are presented to illustrate how various network parameters affect the optimal lifetime-distance factor. We demonstrate quantitatively how the proper balance between distance and lifetime in a transmission schedule can significantly improve the network performance, even under imperfect schedule implementation.

This paper addresses the problem of optimizing the packet transmission schedule in an ad hoc network with end-to-end delay constraints. The emphasis is to determine the proper relative weights assigned to the remaining distance and the remaining lifetime in order to rank the urgency of a packet. We consider a general class of transmission schemes that represent such relative weights using a single lifetime-distance factor, which includes, as special cases, schedules such as Earliest-Deadline-First and Largest-Distance-First. We propose an analytical framework, based on recursive non-homogeneous Markovian analysis, to study the effect of the lifetime-distance factor on packet loss probability in a general multihop environment, with different configurations of peer-node channel contention. Numerical results are presented to demonstrate how various network parameters affect the optimal lifetime-distance factor. We demonstrate quantitatively how the proper balance between distance and lifetime in a transmission schedule can significantly improve the network performance, even under imperfect schedule implementation.

We investigate the impact of medium access control (MAC) design on the reconstruction performance of a 1D random signal field measured by a large scale sensor network. Assuming the sensor density goes to infinity, we show that MAC design affects the decay rate of reconstruction distortion, and thus the efficiency of reconstruction, as the number of received packets M increases. Using a deterministic MAC with uniform spatial sampling, i.e., scheduling sensor transmissions from uniformly spaced locations, results in a faster decay rate of distortion than that using an ALOHA-like random access MAC. In particular, the ratio of the excess reconstruction distortion under random access MACs to that under the MAC with uniform sampling grows as log M+O(log log M). We further show that in the high measurement SNR regime, the benefit from carefully scheduling transmission, instead of random access, is substantial. In the low SNR regime, however, using random access MACs results in little reconstruction performance loss.

The effect of medium access control (MAC) for information retrieval on signal field reconstruction in large-scale sensor networks with finite density is analyzed. Two MAC schemes are compared: the deterministic scheduling and random access. For fixed sensor density, we show that there is a critical threshold of e/sup -/spl lambda/(1+o(1))/, where /spl lambda/ is the throughput of the random access protocol, on the sensor outage probability P/sub out/ beyond which the reconstruction performance of deterministic central scheduling is inferior to that of distributed random access.

The problem of training symbol placement in data packets for channel tracking is considered, where the channel is time-varying Rayleigh flat fading. We use the minimum mean-square error (MMSE) estimator for channel tracking. A minmax approach is considered. We optimize the placement by minimizing the maximum MSE over a packet. It is shown that training symbols should be scattered throughout the packet with equal space to achieve the optimal performance.

The problem of design and placing pilot symbols for the estimation of frequency selective random channels is considered. For both SISO and MIMO channels, the Cramer-Rao bound (CRB) on the mean square error of channel estimators is derived and minimized with respect to the pilot symbols and their placement. It is shown that placing pilot symbols, possibly in multiple clusters, in the middle of the data packet leads to minimum CRB.