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A Game-Theoretic Approach for Energy-Efficient Contention-Based Synchronization in OFDMA Systems Giacomo Bacci, Member, IEEE, Luca Sanguinetti, Member, IEEE, Marco Luise, Fellow, IEEE, and H. Vincent Poor, Fellow, IEEE
Abstract—The purpose of this paper is to provide a novel energyefficient perspective to the problem of contention-based synchronization in orthogonal frequency-division multiple-access communication systems. This is achieved by modeling the terminals and their corresponding receivers at the base station as economic and rational agents that engage in a noncooperative game. In the proposed game, each one trades off its available resources (transmit power and detection strategy) so as to selfishly maximize its own revenue (in terms of probability of correct detection) while saving as much energy as possible and satisfying quality-of-service requirements given in terms of probability of false alarm and timing estimation accuracy. The existence and uniqueness of the equilibrium of the game are studied. In particular, a necessary and sufficient condition on the system parameters is given for the equilibrium to exist. An iterative and distributed algorithm based on best-response dynamics (at the transmit side) and a practical parameter estimation (at the receive side) are proposed to achieve the equilibrium point. Numerical results are used to highlight the effectiveness of the proposed solution and to make comparisons with existing alternatives in terms of power consumption, synchronization time, and estimation accuracy. Index Terms—Best-response dynamic, contention-based synchronization, energy efficiency, game-theory, generalized Nash equilibrium, GLRT, IEEE 802.16, LTE-Advanced, OFDMA, power allocation.
I. INTRODUCTION A. Motivation
T
HE demand for high data rates in wireless communications has led to a strong interest in orthogonal frequency-division multiple-access (OFDMA) technologies
Manuscript received June 11, 2012; revised August 27, 2012 and November 13, 2012; accepted November 13, 2012. Date of publication December 03, 2012; date of current version February 12, 2013. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Samson Lasaulce. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n. PIOF-GA-2011-302520 GRAND-CRU Game-theoretic Resource Allocation for wireless Networks based on Distributed and Cooperative Relaying Units. This work was presented in part at the Fiftieth Annual Allerton Conference on Communications, Control, and Computing, Monticello, IL, USA, October 2012. G. Bacci is with the Department of Information Engineering, University of Pisa, 56126 Pisa, Italy, and also with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: giacomo.bacci@iet. unipi.it;
[email protected]). L. Sanguinetti and M. Luise are with the Department of Information Engineering, University of Pisa, 56126 Pisa, Italy (e-mail: luca.sanguinetti@iet. unipi.it;
[email protected]). H. V. Poor is with the Department of Electrical Engineering, Princeton University, Princeton, NJ, 08544 USA (e-mail:
[email protected]). Digital Object Identifier 10.1109/TSP.2012.2231679
due to their advantages in terms of dynamic channel allocation, spectral efficiency and robustness to multipath distortions. For these reasons, OFDMA-based technologies have been adopted by the WiMAX alliance [1] and the Third-Generation Partnership Project (3GPP) [2] for efficient packet-based mobile broadband communications. To maintain orthogonality among subcarriers of different users and avoid the occurrence of multiple access interference (MAI), uplink signals arriving at the base station (BS) should be aligned to the local time and frequency references [3]. For this purpose, the WiMAX alliance specifies a network entry procedure called initial ranging (IR) by which subscribers can achieve uplink synchronization and power control [4]. A similar procedure called random access (RA) is specified by the 3GPP for the (advanced) long-term evolution (LTE) standard [5]. In their basic forms, the IR and RA functions are contention-based synchronization procedures developing through the following steps. Each terminal that intends to establish a communication link with the BS (also known as eNodeB) achieves downlink synchronization using a common control channel. The synchronization parameters estimated in the downlink are used by each terminal as references in the subsequent uplink phase, during which each terminal notifies its entry request by transmitting a randomly chosen code over a specified set of subcarriers.1 As a result of different positions within the radio coverage area, synchronization signals transmitted by different terminals arrive at the BS with different time delays and power levels. After identifying the active codes and their corresponding timing and power information, the BS broadcasts a response packet indicating which codes have been detected and giving instructions for timing and power adjustments. If a terminal does not receive any response message, after a specified time it performs another synchronization attempt using a higher power level. To minimize the probability of collision, the time between two successive attempts is typically randomized on the basis of some specified contention resolution methods. For instance, the approach adopted in WiMAX relies on the binary exponential backoff (BEB) algorithm [4]. From the above discussion, it follows that code identification as well as multiuser timing and power estimation are the main tasks of the BS in contention-based synchronization processes. These problems have received great attention in the last 1In WiMAX, the entry request of each terminal is generated from a binary phase-shift keying ranging code and is transmitted over groups of adjacent subcarriers arbitrarily positioned within the available spectrum. In LTE, it is obtained by applying different cyclic shifts to a Zadoff-Chu sequence [5] and it is transmitted over a single set of adjacent subcarriers.
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BACCI et al.: A GAME-THEORETIC APPROACH FOR ENERGY-EFFICIENT CONTENTION-BASED SYNCHRONIZATION IN OFDMA
few years and some solutions are currently available (see for example [6]–[11]). All these works are focused on the detection and estimation problems mentioned above, under the assumption that the terminals deterministically increase their transmit powers upon successful synchronization. In this work, we look at the problem from a different perspective by focusing on the joint detection/estimation and power allocation issues. In particular, we derive a low-complexity and scalable procedure that allows each terminal and the BS to locally choose the transmit power and the detection strategy so as to obtain a good tradeoff between detection capabilities and power consumption. This is achieved by modeling the terminals and the BS as economic and rational agents that engage in a noncooperative game [12], [13] in which each one trades off its available resources (transmit power and detection strategy). The main goal of each terminal is to selfishly maximize its own revenue in terms of probability of being detected while saving as much energy as possible and satisfying quality of service (QoS) requirements given in terms of probability of false alarm and accuracy of its timing estimate.
B. Prior Work Game theory provides an analytical framework to study complex interactions among rational entities, and has attracted a significant interest by the wireless communication and signal processing communities in the last few years (see [14]–[16] and references therein). In particular, there exists a substantial literature on power control techniques based on noncooperative game theory [12]. Most of them are focused on the data transmission phase in wireless communications. Among the different formulations available in literature, particularly significant is the energy-efficient approach (see [17] and references therein), which is specifically tailored for a battery-powered mobile population as it aims at capturing the tradeoff between achieving a satisfactory error-rate and saving as much energy as possible. This framework, originally developed for voice traffic [18], has been extended to code-division multiple-access (CDMA) systems [19], [20], multicarrier networks [21], ultrawideband systems [22], and ad-hoc networks [23]. Energy-efficient resource allocation schemes for multicell OFDMA-based networks based on noncooperative game theory have been recently investigated in [24]–[27]. As mentioned before, the focus of the aforementioned works is on the data transmission phase, in which the terminals are already synchronized to the BS references. In this work, we investigate the network association phase, in which the terminals notify the BS of their entries through the procedure summarized in Section I.A. To the best of our knowledge, energy efficiency during this stage has been investigated only in [28], [29] for a CDMA wireless network in a flat-fading scenario, and extended in [30] to include a frequency-selective channel. In this work, we use a similar approach to improve the energy efficiency of contention-based synchronization procedures for wideband OFDMA single-cell systems. Although we adopt a similar optimization criterion, notable differences with respect to [28]–[30] can be highlighted: i) the detection strategy is included in the optimization problem, and not just the detection threshold given a particular code detection technique; ii) the
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parameter estimation accuracy is included in the game, given the particular requirements of OFDMA synchronization; and iii) in [28]–[30], simulations are conducted using the average performance of the detectors, including average auto- and cross-correlation properties of the spreading codes and perfect channel state information (CSI); in this paper, the simulation platform contains more physical-layer details, and all the results are obtained using random channel realizations (based on frequency-selective models), system parameters specified by existing standards (including spreading codes), and estimated parameters fed back by the BS (thus including the impact of imperfect CSI and estimation errors on the resource allocation performance). C. Contributions The main contributions of this paper are as follows. • A novel perspective on contention-based synchronization in OFDMA-based systems is provided. This is achieved by modeling the network elements as economic and rational agents that trade off transmit powers and detection strategies so as to selfishly maximize the probability of correct synchronization using an energy-efficient approach and satisfying given QoS requirements. • A game-theoretic framework is used: i) to identify optimization criteria for system design; ii) to derive a low-complexity and scalable procedure that allows each terminal to regulate its power in a distributed manner on the basis of its estimated signal-to-interference-plus-noise ratio (SINR) at the BS; and iii) to derive a low-complexity detection/estimation scheme allowing the BS to detect the selected codes and to estimate the associated synchronization parameters, without any prior information on the terminals currently in the network association stage. • Numerical results are used to highlight the effectiveness of the proposed solution with respect to existing alternatives based on a deterministic increase of the transmit power (with or without contention resolution methods). It turns out that the proposed solution allows each terminal to be detected with a limited amount of power in a shorter time interval while providing better timing and power estimation accuracy. D. Organization The remainder of the paper is structured as follows.2 Section II describes the system model, whereas Section III formulates the problem and uses the analytical tools of game theory to investigate its solution. Section IV presents an iterative and distributed algorithm to reach the equilibrium point, whereas Section V reports some simulation results and comparisons with alternatives. Conclusions are drawn in Section VI. 2The following notation is used throughout the paper. Matrices and vectors and are the identity matrix and the are denoted by boldface letters. all-zero vector, whereas denotes an diagonal matrix with entries along its main diagonal. We use and for expectation, transposition and Hermitian transposition, resp., for the Euclidean norm of the enclosed vector, and to round to the nearest integer towards zero.
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II. SYSTEM AND SIGNAL MODEL A. System Model We consider an OFDMA-based transmission technology emsubcarriers with frequency spacing . To avoid ploying aliasing problems at the receiver, null subcarriers are placed at both edges of the signal spectrum. The available subcarriers are split into a synchronization subchannel, used for the network association, and several data subchannels, used for data transfer. The former is employed by synchronization terminals (STs) that must complete their synchronization procedure, while the latter are assigned to data terminals (DTs) that entered the network at an earlier stage and have already achieved synchronization. Following [4], the synchronization subchannel is further divided into subbands and a given subband comprises a set of adjacent subcarriers, which is called a tile. We denote the index of the th subcarrier within the th tile by and call the set collecting the subcarrier indices of the th tile. The only constraint in the selection of the is that the tiles must be disjoint, which amounts to indices saying that for . We denote by the number of simultaneously active STs and assume that each ST notifies its entry request by transmitting a synchronization code of length , which is randomly chosen from a specified set . For simplicity, we assume that different STs choose different denoting the set collecting the codes, with indices of the selected codes. This assumption is reasonable in practical systems, since is usually much smaller than the code set cardinality . We assume that DTs have been successfully synchronized to the BS and do not generate interference over the received synchronization channel. On the other hand, the signals transmitted by the STs are not aligned, both in frequency and time domains. Let us denote the carrier frequency offset (CFO) (normalized to the subcarrier spacing ) and the timing error (normalized to the sampling period ) of the th ST by and , respectively. As explained in [31], CFOs are only induced by Doppler shifts and/or downlink estimation errors. We consider low mobility applications and assume that frequency estimation errors in the downlink are within 2% of as specified in [4]. Under such hypotheses, the impact of CFOs on the synchronization process can reasonably be neglected. On the contrary, timing errors cannot be neglected, as they are related to the different (unknown) positions occupied by the users within the cell, and their maximum value corresponds to the round trip propagation delay for a user located at the cell boundary [31], where is the cell radius and is the speed of light. A simple way to counteract the effects of timing errors would be the use of a sufficiently long cyclic prefix (CP) composed by sampling intervals, with being the maximum expected path delay. In this case, timing errors would not produce any interblock interference (IBI), and would appear only as phase shifts at the output of the receiver discrete Fourier transform (DFT) unit. Unfortunately, this solution is not suited for the data section of the frame as it leads to an intolerably large overhead. This implies that a successful synchronization procedure calls not only for identifying the transmitted codes actually buried in the received signal, but also for
providing accurate timing estimates during the synchronization process in order to avoid IBI during the subsequent data transmissions. B. Signal Model To model the received signal, we assume that the channel response experienced by the th ST over the th tile is nearly flat over each tile and independent across tiles (with an amplitude that depends on both large-scale and small-scale fading effects). The validity and impact of this assumption on the system performance will be discussed in detail in Section V.B by means of numerical results obtained with standard channel models. Denoting by the vector collecting the DFT outputs over the th tile , we may write (1) is ST ’s transmit power, and denotes its where channel frequency response within the th tile. In addition, is additive white Gaussian noise with zero mean and covariance matrix , the vector (2) accounts
for
the
phase
shifts
within
a
tile, and , with being the code randomly
chosen by the th ST. For simplicity, in this paper we focus on single-user strategies that operate individually for each . More , we assume the BS to precisely, for each decide in favor of one of the two following hypotheses:3 the code is not present in the observation vector is present in . Although suboptimal, this approach has the advantage of allowing a simple formulation of the detection problem as a composite binary hypothesis test: (3) (4) , and accounts for where the contribution of MAI plus thermal noise. To statistically describe the distribution of , we assume that and in (4) are unknown deterministic parameters, and we model the entries of as independent Gaussian random variables with zero means and (unknown) powers (5) 3As better detailed in Section IV, during contention-based synchronization, detectors, one for each possible , since it does the BS must allocate not know a-priori which codes are selected by the STs. Note that the code constitutes the only temporary means of identification between the th ST and the BS, that will be also used by the BS (on a broadcast downlink channel) to provide feedback to the th ST (e.g., outcome of the test, and estimated parameters, such as the timing offset).
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where
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is terminal ’s received power at the BS, and (6)
is ST ’s average channel power gain across the tiles. For later convenience, the probability density functions of under the hypotheses and are defined as:
(7)
(8)
III. ENERGY-EFFICIENT SYSTEM DESIGN A. Problem Formulation As mentioned in the introduction, the goal of this work is to make each ST locally and selfishly choose its transmit power so as to maximize its own utility, paired with an optimal detection strategy at the BS. Although OFDMA-based 4G candidate technologies, such as IEEE 802.16m [32] and 3GPP LTE [5] standards, allow for cooperation among terminals in the network, the contention-based synchronization is the very first active operation performed by a mobile terminal (after listening to broadcast channels on the downlink) to get successful association to the network. In this phase, it is thus reasonable to assume selfish behavior by the STs, which aim at achieving a good tradeoff between detection capabilities and power consumption. In other words, the utility function to be maximized must be defined so as to guarantee an energy efficient management of the available resources. This tradeoff can be quantified by defining the utility function of the th ST as the ratio of the probability of correct code detection to the transmitted energy per OFDMA symbol , with being the duration of the cyclically extended OFDMA block. This yields (9) where is the vector containing the transmit is the detection strategy adopted at powers of all STs, and the BS to detect (the code selected by the th ST). We have explicitly introduced the dependence of on in but also with affects (9) to emphasize that not only the detection probability of ST . Thus, the maximization of with respect to cannot be performed by means of a unilateral optimization, but rather requires a multidimensional one. The physical interpretation of , which has units of J , can be captured using the finite-state machine of Fig. 1, where the two possible states of a terminal in the network are sketched: the synchronization state, during which a terminal acts as an ST, and the data transmission state, in which it acts as a
Fig. 1. Finite-state machine describing the terminal operational status.
DT. The probability that the synchronization procedure is successfully completed is , and thus the average time spent by an ST in the first state is . As a conserepresents the expected energy consumed quence, by the th ST when transmitting at power .4 To proceed further, we observe that the detection strategy may lead to a wrong detection of the th code in the two following cases: i) the code is detected even though it is not present in the observation vector ; or, ii) the code is detected with an inaccurate timing estimation when it is actually present. The former situation gives rise to a false alarm event, and it can be handled imposing an upper bound on the . On the other hand, probability of its occurrence the latter case may be particularly harmful in OFDMA systems, as it may give rise to a significant IBI during the data transmission phase. A possible solution to circumvent this situation is to make the th ST regulate its power while satisfying a constraint on the mean-square-error (MSE) of its timing estimation error, defined as , where is the timing offset estimate of at the BS. Based on the above considerations, we can formulate our optimization problem in terms of optimal transmit power (at the ST side) and of optimal detection strategy (at the BS side) as follows:5
(10) STs attempting to achieve successful for all synchronization, where: is ST ’s transmit power denoting the maximum transmit power (to be set set, with large enough to allow STs located at the cell boundaries to correctly achieve successful synchronization); is the single-user and are the network QoS detection strategy set; and requirements in terms of maximum probability of false alarm and maximum MSE of the timing estimation error, respectively. Note that the problem in (10) cannot be solved in a centralized fashion by the BS as it actually does not know which STs are transmitting (this is indeed one of the outcomes of the synchronization process). This means that each ST must solve (10) in a decentralized way in order to compute its optimal . Furthermore, (10) cannot be decoupled into subproblems, as depends not only on , but also on all other STs’ 4Although other metrics (based for instance on a global-performance criterion and possibly coordinated by the service provider) can be used, we find the proposed metric a physically sound one to properly capture the description of the problem and to measure how efficient a resource allocation strategy is. 5Strictly speaking, the solution to this problem is not necessarily unique, as operator provides a whole set of values as its output. The equality the stands for all possible values that provide the maximum of the utility function.
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transmit powers . Otherwise stated, any action taken by a user affects the performance of all others. This makes the problem naturally fall within the scope of noncooperative game theory [12]. In this respect, the problem in (10) can be restated as a noncooperative game with complete information [12] defined as in which: is the player set, where player corresponds to the pair composed by the ST using code , and its receiver at the BS; denotes the strategy set for which the constraints in (10) are satisfied; and is player ’s payoff function defined as in (9). By restating (10) as game , in the next subsections we will use the analytical tools of game theory to investigate its solution.
In other words, meeting the constraint on the MSE means restricting ST ’s power strategy set to the subset (19) which depends on the opponents’ strategies . Since not only the utility but also the strategy set depends on , the game belongs to the category of generalized Nash games [13]. For such games, the most widely used solution is the generalized Nash equilibrium (GNE) [12], [13], defined as a set of strategies such that no player can unilaterally improve its own utility. Formally, a vector , with , is a GNE of if for any
B. Optimal Detection Strategy (at the BS Side)
(20)
To satisfy the constraint on the MSE in (10), let us focus on the properties of a generic timing estimator . In general, takes the form [33] (11) where
and are the bias and the variance of the timing estimate , respectively. The bias term can be generally measured through extensive simulations, whereas finding is usually a challenging task. To circumvent this problem, we assume that is well approximated by its Cramér-Rao [33] and rewrite (11) as bound (CRB) (12) from which it follows that the inequality constraint in (10) can be reasonably replaced by (13) In Appendix A, we show that (14) where
is the SINR of the th ST at the BS, given by (15)
and for all strategies , with . In this work, we focus only on pure (i.e., deterministic) strategies6 and study the existence and uniqueness of the corresponding GNEs. Using the considerations above and taking into account that the strategy only impacts on the numerator of (9), the optimization problem in (10) can be reformulated as for all transmit powers such that
(21) from which the optimal detection strategy is easily identified as the solution of the inner maximization. Under the assumption of single-user detection introduced in Section II, the utility function in (9) is independent of the others’ strategies with . can be found This means that the optimal detection strategy using standard optimization techniques. In particular, the solution can be obtained using the Neyman-Pearson theorem and is given by [33] (22) where and are defined as in (7) and is such that (8), and the threshold (23)
Letting (16) the constraint
in (13) is satisfied provided that
and As follows from (7) and (8), computing in (22) requires knowledge of the unknown pa, and . Then, we approximate the likelihood rameters ratio test (LRT) in (22) with the generalized LRT (GLRT) given by (see Appendix B) [33]
(17) (24) with
given by (18)
6This choice is motivated by the fact that there exist no mixed (i.e., statistical) strategies that are more efficient (in the Pareto sense [12]) than any pure (i.e., degenerated mixed) one, assuming such exists.
BACCI et al.: A GAME-THEORETIC APPROACH FOR ENERGY-EFFICIENT CONTENTION-BASED SYNCHRONIZATION IN OFDMA
where
with
and (25)
is the maximum likelihood (ML) estimate of in which obtained as (26) with being a tentative value for we obtain
. From (24), following [34] (27)
where (28) is the incomplete beta function [35]. The above result indicates that, for a given pair , the probability of false alarm is a function of the threshold only. The latter must be chosen is satisfied. such that the identity Note that, unlike [28]–[30], the probability of false alarm (27) does not depend on the transmit power . As better detailed in Section IV, this is of significant relevance for practical implementation purposes as the BS can dispense with any prior information on the active codes. C. Optimal Transmit Power (at the ST Side) Substituting the above results into (21) leads to the problem (29) on for nowhere we have omitted the dependence of tational simplicity. To solve (29), we first need to evaluate the probability of correct detection . For this purpose, we recall from Section II that the channel coefficients can be modeled as independent complex Gaussian random variables with zero means and variances given by . Under these assumptions, we have that [34] (30) where
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being the solution of (33)
The game admits a unique pure-strategy GNE if and only if in (32) is such that (34) Proof: The proof of existence and uniqueness of in (29) follows the same steps described in [28] and proceeds according to the following line of reasoning. First, the probability of correct code detection (30) is proven to be eventually a concave function of . Then, the existence is proven as in [13] and [36]–[39], whereas the arguments illustrated in [40] are used to prove the uniqueness. Next, we observe that the detection strategy based on the GLRT (22) maximizes for a given probability of false alarm irrespectively of all transmit powers. This easily follows from (21) where it is shown that each player can always choose . Hence, all the properties of the solution of (29) apply to as well. This means the optimal action at the GNE is given by with (selected by the th ST) given by (24) (selected by the detector for code at the and BS). Although related to a different application scenario, the results shown in Proposition 1 have a mathematical structure which is similar to those obtained by other relevant works in the field of game-theoretic energy efficiency (see for example [19], [20], [22], and [41]). Unlike previous works, Proposition 1 establishes a necessary and sufficient condition for the GNE to exist. This condition is not present in the aforementioned works and stems from the constrained formulation (10), which makes the game a generalized one (such as that investigated in [28]). As seen, the condition (34) is not always met, as it depends on the number of STs, the tile size , and the QoS and (through ). It is worth observing constraints that, if (34) is not fulfilled, it may happen that the set of power strategies of some users may be empty. In this case, such users will not be able to reach the equilibrium with a resulting degradation of the system performance (see Section V.B for some numerical examples). On the other hand, when (34) is fulfilled the following result holds true. Corollary 1: If the condition (34) is satisfied, at the GNE the th ST would end up transmitting at
is defined as (31)
(35)
with being the SINR of the th ST, defined as in (15). From (16), it follows that there exists a one-to-one correspondence between and for a given vector . This means that the can be equivalently probability of correct detection replaced with , which is a function of rather than of . To proceed further, we introduce the following proposition. Proposition 1: Define
(36)
(32)
Proof: The above result can be derived using the mathematical arguments developed in [28]. It is worth observing that neither (35) nor (36) give a practical method to enforce that each ST noncooperatively (i.e., distributely) reaches the GNE. This easily follows by observing that (35) requires knowledge of whereas (36) depends
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on and . All these parameters are unknown at the STs and cannot be directly estimated. To overcome this problem, in the next section we show how to exploit the GNE analysis provided so far to derive a practical power control algorithm. IV. IMPLEMENTATION To derive a practical algorithm to reach the GNE of in a distributed fashion, we start by assuming that the STs with indices have already chosen their optimal transmit powers. This amounts to saying that . Then, from (15) we have (37) from which using (35) yields (38) for a given requires We see that the computation of knowledge of only, but this information is not available at the th ST. A possible solution is performing the estimation at back to the ST through a the BS and feeding the estimate of reliable reverse link. An estimate of is obtained as [11] (see Appendix B for further details): (39) Since the BS does not have any a-priori knowledge of which codes are currently active, it must estimate the received SINR for all possible codes . The estimated SINRs are then fed back to the STs together with the corresponding code indices. The STs finding their code information in the response message will update the transmit power according to (38) after replacing with . Based on the above considerations, an iterative and distributed algorithm can be derived to let each active user reach the GNE of the proposed game . In the sequel, this scheme is referred to as best-response synchronization algorithm (BRSA), as it is based on best-response dynamics [40] operating as follows. a. Initialization of the game: a1) each active ST computes the SINR level at the equilibrium using (32), in , and are assumed which to be common knowledge across the network; a2) each active ST initializes the to a predetermined value; transmit power a3) each active ST sets ; and a4) the BS sets the optimal detection threshold based on by numerically inverting (27). b. GLRT algorithm: at each step of the algorithm, for each code , the BS ; b1) applies (26) to obtain b2) decides on or according to (24); b3) estimates the received using (39); b4) feeds back the results of the GLRT test and the SINR on the return broadcast channel. c. Best-response algorithm: at each step of the algorithm, each ST
c1) receives the SINR estimated by the BS, and the result of the code detection test (24) based on current estimated parameters; c2) if the GLRT for code is verified and , exits the game, otherwise goes to the next step; c3) adjusts the transmit power according to (40) c4) updates . Note that both the GLRT algorithm (performed by the BS for each available code ) and the best-response power update (implemented by each active ST) follow directly from the solution of the optimization problem (10). A close inspection of steps c1-c4 reveals that the BRSA requires each ST to know only its estimated SINR and the GLRT outcome. This means that it can be performed in a fully decentralized manner, in which the number of STs and the transmit power levels change across time. It is worth emphasizing that the convergence of BRSA to the GNE is ensured for any initial power by the theoretical analysis presented in [40] as long as condition (34) is fulfilled. This result holds true because the relationship (35) describing the best-reponse dynamics possesses the properties of a standard function [40]. Observe that, although in general the properties of uniqueness of the game equilibrium and of the convergence of iterative algorithms approaching it are not necessarily related, in this specific formulation the property of the standard function ensures both GNE uniqueness and BRSA convergence. Note that, in step c1, the ST can extract the relevant details in the downlink broadcast channel using , that serves as a temporary identifier between it and the BS. When the th ST exits the game or, equivalently, when hypothesis is verified, the BS will broadcast the estimated timing offset and the estimated received power. The ST will make use of both to adjust its time scale and transmit power in order to access the subsequent data transmission phase with the minimum impact in terms of IBI [11]. The exit condition on in step c2 is introduced to guarantee a sufficient accuracy of the timing estimation as indicated by the constraint , whereas in step c3 is considered to make sure that the constraints on the maximum transmit powers are met at every step of the BRSA. V. NUMERICAL RESULTS The performance of the BRSA is now investigated by means of numerical results. The simulation parameters are reported below and are chosen in compliance with the IEEE 802.16 family of standards [4]. All numerical results are obtained by averaging 20,000 independent network realizations. A. Simulation Parameters The DFT size is , and the sampling period is ns, corresponding to a subcarrier spacing of kHz. There are unmodulated subcarriers for both the releft and the right guard bands. Out of the maining subcarriers, are reserved for synchronization. The tiles composed of a set of adjacent subcarriers are randomly positioned within the available bandwidth so as to
BACCI et al.: A GAME-THEORETIC APPROACH FOR ENERGY-EFFICIENT CONTENTION-BASED SYNCHRONIZATION IN OFDMA
effectively exploit the frequency diversity offered by the multipath channel. We assume that a single OFDMA synchronization symbol is present within a frame, and that the frame duration is equal to ms. The synchronization codes are chosen from a set composed of binary phase shift keying signafor ) generated tures (i.e., as specified in [4]. We consider a cell radius 3 km, corresponding to a maximum normalized propagation delay . Path gains are modeled as statistically independent and circularly symmetric Gaussian random variables with zero means and power delay profile specified by the 6-tap ITU modified vehicular-A channel model [42]. In these circumstances, the maximum channel impulse response has a time span of samples, and the coherence bandwidth of the kHz. The average channel is approximately given by channel power is normalized with respect to a distance , and a path loss exponent is used. The CP length during the data transmission phase is chosen equal to . This means that the maximum timing estimation error that does not to give rise to IBI during the frame data section is . Hence, the constraint on the maximum MSE translates into . Extensive simulations (not reported here due to space limitations) indicate that the estimate obtained as in (26) is Gaussian-distributed with a bias , where is the delay spread of the channel [43]. Although the channel parameter is generally unknown, it can be roughly upper bounded by . Therefore, combining this result with (13), . In addition, the . maximum probability of false alarm is set to The DTs are supposed to be perfectly aligned with the BS references, whereas the number of STs is fixed at . Without loss of generality, we concentrate on the first ST and assess the performance of the BRSA when its distance from the BS is kept constant, while all other STs with indices are located at random distances uniformly distributed in the range between and . The maximum normalized transmit powers are assumed to be the same for all STs and equal to dB. On the other hand, two different scenarios are envisaged for the initial normalized powers : i) the minimum power (MP) scenario (shown using upper triis fixed to dB by all angular markers), in which STs; and ii) the single-user (SU) scenario (reported with circular markers), in which is chosen equal to , rep. The latter case resenting the optimal power level when minimizes the convergence time of the best-response algorithm [44] and it is used in the sequel as a benchmark for the minimum synchronization time required by the BRSA. Note that, in the SU scenario, knowledge of the average channel gain is required at the th ST. This information can be easily obtained in time division duplexing systems, whereas it calls for additional complexity in systems operating according to a frequency division duplexing mode. B. Network Design Criteria In this subsection, we exploit the theoretical analysis provided in Section III-C to derive some criteria for the network
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Fig. 2. Average normalized power consumption as a function of and ).
Fig. 3. Average synchronization time as a function of and ).
(
(
system design, and make use of the simulation results to illustrate the major findings. We begin by assessing the impact of and on the performance of the BRSA. For this purpose, in Fig. 2 we assume and report the average normalized power expenditure , required by ST 1 from the time it accesses the network until it successfully completes the synchronization procedure, as a function of the number of tiles . Similarly, Fig. 3 shows the average time needed to complete a successful synchronization, obtained by scaling the average number of steps required by the BRSA by . The results of Figs. 2 and 3 indicate that, in both the MP and the SU scenarios, the best performance is achieved for . This is motivated by the following reason. On one hand, the larger the tile size , the larger the processing gain yielded by the spreading code, as is apparent from (15). On the other hand, the smaller , the more accurate the matching between the selectivity of the channel in the frequency domain and the flat-fading assumption adopted in
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Fig. 4. Optimal SINR at the GNE as a function of and ).
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Fig. 5. Average MSE of the timing estimate as a function of and ).
(
Section II to derive the GLRT. The best choice to meet these two conflicting requirements is to choose according to the coherence bandwidth of the channel. In the network under investigation, this amounts to setting and , which is in accordance with the results of Figs. 2 and is not an integer, the optimal choice is to 3. If select the closest acceptable value for . In the case the code length is a prime number, as considered for LTE-compliant and systems [5], the best approach is to set , thus partially sacrificing some synchronization subcarriers, with a tolerable loss on the code cross-correlation performance [11]. The results of Figs. 2 and 3 show a large performance degradation for . This can be explained using the results of Section III.C. For the reader’s convenience, Fig. 4 reports the numerical values of the optimal SINR at the GNE (star markers) as a function of . The SINR levels and are also shown, using dashed and dash-dotted curves, respectively. By inverting (34), it follows that the maximum number of STs that can be simultaneously accommodated in the cell to guarantee the existence and uniqueness of the GNE of is (41) the maxIn the investigated network, we have that for should be smaller than 5. Since we imum number of STs assume , it follows that the condition (34) is not met for . This means that resources are not sufficient to accomSTs while meeting the QoS requirements. modate all the This makes the power consumption as well as the average synchronization time increase, although with a graceful behavior for . The sudden increase in the resources consumed by the pair can be again interpreted using the theoretical analysis of Section III-C, in a twofold manner. On one side, when . On the other side, for . Since at the GNE lies on the global maximum of the unconstrained utility function (i.e., that without the constraint on the MSE) if and only if (as follows from the
(
proof of Proposition 1, not reported for the sake of brevity), it is always preferable to have to ensure a better energy-efficient exploitation of the available resources. To complete the simulation analysis, we assess the accuracy of the timing estimator in (26) once the synchronization process is successfully completed. For this purpose, Fig. 5 illustrates the MSE of the timing estimate for different values of . From the simulation results, we can see that the QoS requirement is largely satisfied by all considered values of . In particular, we note that the best estimation accuracy is again obtained for and for both MP and SU scenarios. C. Performance Assessment Based on the results of Section V-B, in all subsequent simulations we choose and , from which, using (18) and recalling that and , we get dB. From (27), we have that when . Moreover, the optimal SINR turns out to be dB, from which, using (30) and (31), we . get The BRSA is compared with two alternative solutions relying on a deterministic increase of the transmit power. The first one is referred to as the deterministic synchronization algorithm (DSA), whereas the second one is called the BEB-DSA [4]. Both differ from the BRSA in the transmit power update (step c3) only, as follows: if the selected code is not successfully detected, the th ST updates its transmit power according to (42) where is a design parameter common to all STs. For the DSA, , whereas for BEB-DSA is an integer number , with being the randomly chosen in the interval current value of ST ’s backoff window. The parameter of BEB-DSA is referred to as the backoff counter and indicates how many OFDMA synchronization symbols the th ST must
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Fig. 6. Average normalized power consumption as a function of the normalized ( and ). distance
Fig. 7. Average synchronization time as a function of the normalized distance ( and ).
wait before re-transmitting using . During the first synchronization attempt, the backoff window size is set to and it is doubled after each unsuccessful attempt. After successive unsuccessful attempts, is reset to its . In all subsequent simulations, we assume initial value dB, , and . Similarly to the BRSA, we assume that the maximum normalized transmit powers for both schemes are the same for all STs and such that dB. The initial powers are chosen equal to , with dB. and as functions of , Figs. 6 and 7 show i.e., the normalized distance from the BS of the ST of interest, using lower triangular and square markers to report the results of the DSA and BEB-DSA, respectively. As seen, the BRSA provides better results in terms of both energy efficiency and . As expected, the fairness for all investigated values of SU initialization requires the minimum average time for a successful synchronization, whereas the MP initialization guarantees the minimum amount of power expenditure. The BEB-DSA
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requires roughly the same power consumption as the BRSA, but at the expense of an increased average time per acquisition. The DSA is faster than the BEB-DSA, but requires a significant amount of battery drain. On the contrary, BRSA maintains the average acquisition time limited up to the maximum of about two frames for any BS-terminal distance in the SU initialization case, and less than five frames in the MP initialization case for the far users, and requires a limited amount of power expenditure (around 5 dB above the noise power for the far users in both initialization schemes). Therefore, the BRSA outperforms the DSA both in terms of power expenditure and of time needed for successful synchronization, at the expense of an increased amount of feedback information from the BS. Currently, IEEE 802.16m [32] and 3GPP LTE [5] standards provide feedback for every detected code (in terms of corrections to be applied both to timing offsets and to transmit powers). In the proposed method, we only require the BS to broadcast the outcome of the GLRT (1 bit), and the received SINR for each code in . Since the number of codes is usually on the order of tens to hundreds, the amount of extra resources needed on the downlink channel is limited, also considering that preliminary experimental results (not reported for the sake of brevity) show that introducing a 1-byte SINR quantization does not significantly affect the numerical performance. We now observe that the analysis presented in Section III is valid under the hypothesis of a sufficiently large power constraint that allows far users to reach the optimal SINR even in the presence of a bad channel realization. To properly set this parameter, consider an SU scenario in which the single ST is placed at . To meet , we just need the channel power gain (averaged across the tiles as in (6)) to be higher than . Since the channel powers are normalized with respect to , in the considered scenario it is sufficient that be higher than dB. Since the average value of is dB, the probability of not meeting is negligible. When considering , it might happen (with a low probability considering that channel power gains are averaged across tiles than span across a bandwidth ), that some near STs show , thereby preventing ST from meeting . However, this situation usually occurs only for a short time interval since “strong” users are synchronized very fast, and the new incoming users (randomly placed in the cell) are likely not to be “strong” again. This allows the “weak” ST to eventually achieve and enter the network (although after a longer time interval). To support this observation, note that throughout our experiments channel realizations (obtained by averaging at least per simulation point) we never encountered a situation in which an ST was not able to achieve . Finally, observe that the design of plays a more important role for BEB-DSA and DSA rather than BRSA. While increasing does not substantially affect the performance of BRSA, a large degradation is observed for both BEB-DSA and DSA. This is because, for a given incremental power step, increasing forces STs to remain in the collision phase for a longer time interval before resetting their powers to . For the sake of completeness, in Figs. 8 and 9 we compare the estimation accuracy of the investigated solutions in terms of and the normalized variance of the (unbiased) power
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Fig. 8. Average MSE of the timing estimate as a function of the normalized ( and ). distance
Fig. 9. Average normalized variance of the power estimate as a function of the ( and normalized distance ).
estimate, given by , as func. The normalized CRB of the received power, detions of fined as with given in Appendix A, is also reported for comparison. As before, the BRSA represents the best allocation scheme, whereas the DSA and BEB-DSA exhibit a significant loss for values of larger than 0.6. Finally, Figs. 10 and 11 show and for the invesof STs ranges from 2 to tigated solutions when the number . The user of interest is placed at distance . Comparisons are similar to the ones shown above and lead to similar conclusions: the proposed BRSA is particularly suitable for a bursty-traffic scenario, with messages composed of a small number of packets, and in which users are required to be synchronized in a limited amount of time. This makes it particularly suited for applications in which a refinement of the synchronization parameters is periodically required. Nowadays, the
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Fig. 10. Average normalized power consumption as a function of number of STs ( and ).
Fig. 11. Average synchronization time as a function of number and ).
of STs (
common procedure adopted by current standards for synchronization refinement is known as periodic ranging [5], [32]. The latter is a process by which any mobile terminal periodically adjusts its transmission parameters in order to stay synchronized with the BS even during its idle states, thereby reducing the transmission latency but at the same time the battery life. Since the proposed solution enables a fast initial synchronization with low power consumption (especially when far terminals are considered), it can be used for reducing the frequency of periodic ranging procedures, thereby further increasing the energy efficiency of the mobile terminals. VI. CONCLUSION In this work, we have proposed a game-theoretic approach to derive an energy-efficient solution for contention-based synchronization in OFDMA-based systems. A noncooperative game has been formulated in which each terminal and the
BACCI et al.: A GAME-THEORETIC APPROACH FOR ENERGY-EFFICIENT CONTENTION-BASED SYNCHRONIZATION IN OFDMA
base station are allowed to locally and selfishly choose the transmit power as well as the detection strategy to maximize the probability of correct terminal synchronization while saving as much energy as possible. This is achieved by controlling the performance of the network in terms of probability of false alarm and estimation accuracy of the timing errors. We have shown that the proposed game admits a unique generalized Nash equilibrium under some mild conditions on the system parameters. An iterative algorithm based on best-response dynamics has been derived to let each user achieve the equilibrium point in a distributed manner, using the unknown parameters estimated at the BS (through a low-complexity method that follows from the resource allocation optimization problem). Numerical results based on realistic network parameters and widely agreed-upon channel models have shown that the proposed solution outperforms deterministic-increase approaches (both with and without contention resolution methods) in terms of average transmit power and synchronization time as well as in terms of accuracy of the parameter estimation. This is achieved at the expense of an increased amount of feedback information from the BS. Further work is needed to assess the impact of quantized levels for both the signal-to-interference-plus-noise ratios and the transmit powers, with the former particularly important to significantly reduce the amount of feedback required across the network. It is worth observing that the approach developed in this work can also be expedient to optimize the performance and the efficiency of other radio networks. As an example, in [45] a similar formulation for the utility function is used to investigate the tradeoff between detection capabilities and power consumption for a distributed radar sensor network.
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with (47) and
From (46), it follows that
(48) and defining [33]
Using (47), recalling that , we get (14). From
(49) where (50) is the gradient of with respect to (50) into (49) yields
. Substituting (46) and
(51)
APPENDIX B Maximizing
in (7) with respect to
produces (52)
from which it follows that (53)
APPENDIX A In this Appendix, we compute the CRBs for the joint estimation of and . Let us define the set of unknown paand denoting the real and the rameters, with imaginary parts of vector , respectively. Using the above definitions and the pdfs given in (7)–(8), the Fisher information matrix is found to be [33] (43)
in (8) with respect Looking for the maximum of to while keeping and fixed yields (26), where takes the form (25). Maximizing with respect to using as in (26) leads to (54) with
. Substituting this result back into and maximizing with respect to yields (55)
where
from which we get (44)
(56)
and (45) The inverse of
is equal to
Substituting (53) and (56) into (22) yields (57)
(46)
which can be equivalently rewritten as in (24) with . Using the invariance property of the ML estimator, it follows that the estimate of the received power
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can be obtained as using (25) and (54), as
or, equivalently, (58)
It is worth observing that, if the timing offset is perfectly estimated (i.e., ), then (59) and (60) From (59) and (60), it follows that and are biased estimates of and , respectively. Using (59), we can see that takes the form . an unbiased estimate of Recalling (55), (61) is found to From the above results, an unbiased estimate of , from which, using (61), we obtain be (62) Combining (61) and (62) with (15), the estimated SINR (39) easily follows.
in
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[15] E. A. Jorswieck, E. G. Larsson, M. Luise, H. V. Poor, and A. Leshem, “Game theory in wireless communications,” IEEE J. Sel. Topics Signal Process, vol. 6, no. 2, pp. 73–75, Apr. 2012. [16] A. Attar, T. Başar, M. Debbah, H. V. Poor, and Q. Zhao, “Introduction to the issue on game theory in signal processing,” IEEE J. Sel. Areas Commun., vol. 30, no. 1, pp. 1–3, Jan. 2012. [17] E. Belmega, S. Lasaulce, and M. Debbah, “A survey on energy-efficient communications,” presented at the IEEE Symp. Personal, Indoor, Mobile Radio Commun. (PIMRC), Istanbul, Turkey, Sep. 2010. [18] H. Ji and C.-Y. Huang, “Non-cooperative uplink power control in cellular radio systems,” Wireless Netw., vol. 41, no. 3, pp. 233–240, Mar. 1998. [19] D. Famolari, N. B. Mandayam, D. J. Goodman, and V. Shah, “A new framework for power control in wireless data networks: Games, utility and pricing,” in Wireless Multimedia Network Technologies, R. Ganesh, K. Pahlavan, and Z. Zvonar, Eds. Boston, MA, USA: Kluwer Academic, 1999, pp. 289–310. [20] D. J. Goodman and N. B. Mandayam, “Network assisted power control for wireless data,” in Proc. IEEE Veh. Technol. Conf. (VTC), Rhodes, Greece, May 2001, pp. 1022–1026. [21] F. Meshkati, M. Chiang, H. V. Poor, and S. C. Schwartz, “A game-theoretic approach to energy-efficient power control in multicarrier CDMA systems,” IEEE J. Sel. Areas Commun., vol. 24, no. 6, pp. 1115–1129, Jun. 2006. [22] G. Bacci, M. Luise, H. V. Poor, and A. M. Tulino, “Energy-efficient power control in impulse radio UWB wireless networks,” IEEE J. Sel. Topics Signal Process, vol. 1, no. 3, pp. 508–520, Oct. 2007. [23] O. Ileri, S.-C. Mau, and N. B. Mandayam, “Pricing for enabling forwarding in self-configuring ad hoc networks,” IEEE J. Sel. Areas Commun., vol. 23, no. 1, pp. 151–162, Jan. 2005. [24] Z. Han, Z. Ji, and K. Liu, “Non-cooperative resource competition game by virtual referee in multicell OFDMA systems,” IEEE J. Sel. Areas Commun., vol. 25, no. 6, pp. 1079–1090, Aug. 2007. [25] G. Miao, N. Himayat, G. Li, and S. Talwar, “Distributed interference-aware energy-efficient power optimization,” IEEE Trans. Wireless Commun., vol. 10, no. 4, pp. 1323–1333, Apr. 2011. [26] S. Buzzi, G. Colavolpe, D. Saturnino, and A. Zappone, “Potential games for energy-efficient power control and subcarrier allocation in uplink multicell OFDMA systems,” IEEE J. Sel. Topics Signal Process., vol. 6, no. 2, pp. 89–103, Apr. 2012. [27] G. Bacci, A. Bulzomato, and M. Luise, “Uplink power control and subcarrier assignment for an OFDMA multicellular network based on game theory,” presented at the Int. Conf. Perf. Eval. Method. Tools (ValueTools), Paris, France, May 2011. [28] G. Bacci and M. Luise, “A game-theoretic perspective on code synchronization for CDMA wireless systems,” IEEE J. Sel. Areas Commun., vol. 30, no. 1, pp. 107–118, Jan. 2012. [29] G. Bacci and M. Luise, “A pre-Bayesian game for CDMA power control during network association,” IEEE J. Sel. Topics Signal Process., vol. 6, no. 2, pp. 76–88, Apr. 2012. [30] G. Bacci, “Energy-efficient power control for CDMA code acquisition over frequency-selective channels,” IEEE Commun. Lett., vol. 16, no. 3, pp. 364–367, Mar. 2012. [31] M. Morelli, “Timing and frequency synchronization for the uplink of an OFDMA system,” IEEE Trans. Commun., vol. 52, no. 2, pp. 296–306, Feb. 2004. [32] “IEEE Standard for Local and Metropolitan Area Networks—Part 16: Air Interface for Broadband Wireless Access Systems—Amendment 3: Advanced Air Interface,” IEEE 802.16 Broadband Wireless Access Working Group, Tech. Rep. IEEE 802.16m-2011, 2011. [33] H. V. Poor, An Introduction to Signal Detection and Estimation, 2nd ed. New York, NY, USA: Springer, 1994. [34] P. Lombardo and D. Pastina, “Multiband coherent radar detection against compound-Gaussian clutter,” IEEE Trans. Aerosp. Electron. Syst., vol. 35, no. 4, pp. 1266–1282, Oct. 1999. [35] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. New York, NY, USA: Dover, 1965. [36] D. Debreu, “A social equilibrium existence theorem,” in Proc. Nat. Acad. Sci., 1952, vol. 38, pp. 886–893. [37] I. L. Glicksberg, “A further generalization of the Kakutani fixed point theorem with application to Nash equilibrium points,” in Proc. Nat. Acad. Sci., 1952, vol. 38, pp. 170–174. [38] K. Fan, “Fixed point and minimax theorems in locally convex topological linear spaces,” in Proc. Nat. Acad. Sci., 1952, vol. 38, pp. 121–126.
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[39] K. Arrow and G. Debreu, “Existence of an equilibrium for a competitive economy,” Econometrica, vol. 22, no. 3, pp. 265–290, July 1954. [40] R. D. Yates, “A framework for uplink power control in cellular radio systems,” IEEE J. Sel. Areas Commun., vol. 13, no. 9, pp. 1341–1347, Sept. 1995. [41] F. Meshkati, A. J. Goldsmith, H. V. Poor, and S. C. Schwartz, “A gametheoretic approach to energy-efficient modulation in CDMA networks with delay QoS constraints,” IEEE J. Sel. Areas Commun., vol. 25, no. 6, pp. 1069–1078, Aug. 2007. [42] Guidelines for Evaluation of Radio Transmission Technology for IMT2000, Recommendation ITU-R M.1225, 1997. [43] M. Morelli, L. Sanguinetti, and H. V. Poor, “A robust ranging scheme for OFDMA-based networks,” IEEE Trans. Commun., vol. 57, no. 8, pp. 2441–2452, Aug. 2009. [44] G. Bacci, “Distributed power control techniques based on game theory for wideband wireless networks,” Ph.D. dissertation, Univ. of Pisa, Pisa, Italy, 2008. [45] G. Bacci, L. Sanguinetti, M. S. Greco, and M. Luise, “A game-theoretic approach for energy-efficient detection in radar sensor networks,” presented at the IEEE Sensor Array Multich. Signal Process. Workshop (SAM), Hoboken, NJ, Jun. 2012.
Giacomo Bacci (S’07–M’09) received the B.E. and the M.E. degrees in telecommunications engineering and the Ph.D. degree in information engineering from the University of Pisa, Pisa, Italy, in 2002, 2004, and 2008, respectively. Since 2005, he has been with the Department of Information Engineering at the University of Pisa, where he is currently a Postdoctoral Research Fellow. In 2006–2007, he was a visiting student research collaborator at the Department of Electrical Engineering at Princeton University, Princeton, NJ, USA. In 2008, he joined Wiser srl, Livorno, Italy, as a software engineer. From May 2012 to April 2013, he was also enrolled as a Visiting Postdoctoral Research Associate at the Department of Electrical Engineering, Princeton University. His research interests are in the areas of digital communications, signal processing, and estimation theory. His current research topics focus on resource allocation for multiple-access and relay-based wireless networks, time delay estimation for satellite positioning systems and wireless communications, and channel coding for IMT-advanced technologies. Dr. Bacci is the recipient of the FP7 Marie Curie International Outgoing Fellowships for career development (IOF) 2011 GRAND-CRU Game-Theoretic Resource Allocation for wireless Networks Based on Distributed and Cooperative Relaying Units. Luca Sanguinetti (S’04–M’06) received the Laurea Telecommunications Engineer degree (cum laude) and the Ph.D. degree in information engineering from the University of Pisa, Pisa, Italy, in 2002 and 2005, respectively. Since 2005 he has been with the Department of Information Engineering of the University of Pisa. In 2004, he was a visiting Ph.D. student at the German Aerospace Center (DLR), Oberpfaffenhofen, Germany. During the period June 2007 to June 2008, he was a Postdoctoral Associate in the Department of Electrical Engineering at Princeton University, Princeton, NJ, USA. During the period June 2010 to September 2010, he was selected
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for a research assistantship at the Technische Universitat München. He is currently an Assistant Professor at the Department of Information Engineering of the University of Pisa. His expertise and general interests span the areas of communications and signal processing, estimation, and detection theory. Dr. Sanguinetti is currently serving as an Associate Editor for the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS. Marco Luise (M’85–SM’94–F’12) received the M.E. and Ph.D. degrees in electronic engineering from the University of Pisa, Pisa, Italy, in 1984 and 1989, respectively. He was formerly a Research Fellow of the European Space Agency (ESA) at ESTEC Noordwijk, The Netherlands, a Researcher of the Italian National Research Council (CNR), at the Centro Studio Metodi Dispositivi Radiotrasmissioni (CSMDR), Pisa, Italy, and an Associate Professor at the Department of Information Engineering of the University of Pisa, where he is currently a Full Professor of telecommunications. His main research interests lie in the broad area of communication theory, with particular emphasis on wireless communications, mobile and satellite communications, positioning systems, and software-defined radios. Prof. Luise served as an Editor of the IEEE TRANSACTIONS ON COMMUNICATIONS and of the European Transactions on Telecommunications. He was the founder and first Co-Editor-in-Chief of the International Journal of Navigation and Observation and is currently an Associate Editor of the Journal of Communications and Networks. Recently, he was the General Chairman of EUSIPCO 2006, the General Co-Chair of European Wireless 2010, and will be the General Co-Chair of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP) 2014. H. Vincent Poor (S’72–M’77–SM’82–F’87) received the Ph.D. degree in electrical engineering and computer science (EECS) from Princeton University, Princeton, NJ, USA, in 1977. From 1977 until 1990, he was on the faculty of the University of Illinois at Urbana-Champaign. Since 1990, he has been on the faculty at Princeton, where he is the Michael Henry Strater University Professor of Electrical Engineering and Dean of the School of Engineering and Applied Science. His research interests are in the areas of stochastic analysis, statistical signal processing, and information theory, and their applications in wireless networks and related fields such as social networks and smart grid. Among his publications in these areas are the recent books Classical, Semi-classical and Quantum Noise (Springer, 2012) and Smart Grid Communications and Networking (Cambridge Univ. Press, 2012). Dr. Poor is a member of the National Academy of Engineering and the National Academy of Sciences, a Fellow of the American Academy of Arts and Sciences, and an International Fellow of the Royal Academy of Engineering (U.K.). He is also a Fellow of the Institute of Mathematical Statistics, the Acoustical Society of America, and other organizations. In 1990, he served as President of the IEEE Information Theory Society, and from 2004 to 2007, he served as the Editor-in-Chief of the IEEE TRANSACTIONS ON INFORMATION THEORY. He received a Guggenheim Fellowship in 2002 and the IEEE Education Medal in 2005. Recent recognition of his work includes the 2010 IET Ambrose Fleming Medal, the 2011 IEEE Eric E. Sumner Award, the 2011 Society Award of the IEEE Signal Processing Society, and honorary doctorates from Aalborg University, the Hong Kong University of Science and Technology, and the University of Edinburgh.
