I. INTRODUCTION
Throughput per Pass for Data Aggregation from a Wireless Sensor Network via a UAV ANDREA GIORGETTI, Member, IEEE MATTEO LUCCHI, Student Member, IEEE MARCO CHIANI, Fellow, IEEE University of Bologna MOE Z. WIN, Fellow, IEEE M.I.T. Data retrieval from a sensor field by means of unmanned aerial vehicle (UAV) has increasing interests for both commercial, military, and homeland security applications. In these situations, the design of energy-efficient communication links between sensor field and UAV is crucial, owing to battery powered sensor nodes. We propose an energy-efficient cooperative transmission scheme for wireless sensor networks (WSNs) where data gathered by sensor nodes need to be collected into a far receiver. In particular, we consider a network composed of sensor nodes that share a common message that has to be transmitted asynchronously toward a fusion center onboard a UAV. We consider that the communication channels between the nodes and the fusion center are subject to fading and noise. Due to the far communication distance and energy constraint at each node, the fusion center must be able to reliably receive the weak and noisy signals. In our approach the fusion center consists of a Rake receiver capable of collecting multiple replicas of the same information from the nodes in the WSN. The performance of the proposed cooperative diversity scheme is then studied in terms of throughput, bit error probability, and energy efficiency. The results obtained show that, as the number of nodes increases, the proposed approach increases network lifetime, communication reliability, and throughput.
Manuscript received June 25, 2009; revised March 14, 2010; released for publication August 2, 2010. IEEE Log No. T-AES/47/4/942891. Refereeing of this contribution was handled by V. Krishnamurthy. This research was supported, in part, by the University of Bologna Grant Internazionalizzazione, the European Commission under the FP7 ICT integrated project CoExisting Short Range Radio by Advanced Ultra-WideBand Radio Technology (EUWB) Grant 215669, the National Science Foundation under Grant ECCS-0901034, the Office of Naval Research Young Investigator Award N00014-11-1-0397, and the MIT Institute for Soldier Nanotechnologies. This paper was presented in part at the Eight International Symposium on Wireless Personal Multimedia Communications (WPMC’05), Aalborg, Denmark, Sept. 19—22, 2005. Authors’ addresses: A. Giorgetti, M. Lucchi, and M. Chiani, DEIS, WiLAB, University of Bologna, Via Venezia 52, 47521 Cesena, Italy, (E-mail:
[email protected]); M. Z. Win, Laboratory for Information and Decision Systems (LIDS), M.I.T., Room 32-D658, 77 Massachusetts Ave., Cambridge, MA 02139. c 2011 IEEE 0018-9251/11/$26.00 ° 2610
Recent progress in microelectronics and wireless communications have enabled the development of low cost, low power, multifunctional sensors, which has allowed the birth of new type of networks named wireless sensor networks (WSNs) [1]. The main features of such networks are: the nodes are positioned randomly over a given field with a high density; each node operates both like sensor (for collection of environmental data) as well as transceiver (for transmission of information to the data retrieval); the nodes are not rechargeable [2, 3]. Typical scenarios include a sink, which periodically triggers the WSN, and a large number of nodes deployed in a given geographical area without detailed planning [4]. In such scenarios, the goal is to collect observations from all sensors to a far receiver [5, 6], in which the receiver may be located onboard unmanned aerial vehicles (UAVs) [7], high altitude platforms (HAPs) [8], or low Earth orbit (LEO) satellites [9]. This is a practical example of reachback communication, characterized by the high density of nodes that transmit data reliably and efficiently towards a far receiver. This problem has been investigated from the information-theoretic point of view in [10]—[12]. In the literature a few technical solutions have been proposed. The aggregate transmission of relay nodes is proposed in [13], while a distributed algorithm for a broadcast communication is presented in [10]. In [7] a different solution based on the ultrawideband (UWB) transmission technique that does not require stringent network synchronization [14, 15] is proposed and analyzed. The problem of transmitting information from a sensor to a far receiver lies in the more general framework of cooperative communications. This paradigm has recently attracted considerable attention in wireless cellular and ad-hoc networks as a way to share resources through distributed transmission and processing. Through this concept, it is possible to realize a new form of diversity to mitigate the effects of severe fading that has been termed cooperative diversity. With the aim to increase network capacity and reliability, the cooperation can be realized in various forms: for example through the adoption of distributed space-time codes in wireless ad-hoc networks [16—18], the use of code division multiple access (CDMA) signaling [19, 20], or by means of practical opportunistic relaying [21—23]. We consider the scenario in which each node transmits a common shared message directly to the receiver onboard the UAV whenever it receives a broadcast message (triggered for example by the vehicle).1 We assume that the communication 1 This common message can be obtained by a “Gossip Phase” where the information is shared among sensors via efficient flooding [7, 10, 15].
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channels between the local nodes and the receiver are subject to fading and noise. The receiver onboard UAV which we refer to as fusion center, must be able to fuse the weak and noisy signals in a coherent way to receive the data reliably. In this paper, we analyze a cooperative diversity concept as an effective solution to the reachback problem. In particular, we propose a spread spectrum (SS) transmission scheme in conjunction with a fusion center that can exploit cooperative diversity, without requiring stringent synchronization between nodes. The idea consists of simultaneous transmission of the common message among the nodes and a Rake reception at the fusion center. The proposed solution is mainly motivated by two goals: the necessity to have simple nodes (to this aim we move the computational complexity to the receiver on board the UAV), and the importance to guarantee high levels of energy efficiency of the network, thus increasing the network lifetime. We then analyze the proposed scheme in order to better understand the effectiveness of the approach presented. The performance metrics considered here are both the theoretical limit on the maximum amount of data that can be collected by the fusion center, as well as the error probability with a given modulation scheme. Since we deal with a WSN, both of these performance are evaluated taking into consideration the energy efficiency of the network. The remainder of the paper is organized as follows. In Section II, we introduce the system model of the WSN and the fusion center. The average mutual information and the throughput of the network are evaluated in Section III. In Section IV, the performance of the cooperative scheme in terms of error probability is evaluated. In Section V, some numerical results for throughput and error probability are presented confirming the validity of the proposed transmission scheme. Finally, conclusions are given in Section VI. II. SYSTEM DESCRIPTION We consider a WSN with N nodes deployed randomly over a wide planar area (Fig. 1). These nodes collect data (e.g., environmental such as temperature, pressure, humidity, etc.) that need to be transmitted to the fusion center onboard the UAV whenever a message triggered from the vehicle is received by the nodes. As previously stated, all nodes share the same data. A. Channel Model The channel for each communication link between a node and the fusion center is modeled with path-loss and fading. In particular, we consider a free-space path-loss model for the link between the ith node
(with i = 1, : : : , N) and the UAV, given by μ ¶2 1 4¼di f0 PL(di ) = GT GR c
(1)
where GT and GR are the transmitting and receiving antenna gains, respectively, c is the speed of light, and f0 is the carrier frequency. The distance di between the ith node and the receiver can be written as q 2 (2) di = (xi ¡ xUAV )2 + (yi ¡ yUAV )2 + zUAV where (xi , yi , 0) are the coordinates of the ith node and (xUAV , yUAV , zUAV ) are the coordinates of the UAV with respect to a reference coordinate system. Aeronautical channel models have attracted attention for their peculiar propagation characteristics owing to a strong direct line-of-sight (LOS) component in addition to many weaker random components due to local scattering [24]. Accordingly, it has been shown recently that Rician fading is a good model for aeronautical [25] and ship-to-ship radio [26] channels. The Rice fading is characterized by a Rice factor K which is the ratio of the power of the LOS and that of the non-LOS (NLOS) components. Therefore, in our analysis we consider independent frequency-flat2 Ricean fading channels between the nodes and the UAV. In particular, the equivalent low-pass representation of the channel between the ith node and the UAV is modeled by a complex gain hi = jhi j ¢ ejμi with phases μi uniformly distributed between 0 and 2¼, and Rice distributed amplitudes jhi j. For the sake of convenience we include the path-loss in the fading model as3 −i = Efjhi j2 g =
1 PL(di )
(3)
and we consider the scenario in which all the N channels have the same Rice factor K [27]. B. Transmission Technique We consider a DSSS transmission scheme such as in CDMA [28] or impulse radio UWB [29]—[31]. In this case, the equivalent low-pass (ELP) representation of the transmitted signal from the ith node can be written as p X aj C(t ¡ jTs ¡ ±i ) (4) s(i) (t) = 2 j
where aj is the jth transmitted symbol with Efjaj j2 g = PT , and the delays ±i , i = 1, : : : , N, account for the asynchronism among the nodes. The spreading waveform is composed of M chips with duration Tc 2 The extension to frequency-selective fading is straightforward by introducing virtual nodes. 3 We use Ef¢g to denote the expectation operator.
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Fig. 1. WSN and the UAV.
as C(t) =
M¡1 X k=0
ck g(t ¡ kTc )
(5)
where ck 2 f¡1, 1g. The symbol duration is thus Ts = MTRc and g(t) represents the chip waveform with +1 energy ¡1 g 2 (t)dt = Tc . We assume that each node transmits with the same power and same spreading sequence fck gM¡1 k=0 . In the following, we denote by Es = PT =Rs the transmitted energy per symbol of each node, where Rs = 1=Ts is the symbol rate. Now, considering the channel model adopted, the ELP received signal at the fusion center can be written as N X sr (t) = hi s(i) (t ¡ ¿i ) + º(t) (6) i=1
where hi is the complex channel gain between the ith node and the fusion center, ¿i is the propagation delay between the ith node and the UAV, and º(t) is the complex additive white Gaussian noise (AWGN) with two-sided power spectral density 2N0 . The instantaneous received power at the fusion center from the ith node is PR(i) = PT jhi j2 , and, due to (3), the average received power is therefore P¯R(i) = PT =PL(di ). It is clear from (6) that the received signal sr (t) is the result of the superposition of the common message transmitted from different nodes. Since all nodes use the same spreading sequence, although 2612
individual signals experiences independent flat-fading, this composite signal can be thought as the signal received from a single node through a “virtual” frequency-selective multipath channel.4 That is, the received signal is composed of replicas of the same transmitted signal with different amplitudes, delays, and phases. As a result we can employ a Rake receiver as fusion center to combine these replicas to decode the data as shown in Fig. 2. In order to keep the complexity low, we propose two solutions depending on the specific application of the network. The first one is devoted to applications where an instantaneous detection of the signal is not required. In fact, some applications can tolerate great delays, so in principle data can be collected by the UAV and decoded “off-line.” In this case, the fusion center can be implemented via software. Therefore, the receiver complexity could be overcome by a software implementation of the receiver (including channel estimation, synchronization, combining, etc.) at the expense of a non real time availability of the data. Conversely, if the application requires stringent delay constraints, it is possible to use a Rake with a limited number of fingers (equals to Nsel ) that 4 Note that the scenario of interest here cannot be interpreted as a spatial multiplexing MIMO system [32, 33] since all nodes are transmitting the same data stream.
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Fig. 2. ELP representation of Rake receiver adopted as fusion center.
combines only the Nsel signals, namely partial Rake (PRake) [34]. As we show in the following, the latter solution gives a good trade-off between reliability and energy consumption. C. Synchronization and Transmission Bandwidth Requirements As previously stated, the Rake receiver can combine coherently the signals from all nodes provided that they are resolvable. Due to the properties of the Rake receiver, this does not require any form of coordination among the nodes prior to transmission. Such asynchronous transmission results in simple network design, provided that the maximum excess delay is significantly smaller than the symbol duration, Ts . To understand typical values of the maximum excess delay, i.e., the delay between the first and the last received replicas, let us consider a scenario where nodes are positioned on a square area with side L. Each node transmits to the UAV whenever it receives a trigger message from the vehicle. When the UAV is located at the center of the sensors field at an altitude zUAV , the path lengths difference between the closest node (at the center of the area) q and the farthest one (at 2 the corner of the area) is ¢d = zUAV + L2 =2 ¡ zUAV . Therefore, the time difference between the reception of the symbol from the two nodes is ¢t = 2¢d=c, where the factor 2 accounts for the round-trip delays.5
5 For
example, L = 1 Km and zUAV = 1 Km correspond to ¢t = 1:4 ¹s which is typically encountered in outdoor propagation environments, where the Rake receiver is used to exploit multipath fading. This means that in order to reduce ISI, without requiring synchronization among nodes, the symbol rate Rs should be much less than 1=¢t, i.e., Rs ¿ 714 Kbit/s. For sensor network applications that do not require high data rate, this is a reasonable limit for Rs . In this case, the synchronization is guaranteed by the geometry of the network itself. Otherwise, it would require some form of synchronization among the nodes.
As far as the required bandwidth of the SS signal is concerned, it is important to note that in order to guarantee resolvable paths, the chip duration Tc should be less than most of the inter-arrival times, between the adjacent paths. Since nodes positions are random, the corresponding delays ¿i = di =c are random variables (RVs). Note that the statistical distribution of inter-arrival time is dependent on the sensor field geometry, the nodes density (i.e., nodes per unit area), and the UAV position. In general, we can state that the average inter-arrival time increases as the nodes density decreases. In Section V, we give a numerical example to illustrate the bandwidth required for the resolvable condition. D. Fusion Center Model Since all nodes transmit the same message toward the UAV, the transmission scheme can be represented conveniently as a single-input single-output (SISO) system where a single transmitting “virtual” source, transmits over a single “virtual” frequency-selective multipath channel to the fusion center, represented by a Rake receiver. The virtual frequency-selective fading channel can be represented by a channel impulse response (CIR) with N paths, and the corresponding power dispersion profile (PDP). For the spreading waveforms with ideal correlation properties, intersymbol interference (ISI) and self-interference are negligible, and thus the Rake receiver can be represented as a maximal ratio combiner (MRC). Such a representation is depicted in Fig. 3. In the figure, ni represent the noise terms at the output of each finger. III. PERFORMANCE LIMITS FOR UNCONSTRAINED INPUT SIGNALING The signal at the output of the Rake combiner at the sampling instant is Y=X¢
N X i=1
jhi j2 +
N X i=1
jhi j2 ni
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(7)
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and random positions of the nodes. The approach used to achieve this goal consists in the following three steps. 1) Compute the local ergodic mutual information (averaging over fading), ¯ p) = E fC(s, p, h)g [bits/s/Hz] C(s, h
Fig. 3. Compact representation of ELP transmission system. For simplicity, without loss of generality matched filter and spreading/despreading blocks are not shown. Ideal Rake is represented as an MRC.
where X is the transmitted signal and the second term represents the thermal noise at the combiner output with power N N X X ¾2 = jhi j2 Efjni j2 g = ¾n2 ¢ jhi j2 (8) i=1
i=1
¢
channel gains h =(h1 , h2 , : : : , hN ), the transmission scheme considered is equivalent to a SISO system affected by AWGN with power ¾2 , and the instantaneous mutual information, when channel state information (CSI) is available at the receiver, is (9)
where SNR(h) is the instantaneous SNR given by SNR(h) = ½ ¢
N X i=1
jhi j2
(10)
with ½ = EfjXj2 g=(N0 Rs ) = Es =N0 . Since the channel gains depend on the relative positions between the nodes and the UAV, i.e., h = h(s, p) with s the distance covered by the UAV from the beginning of the trajectory and p = (x1 , y1 , x2 , y2 , : : : , xN , yN ) the vector of nodes positions,6 the expression of the instantaneous mutual information can be rewritten as C(s, p, h) = log2 (1 + ½kh(s, p)k2 )
(11)
where k ¢ k2 denotes the norm squared of a given vector. Another interesting metric related to the capacity is the throughput defined as the total amount of bits per unit bandwidth that the sensors network can reliably transmit to the UAV in a single passage over the sensor field. In particular, our goal is to evaluate the average mutual information and throughput where averages are over random fluctuations of the channel 6 For
the sake of convenience, the position is denoted by s instead of the coordinates (xUAV , yUAV , zUAV ).
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for a fixed s and p. 2) For a uniform UAV speed v [m/s] over the trajectory, we can integrate the local ergodic mutual information over the pass in order to calculate the throughput per pass as [35] Z Z ¢
T (p) =
flying time
¯ ¢ t, p)dt = C(v
¯ p) ds C(s, v trajectory
[bits/Hz]
(13) i.e., the total amount of data transmitted per unit bandwidth.7 3) Compute the average throughput per pass T¯ = Ep fT (p)g [bits/Hz]
(14)
over random positions of nodes.
and ¾n2 = Efjni j2 g = N0 Rs is the noise power of each path before the MRC. For a given instantaneous
C(h) = log2 (1 + SNR(h)) [bits/s/Hz]
(12)
In general, the term kh(s, p)k2 that appears in (11) represents an RV for a fixed position of the UAV and nodes, and it can be viewed as a random process in time (or space) as the UAV moves along its trajectory, i.e., by varying s. Thus mutual information in (11) can also be viewed as a random process as was observed in [36]—[38]. Looking at the geometry of the scenario considered and the finiteness of the sensor field, we note that the instantaneous mutual information (11) is not a stationary process when the UAV moves along its trajectory. Despite this, it is reasonable to assume that the instantaneous mutual information is ergodic in a certain temporal (or spatial) interval around a given UAV position. Once the local ergodic mutual information is evaluated in the first step, we can then integrate the mutual information over the trajectory, i.e., by varying the position s, in order to obtain the throughput. In practice, we decompose the UAV trajectory into a number of segments in which the mutual information is assumed ergodic. Note that the throughput is an RV due to the random position of the nodes. We can also analyze the outage throughput, namely the probability that the throughput is below a certain threshold. It will be apparent that the average throughput, instead of its outage, is sufficient as the number of nodes becomes large (N > 10), i.e., the variance of the throughput becomes small, and thus its average becomes representative of the performance of the system. 7 In this paper we define the throughput according to [35], as volume of data transferred; other possible definitions are in terms of transfer rate.
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Similarly, it is interesting to evaluate the average mutual information at a given UAV position s averaged over the fading and nodes positions as ¯¯ ¯ p)g: C(s) = Ep fC(s,
(15)
We use (14) and (15) in Section V to investigate the maximum attainable mutual information.
The capacity limits described in Section III are achieved with Gaussian signaling, i.e., with symbols X having a Gaussian distribution. Following a similar method, here we evaluate the performance limits of the network under the constraint of binary signaling. Complementary to the results in the previous section, the analysis with binary modulation is useful to evaluate practical performance limits when energy consumption and complexity of nodes are major issues. In particular, restricting possible symbols to p the p binary signaling X 2 f¡ PT , + PT g, and assuming hard decision on the output Y, the transmission system can be modeled as a binary symmetric channel (BSC) with crossover probability Pe . We now evaluate the throughput per pass and the average bit error probability (BEP) for this transmission scheme. Let us start by defining the instantaneous SNR for the ith Rake finger as PT jhi j2 E = s jhi j2 : N0 Rs N0
Starting from the expressions (16) and (17), the BEP conditioned on the channels amplitudes or ¢
equivalently the SNR in each path ° =(°1 , : : : , °N ) can be rewritten as
0v u N 1 u X °i A : Pe (°) = Q @t2
(19)
i=1
IV. PERFORMANCE LIMITS WITH BINARY SIGNALING
°i =
A. Bit Error Probability Analysis
(16)
The BEP conditioned on the channels amplitudes on each finger can be written as Ãs ! Es 2 Pe (s, p, h) = Q 2 kh(s, p)k (17) N0 where Q(¢) is the Gaussian Q-function defined in [39]. Considering that Pe (s, p, h) is the crossover probability of the equivalent BSC, the instantaneous mutual information can be written as CBSC (s, p, h) = 1 + Pe log2 (Pe ) + (1 ¡ Pe ) log2 (1 ¡ Pe ) [bits/s/Hz]: (18) Using (18) in steps 1—3 of Section III, the average throughput of the network can be obtained as follows: ¯ first evaluating the mutual information C BSC (s, p) averaged over fading as in (12), then integrating it over the trajectory TBSC (p) as in (13), and finally obtaining the average throughput over nodes positions T¯BSC as in (14). Moreover, the average mutual ¯¯ information C (s) along the trajectory can be BSC
evaluated by further averaging over nodes positions as in (15).
Then, the BEP averaged over the Rice fading, can be obtained by averaging Pe (°) over the distribution of the °i s with probability distribution function (pdf) μ ¶ μ r ¶ f°i (°) =
K +1 ° exp ¡K ¡ (1 + K) °¯ i °¯ i
I0 2
K(1 + K)
° °¯ i
°¸0
(20)
,
where the term °¯ i is the average SNR per path (or finger) 1 E °¯ i = Ef°i g = s : (21) N0 PL(di ) Unfortunately, this cannot be performed in closed form due to the difficulties in evaluating the integrals involved. In order to obtain a useful closed-form formula, we compute the average error probability P¯e (s, p) = E° fPe (°)g by introducing the approximation proposed in [40] ³ ³ ´ ´ 1 Q(x) » exp ¡ 12 x2 + 14 exp ¡ 23 x2 (22) = 12 that avoids problems with the averaging of the error function over Rice fading. Therefore, the average BEP can be well approximated as ) (N Y 1 exp(¡°i ) P¯e (s, p) » E = 12 ° i=1 ) (N Y 1 + E° exp(¡4°i =3) : (23) 4 i=1
For independent Rice distributed fading in each path, the average BEP becomes μ ¶ N 1 Y 1+K °¯ i K P¯e (s, p) » exp ¡ = 12 1 + °¯ i + K 1 + °¯ i + K i=1
+
μ ¶ N 1 Y 3(1 + K) 4°¯ i K exp ¡ : 4 3 + 4°¯ i + 3K 3 + 4°¯ i + 3K i=1
(24) This formula gives the BEP expression as a function of the average SNRs (21), which in turn depends on the distances (2) between the nodes and the UAV. Similarly to (15), we can obtain average performance over nodes positions by further averaging (24) as ¯ P¯ (s) = E fP¯ (s, p)g: (25) e
p
e
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Fig. 4. Sensors field with random positions of nodes (+) and UAV trajectory (dashed line).
In the next section we illustrate the results of several simulations for the Rake-based cooperative scheme proposed, with a number of fingers equal to the number of nodes N in the network. V. NUMERICAL RESULTS We consider a scenario that consists of a square area with side L = 1 Km, N = 100 uniformly distributed nodes, and a UAV that flies with speed v = 100 Km/h for a trajectory with length S = 3 Km at a constant altitude zUAV = 1 Km over the area. Fig. 4 shows an example of the sensors field and the UAV trajectory. The carrier frequency of the transmission is f0 = 2:4 GHz. The free space path-loss model in (1) and Ricean fading with K = 10 dB are assumed. The antenna gains are GT = 0 dB for the nodes and GR = 6 dB for the receiver. The one-sided power spectral density of the AWGN at the fusion center is N0 = KB Tsys , where KB = 1:38 ¢ 10¡23 J/K is the Boltzmann constant, and Tsys = T0 F is the noise temperature with T0 = 290 K and a receiver noise figure F = 5 dB. Supposing that all the nodes transmit with the same energy per symbol Es , the total energy per symbol spent by the WSN is Estot = N ¢ Es . Unless otherwise stated, we assume Es = 10 pJ and a Rake receiver with a number of fingers equal to the number of nodes N. As explained, the mutual information expression in (12) and the average BEP formula in (24) are conditioned on the PDP, or more explicitly on the 2616
power of each path, (3), that depends on nodes positions, the scenario geometry, etc. This profile can be evaluated numerically for a given sensor field, UAV altitude and trajectory, the number and positions of the nodes, and the path-loss model adopted. Figs. 5 and 6 show two normalized PDPs for two different UAV positions. In these figures the normalization is carried out with respect to the first path indexed by i = 1, which has the maximum power and minimum delay, i.e., PDP is given by ®i2 = −i =−1 as a function of the excess delays ¿i ¡ ¿1 with i = 1, : : : , N. Comparison between these figures shows that the second profile has powers roughly equal in amplitude, while in the first one, differences are much more pronounced. The reason behind these differences is related to the position of the UAV, and in fact Fig. 5 corresponds to the UAV that is far from the sensors field while Fig. 6 corresponds to the UAV above the network, xUAV = yUAV = 0. To evaluate the bandwidth required to resolve adjacent paths, Fig. 7 shows the cumulative distribution function (CDF) of the inter-arrival time between the received replicas for the two UAV positions considered in Figs. 5 and 6, and for a different number of nodes. For example, considering a scenario with N = 30 nodes with the UAV located at the beginning of the trajectory, we observe that 20% of paths have an inter-arrival time lower than 20 ns, which corresponds to a bandwidth in the order of
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Fig. 5. Normalized PDP of channel when UAV is in xUAV = ¡1500 m, yUAV = 0 m (outside sensors field).
Fig. 6. Normalized PDP of channel when UAV is in xUAV = 0 m, yUAV = 0 m (above sensors field).
50 MHz. On the other hand, when the UAV is above the network and N = 100, the corresponding minimum resolvable delay must be around 2 ns, that correspond to a bandwidth of 500 MHz. In this case, the UWB
impulse radio technology is mandatory to support the cooperative communication proposed. Figs. 7, 5, and 6, can also be useful to derive the maximum node spatial density that guarantees resolvability for a
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Fig. 7. CDF of inter-arrival time between adjacent paths in four different scenarios.
¯¯ as function of UAV position. Fig. 8. Average mutual information profile C(s)
given percentage of the paths when the transmission bandwidth is known. A. Mutual Information and Throughput results Following the approach developed in Section III and IV, we plot the mutual information along the UAV trajectory for both signaling schemes considered. ¯¯ and In particular, as shown in Figs. 8 and 9, C(s) ¯¯ C BSC (s) are plotted as a function of UAV position s = xUAV for a different number of nodes, fixing 2618
the energy per transmitted symbol Es . Due to the symmetry of the scenario, the curves presented are symmetric. Moreover, as expected, with binary signaling (Fig. 9) the mutual information saturates to 1 bit/s/Hz when N, or equivalently the SNR, becomes high. The average throughput as a function of the energy per transmitted symbol Es is plotted in Fig. 10 for a different number of nodes. As shown in Fig. 10, the amount of information bits per unit bandwidth for a given number of nodes, is directly proportional
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¯¯ Fig. 9. Average mutual information profile C BSC (s) as function of UAV position.
Fig. 10. Average throughput per pass T¯ as function of transmitted symbol energy per node Es , for different number of cooperative nodes in network.
to the transmit energy Es , and approaches a linear behavior for large energy values. This linear behavior is justified by the fact that, as shown in (11), the mutual information has a logarithmic dependence with Es and the energy plotted in Fig. 10 is in logarithmic scale. Note that for a given Es , equivalently the node (or network) lifetime, there is a significant improvement in throughput obtained by increasing the number of nodes. Alternatively, it is possible to keep constant the average throughput and reduce the transmit energy, by simply increasing the number of
nodes. For instance, a throughput of 440 bits/Hz can be obtained by a single node with energy Es = 1 nJ or by 10 nodes with energy Es = 83 pJ, thus increasing the network lifetime considerably. This throughput, with a symbol-rate equal to Rs = 1 Msymbols/s, means that it is possible to collect data volumes up to 55 Mbytes/pass. Obviously this result is derived under an information-theoretic framework, thus it should be considered as an upper bound of practical attainable performance. Adopting a binary signaling the average throughput T¯BSC evaluated using expression (14)
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Fig. 11. Average throughput per pass T¯BSC as function of transmitted symbol energy per node Es , for different number of cooperative nodes in network.
Fig. 12. Average BEP, equation (25), as function of UAV position for different number of cooperative nodes. Different values of Es correspond to fixed average throughput T¯BSC = 100 bits/Hz.
is depicted in Fig. 11. As we can see, the amount of information bits per unit bandwidth is directly proportional to the energy Es and N, but saturates accordingly to the mutual information behavior. B. Bit Error Probability Results In Fig. 12, the average BEP (25) as a function of UAV position, for a different number of nodes in the network, is reported. In the figure, different values of Es correspond to the same average throughput 2620
T¯BSC = 100. The figure confirms that the proposed cooperative approach offers good results, both in terms of communication reliability and energy efficiency. For example, we can guarantee the same average throughput with a single node and a transmitted energy Es = 231 pJ, or with N = 5 nodes and Es = 35:7 pJ. Looking at the total energy spent by the network Estot , we can note that increasing the number of nodes decreases the total energy owing to the diversity provided by the transmission scheme.
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Fig. 13. Transmitted symbol energy per node Es , required to reach average throughput T¯BSC = 100 bits/Hz, as function of number of cooperative nodes N.
Note that the diversity gain saturates as the number of nodes goes to infinity. In fact, as confirmed in Fig. 12, while increasing N from 1 to 50 reduces the total energy spent by the network Estot by 26.8%, with a further increase of N from 50 to 100, Estot does not reduce anymore. Keeping the throughput fixed, in Fig. 13 we report the node energy as a function of the number of nodes. As we can see, the required symbol energy decreases as the number of cooperative nodes increases. Finally, to overcome the drawback of high receiver complexity, we consider a PRake with a limited number of fingers Nsel < N which is able to fuse only the first (or strongest on average) Nsel paths. The adoption of a PRake scheme could also be useful to reduce the energy consumption of the network in those scenarios where only a limited number of nodes transmits its data in a passage. In other words, a possible way to increase the network lifetime at the expense of reducing the throughput of the network, could be to select Nsel nodes among N to transmit in a given passage. By selecting different subsets of Nsel nodes in each passage, the energy consumption will be distributed among all N nodes, thus reducing the energy consumption by a factor N=Nsel . Fig. 14 shows the result obtained with this receiver considering a WSN with N = 100 nodes and a different number of fingers. This figure quantifies the trade-off between complexity and energy consumption. As previously explained, the adoption of a PRake could be useful to reduce the energy consumption of the network when combined with a scenario where for each UAV
passage only a selected number of nodes transmit its data. Fig. 15 shows the average throughput T¯BSC as a function of the number of selected nodes Nsel that transmit and the average energy consumption for the transmission. This figure shows that we can achieve an energy saving (as a percentage of Es ) selecting a low number of transmit nodes at the expense of a reduced throughput. C.
Scaling
For the sake of simplicity, the previous results are derived with parameters such as the UAV altitude and the area of the network that are reasonable for practical applications in the scenario considered. These numerical results can be easily extended by means of proper scaling factors to other similar scenarios. For instance, if we change the noise power spectral density by a factor ¨ , i.e., N00 = N0 ¢ ¨ , to obtain the same network performance, we need to have an energy scaled by the same factor Es0 = Es ¢ ¨ . Similarly, for a given geometry of the scenario, i.e., the ratios zUAV =L and S=L, changing all the distances by a factor ¨ we have to scale the energy Es0 = Es ¢ ¨ 2 to maintain the same performance. As far as the UAV speed is concerned, replacing the speed with v ¢ ¨ the corresponding throughput will be scaled by a factor 1=¨ . VI. CONCLUSIONS In this work, we have proposed a new approach for cooperative transmission for reachback communications in WSN. In particular, we have
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Fig. 14. Average BEP, (25), as function of UAV position with N = 100 nodes, Es = 1:69 pJ, and PRake with Nsel fingers.
Fig. 15. Average throughput per pass T¯BSC as function of number of selected nodes Nsel and average energy consumption (as percentage of transmitted energy Es = 1:69 pJ) required for transmission.
considered a scenario with sensor nodes, randomly scattered over a given area, transmitting a common information to the UAV. For such a scenario, we have introduced a cooperative communication concept to guarantee energy efficiency and communications reliability. The cooperation has been obtained by means of an SS technique, combined with a Rake receiver that acts as a fusion center, to collect multiple repetitions of the same information transmitted by the nodes. We have validated the proposed idea in terms of a trade-off between performance and energy 2622
consumption. In particular, we have considered two figures of merit related to performance: the information-theoretic throughput and the BEP. In both cases, cooperation provides significant advantages in terms of performance and energy efficiency as the number of nodes increases. ACKNOWLEDGMENTS The authors would like to thank Dr. L. Reggie Brothers for helpful discussions, and Dr. Tony Q. S. Quek for comments and careful reading of the manuscript.
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REFERENCES [1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
Akyildiz, I. F., et al. A survey on sensor networks. IEEE Communications Magazine, 40, 8 (Aug. 2002), 102—114. Tubaishatand, M. and Madria, S. Sensor networks: An overview. IEEE Potentials, 22, 2 (Apr./May 2003), 20—23. Chong, C. Y. and Kumar, S. P. Sensor networks: Evolution, opportunities, and challenges. Proceedings of the IEEE, 91, 8 (Aug. 2003), 1247—1256. Verdone, R., et al. Process estimation through a self-organizing collaborative wireless sensor network. In Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM 2004), vol. 5, Dallas, TX, Nov. 2004, 3193—3199. Buratti, C., Giorgetti, A., and Verdone, R. Simulation of an energy efficient carrier sensing multiple access protocol for clustered wireless sensor networks. In Proceedings of the IEEE International Workshop on Wireless Ad-hoc Networks (IWWAN2004), Oulu, Finland, June 2004, 325—329. Buratti, C., Giorgetti, A., and Verdone, R. Cross layer design of an energy efficient cluster formation algorithm with carrier sensing multiple access for wireless sensor networks. EURASIP Journal on Wireless Communications and Networking, 2005, 5 (Dec. 2005), 672—685. Quek, T. Q. S., Win, M. Z., and Chiani, M. Distributed diversity in ultrawide bandwidth wireless sensor networks. In Proceedings of the IEEE Vehicular Technology Conference (VTC2005-Spring), vol. 2, Stockholm, Sweden, May 2005, 1355—1359. Tozer, T. C. and Grace, D. High-altitude platforms for wireless communications. IEE Electronics and Communications Engineering Journal, 13, 3 (June 2001), 127—137. De Fina, S., Ruggieri, M., and Bosisio, A. V. Exploitation of the W-band for high capacity satellite communications. IEEE Transactions on Aerospace and Electronic Systems, 39, 1 (Jan. 2003), 82—93. Servetto, S. D. Distributed signal processing algorithms for the sensor broadcast problem. In Proceedings of the 37th Annual Conference on Information Sciences and Systems (CISS), Baltimore, MD, Mar. 2003. Barros, J. and Servetto, S. D. Network information flow with correlated sources. IEEE Transactions on Information Theory, 52, 1 (Jan. 2006), 155—170. Yang, Z. and Tong, L. Cooperative sensor networks with misinformed nodes. IEEE Transactions on Information Theory, 51, 12 (Dec. 2005), 4118—4133. Scaglione, A. and Hong, Y-W. Opportunistic large array: Cooperative transmission in wireless multihop ad hoc networks to reach far distances. IEEE Transactions on Signal Processing, 51, 8 (Aug. 2003), 2082—2092. Quek, T. Q. S. and Win, M. Z. Analysis of UWB transmitted-reference communication systems in dense multipath channels. IEEE Journal on Selected Areas in Communications, 23, 9 (Sept. 2005), 1863—1874.
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
Quek, T. Q. S., Dardari, D., and Win, M. Z. Energy efficiency of dense wireless sensor networks: To cooperate or not to cooperate. IEEE Journal on Selected Areas in Communications (Special Issue on Cooperative Communications and Networking), 25, 2 (Feb. 2007). Laneman, J. N. and Wornell, G. W. Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks. IEEE Transactions on Information Theory, 49, 10 (Oct. 2003), 2415—2425. Gamal, H. E. and Aktas, D. Distributed space-time filtering for cooperative wireless networks. In Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM 2003), vol. 4, San Francisco, CA, Dec. 2003, 1826—1830. Conti, A., Tralli, V., and Chiani, M. Pragmatic space-time codes for cooperative relaying in block fading channels. Eurasip Journal on Advances in Signal Processing (Special Issue on Wireless Cooperative Networks), 2008 (July 2008), 1—12. Sendonaris, A., Erkip, E., and Aazhang, B. User cooperation diversity–Part I: System description. IEEE Transactions on Communications, 51, 11 (Nov. 2003), 1927—1938. Sendonaris, A., Erkip, E., and Aazhang, B. User cooperation diversity–Part II: Implementation aspects and performance analysis. IEEE Transactions on Communications, 51, 11 (Nov. 2003) 1939—1948. Bletsas, A., Shin, H., and Win, M. Z. Outage-optimal cooperative communications with regenerative relays. In Proceedings of the 40th Conference on Information Sciences and Systems (CISS 2006), Princeton, NJ, Mar. 2006, invited paper. Bletsas, A., Shin, H., and Win, M. Z. Cooperative communications with outage-optimal opportunistic relaying. IEEE Transactions on Wireless Communications, 6, 9 (Sept. 2007), 3450—3460. Bletsas, A., Shin, H., and Win, M. Z. Outage optimality of opportunistic amplify-and-forward relaying. IEEE Communications Letters, 11, 3 (Mar. 2007), 261—263. Bello, P. A. Aeronautical channel characterization. IEEE Transactions on Communications, COM-21, 5 (May 1973), 548—563. Haas, E. Aeronautical channel modeling. IEEE Transactions on Vehicular Technology, 51, 2 (Mar. 2002), 254—264. Cuevas-Ruíz, J. L. and Delgado-Penín, J. A. Channel modeling and simulation in HAPS systems. In Proceedings of the Fifth European Wireless Conference, Barcelona, Spain, Feb. 2004. Stuber, G. L. Principles of Mobile Communication (2nd ed.). Norwell, MA: Kluwer Academic Publishers, 2001. Pursley, M. The role of spread spectrum in packet radio networks. Proceedings of the IEEE, 75, 1 (Jan. 1987), 116—134. Win, M. Z. and Scholtz, R. Impulse radio: How it works. IEEE Communications Letters, 2, 2 (Feb. 1998), 36—38.
GIORGETTI ET AL.: THROUGHPUT PER PASS FOR DATA AGGREGATION FROM A WIRELESS SENSOR NETWORK
2623
[30]
[31]
[32]
[33]
[34]
[35]
Win, M. Z. and Scholtz, R. Ultra-wide bandwidth time-hopping spread-spectrum impulse radio for wireless multiple-access communications. IEEE Transactions on Communications, 48, 4 (Apr. 2000), 679—691. Foerster, J. R. The performance of a direct-sequence spread ultra wideband system in the presence of multipath, narrowband interference, and multiuser interference. In Proceedings of the IEEE Conference on Ultra Wideband Systems and Technologies, Baltimore MD, May 2002, 87—92. Winters, J. H. On the capacity of radio communication systems with diversity in Rayleigh fading environment. IEEE Journal on Selected Areas in Communications, SAC-5, 5 (June 1987), 871—878. Foschini, G. J. Layered space-time architecture for wireless communication a fading environment when using multiple antennas. Bell Labs Technical Journal, 1, 2 (Autumn 1996), 41—59. Win, M. Z., Chrisikos, G., and Sollenberger, N. R. Performance of Rake reception in dense multipath channels: Implications of spreading bandwidth and selection diversity order. IEEE Journal on Selected Areas in Communications, 18, 8 (Aug. 2000), 1516—1525. Ryan, W. E., Han, L., and Quintana, P. A. Design of a low-orbit-to-geostationary satellite link for maximal throughput. IEEE Transactions on Communications, 45, 8 (Aug. 1997), 988—996.
[36]
[37]
[38]
[39]
[40]
Ozarow, L. H., Shamai, S., and Wyner, A. D. Information theoretic considerations for cellular mobile radio. IEEE Transactions on Vehicular Technology, 43, 2 (May 1994), 359—378. Giorgetti, A., et al. MIMO capacity, level crossing rates and fades: The impact of spatial/temporal channel correlation. International Journal of Communications and Networks (Special Issue on Coding and Signal Processing for MIMO Systems), 5, 2 (June 2003), 104—115. Wang, S. and Abdi, A. On the second-order statistics of the instantaneous mutual information of time-varying fading channels. In Proceedings of the IEEE International Workshop on Signal Processing Advances for Wireless Communications (SPAWC’05), New York, June 2005, 405—409. Proakis, J. G. Digital Communications (4th ed.). New York: McGraw-Hill, 2001. Chiani, M., Dardari, D., and Simon, M. K. New exponential bounds and approximation for the computation of error probability in fading channels. IEEE Transactions on Wireless Communications, 2, 4 (July 2003), 840—845.
Andrea Giorgetti (S’98–M’04) received the Dr. Ing. degree (magna cum laude) in Electronic Engineering and the Ph.D. degree in electronic engineering and computer science, both from the University of Bologna, Bologna, Italy, in 1999 and 2003, respectively. In 2003, he was with the Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni (IEIIT-BO), research unit at Bologna of the National Research Council (CNR), Bologna, Italy. In 2005 he was a researcher with the National Research Council, and since 2006 he is an assistant professor at the II Engineering Faculty, University of Bologna, where he joined the Department of Electronics, Computer Sciences and Systems (DEIS), and the Wireless Communications Laboratory (WiLAB). During the spring of 2006 he was with the Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology (MIT), Cambridge, MA. Since then he is a Research Affiliate of LIDS, MIT. His research interests include ultra-wide bandwidth communications systems, active and passive localization, wireless sensor networks, and multiple antenna systems. Dr. Giorgetti was TPC cochair of the Wireless Networking Symposium at the IEEE International Conference on Communications (ICC 2008), Beijing, China, May 2008, and TPC cochair of the MAC track of the IEEE Wireless Communication & Networking Conference (WCNC 2009), Budapest, Hungary, April 2009, both as a representative of the IEEE Radio Communications Committee (RCC). 2624
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Matteo Lucchi received the Dr. Ing. degree (magna cum laude) in information and communication technology engineering and the Ph.D. degree in electronic engineering and computer science, both from the University of Bologna, Italy, in 2004 and 2008, respectively. He was a system engineer at Senet s.r.l. (2006—2008) and now is at Winet s.r.l. developing MAC, routing and synchronization protocols for wireless sensor networks. His research interests include wireless sensor networks, distributed detection and cooperative communication.
Marco Chiani (M’94–SM’02–F’11) was born in Rimini, Italy, in April 1964. He received the Dr. Ing. degree (magna cum laude) in electronic engineering and the Ph.D. degree in electronic and computer science from the University of Bologna in 1989 and 1993, respectively. He is a full professor of telecommunications and the current director of the Industrial Research Center on ICT, University of Bologna, Italy. During the summer of 2001 he was a visiting scientist at AT&T Research Laboratories in Middletown, NJ. He is a frequent visitor at the Massachusetts Institute of Technology (MIT), where he presently holds a Research Affiliate appointment. He is leading the research unit of University of Bologna on cognitive radio and UWB (European project EUWB), on Joint Source and Channel Coding for wireless video (European projects Phoenix-FP6 and Optimix-FP7), and is a consultant to the European Space Agency (ESA-ESOC) for the design and evaluation of error correcting codes based on LDPCC for space CCSDS applications. Dr. Chiani’s research interests include wireless communication systems, MIMO systems, wireless multimedia, low density parity check codes (LDPCC) and UWB. In January 2006 Dr. Chiani received the ICNEWS award “For Fundamental Contributions to the Theory and Practice of Wireless Communications.” He was the recipient of the 2008 IEEE ComSoc Radio Communications Committee Outstanding Service Award. He has chaired, organized sessions, and served on the Technical Program Committees at several IEEE International Conferences. He is the past chair (2002—2004) of the Radio Communications Committee of the IEEE Communication Society and past Editor of Wireless Communication (2000—2007) for IEEE Transactions on Communications. GIORGETTI ET AL.: THROUGHPUT PER PASS FOR DATA AGGREGATION FROM A WIRELESS SENSOR NETWORK
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Moe Z. Win (S’85–M’87–SM’97–F’04) received both the Ph.D. in electrical engineering and M.S. in applied mathematics as a Presidential Fellow at the University of Southern California (USC) in 1998. He received an M.S. in electrical engineering from USC in 1989, and a B.S. (magna cum laude) in electrical engineering from Texas A&M University in 1987. He is an associate professor at the Massachusetts Institute of Technology (MIT). Prior to joining MIT, he was at AT&T Research Laboratories for five years and at the Jet Propulsion Laboratory for seven years. His research encompasses developing fundamental theories, designing algorithms, and conducting experimentation for a broad range of real-world problems. His current research topics include network localization and navigation, network interference, intrinsic wireless secrecy, ultra-wide bandwidth systems, adaptive diversity techniques, optical transmission systems, and space communications systems. He is an IEEE Distinguished Lecturer and elected Fellow of the IEEE, cited for “contributions to wideband wireless transmission.” He was honored with two IEEE Technical Field Awards: the IEEE kiyo Tomiyasu Award (2011) for “fundamental contributions to high-speed reliable communication over optical and wireless channels” and the IEEE Eric E. Sumner Award (2006, jointly with R. A. Scholtz), for “pioneering contributions to ultra-wide band communications science and technology.” Together with students and colleagues, his papers have received several awards including the IEEE Communications Society’s Leonard G. Abraham Prize Paper Award (2011), the IEEE Aerospace and Electronic Systems Society’s M. Barry Carlton Award (2008), the IEEE Society’s Guglielmo Marconi Best Paper Award (2008) and the IEEE Antennas and Propagation Society’s Sergei A. Schelkunoff Transactions Prize Paper Award (2003). Highlights of his worldwide educational and research collaborations are the Copernicus Fellowship (2011), the Royal Academy of Engineering Distinguished Visiting Fellowship (2009), and the Fulbright Foundation Senior Scholar Lecturing and Research Fellowship (2004). Other recognitions include the Outstanding Service Award of the IEEE ComSoc Radio Communications Committee (2010), the Laurea Honoris Causa from the University of Ferrara, Italy (2008), the Technical Recognition Award of the IEEE ComSoc Radio Communications Committee (2008), Wireless Educator of the Year Award (2007), the U.S. Presidential Early Career Award for Scientists and Engineers (2004), the AIAA Young Aerospace Engineer of the Year (2004), and the Office of Naval Research Young Investigator Award (2003). Professor Win is an elected Member-at-Large on the IEEE Communications Society Board of Governors (2011—2013). He was the chair (2004—2006) and secretary (2002—2004) for the Radio Communications Committee of the IEEE Communications Society. He served as the technical program chair for the IEEE Wireless Communications and Networking Conference in 2009, the IEEE Conference on Ultra Wideband in 2006, the IEEE Communication Theory Symposia of ICC (2004) and Globecom (2000), and the IEEE Conference on Ultra Wideband Systems and Technologies in (2002); technical program vice-chair for the IEEE International Conference on Communications (2002); and the tutorial chair for ICC (2009) and the IEEE Semiannual International Vehicular Technology Conference (Fall 2001). He is currently an editor for IEEE Transactions on Wireless Communications. He served as area editor for Modulation and Signal Design (2003—2006), editor for Wideband Wireless and Diversity (2003—2006), and editor for Equalization and Diversity (1998—2003), all for the IEEE Transactions on Communications. He was guest-editor for the Proceedings of the IEEE (Special Issue on UWB Technology & Emerging Applications) in 2009 and IEEE Journal on Selected Areas in Communications (Special Issue on Ultra-Wideband Radio in Multiaccess Wireless Communications) in 2002. 2626
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