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Bio-Inspired Decentralized Radio Access Based on Swarming Mechanisms Over Adaptive Networks Paolo Di Lorenzo, Member, IEEE, Sergio Barbarossa, Fellow, IEEE, and Ali H. Sayed, Fellow, IEEE

Abstract—The goal of this paper is to study the learning abilities of adaptive networks in the context of cognitive radio networks and to investigate how well they assist in allocating power and communications resources in the frequency domain. The allocation mechanism is based on a social foraging swarm model that lets every node allocate its resources (power/bits) in the frequency regions where the interference is at a minimum while avoiding collisions with other nodes. We employ adaptive diffusion techniques to estimate the interference profile in a cooperative manner and to guide the motion of the swarm individuals in the resource domain. A mean square performance analysis of the proposed strategy is provided and confirmed by simulation results. The proposed approach endows the cognitive network with powerful learning and adaptation capabilities, allowing fast reaction to dynamic changes in the spectrum. Numerical examples show how cooperative spectrum sensing remarkably improves the performance of the resource allocation technique based on swarming. Index Terms—Diffusion adaptation, distributed resource allocation, distributed spectrum estimation, self-organization, swarming.

I. INTRODUCTION

C

OMMUNICATION strategies over radio networks are concerned with efficient techniques for dynamic access to spectral resources [1], [2] and for self-organization (SO) capabilities. SO is important in femtocell networks, where the deployment of a potentially large number of user-operated femto-access points makes centralized schemes hard to implement and prone to heavy signaling traffic. While decentralized resource allocation strategies are appealing, relying on pure decentralization can lead to inefficient implementations. A more viable approach consists in endowing the radio nodes with the capability to learn from the environment and to exchange information only with immediate neighbors in order to identify the most appropriate radio resources. Manuscript received October 01, 2012; revised February 02, 2013, April 03, 2013; accepted April 03, 2013. Date of publication April 16, 2013; date of current version May 22, 2013. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Huaiyu Dai. This work was supported by the TROPIC Project, Nr. 318784. The work of A. H. Sayed was supported in part by the NSF grants CCF-1011918 and CCF-0942936. Part of this work was presented at the European Signal Processing Conference (EUSIPCO), Barcelona, Spain, August–September 2011. P. Di Lorenzo and S. Barbarossa are with the Department of Information, Electronics, and Telecommunications (DIET), Sapienza University of Rome, 00184 Rome, Italy (e-mail: [email protected]; sergio@infocom. uniroma1.it). A. H. Sayed is with the Electrical Engineering Department, University of California, Los Angeles, CA 90095 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2013.2258342

In cognitive radio networks, opportunistic (or secondary) users (SU’s) are allowed to use temporally unoccupied communication resources, such as frequency bands, time slots or user codes, under the constraint of not interfering (or producing a tolerable interference) with licensed (or primary) users (PU’s). The opportunistic users should be able to sense the resources, use them, and release them as soon as primary users demand access. Overview surveys on cognitive radios and dynamic spectrum access methods appear in [3], [4]. Dynamic access techniques have been studied in a series of works, such as [5]–[12]. In all these works it has been emphasized that the sensing and access strategies should be designed jointly in order to optimize system performance. In particular, the authors of [8] show how to maximize the throughput of a secondary user by considering jointly the tasks of identifying spectral opportunities, sensing and accessing radio resources. These previous works concentrate on the decisions about whether to access the available channels or not. In [10], for instance, it was shown how to determine the decision thresholds in order to maximize the opportunistic throughput, in a multicarrier setup, for a given set of rates over the available subcarriers. In [11] it was then shown, within the same multicarrier framework, that a substantial performance improvement can be obtained by choosing decision thresholds and performing power allocation jointly, rather than separately. The uncoordinated access from multiple secondary users was addressed in [9]. Game-theoretic approaches have also been proposed, as a way to derive decentralized access strategies. In particular, in [12] the multiuser access problem was formulated as a game whose players are the secondary nodes, and their aim is to maximize their rate under the constraint of inducing no interference at all, or only limited interference, to the primary users. It is only natural that the deployment of cognitive terminals can benefit from decentralized radio access and sensing strategies. The use of distributed sensing strategies was proposed, for example, in [13], [14], where cooperative spectrum sensing techniques exploited the intrinsic sparsity of the radio resource allocation. The decentralized approach that is pursued in this work is inspired by the behavior observed in nature and is meant to endow cognitive nodes with adaptation and learning abilities. Biological networks tend to exhibit robust behavior and are capable of solving difficult organizational tasks through local cooperation among the individual agents without central control. In the bio-inspired approach, the network nodes are modeled as a population of simple agents interacting with the surrounding environment: while each individual has relatively limited capabilities, it is the collaborative behavior of the population that leads to the emergence of global patterns of behavior

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and cognition enabling them to handle complex tasks. Bio-inspired models for network synchronization and for resource allocation over cognitive networks have already been studied in a series of works, such as [15]–[21]. A useful survey article is [15], while [16] focuses on the practical relevance of bio-inspired solutions. Reference [17] shows how a simple self-synchronization mechanism, inspired by biological systems, can form the basic tool for achieving globally optimal distributed decisions in a wireless sensor network. In [18], the authors developed a decentralized scheduling scheme over a network of self-organizing devices that are modeled as pulse-coupled oscillators. Recent works also illustrate how cooperation over adaptive networks can model collective animal behavior and self-organization in biological networks such as birds flying in formation [22], fish foraging for food [23], or bacteria motility [24]. The application of swarming mechanisms to the solution of decentralized resource allocation problems was proposed in [25], where the resource allocation mechanism mimics the motion of a flock of birds searching for food, assuming a static interference profile and ideal communication channels among swarm individuals. The extension to random interactions among individuals was carried out in [26], to accommodate for random packet drops and quantization noise. In parallel, a distributed mechanism was proposed in [22], based on diffusion adaptation schemes [29]–[33], to guide the motion of a swarm of birds in dynamic environments, through local cooperation. In this paper we combine the swarm-based resource allocation scheme from [25], [26] with the diffusion adaptation strategies from [29], [30]. The resulting bio-inspired network cooperatively estimates the interference profile in the resource domain of a cognitive network and allocates resources through purely decentralized mechanisms. The resource allocation mechanism is based on a social foraging swarm model that emulates the motion of a swarm of birds searching for food. The “movement” of the resources in the resource domain is guided by diffusion adaptation, which estimates and learns the interference profile through local cooperation. The resulting network is able to learn and adapt its behavior to variations in the environment. Through a real-time adaptive diffusion process, the nodes share information locally and cooperate in order to estimate the interference profile in real-time and without the need for a central processor. In comparison with other distributed approaches that rely on, for example, consensus-based techniques [17], [36]–[38], adaptive networks rely on single time-scale iterations and enhance the diffusion of information through the network by exploiting the temporal and spatial diversity of the data in real-time. In addition, it is shown in [34] that diffusion networks outperform consensus networks in terms of mean-square-error performance, convergence rate, and mean-square stability. For this reason, we shall focus on diffusion strategies. The basic contributions of this paper are: (a) the extension of the social foraging model proposed in [25] to incorporate Quality of Service (QoS) requirements; (b) the combination of a distributed spectrum estimation technique based on diffusion adaptation [30] with the swarm-based resource allocation; (c) the derivation of the mean square properties of the diffusion adaptive filter applied to the spectrum estimation problem; and (d) the application of the proposed procedure to the dynamic

resource allocation problem. As will be shown in the paper, the incorporation of QoS requirements induces an interesting interplay between the swarming algorithm and the estimation step, so that the swarming mechanism turns out to depend not only on the estimation step but also on the quality of the estimates. The paper is organized as follows. In Section II we describe the swarm model, formulating the search of available slots as the distributed minimization of a global potential function. In Section III, we incorporate into the swarm model QoS constraints like, e.g., resource allocation with guaranteed signal to noise interference ratio (SNIR). Section IV illustrates the proposed distributed spectrum estimation technique based on diffusion adaptation. We first introduce a basis expansion model, which is useful to model the PU’s transmission, allowing distributed cooperative sensing. Then, we employ a vector version of the adapt-then-combine (ATC) diffusion algorithm from [30], which enables the network to learn and track the interference profile. A convergence and mean-square performance analysis of the proposed ATC diffusion filter, applied to the spectrum estimation problem, is also derived. In Section V, combining the diffusion step from Section IV and the swarming behavior from Section III, we illustrate how the proposed adaptive swarming algorithm performs dynamic resource allocation. Section VI provides some numerical examples aimed at illustrating the theoretical findings and assessing the performance and adaptation capabilities of the proposed technique. Finally, in Section VII we draw some conclusions. II. SWARM MODEL In this section, we describe an improved version of the swarm-based resource allocation strategy proposed in [25]. The problem we wish to solve is the assignment of frequency slots to cognitive (or femto) users in order to minimize interference towards primary (or macrocell) users and avoid conflicts among the cognitive users, while keeping the spread in the resource domain as limited as possible. A centralized controller knowing the spatial distribution of the primary users’ activity in the resource domain, as perceived by each cognitive node, could solve this non-trivial assignment problem. However, besides the computational complexity aspects, a centralized approach would require considerable signaling between the secondary nodes and the controller. Furthermore, since femto-access points are owner-operated devices, they are not necessarily under the control of a central authority. It is then of interest to examine decentralized resource assignment techniques. We formulate the problem as follows. We consider a set of synchronous secondary users interested in using resources in the frequency domain, trying to access frequency slots that are vacant. The resource selected by agent is described by a scalar denoting the frequency sub-channel that will end up being selected by agent . We denote by the interference power over the slot having coordinate (i.e., a frequency subchannel) perceived by node . The goal of node is to select the frequency slot, having coordinate , where is at a minimum. At the same time, each node wants to prevent conflicts with the other SU’s, while avoiding an excessive spread over the resource domain. The mutual

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interference among the SU’s can be modeled as an undirected graph , where denotes the set of nodes and is the edge set, whose vertices are the SU nodes and there is a link (edge) between two nodes if the distance between them is less than a coverage radius dictated by the node’s transmit power. The interference graph is described by the adjacency matrix , composed of nonnegative entries , the degree diagonal matrix , whose diagonal entries are , and the Laplacian , defined as . The set of neighbors of a node is , defined as . Node interferes with node if is a neighbor of (or ). The resource allocation problem can then be formulated mathematically as the search of the resource vector that minimizes in a distributed fashion a global potential function given by the sum of the interference perceived by the whole set of nodes plus an attraction/repulsion term:

The simplest way to implement the minimization of (1) in a distributed fashion is to use a gradient descent optimization procedure. In the application at hand, the search procedure should take into account that the resource domain (i.e., the frequency bandwidth) is bounded. This constraint can be incorporated by using a projected gradient algorithm. More specifically, let us indicate with the resource domain for user . Furthermore, considering again the swarm analogy, the occupied zones in the resource domain take the role of “dangerous” regions that must be avoided by the swarm individuals, while idle bands represent regions rich in food that the agents should occupy by reducing their speed. Thus, mimicking this natural learning capability, we consider a distributed minimization of (1) based on a projected scaled gradient descent optimization, so that every node starts with an initial guess, let us say , and then updates its resource allocation in time according to the following discrete-time implementation:

(1) where . The second term on the right-hand side of (1) represents an attraction/repulsion potential function given by (2) This function incorporates a short range repulsion term , whose effect is to avoid collisions among the cognitive nodes, and a long range attraction term , whose goal is to induce a swarm cohesion behavior, e.g., to avoid an excessive spread of the selected radio resources in the frequency domain. In summary, minimizing (1) leads the system to dynamically allocate its resources in frequency regions where there is less interference while avoiding conflicts among users and limiting the spread of the occupied domain. Remark 1: The function (1) is reminiscent of the social utility function used in [27], [28] to model a swarm moving in search of forage. In [27], [28], the swarm was supposed to move in space in order to maximize a function having the same form as in (1), except that the first term had the meaning of a spatial distribution of food, whereas in our case we wish to minimize a function whose first term represents the interference sensed by the cognitive users. In spite of the similarities of the mathematical problems, it is important to remark that while the swarming model studied in [27], [28] assumes full connectivity, in our case every node interacts only with a few neighbors. We will see that this makes a significant difference in the final result because it enables spatial reuse of radio resources. Remark 2: Differently from [25]–[28], where the authors used a fixed profile , in this paper we consider the possibility of time variability of the interference profile sensed by each node, i.e., . This is an important difference because it enables the swarm to dynamically allocate resources, tracking the changes in the interfering environment and reacting accordingly. A similar scenario arises in the modeling of bird flight formations through adaptive networks [22], where the total upwash function evolves dynamically as the birds move in search for the optimal location.

(3) , where is the time index, denotes projection onto the set , is a positive iteration-dependent step-size, and denotes the function defined as (4) where

and are the derivatives of and with respect to , respectively. The step-size , where is a monotonically increasing function of the interference power perceived at time by every node at its current position on the resource domain. Examples include linear, quadratic, logarithmic functions, etc. The goal is to accelerate the shift of resources when high interference is perceived and, at the same time, to slow down the reallocation of resources that are momentarily allocated over idle sub-bands. This adaptive behavior improves the reaction capability of the algorithm to changes in the environment. The upper bound is chosen in order to guarantee convergence of the projected gradient algorithm. The interested reader can refer to [25], [26] for a detailed convergence analysis. In this paper we consider an attraction/repulsion coupling function in (4) having a linear attraction term, i.e., (5) and an unbounded repulsion term of the form (6) and . These choices are infor some positive constants strumental to endow the system with the desired behavior and they are simple enough to allow for mathematical tractability. Other choices of the attraction/repulsion functions are also possible, see, e.g., [26], [27]. Actually, there is a unique distance at which the attraction and repulsion forces balance each other: the so-called equilibrium distance in the biological literature [39],

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[40]. This distance can be properly adjusted through the selection of the parameters and . To avoid conflicts among the allocations of different users, in our setting we choose the equilibrium distance to be proportional to the bandwidth of the frequency subchannel in the resource domain so that, at convergence of the swarming algorithm, resources of secondary users do not overlap on the same channel. Then, assuming that Tx/Rx filters shape the SU’s waveforms in order to have negligible interference between consecutive subchannels, the repulsion mechanism, properly defined over an interference graph, is capable of handling the mutual interference among secondary users. We further note that the coefficients depend on the distance between the nodes because two nodes interfere with each other only if they are spatial neighbors. Hence, in our setting, two nodes and with no direct link between them in the interference graph (i.e., with ), are allowed to end up with the same allocation in the resource domain; this occurrence is what is known as spatial reuse of frequency.

is the Lagrange multiplier associated with the -th where constraint of problem (8). The function

III. SWARM ADAPTATION INCORPORATING QOS CONSTRAINTS Radio resource management needs to take into account Quality of Service (QoS) requirements. For example, it may be necessary to enforce a minimum signal to noise plus interference ratio (SNIR). In practice, the SNIR value is not known and then it has to be estimated. Let us denote by the SNIR value estimated over the channel indexed by the coordinate . Denoting by the useful signal power received by the cognitive user over the channel , can be expressed as (7) where denotes the interference power estimated over the channel . In practice, since the estimate is affected by errors, the QoS constraint must be formulated in probabilistic terms. More specifically, we require the probability that value falls below a given threshold to be lower the than a fixed probability . Accordingly, the resource allocation problem can be reformulated as the solution of the following constrained optimization problem:

(8) given by (1). The constraint can be written directly with in terms of the interference value as: (9) . Hence, the Lagrangian associated with the where constrained problem (8) is

(11) can be interpreted as a penalized interference profile, where the penalty is proportional to the probability of violating the QoS constraint over each channel . Solving the constrained optimization problem (8) may be difficult in practice. Alternatively, we can approximate the minimization of the Lagrangian function in (10), by treating the coefficients as given positive weighting coefficients. One possible distributed iterative mechanism to minimize (10) under these conditions is again based on a projected gradient algorithm:

(12) where we have substituted the estimated interference level with its penalized version , so that . The effect of introducing the penalty is twofold. First, it penalizes the high interference spectrum regions that violate the SNIR constraint, thus facilitating the resource allocation task. Second, it increases the interference value of spectrum regions having a small sensed interference but a large variance of the interference estimate, thus preventing resource allocation over unreliable channels. It is useful to remark that the new formulation (11) incorporating the penalty term requires knowledge of the statistical distribution of the interference to be able to compute the probabilities involved in (11). The pdf of the interference estimate depends on the estimator. In the following, we provide an illustrative example involving one of the most common interference estimators, which is based on energy detection. Let us consider a general observation model where the observation over channel is composed of a sequence of time samples: , , where represents the interference (primary) signal, while is additive white Gaussian noise. The energy detector consists in estimating the energy of the received sequence (13) and comparing it with a threshold. Under relatively mild conditions, and according to the central limit theorem, tends to be asymptotically normally distributed if is large enough ( is often sufficient in practice). That is, for large , we can approximate the pdf of as follows [35]:

(10)

(14)

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where is the average interference (primary) signal power. In this way, for large , the probability that the estimated interference exceeds a certain threshold is given by: (15) where

is the true interference on channel

, is the standard deviation of is the tail probability of a zerothe estimation error, and mean unit-variance Gaussian random variable. Expression (15) cannot be directly used in (11) to build the penalized interference profile because its value depends on the true interference power , which is in general unknown to the cognitive users. An adaptive implementation can be used by substituting the true value of the interference with its current estimate , given by the online outcome of the energy detector in (13). The result is used by the swarm-based algorithm in (12) to allocate resources on the frequency axis. Applying an energy detector over each frequency subchannel is the simplest form of spectrum estimation. Of course, it is expected that more sophisticated cooperative sensing techniques lead to better performance with respect to a non-cooperative approach like the one in (13). Thus, in the next section, we show perhow to adaptively estimate the interference profile ceived by a cognitive node in a distributed manner by exploiting local cooperation. IV. DISTRIBUTED SPECTRUM ESTIMATION BASED DIFFUSION ADAPTATION

ON

Consider active PU’s transmitters and let denote the signal received at time by the SU , given by the superposition of the transmitted signals convolved with a linear, and possibly time-varying, fading tapped-delay-line channel with impulse response , and observed in the presence of additive white noise . The signal is further sampled at frequency , so that at time , we have

transmitted by the PU’s are known, every cognitive user can estimate the channel gains from a number of measurements. The training is usually repeated at regular intervals to accommodate the fact that the channel state can vary (albeit slowly) over time. In the following, we introduce a basis expansion model, which is useful to model the PU’s transmission, allowing distributed cooperative sensing. A. PSD Basis Expansion Let denote the power spectral density (PSD) of the signal transmitted by the -th primary user. The PSD can be represented as a linear combination of some preset basis functions, say, as: (17) where is the vector of basis functions evaluated at frequency , is a vector of weighting coefficients representing the power transmitted by the -th PU over each basis, and is the number of basis functions. For sufficiently large, the basis expansion in (17) can well approximate the transmitted spectrum. Several choices for the set of basis are possible. In particular, we consider continuously differentiable basis functions, such as raised cosines, Gaussian pulses, etc. The propagation medium introduces a frequency-selective channel gain between primary and secondary users. Letting be the channel transfer function between the -th primary user transmitter and the -th secondary user and considering a single source , the PSD received by node can be expressed as (18) active PU’s, each SU Considering now the presence of senses the aggregate effect of the power spectra that are transmitted by all active primary users. Thus, the PSD at SU can be expressed as:

(16) samReceived data are parsed into blocks each containing ples, where is chosen equal to the channel coherence incan be conterval, so that the impulse response sidered invariant in each block. These blocks are indexed by so that , with . For example, in frame-based communications (such as WiFi, WiMAX, and LTE), could correspond to the length of the preamble within a certain frame, and nodes could perform a sensing step at the end of each preamble. In the following, it is assumed that the channels are known for every node at every sample time . This assumption is reasonable in practice for the reasons we outline next. Many communication systems operating in licensed bands use pilot signals to ensure synchronization with the receiver. If we assume that the pilot tones

(19) where , with and denoting the collection of expansion coefficients for all primary user and for the noise power at the -th receiver node, respectively. Furthermore, denotes the vector of channel gains between every transmitter and the -th receiver, and (20) with denoting the Kronecker product operation. Expression (19) models the power received by node in terms of an unknown vector ; this vector represents the expansion of the received power in the basis defined by the vectors .

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B. Diffusion Adaptation

the interference profile variations; thus enabling the swarming mechanism to dynamically allocate resources on the frequency domain. Using its local estimates , and using (19), every node can determine an estimate for the interference profile received by node at the frequency location at time as:

The sensing strategy aims at obtaining by relying on estimates for , which can be obtained by computing the fast Fourier transform of , namely , inside the -th coherence block of length samples, and evaluating the average . periodogram estimate, say, as Thus, at every block-time index , every node observes noisy measurements of the PSD described by (19) over frequency samples in the interval , according to the model: (21) are modeled as known deterministic regression where vectors. The temporal index in the regressor expression takes into account the possibility of node mobility and possible variations in the channel conditions over time. The term denotes observation noise and is assumed to have zero mean and variance . Collecting measurements over contiguous channels, we obtain a vector linear model: (22) where , and is a zero mean random vector with covariance matrix . Given the interference measurements across all secondary users, these users can now cooperate to estimate the modeling vector in a distributed and adaptive manner. They can do so by seeking to minimize the following cost function: (23) The minimization of (23) can be computed using a centralized algorithm, which can be run by a fusion center once all nodes transmit their data , for all , to it. However, our emphasis is on a distributed solution, where the nodes estimate the interference profile by relying solely on in-network processing through the exchange of data only between neighbors. Several diffusion adaptation schemes have been developed for such purpose in [29], [30]. In this paper, we employ a vector version of the Adapt-then-Combine (ATC) algorithm without measurement exchange from [30]. For the vector minimization problem in (23), the ATC algorithm reads as follows:

(25) Since (24) can be expressed as a linear recursion, assuming suffiGaussian observation noise in (22) (i.e., assuming ciently large), the local interference estimate in (25) is also Gaussian distributed so that the SNIR constraint in (9) is given by:

(26) which is similar to what we have already obtained in (15). Again, since the true interference value is not known, an adaptive implementation of (26) can be obtained by substituting the true value of the interference with its current estimate , given by the current outcome (25) of the diffusion filter in (24). The expressions in (25), (26) can then be used in (12) to update the swarming algorithm. To evaluate (26), we still need an expression for the standard deviation of the estimation error on the channel achieved by the diffusion filter in (24) at convergence. In the next section, we carry out a mean-square performance analysis of the diffusion scheme in (24), providing closed form expressions for the mean-square deviation obtained by each node at convergence. C. Performance Analysis In this section we analyze the performance of the diffusion algorithm (24) by extending the approach of [30] to the case of a vector linear model given in (22). In what follows we view the estimates as realizations of a random process and analyze the performance of the algorithms in terms of their mean square behavior. We consider a general algorithmic form that includes various diffusion algorithms as special cases. Thus, we consider a general diffusion filter of the form:

(24) where is a positive step-size chosen by node . The first step in (24) involves local adaptation where node updates using the new observations . The second step in (24) is a combination step where the intermediate estimates , from the neighborhood , are combined through the coefficients . The combination matrix satisfies , and if . The resulting estimate of node at time is denoted by . The notation refers to a column vector with all its entries equal to one. In the case in which the unknown parameter varies slowly with time, the ATC diffusion algorithm allows online tracking of

(27) , and are generic non-negative real coefficients corresponding to the entries of the matrices , , and , respectively, satisfying (28) Different types of algorithms can be obtained as special cases . The ATC of (27) by choosing different matrices

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diffusion algorithm without measurement exchange in (24) is obtained by choosing and . To proceed with the analysis, we assume a linear measurement as in (22). Using (27), we define the error quantities , , and the global vectors: .. .

.. .

where denotes the Euclidean norm of its vector argument. Likewise, the induced block maximum norm of a block matrix with blocks of size is defined as: (40) Following [32] and applying the triangle inequality of norms to (38), we find that

.. . (29)

We also introduce the diagonal matrix (41) (30) Since

and the extended weighting matrices (31) deLet note the vector of channel gains of the network at time . Since each matrix depends on the channel gains between node and the PU’s at time , we introduce the quantities

and

are left-stochastic matrices, it holds that . Therefore, for the vector to converge to zero, it suffices to require (42) Then, exploiting the block-diagonal structure of the matrices and , we can conclude that is asymptotically unbiased if the step-sizes are small enough and satisfy: (43)

(32) (33) so that we have (34)

where denotes the -th matrix block of , and denote the maximum eigenvalue of the Hermitian matrix . Mean-Square Performance: In this section we examine the mean-square performance of the adaptive diffusion strategy (27). Following the energy conservation arguments of [29], [30], [43], we evaluate the weighted norm of for :

(35) (36)

(44) where is an arbitrary Hermitian positive-semidefinite matrix that we are free to choose, and

(37)

(45)

or, equivalently,

In the following mean-square analysis, we assume that the channel gain vector , for all , where is a fixed constant vector and is a finite time instant. Mean Stability: Let us assume the regression data to be temporally white and spatially independent. Taking the expectation of (37), and considering the evolution of the system for , we get (38) where . The algorithm (37) converges in the mean if the matrix is a stable matrix. To proceed, we call upon results from [30]–[33]. Following [31], let denote a vector that is obtained by stacking subvectors on top of each other (as is the case with ). The block maximum norm of is defined as (39)

If we let (46) then we can rewrite (44) as a variance relation of the form (47) is the trace operator. We further introduce the nowhere tation , and , where the notation stacks the columns of the matrix on top of each other, and is the inverse operation. We will also use the notation or interchangeably to denote the same square weighted quantity . Using the Kronecker product property [43], we can rewrite in (45) as , where the matrix is given by

(48)

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Then, using the property , and taking the limit of (47) as , we can recast (47) as follows: (49) Expression (49) is a useful result as it allows us to derive several performance metrics through the proper selection of the free weighting parameter (or ), as was done in [30]. Indeed, the steady-state mean-square deviation (MSD) at node is defined as: (50) The MSD at node can be obtained by weighting with a block matrix that has an identity matrix at block and zeros elsewhere. We denote the vectorized version of this matrix by , with denoting the column vectors with a unity entry at position and zeros elsewhere. Then, if the step sizes are small enough so that the matrix is stable and invertible, the free parameter can be chosen as . Thus, from (49), the MSD of node is given by

V. ADAPTIVE SWARMING FOR DYNAMIC RADIO ACCESS Combining the adaptive diffusion step (24), for estimating and tracking the interference profile, with the swarming update (12), for dynamic resource allocation, we arrive to the following adaptive algorithm to coordinate the learning and adaptation capabilities of the bio-inspired cognitive network. Adaptive Swarming Algorithm with QoS Constraints For each node , start with . Every node then performs the following steps for : 1) The node knows the position of its resource on the frequency domain and has access to the local data . 2) Perform an adaptation step to estimate the vector : (56) 3) Perform a combination step that combines the intermediate estimates in the neighborhood: (57)

(51) The network MSD is defined as the average MSD across all nodes in the network and is given by

4) Compute the current estimate of the interference spectrum in the current position , according to (25), and evaluate the penalized interference profile as:

(52) Similarly to what we have done for the MSD at node , from (49), the network MSD can be obtained as:

(58) with given by the square root of (55). 5) Update the position of resource as:

(53) . In the simulation section, we where will illustrate how these theoretical expressions match well with simulation results. Expression (49) is also useful to compute the variance of the estimation error on the channel achieved by the diffusion filter in (24) at convergence. Indeed, exploiting (25), we have:

(54) where . Thus, as previously done for (51) and (53), exploiting (54) we have: (55) where . The expressions in (25), (26), with given by (55), can then be used in (12) to update the swarming algorithm.

(59)

Remark 3: The adaptive swarming algorithm needs to evaluate the variance in (55) in order to compute step 4 of the Adaptive Swarming Algorithm with QoS Constraints. In this paper, considering a static network (static topology, noise, and channels), and since the first part of expression (55) is fixed and equal for each node, we assume that it can be computed offline and stored at each node. The second part can be computed locally, by each node, and it depends on the resource location currently chosen by node in the frequency domain. In general, the swarming methods that do not incorporate the QoS requirements, i.e., that assume for all in (59), lead to fully adaptive and decentralized algorithms and do not need any precomputed parameters. Further investigations are justified to derive a fully adaptive and decentralized mechanism in the presence of the QoS constraints.

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Fig. 2. Spectrum estimation through diffusion adaptation, and example of resource allocation through swarming.

Fig. 1. Interference graph. The square nodes denote primary users and the dot nodes denote secondary users.

VI. SIMULATION RESULTS In this section, we provide numerical examples to illustrate the main features of the proposed technique combining the swarm-based resource allocation method, illustrated in Sections II and III, and the distributed cooperative sensing algorithm using diffusion adaptation, shown in Section IV. All the numerical results were obtained using Matlab. Numerical Example 1—Performance: We consider a connected network composed of 15 SU’s, plus the inclusion of two PU’s. The interference graph among the SU’s coincides with the network topology shown in Fig. 1, where the dots represent SU’s whereas the squares refer to PU’s. We consider a , polynomial path loss model where is the distance between the -th PU and the -th SU, is a reference distance. The cognitive SU’s scan and channels over the frequency axis, which is normalGaussian basis funcized between 0 and 1, and use tions to model the expansion of the transmitted spectrum. The Gaussian basis functions have amplitude normalized to one, and . To estimate the spectrum profile, we emvariance ploy the ATC diffusion algorithm in (24) where the step-sizes , for all . Furthermore, we consider are set equal to a combination matrix that simply averages the intermediate for all . estimate from the neighborhood, hence, in (21) is assumed to be Gaussian The sampling noise with a variance dependent on the interference level on the fre, according to , where quency the receiver noise variance is set equal to (Interference to Noise ratio (INR) equal to 5 dB, with respect to the transmitted spectrum in Fig. 2), for all , and . We assume the presence of 15 resources (to be allocated) that are initially scattered randomly across the frequency spectrum. At the -th iteration of the updating rule (12), each node communicates to its neighbors the position it intends to occupy, i.e., the representing a frequency subchannel. In the appliscalar cation at hand, there is an intrinsic quantization of the frequency resources given by the subchannel bandwidth. In our implementation, we let the system evolve according to (3) until successive

Fig. 3. Steady-state MSD versus node index.

differences in allocation become smaller than the bandwidth of a frequency subchannel. At that point, the evolution stops and every SU is allowed to transmit over the selected channel. We consider an interference profile as in Fig. 2, where the dashed curve depicts the true spectrum transmitted by the two PU’s, whereas the solid curve represents the estimation at convergence through ATC diffusion. From Fig. 2, we can notice how diffusion adaptation fits well the spectrum profile. in (16) are esIn practice, the channel realizations timated and subject to noisy distortions. It is then of interest to check how sensitive is the proposed estimation strategy to errors in the channel estimation. To do so, we model the channel realizations as Gaussian random variables, with expected value . To evalgiven by the true channel coefficient, and variance uate the performance of the distributed estimation technique in the presence of channel estimation errors, in Fig. 3 we show the steady-state MSD of the ATC diffusion algorithm, for each node in the network, considering different values of the error . The settings are the same of the previous simulavariance tion, which leaded to Fig. 2. The steady-state values are obtained by averaging over 200 independent experiments and over 100 time samples after convergence. We also compare the obtained results with the theoretical findings in (51), which are depicted as diamonds in Fig. 3. As expected, from Fig. 3, we can notice

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Fig. 4. Convergence speed versus iteration index, for different swarming algorithms.

how, reducing the variance of the error in the channel estimation, the diffusion strategy gets better estimation performance. Further, it can be observed that the simulation results match well the theoretical values. An example of resource allocation is shown in Fig. 2, where the dots on the frequency axis represent the final frequency sub-channels chosen at convergence by the network nodes. The , . We further parameters of the swarm are considered the parameters and for all , the , and . The step size is fixed and threshold equal to 0.05, thus leading to a simple gradient descent version of the algorithm in (12). It is evident how the resources avoid the positions occupied by primary users, tend to keep the spread as small as possible while avoiding collisions among the allocations of different users. To learn the spectrum profile and adapt its resource allocation accordingly, the swarming algorithm needs time to converge. Clearly, in a resource allocation problem, a distributed technique is appealing only if it guarantees convergence in a few iterations. It is then of interest to check the average number of iterations needed by the proposed swarming algorithms to learn the spectrum and perform a resource allocation. In this example, we assume the presence of the interference profile in Fig. 2, which is learnt through local cooperation by the adaptive method in (24). To show the learning and adaptation capability of the cognitive network based on the swarming algorithm aided by the cooperative adaptive method in (24), in Fig. 4 we report the average behavior of the interference level perceived by the swarm versus the iteration index, averaged over 200 independent realizations. We compare the results obtained with the alternative techniques illustrated before: i) the basic swarming algorithm in (3) (where for all ); ii) the adaptive swarming method in (3) (with , where , for all ); iii) and the adaptive swarming method with penalized , interference profile in (12) (with where and , for all ). The other parameters are the same of the previous simulations. From Fig. 4, we can observe that the final interference level, which represent the noise level, is always the same in all cases. This means

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Fig. 5. Cumulative distribution function (CDF) of the Signal to Noise plus Interference Ratio perceived at convergence, for different swarming algorithms.

that the swarm always performed resource allocations in the interference-free regions of the spectrum, thus proving the excellent capabilities of spectrum estimation of the diffusion technique in (24). Since the adaptive algorithm in (3) accelerates the shift of resources perceiving a high interference, it outperforms the basic swarming algorithm in terms of convergence/reaction time needed by the algorithm to perform a resource allocation on idle bands. Furthermore, introducing the constraint in (9) in the adaptive method (12), the algorithm speeds up thanks to the fact that high interference regions are further penalized, thus incrementing the capability of the algorithm to move out resources from primary regions. To assess the effectiveness of the distributed resource allocation strategy, in Fig. 5 we report the cumulative distribution function (CDF) of the SNIR, averaged over 5000 independent realizations, that the secondary network achieves after convergence of the swarming mechanism. We compare the results obtained with the alternative techniques illustrated before: i) the for all basic swarming algorithm in (3) (where ); ii) the basic swarming method with penalized interference , and for all , profile in (17) (with iii) the adaptive swarming method in (3) (with , where , and , for all ); iv) and the adaptive swarming method with penalized interfer, where ence profile in (12) (with and , for all ). In this example, the spectrum estimation has been carried out using the non cooperative energy detection scheme from (13). The other parameters are the same of the previous simulations, and in particular, for all , the threshold , and . As we notice from Fig. 5, the basic swarming algorithm shows the worst performance. This happens because some resources can get stuck in regions occupied by the primary users but having a low gradient. This leads to the low final SNIR. Conversely, using the adap, tive scaling method in (3) (with , for all ), the agents move faster towards where the interference-free region due to the increment of the average profile gradient and the cohesion force, thus making the overall

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Fig. 6. Cumulative distribution function (CDF) of the Signal to Noise plus Interference Ratio perceived at convergence, for different cooperation strategies.

Fig. 7. Percentage of collisions versus interference to noise ratio, for different cooperation strategies.

swarm experience a smaller total interference. This means that the performance can be considerably improved if every node adapts its scaling function according to both interference value and its gradient. Furthermore, as we can notice from Fig. 5, ) helps imthe inclusion of the constraint in (9) (with prove the performance of the resource allocation. In fact, such a constraint further penalizes the spectrum regions with high interference because in those regions the estimation variance is also higher. Consequently, the swarming mechanism incorporating the SNIR constraint facilitates the shift of the resources out of the regions occupied by the primary (macro) users. From Fig. 5, we also notice that the basic swarming algorithm does not satisfy the QoS requirement, whereas the inclusion of the , for all ) helps the method constraint in (9) (with to provide a better quality of service, thus satisfying the QoS requirement. To illustrate the performance of cooperation among secondary nodes, in Fig. 6 we report the behavior of the cumulative distribution function of the Signal to Interference plus Noise Ratio (SNIR) at convergence, comparing the results obtained using the non-cooperative approach based on the simple energy detector in (13), and the cooperative learning approach in (24), for the spectrum sensing step. From Fig. 6, we note that, since cooperation improves estimation accuracy, each resource tends to move towards the interference-free regions, thus improving the system performance. What is also interesting to observe from Fig. 6 is that, for a given sensing strategy, the system performance may be improved by simply increasing the cohe. Indeed, sion strength, acting on the attraction parameter increasing , the agents tend to form cohesive blocks that exert an attraction towards the agents trapped by mistake over the subchannels occupied by the primary users, because of local estimation errors. This shows that swarm cohesion can induce a positive intrinsic robustness against individual errors, thus introducing a further level of cooperation among the cognitive users. Numerical Example 2—Collision Avoidance and Spatial Reuse of the Channels: As previously mentioned, the proposed

swarming algorithm is able to avoid conflicts among the allocations of neighbor users by properly selecting the equilibrium distance to be proportional to the bandwidth of the frequency subchannel in the resource domain so that, at convergence of the swarming algorithm, resources of secondary users do not overlap on the same channel. The presence of estimation noise affects the capability of the swarm of avoiding collisions. Thus, to assess the robustness of the collision avoidance mechanism based on swarming, in Fig. 7 we show the behavior of the percentage of collisions between spatial neighbors versus the interference to noise ratio, for different cooperation strategies. The results are averaged over 500 independent simulations. We consider the adaptive scaling method in (3) , where , (with for all ), and the other parameters are the same of the simulation in Fig. 2. From Fig. 7, we can see, as expected, that the number of collisions tends to zero as the noise decreases (INR increases). At the same time, we can also notice how the collision avoidance capability of the swarm improves if it adopts a cooperative sensing strategy, thanks to the better accuracy in the spectrum estimation. Finally, we can also see , we can reduce how, controlling the repulsion coefficient the average number of collisions. An interesting byproduct of the proposed collision avoidance method is that, since the interference among SU’s is described through a graph, only spatial neighbors will avoid overlap on the same channels, whereas two nodes sufficiently far away from each other are allowed to end up with the same allocation in the resource space, thus leading to spatial reuse of frequency in a totally decentralized fashion. As an example, in Fig. 2, observe that the number of allocated channels is less than the number of requested resources. This means that a certain number of nodes have picked up the same channels, but without leading to collisions. To quantify the capability of the proposed method to provide spatial reuse of the channels in the presence of estimation errors, in Fig. 8, we illustrate the behavior of the channel reuse parameter, defined as the ratio between the number of resources to be allocated and the number of allocated channels,

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Fig. 8. Channel reuse parameter versus Interference to noise ratio, for different cooperation strategies.

versus the interference to noise ratio, for different cooperation strategies. The results are averaged over 500 independent simulations. We consider the adaptive scaling method in (3) (with , where , for all ), and the other parameters are the same of the simulation in Fig. 2. A reuse factor of about two, achieved in Fig. 8 for low noise values, means that the system is able to accommodate roughly the double of requirements with respect to the number of available channels. From the same figure, we may also notice that this characteristic is affected by estimation errors. In fact, at low interference to noise ratios, i.e., for large noise, the reuse factor tends to one. Furthermore, performance improves by adopting a cooperative sensing strategy with respect to a non-cooperative approach. Finally, we can notice how an increment of the leads to a lower spatial reuse of the chanrepulsion constant nels due to the larger spread of the resource allocation over the resource domain. Form this last observation, it is useful to highlight that the cohesion aspect of the swarm plays a central role in our application not only because it limits the spread in the frequency occupancy, but principally because it induces a spatial reuse of radio resources. Numerical Example 3—Learning and Adaptation: We show now an example of learning and adaptation of the cognitive network based on the adaptive swarming algorithm. Natural swarms are adaptive systems whose individuals cooperate in order to improve their food search capabilities and to increase their robustness against predators’ attacks. We show next that the proposed resource allocation increases, as a by-product, the network robustness against the intrusion of a primary user (predator). We consider again the network topology depicted in Fig. 1, where the two PU’s start emitting at different times, thus causing a dynamic change of the occupied spectrum. Our goal is to test the dynamic response of the network to this changing environment. The parameters are the same considered in the previous simulation. In Fig. 9 we show an example of spectrum estimation and swarm-based resource assignment in the case the PU’s interference is dynamic. As before, the dots on the frequency axis represent the final channels chosen at convergence

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Fig. 9. Resource allocation in dynamic environment.

Fig. 10. ATC diffusion learning curve, in terms of MSD.

by the network nodes. At the beginning of time, the two PU’s are silent, and the first PU starts to transmit only at the iteration . The first PU becomes silent at iteration while, at the same time, the second PU starts to transmit. After , the two PU’s are both transmitting at the iteration same time. In particular, in Fig. 9 it is shown the evolution of the spectrum estimation and resource allocation at 4 different , 450, 675, 900. We notice from Fig. 9 time iterations, how diffusion adaptation fits always well the spectrum profile, thus proving good tracking performance. To give an example of the tracking capability of the ATC diffusion filter, in Fig. 10, we show the learning curve of the algorithm in terms of MSD, averaged over 200 independent experiments. As we can see, ATC diffusion reacts to the changes in the environment, learning the spectrum profile through local cooperation. At the same way, from Fig. 9, we also notice how the swarm reacts to the PU’s activations, avoiding to select radio channels occupied by primary transmissions. Resorting again with the swarm analogy, PU’s take now the role of predators whose positions must be avoided by the swarm individuals. In this context it is reasonable that the swarm agents closer to the

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and learning, including resource allocation with QoS constraints and cooperative sensing. A diffusion adaptation scheme, which estimates and learns the interference profile through local cooperation, guides the dynamic resource reallocation process. A mean-square performance analysis for the diffusion adaptation filter has been also derived and confirmed by simulation results. Finally, the procedure has been applied to the dynamic resource allocation problem in the frequency domain. Numerical results show the performance improvement in the resource allocation due to the cooperative estimation of the spectrum. Furthermore, it is shown how the proposed technique endows the resulting bio-inspired network with powerful learning and adaptation capabilities.

Fig. 11. Average perceived interference versus iteration index.

predator’s positions move faster to avoid the dangerous zones. To allow this adaptive swarming behavior, in this example, we have considered a time-varying step size that depends on the perceived interference through a linear scaling function, , where e.g. and , for all . As a consequence, the swarm model in (3) accelerates the motion of the resources perceiving a high interference, improving the reaction time needed by the algorithm to perform a resource allocation on idle bands in case of a PU’s activation. To give an example of the time needed by the algorithm to react to the PU’s intrusions and adjust the resource allocation consequently, in Fig. 11 we show the behavior of the instantaneous perceived interference versus the iteration index. The three peaks correspond to the PU’s activation times. From Fig. 11, we notice how the adaptive swarming algorithm needs only a few iterations to leave the PU’s regions. This positive behavior is due to the adaptation of the algorithm to the perceived interference, determining that resources allocating on high interference regions move faster due to the increment of the profile gradient and the cohesion force. VII. CONCLUSIONS In this paper we have proposed a dynamic resource allocation technique combining a distributed diffusion algorithm, for implementing cooperative sensing, with a swarming technique, for allocating resources in a parsimonious way (i.e., avoiding unnecessary spread in the frequency domain), yet avoiding collisions. In the swarm analogy, the dynamic interference distribution over the frequency domain takes the role of the food spatial distribution. Furthermore, the occupied zones in the resource domain take the role of dangerous regions that must be avoided by the swarm individuals as fast as possible, while idle bands represent regions rich of food that the agents have to occupy reducing their speed. The swarm mechanism includes an attraction force, useful to minimize the spread over the resource domain, and a repulsion force, useful to avoid collisions among swarm members. We have illustrated how inspiration form natural swarms can lead to different level of adaptation

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[41] F. Khan, LTE for 4G Mobile Broadband—Air Interface Technologies and Performance. Cambridge, U.K.: Cambridge Univ. Press, 2009. [42] B. T. Polyak, Introduction to Optimisation. New York: Optimization Software, Inc., 1987. [43] A. H. Sayed, Adaptive Filters. New York, NJ: Wiley, 2008.

Paolo Di Lorenzo (S’10–M’13) received the M.Sc. degree in 2008 and the Ph.D. in electrical engineering in 2012, both from University of Rome “La Sapienza,” Italy. He is currently a postdoctoral researcher in the Department of Information, Electronics and Telecommunications, University of Rome, “La Sapienza.” During 2010, he held a visiting research appointment in the Department of Electrical Engineering, University of California at Los Angeles (UCLA). He has participated in the European research project FREEDOM on femtocell networks. He is currently involved in the European projects SIMTISYS, on moving target detection through satellite constellations, and TROPIC, on distributed computing, storage and radio resource allocation over cooperative femtocells. His primary research interests are in statistical signal processing, distributed optimization algorithms for communication and sensor networks, graph theory, game theory, and adaptive filtering. Dr. Di Lorenzo received three Best Student Paper awards, respectively, at the IEEE SPAWC’10, EURASIP EUSIPCO’11, and IEEE CAMSAP’11, for works in the area of signal processing for communications and synthetic aperture radar systems. He is a recipient of the 2012 Italian national group on telecommunications and information theory (GTTI) award for the Best Ph.D. Thesis in information technologies and communications.

Sergio Barbarossa (S’84–M’88–F’12) received the M.Sc. degree in 1984 and the Ph.D. degree in electrical engineering in 1988, both from the University of Rome “La Sapienza,” Rome, Italy. He has held positions as a Research Engineer with Selenia SpA (1984–1986) and with the Environmental Institute of Michigan (1988), as a Visiting Professor with the University of Virginia (1995 and 1997) and with the University of Minnesota (1999). He has taught short graduate courses at the Polytechnic University of Catalunya (2001 and 2009). Currently, he is a Full Professor with the University of Rome “La Sapienza.” His current research interests lie in the area of signal processing for self-organizing networks, bio-inspired signal processing, femtocell networks, mobile cloud computing, graph theory, game theory, and distributed optimization algorithms. He is the author of a research monograph titled “Multiantenna Wireless Communication Systems.” He has been the scientific coordinator of the European projects WINSOC, on wireless sensor networks, and FREEDOM, on femtocell networks. He is currently the scientific coordinator of the European Project TROPIC, on cloud computing over small cell networks. He is also a principal investigator in the European Project SIMTISYS, on the radar monitoring of maritime traffic from satellites. Dr. Barbarossa has been nominated as an IEEE Fellow for his contributions to signal processing, sensor networks, and wireless communications. He received the 2010 EURASIP Technical Achievements Award for his contributions to synthetic aperture radar, sensor networks, and communication networks. He received the 2000 IEEE Best Paper Award from the IEEE Signal Processing Society. He is the coauthor of papers that received the Best Student Paper Award at ICASSP 2006, SPAWC 2010, EUSIPCO 2011, and CAMSAP 2011. From 1997 until 2003, he was a member of the IEEE Technical Committee for Signal Processing in Communications. He served as an Associate Editor for the IEEE TRANSACTIONS ON SIGNAL PROCESSING for two terms (1998–2000 and 2004–2006). He is now a member of the IEEE SIGNAL PROCESSING MAGAZINE Editorial Board. He has been the General Chairman of the IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC) 2003 and he is the Technical Co-Chair of SPAWC 2013. He has been the Guest Editor for Special Issues on the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, EURASIP Journal of Applied Signal Processing, EURASIP Journal on Wireless Communications and Networking, and the IEEE SIGNAL PROCESSING MAGAZINE. In 2012, he was nominated IEEE Distinguished Lecturer from the Signal Processing Society.

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Ali H. Sayed (S’90–M’92–SM’99–F’01) received the M.S. degree in electrical engineering from the University of Sao Paulo, Sao Paulo, Brazil, in 1989 and the Ph.D. degree in electrical engineering from Stanford University, Stanford, CA, USA, in 1992. He is Professor of Electrical Engineering with the University of California, Los Angeles (UCLA), where he leads the Adaptive Systems Laboratory. He has published widely, in the areas of adaptation and learning, statistical signal processing, distributed processing, and bio-inspired cognition. He is coauthor of the textbook Linear Estimation (Englewood Cliffs, NJ: Prentice-Hall, 2000), of the research monograph Indefinite Quadratic Estimation and Control (Philadelphia, PA: SIAM, 1999), and co-editor of Fast Algorithms for Matrices with Structure (Philadelphia, PA: SIAM, 1999). He is also the author of the textbooks Fundamentals of Adaptive Filtering (Hoboken, NJ: Wiley, 2003), and Adaptive Filters (Hoboken, NJ: Wiley, 2008). He has contributed several encyclopedia and handbook articles.

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Dr. Sayed is a Fellow of IEEE for his contributions to adaptive filtering and estimation algorithms. He has served on the Editorial Boards of several publications. He has also served as the Editor-in-Chief of the IEEE TRANSACTIONS ON SIGNAL PROCESSING from 2003 to 2005, and the EURASIP Journal on Advances in Signal Processing from 2006 to 2007. He has served on the Publications (2003–2005), Awards (2005), and Conference Boards (2007–present) of the IEEE Signal Processing Society. He also served on the Board of Governors of the IEEE Signal Processing Society from 2007 to 2008 and as Vice President of Publications of the same Society from 2009 to 2011. His work has received several recognitions, including the 1996 IEEE Donald G. Fink Award, the 2002 Best Paper Award from the IEEE Signal Processing Society, the 2003 Kuwait Prize in Basic Sciences, the 2005 Terman Award, the 2005 Young Author Best Paper Award from the IEEE Signal Processing Society, the 2012 Technical Achievement Award from the IEEE Signal Processing Society, and the 2012 Best Paper Award from the same society. He has served as a 2005 Distinguished Lecturer of the IEEE Signal Processing Society and as General Chairman of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2008.