Antonio G. Marques

A Unified Approach to QoS-Guaranteed Scheduling for Channel-Adaptive Wireless Networks

Scheduling amounts to allocating optimally channel, rate and power resources to multiple connections with diverse quality-of-service (QoS) requirements. It constitutes a throughput-critical task at the medium access control layer of todays wireless networks that has been tackled by seemingly unrelated information-theoretic and protocol design approaches. Capitalizing on convex optimization and stochastic approximation tools, the present paper develops a unified framework for channel-aware QoS-guaranteed scheduling protocols for use in adaptive wireless networks whereby multiple terminals are linked through orthogonal fading channels to an access point, and transmissions are (opportunistically) adjusted to the intended channel. The unification encompasses downlink and uplink with time-division or frequency-division duplex operation; full and quantized channel state information comprising a few bits communicated over a limited-rate feedback channel; different types of traffic (best effort, non-real-time, real-time); uniform and optimal power loading; off-line optimal scheduling schemes benchmarking fundamentally achievable rate limits; as well as on-line scheduling algorithms capable of dynamically learning the intended channel statistics and converging to the optimal benchmarks from any initial value. The take-home message offers an important cross-layer design guideline: judiciously developed, yet surprisingly simple, channel-adaptive, on-line schedulers can approach information-theoretic rate limits with QoS guarantees.

Sampling of Graph Signals With Successive Local Aggregations

A new scheme to sample signals defined on the nodes of a graph is proposed. The underlying assumption is that such signals admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the so-called graph-shift operator. Instead of using the value of the signal observed at a subset of nodes to recover the signal in the entire graph, the sampling scheme proposed here uses as input observations taken at a single node. The observations correspond to sequential applications of the graph-shift operator, which are linear combinations of the information gathered by the neighbors of the node. When the graph corresponds to a directed cycle (which is the support of time-varying signals), our method is equivalent to the classical sampling in the time domain. When the graph is more general, we show that the Vandermonde structure of the sampling matrix, critical when sampling time-varying signals, is preserved. Sampling and interpolation are analyzed first in the absence of noise, and then noise is considered. We then study the recovery of the sampled signal when the specific set of frequencies that is active is not known. Moreover, we present a more general sampling scheme, under which, either our aggregation approach or the alternative approach of sampling a graph signal by observing the value of the signal at a subset of nodes can be both viewed as particular cases. Numerical experiments illustrating the results in both synthetic and real-world graphs close the paper.

Dynamic Resource Management for Cognitive Radios Using Limited-Rate Feedback

Tailored for the emerging class of cognitive radio networks comprising primary and secondary wireless users, the present paper deals with dynamic allocation of subcarriers, rate and power resources based on channel state information (CSI) for orthogonal frequency-division multiple access (OFDMA). Users rely on adaptive modulation, coding and power modes that they select in accordance with the limited-rate feedback they receive from the access point. The access point uses CSI to maximize a generic concave utility of the average rates in the network while adhering to rate and power constraints imposed on the primary and secondary users to respect cognitive radio related hierarchies. When the channel distribution is available, optimum dual prices are found to optimally allocate resources across users dynamically per channel realization. In addition, a simple yet optimal online algorithm that does not require knowledge of the channel distribution and iteratively computes the dual prices per channel realization is developed using a stochastic dual approach. Analysis of the computational and feedback overhead along with simulations assessing the performance of the novel algorithms are also provided.

Optimizing power efficiency of OFDM using quantized channel state information

Emerging applications involving low-cost wireless sensor networks motivate well optimization of orthogonal frequency-division multiplexing (OFDM) in the power-limited regime. To this end, the present paper develops loading algorithms to minimize transmit-power under rate and error probability constraints, using three types of channel state information at the transmitter (CSIT): deterministic (per channel realization) for slow fading links, statistical (channel mean) for fast fading links, and quantized (Q), whereby a limited number of bits are fed back from the transmitter to the receiver. Along with optimal bit and power loading schemes, quantizer designs and reduced complexity alternatives with low feedback overhead are developed to obtain a suite of Q-CSIT-based OFDM transceivers with desirable complexity versus power-consumption tradeoffs. Numerical examples corroborate the analytical claims and reveal that significant power savings result even with a few bits of Q-CSIT

Stationary Graph Processes and Spectral Estimation

Stationarity is a cornerstone property that facilitates the analysis and processing of random signals in the time domain. Although time-varying signals are abundant in nature, in many practical scenarios, the information of interest resides in more irregular graph domains. This lack of regularity hampers the generalization of the classical notion of stationarity to graph signals. This paper proposes a definition of weak stationarity for random graph signals that takes into account the structure of the graph where the random process takes place, while inheriting many of the meaningful properties of the classical time domain definition. Provided that the topology of the graph can be described by a normal matrix, stationary graph processes can be modeled as the output of a linear graph filter applied to a white input. This is shown equivalent to requiring the correlation matrix to be diagonalized by the graph Fourier transform; a fact that is leveraged to define a notion of power spectral density (PSD). Properties of the graph PSD are analyzed and a number of methods for its estimation are proposed. This includes generalizations of nonparametric approaches such as periodograms, window-based average periodograms, and filter banks, as well as parametric approaches, using moving-average, autoregressive, and ARMA processes. Graph stationarity and graph PSD estimation are investigated numerically for synthetic and real-world graph signals.

Resource Allocation for Interweave and Underlay CRs Under Probability-of-Interference Constraints

Efficient design of cognitive radios (CRs) calls for secondary users implementing adaptive resource allocation schemes that exploit knowledge of the channel state information (CSI), while at the same time limiting interference to the primary system. This paper introduces stochastic resource allocation algorithms for both interweave (also known as overlay) and underlay cognitive radio paradigms. The algorithms are designed to maximize the weighted sum-rate of orthogonally transmitting secondary users under average-power and probabilistic interference constraints. The latter are formulated either as short- or as long-term constraints, and guarantee that the probability of secondary transmissions interfering with primary receivers stays below a certain pre-specified level. When the resultant optimization problem is non-convex, it exhibits zero-duality gap and thus, due to a favorable structure in the dual domain, it can be solved efficiently. The optimal schemes leverage CSI of the primary and secondary networks, as well as the Lagrange multipliers associated with the constraints. Analysis and simulated tests confirm the merits of the novel algorithms in: i) accommodating time-varying settings through stochastic approximation iterations; and ii) coping with imperfect CSI.

Optimal Cross-Layer Resource Allocation in Cellular Networks Using Channel- and Queue-State Information

Algorithms that jointly allocate resources across different layers are envisioned to boost the performance of wireless systems. Recent results have revealed that two of the most important parameters that critically affect the resulting cross-layer designs are channel- and queue-state information (QSI). Motivated by these results, this paper relies on stochastic convex optimization to develop optimal algorithms that use instantaneous fading and queue length information to allocate resources at the transport (flow-control), link, and physical layers. Focus is placed on a cellular system, where an access point exchanges information with different users over flat-fading orthogonal channels. Both uplink and downlink setups are considered. The allocation strategies are obtained as the solution of a constrained utility maximization problem that involves average performance metrics. It turns out that the optimal allocation at a given instant depends on the instantaneous channel-state information (CSI) and Lagrange multipliers, which are associated with the quality-of-service (QoS) requirements and the operating conditions of the system. The multipliers are estimated online using stochastic approximation tools and are linked with the window-averaged length of the queues. Capitalizing on those links, queue stability and average queuing delay of the developed algorithms are characterized, and a simple mechanism is devised to effect delay priorities among users.

Power control for cooperative dynamic spectrum access networks with diverse QoS constraints

Dynamic spectrum access (DSA) is an integral part of cognitive radio technology aiming at efficient management of the available power and bandwidth resources. The present paper deals with cooperative DSA networks, where collaborating terminals adhere to diverse (maximum and minimum) quality-of-service (QoS) constraints in order to not only effect hierarchies between primary and secondary users but also prevent abusive utilization of the available spectrum. Peer-to-peer networks with co-channel interference are considered in both single- and multi-channel settings. Utilities that are functions of the signal-to-interference-plus-noise ratio (SINR) are employed as QoS metrics. By adjusting their transmit power, users can mitigate the generated interference and also meet the QoS requirements. A novel formulation accounting for heterogeneous QoS requirements is obtained after introducing a suitable relaxation and recasting a constrained sum-utility maximization as a convex optimization problem. The optimality of the relaxation is established under general conditions. Based on this relaxation, an algorithm for optimal power control that is amenable to distributed implementation is developed, and its convergence is established. Numerical tests verify the analytical claims and demonstrate performance gains relative to existing schemes.

Optimal Selective Forwarding for Energy Saving in Wireless Sensor Networks

Scenarios where nodes have limited energy and forward messages of different importances (priorities) are frequent in the context of wireless sensor networks. Tailored to those scenarios, this paper relies on stochastic tools to develop selective message forwarding schemes. The schemes will depend on parameters such as the available battery at the node, the energy cost of retransmitting a message, or the importance of messages. The forwarding schemes are designed for three different cases: 1) when sensors maximize the importance of their own transmitted messages; 2) when sensors maximize the importance of messages that have been successfully retransmitted by at least one of its neighbors; and 3) when sensors maximize the importance of messages that successfully arrive to the sink. More sophisticated schemes will achieve better importance performance, but will also require information from other sensors. The results contribute to identify the variables that, when made available to other nodes, have a greater impact on the overall network performance. Suboptimal schemes that rely on local estimation algorithms and entail reduced computational cost are also designed.

Reconstruction of Graph Signals Through Percolation from Seeding Nodes

New schemes to recover signals defined in the nodes of a graph are proposed. Our focus is on reconstructing bandlimited graph signals, which are signals that admit a sparse representation in a frequency domain related to the structure of the graph. Most existing formulations focus on estimating an unknown graph signal by observing its value on a subset of nodes. By contrast, in this paper, we study the problem of inducing a known graph signal using as input a graph signal that is nonzero only for a small subset of nodes. The sparse signal is then percolated (interpolated) across the graph using a graph filter. Alternatively, one can interpret graph signals as network states and study graph-signal reconstruction as a network-control problem where the target class of states is represented by bandlimited signals. Three setups are investigated. In the first one, a single simultaneous injection takes place on several nodes in the graph. In the second one, successive value injections take place on a single node. The third one is a generalization where multiple nodes inject multiple signal values. For noiseless settings, conditions under which perfect reconstruction is feasible are given, and the corresponding schemes to recover the desired signal are specified. Scenarios leading to imperfect reconstruction, either due to insufficient or noisy signal value injections, are also analyzed. Moreover, connections with classical interpolation in the time domain are discussed. Specifically, for time-varying signals, where the ideal interpolator after uniform sampling is a (low-pass) filter, our proposed approach and the reconstruction of a sampled signal coincide. Nevertheless, for general graph signals, we show that these two approaches differ. The last part of the paper presents numerical experiments that illustrate the results developed through synthetic and real-world signal reconstruction problems.