Channel Sharing for Underwater Acoustic Networks. Borja M. Peleato-Iñarrea Advisor: Milica Stojanovic

Channel Sharing for Underwater Acoustic Networks. Borja M. Peleato-Iñarrea Advisor: Milica Stojanovic January 15, 2007

Abstract This thesis proposes two channel sharing protocols for cellular and ad-hoc underwater networks. The protocols exploit the long delays and absorption in the underwater channel to increase the throughput over the one achieved by existing radio-environment protocols.

Acknowledgements There are many people whom I would like to thank in this, my first, opportunity of doing so. However, if I named them all, the acknowledgements would have to be structured as a chapter. First of all, I want to thank Milica not only for her advice concerning this thesis, but also for helping me start my future career and for her positive attitude, which has encouraged me in my work. Ethem s help in using Matlab and Marçal s source files have also given me a way out whenever I got stuck. This thesis would have taken me much longer without them, so thanks to both for making my work easier. If I have been able to get up to here, it has been because of the CFIS staff. With hard work and dedication they have created a great program which encourages the love of knowledge. The support that I found there gave me the confidence to come to MIT. I also met some of my best friends there: the spammers (Bird, Nai, Pino, Jabot, Marcel, Ricky, Jota and Txema), the chapapotes (Rouche and Pau), Maxim, and the rest of the ETShiTB (Uri and LoMolina). Finally, a very special thanks to my family for their support, to my ptv friends (Josemi, Javi, Luis, Gon, Baghee, Charlie, Nacho, Miga, Jokin, Josu, Jorge...) for being always with me and to Gemma and Txoko for their effusive wellcome! 1

Contents 1 Introduction 5 2 Cellular network 7 2.1 Introduction................................ 7 2.2 Scenario.................................. 7 2.3 Protocol Description........................... 9 2.3.1 Main idea............................. 9 2.3.2 The protocol........................... 9 2.4 Case study................................. 13 2.4.1 Results............................... 15 2.4.2 Choosing the parameters..................... 17 2.4.3 Parameter sensitivity....................... 20 2.4.4 Error sensitivity.......................... 21 2.5 Small cells................................. 22 2.6 Further work............................... 23 2.7 Conclusion................................. 25 3 Ad-hoc network 26 3.1 Introduction................................ 26 3.2 Protocol description........................... 27 3.2.1 Basic protocol........................... 27 3.2.2 Deferred transmissions...................... 30 3.2.3 Back-offs.............................. 30 3.3 Tolerance to interference......................... 32 3.4 Adjusting t min for a given statistical deployment............ 34 3.5 Fairness.................................. 36 3.6 Simulation Results Without Acknowledgements............ 36 3.6.1 Some special cases........................ 37 3.6.2 Study of the parameters involved................ 40 3.7 Acknowledgements............................ 44 3.8 Simulation Results with ACKs...................... 45 3.8.1 Differences with/without ACK.................. 47 3.8.2 Average example......................... 48 3.8.3 Special case t min = 2T...................... 50 2

3.8.4 Optimal t min and T W min..................... 52 3.9 Conclusion and further work....................... 53 4 Conclusion 55 A Waiting times in the Ad-hoc protocol 58 B Protocol implementation 68 3

List of Figures 2.1 Channel reuse pattern for N=3,4,7,9................... 8 2.2 Main idea of the cellular protocol..................... 10 2.3 Illustration of the first schedule..................... 12 2.4 Illustration of the downlink schedule.................. 14 2.5 (3,3)-hybrid downlink interference level................. 17 2.6 (3,3)-hybrid uplink interference level.................. 18 2.7 (3,3)-hybrid bidirectional interference level............... 19 2.8 (4,1)-hybrid interference level for different radii and frequencies... 20 2.9 (3,4)-hybrid error sensitivity....................... 21 2.10 (7,1)-hybrid error sensitivity....................... 22 2.11 (7,13)-hybrid with small cells...................... 23 2.12 (7,9)-hybrid without division of the interval.............. 24 3.1 Ad-hoc protocol illustration....................... 29 3.2 State diagram without acknowledgements................ 32 3.3 D for SIR=10dB in terms of the distance between the nodes.... 33 3.4 Different hand-shake lengths....................... 34 3.5 Influence of t min on the hand-shake duration without ACKs..... 35 3.6 Throughput and power waste when t min = 2T without ACKs..... 38 3.7 Throughput when t min = T D/c = T 2 without ACKs......... 39 3.8 Throughput when t min = T 2 D/c = 0 without ACKs......... 40 3.9 Optimal t min without ACKs....................... 41 3.10 Throughput in terms of t min....................... 41 3.11 Throughput in terms of the tolerance to interference ( D)...... 42 3.12 Hops and end-to-end packets in terms of the transmission range... 43 3.13 Power waste and delay in terms of the transmission range....... 43 3.14 State diagram with acknowledgements................. 46 3.15 Hand-shake duration with ACKs.................... 47 3.16 Performance metrics in an example with ACKs............ 49 3.17 Performance metrics for t min = 2T with ACKs............. 51 3.18 Optimal t min and T W min with ACKs.................. 52 A.1 Collision between two data packets................... 59 A.2 Collision between two data packets II.................. 61 A.3 Proof environment............................. 63 4

Chapter 1 Introduction Wireless Sensor Networks (WSN) offer fast, inexpensive, and easy deployment for a wide range of terrestrial applications. Consequently, the way of spreading them over different kinds of environments has lately become an active field of study and many protocols have been proposed to overcome the different problems that have arisen: multipath and hidden terminals in urban areas, long delays in satellites and interference in dense networks. Recently, WSN have sparked interest for underwater applications. However, there are many aspects of underwater wireless communications, as well as system deployment considerations, that make these systems very different from their terrestrial counterparts. For one, underwater sensor networks are neither small, nor cheap. Hence, they cannot be treated as disposable. In addition, transmission distances and energy consumption are much greater than those typically found in radio systems on land. Finally, electromagnetic waves do not propagate in water and thus acoustic signals have to be used. Acoustic propagation imposes fundamental challenges on the communication system design. In this thesis we focus on the design of efficient Medium Access Protocols (MAC) for future underwater WSNs. In particular, the underwater channel is characterized by low band-width and long propagation delay. Sound propagates in water at an approximate speed of c = 1500 m and is absorbed according to Thorp s equation: sec A( db km ) = 0.11 f 2 1 + f 2 + 44 f 2 4100 + f 2 +.000275 f 2 +.003 (1.1) where f represents the signal frequency. For distances longer than a few tens of meters, the useful bandwidth narrows to the order of khz and the propagation delays become too long to be neglected (as it is the case in radio environments). Sensors usually need to be battery powered and cannot be replaced easily; therefore, energy is a scarce resource that has to be saved. The main source of energy waste for an acoustic modem is, by far, transmitting. In most cases there is a very high noise level, which together with the high attenuation of the signal with distance, makes it necessary to use high transmission power. Consequently, it is very important to avoid packet collisions at the receiver when sending long data packets. 5

The performance metric which suffers most from the limitations described above is the efficiency, defined as efficiency = (info bits sent) t bit total time (transmission bandwith) (bits per Hz) channel bandwidth Additionally, the existing underwater modems are half-duplex (they cannot transmit and receive at the same time) so the time efficiency for bidirectional communications is always under 1 2. However, the underwater channel also has two particularities that can be used as advantages over half-duplex radio channels: long delays and high absorption. When the delays are long enough, two otherwise colliding packets can cross in the middle allowing simultaneous transmissions within reach of one another. Theoretically, this allows all the N nodes in a fully connected network to achieve an efficiency of 1 2, while in a radio environment the upper bound would be 1 N. The second advantage comes from the high attenuation of the signal due to absorption: relatively small distance increases can cause great reductions in the level of interference. Consequently, the required distance from the receiver to the interfering node in order to achieve a certain Signal to Interference Ratio (SIR) is much smaller. In this thesis we explore some ways of increasing the efficiency in both centralized and ad-hoc networks by exploiting the benefits of the long propagation delays and attenuation in the underwater channel. The thesis is organized as follows: In Chapter 2 we develop a hybrid time-frequency channel assignment scheme for cellular networks that offers better efficiency and higher SIR than plain FDMA. In Chapter 3 we propose a protocol for ad-hoc networks named DACAP based on variable hand-shake lengths to maximize throughput. Finally, chapter 4 summarizes the thesis and the appendix provides the proofs and implementation directions for the DACAP protocol. 6

Chapter 2 Cellular network 2.1 Introduction When we try to extend the work done on radio cellular networks to the underwater environment we come up with differences that cause losses in efficiency. The first of these is the long and variable propagation delay that makes the feedback between base station and nodes difficult and inefficient. Satellite networks have this same problem, and it is solved very efficiently by synchronizing all earth stations to the satellite s time base in a TDMA scheme. Underwater networks also have the problem of the interference between adjacent cells. In satellite networks this is solved with directional antennas and long distances; however, we cannot use these underwater. WLANs have a similar problem with interference and it is solved by clustering, with the consequent efficiency loss. Each cell in a cluster is assigned a different channel (band or code), outside of which the users cannot transmit. The number of cells per cluster is determined by the Signal to Interference Ratio (SIR) requirements so as to ensure a minimum distance to the nearest co-channel cell. Here we propose a hybrid channel sharing scheme which avoids the strongest components of the interference by clustering and the weakest ones by scheduling. The schedule uses the long delays and absorption of the underwater channel to achieve higher efficiencies than either of the two strategies could if used alone. 2.2 Scenario We consider a network of hexagonal cells, each with a base station (or sink, or master node) in the center, and users arbitrarily deployed. Base stations must be loosely synchronized to a common time base, and the rest of the nodes rely on them to correct possible clock drifts. In a shallow water network, when the depth is short compared with the cell radius, base stations can be floating buoys synchronized via radio. The rest of the users in a cell communicate only with the base station, but the link can be either unidirectional (only uplink or only downlink) or bidirectional. 7

To reduce the interference, the channel is divided into several non-interfering sub-channels, which are assigned to the cells in such a way that adjacent cells do not interfere. A group of cells with a complete set of different sub-channels is called a cluster. The distance between two cells with the same sub-channel (co-channel cells) is maximized by repeating the same cluster structure throughout the whole network. In order to tessellate, the number N of cells in a cluster (and therefore the number of sub-channels) must satisfy the following equation[15]: N = i 2 + ij + j 2 (2.1) where i and j are integers. Fig.2.1 illustrates the first four values N=3,4,7,9. A B C A C A B A B C A C A B A B C A A B A B C D C B A B A D C D A B A B A B D C C F G G E A B B D C C F G E A B C A D E F G H I G C A B E F D E B C C A B C C A B C A B D C B A C D A B F G E A D C F G A B B C D E H I C A F D N=3 N=4 N=7 N=9 Fig. 2.1: Channel reuse pattern with N cells per cluster. Each letter represents a different sub-channel. In radio networks, the attenuation of the signal is mainly due to spreading ( 1 ; α = lossexponent). Therefore, each cluster size has a uniquely associated distance α SIR regardless of the cell radius. The reason behind the traditional N=7 reuse pattern is that it yields an SIR over 17.8 db, while the U.S. AMPS cellular system provides sufficient voice quality when the SIR is greater than 18 db [15]. The few cases in which such requirement is not fulfilled are not worth the efficiency loss resulting from an increase in N. In the underwater environment, absorption, which depends exponentially on the distance, also plays an important role in the signal attenuation. Hence, the absolute distances have to be taken into account as well as the relative ones. If the cell radius is large, the interference from the nearest co-channel cell might be negligible compared to the signal, but the interference increases faster than the signal when the radius is reduced. Consequently, short radii require more cells per cluster to achieve the same SIR. When it comes to maximizing the Hz capacity of a cellular network for a given m 2 SIR, the solution is to make the cells as small as possible, increasing the number of cells per cluster accordingly. In the end, the cells would end up with radii of only a few meters and the bandwidth divided into hundreds of sub-bands (or codes). The small cells might not be a problem in dense networks, but the link between the base station and the users sometimes requires a minimum bandwidth (or there are a limited number of available codes). Our protocol can reduce the cell radius as much as necessary without increasing the cluster size, and always achieving a higher theoretical efficiency than FDMA or CDMA. 8

2.3 Protocol Description 2.3.1 Main idea When a node starts transmitting in a radio network, all others within reach must defer their transmissions to avoid colliding at the receiver. In underwater networks, on the contrary, several nodes can be transmitting or receiving packets simultaneously if they are far enough. For instance, if a node transmits a radio signal (3 10 8 m ) during 1 ms, that signal is heard by all receivers within 300 km, sec but if that same signal were underwater and acoustic (1500 m ), only those within sec 1.5 m would be affected, while all others could be receiving. Hence, it is possible to establish a transmit-receive/sleep schedule for each cell so that they do not interfere during the listening period and interferences add up during the sleep or transmitting periods. A very simple example of this principle is shown in Fig. 2.2. A total of 9 packets are exchanged in 6 time slots of the same length as the packets, i.e., 1.5 Erlangs. In a half-duplex radio environment only one packet can be transmitted in each slot, so the traffic can never be over 1 Erlang. By applying this strategy to a FDMA or CDMA cellular network, the interference from the closest cells is avoided without need to assign them different channels, thus reducing the size of the cluster with the consequent efficiency gain. In a further extension of the protocol we will take into account the fact that nodes which are close to the base station can tolerate higher interference levels than those which are far. If such distances are known, some interference restrictions can be relaxed and the duty cycle of the schedule increased. 2.3.2 The protocol Two adjacent cells cannot be using the same channel at the same time, otherwise a node close to the border between the two would hear both signals simultaneously and with the same strength. Pure TDMA (all cells share the same channel and take turns to transmit) is inefficient, so we will combine it with FDMA or CDMA using clusters of N hybrid cells, where N hybrid 3. In the usual cellular structure (assumed FDMA henceforth, but it could be CDMA), cells transmit continuously and N F DMA is fixed as the smallest that still provides the required SIR at every point of the cell. The efficiency is then given by 1 N F DMA. The points near the border of the cell are far from their base station and close to the interfering ones so those are the ones that require a greater N F DMA, limiting the efficiency. On the other hand, as they get closer to the center of the cell, the useful signal strengthens quickly and the interference becomes negligible. We will establish a schedule for each cell so that the strong components of the interference do not arrive to the peripheral nodes during their receiving period. This allows for a reduction of the cluster size to N hybrid < N F DMA. The sleep period introduces a time inefficiency, but, as we are about to see, the overall efficiency is higher nevertheless. 9

1 Ra c 2 c X 3 c a X b Rb a Ra b a X Rc b 4 Ra c 5 c X 6 Rb c Rc a X b Rb a b a X Rc b a 1 2 3 4 5 6 b c Fig. 2.2: Period of six time slots in a transmission schedule. Slots, packets and propagation delay between two nodes have all the same duration. In the above plot, a crossed node is receiving interference during that slot, an Rx inside the node means that it spends the slot receiving a packet from node x, and an arrow coming out from a node means it is transmitting a packet. Interference in the lower plot is represented by a black shade behind the packet being transmitted. 10

First approach: distance ignorant dense networks If the position of the nodes is not known, strong interference must always be avoided. So far, the network has been divided into clusters of N hybrid cells, but the first layers of co-channel cells are still too close to tolerate the interference. Such interference must then be avoided by means of a schedule. All co-channel cells are synchronized and share the same schedule. Denoting by T the propagation delay between a node at the edge of the cell and its base station (T = R ; R=Radius, c=sound speed), whichever of the two is c transmitting must finish doing it at least T seconds before the harmful interference reaches the receiver. The closest co-channel cells are separated by a distance of 3Nhybrid R meters. The signal from one takes at least ( 3N hybrid 1)T sec to reach the other cell s receiver (assuming the base station is playing the same role in both cells: either transmitter or receiver). As all co-channel cells share the same schedule, the transmission/receiving period can last ( 3N hybrid 2)T sec at most (See Fig. 2.3). After transmitting, the nodes must wait until the harmful interferences cease before starting to transmit again. The distances to the first layers of co-channel cells are given by 3k N hybrid R where k = 1, 3, 4, 7, 9... according to equation 2.1. Hence, a node will have to wait 3N hybrid T seconds to avoid the interference from the first layer, 9N hybrid T for the second and so on. Let k 0 be the highest k whose interference needs to be avoided, then the transmitter has to wait 3k 0 N hybrid T seconds before starting a new slot. This leaves us an efficiency given by η time = D 2 D 2 + D η total = η time η freq = D 2 D 2 + D 1 N hybrid where D = 3N hybrid is the length of the transmitting period and D = 3k 0 N hybrid is the length of the idle one. Extension when the distance is known: The previous scheme provides a very high protection against interference, but FDMA offers higher efficiency when requiring less than 19 cells per cluster. Under such conditions, our scheme outperforms FDMA only at networks with small cells: for example, if the cell radius is 50 meters and the carrier frequency 30 khz, FDMA requires over 25 cells per cluster to achieve SIR>10dB, but with a cell radius of 1 km, N=3 cells are enough for FDMA to ensure SIR>25 db. However, a slight variation can be implemented in the hybrid protocol to outperform FDMA in nearly all cases. If the base station knows the approximate distance to each of the nodes, for example by timing the round-trip time, it can reserve part of its active period for 11

D R t=t t=(d-2) T t=(d-1) T t=(d-2+d') T=0 Fig. 2.3: The co-channel cells are separated by a distance D R where D = 3N hybrid. If they start transmitting at t=0, they have to stop at t = (D 2) T in order for a node at the edge of the cell to hear the whole transmission without interference. 12

peripheral nodes and use the rest for communication with closer ones. All nodes are assumed to use the same transmission power, even the base station, therefore the signal level received by/from the inner nodes is higher than at/from the outer area, allowing for higher interference levels too. The scheme proposed in the previous section can be adapted to protect only the outer nodes: The idle interval (D T ) between two active periods must remain the same, and peripheral nodes can only transmit/receive during the first (D 2)T seconds after the idle period, but the length of the active interval can be increased as much as necessary while transmitting to near-by nodes. The efficiency is now given by: (D 2)X η time = (D 2)X + D and (D 2)X η total = η time η freq = (D 2)X + D 1 N hybrid where X 1 represents the ratio of the active period to the portion without interference. By doing this, we can improve the efficiency of any FDMA scheme with more than 3 cells per cluster while ensuring the same SIR at peripheral nodes. However, if N F DMA is small, X will need to be large, and the interval without interference will be shorter. 2.4 Case study Henceforth, the nodes whose communication is threatened by the interference will be assumed to be those in the outer half of the cell (distance to the base station over 2radius), adding up to half the total number of nodes in the cell. We will refer 2 to those nodes as outer nodes. Assuming that the base station divides the channel fairly among all the nodes, X will be 2 in the above formulaes. In practical terms X=2 means that the base station divides its active interval in two parts: the first, with low interference, reserved for outer nodes, and the second, with strong interferences, to communicate with the rest. Higher values of X increase the efficiency, but the additional transmitting time can only be used by central nodes. Let us describe in detail the schedules for each kind of communication: Downlink only All co-channel base stations start transmitting at t=0 the packets for their outer nodes, and continue doing so until t=(d-2)t. At that point, they start transmitting the packets for the inner half of the nodes during another (D-2)T seconds. A node located on the edge of the cell would hear the first group of packets between t=t and t=(d-1)t, and the interference from the closest co-channel cell will reach it after t=(d-1)t, so there is no overlapping. 13

The distance to the farthest co-channel cell whose interference needs to be avoided is D R meters (distance between the centers of both cells). Its interference will reach the edge of our cell at t=(d -1)T. The signal only lasts 2D-4 seconds, but it has to traverse the whole cell, so it will not be over until t=(2d-4+d +1)T. After that, the outer nodes can start receiving without interference again. Consequently, the base station should start a new transmission interval at t=(2d-4+d )T. Summarizing, the base station must transmit from t=0 to t=(d-2)t to the outer nodes, from t=(d-2)t to t=(2d-4)t to the inner nodes and start the cycle again at t=(2d-4+d )T. D' R D R t=(d-2)t t=(d-1)t t=(2d-4)t t=(2d-4+d')t t=0 Fig. 2.4: The transmission starts at t=0 with the train of packets for nodes on the outer region (receiving section shaded black) Nodes in the outer region receive their packets without interference. Uplink only If the base station is a sink where all nodes must send their information, the schedule is more complicated. A transmission can start from any point in the cell and the base station must receive the packets from outer nodes without interference. It is possible to design a schedule such that nodes located at a distance r from the sink transmit from t = r (D R r to t = (modulus c c (2D+D -4)T) without creating harmful interference. However, we will restrict all transmission intervals to (D-2)T seconds, sacrificing some efficiency for the sake of simplicity. 14

The schedule for the downlink case increased the efficiency by doubling the length of the transmission interval with respect to the one proposed in the first approach; equivalently, the length of the receiving interval is now doubled. If the sink multiplexes its users in a TDMA frame, it is enough to assign slots during the first half of the (2D-4)T receiving period to outer nodes and the rest to inner nodes. After the receiving period is over, the sink will stay idle for D T seconds, just as in all the preceding cases. If, on the other hand, the sink assigns a sub-band (or code) to each node, doubling the length of the receiving period does not improve the efficiency because it will only be receiving from half of the nodes at any given instant. The improvement then comes from reusing the same code (or sub-band) for two nodes located in different areas (inner and outer). The schedule is the following: all nodes transmit during (D-2)T seconds but those located in the outer region start at t = T r c and those in the inner circle at t = (D 1)T r c, where r is the distance to the sink. After a node stops transmitting, it waits for (D-2+D )T seconds and starts the cycle again. Bidirectional If bidirectional communication is needed with half-duplex underwater modems, the preceding two schemes will be alternated. With an idle time of (D -1)T sec after the downlink period and (D +1)T sec after the uplink, the efficiency does not change. In all three cases the base station is busy during (2D-4)T seconds and the entire cycle lasts (2D-4+D ), consequently the time efficiency is: η time = 2D 4 2D + D 4 The choice of D and D (or, equivalently, N hybrid and k 0 ) is not trivial. Due to the particularities of the hexagonal topology, some configurations provide lower interference than expected. The next section shows an example which presents unexpectedly low interference for both regions. Among other advantages, it is compatible with power control mechanisms because all nodes receive with low interference. 2.4.1 Results This section presents several numerical calculations of the interference level of the (3,3)-hybrid ((N hybrid, k 0 )=(3,3)). We assume a transmitting power of 1W (0 When no downlink is needed, the efficiency can be further increased if inner nodes transmit during tɛ( R+r c, R r c ) and finish 2 R r c seconds earlier, so that the waiting period is T seconds shorter. Unfortunately, this implementation is incompatible with downlink communication. 15

1 db), which fades with the distance due to spreading as by Thorp s equation (in db ): km dist 1.5 and absorption given 0.11 f 2 1 + f 2 + 44 f 2 4100 + f 2 +.000275f 2 +.003 where f is the carrier frequency in khz. The cell radius is 1 km and the carrier frequency is 30 khz (absorption=8 db/km). The interference level of 16-FDMA (FDMA or CDMA scheme with 16 cells per cluster) is plotted jointly with the one under study as a reference for comparison. We will start by plotting in Fig.2.5 the interference level at the center, side and vertex of a hexagonal cell when only base stations transmit (just downlink). According to the equations, the closest interfering layer during the first half of the active interval will be at least 3 12 km apart (k 0 =4). Such case would provide a SIR equivalent to 12-FDMA. However, despite the fact that the schedule is designed to avoid interference only from the first two co-channel cell layers (k=1,3), this particular example also avoids the interference from the third layer (k=4). Furthermore, the long gap between the third and fourth layers (k=4 to k=7) enhances the SIR improvement. The efficiency is given by: η total = 1 2 3Nhybrid 4 N nybrid 2 3N hybrid 4 + 3N hybrid k = 0.0926 which is higher than the 0.0833 of 12-FDMA. Therefore, this scheme simultaneously achieves better efficiency than 12-FDMA and better SIR than 16-FDMA (50% more efficiency and 3dB more SIR than 16-FDMA or 10% better efficiency and 10 db more SIR than 12-FDMA ). Additionally, the plots in the first row show that the interference level at the central area is low during the second half of the interval. Therefore, inner nodes can also receive their packets without strong interference, thus allowing the base station to reduce its transmitting power if necessary. This holds as long as N hybrid 4. The results for the uplink case are similar. Fig.2.6 shows the interference level in the worst case (minimum distance to the transmitter in each co-channel cell) During the first half of the receiving period, the base station barely hears any interference. This is the interval during which the weak packets from far nodes will arrive, while those from nodes in the inner circle will arrive during the second half. It might seem that the interference during the second half of the interval is too much even for nodes close to the center, but this is mainly due to the fact that we are plotting the worst case. If necessary, the interference could be reduced at the cost of some efficiency by increasing N hybrid. Finally, Fig. 2.7 shows that the results for the bidirectional case are very similar to the ones already presented. 16

60 whole period (3,3) hybrid 16 FDMA 60 Interval with useful signal (3,3) hybrid 16 FDMA 70 70 Interference level (db) 80 90 100 Interference level (db) 80 90 100 110 110 120 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 time (sec) 120 0 0.2 0.4 0.6 0.8 1 1.2 time (sec) 60 whole period hybrid 16 FDMA 60 Interval with useful signal (3,3) hybrid 16 FDMA 70 70 Interference level (db) 80 90 100 Interference level (db) 80 90 100 110 110 120 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 time (sec) 120 0.6 0.8 1 1.2 1.4 1.6 1.8 time (sec) 60 whole period (3,3) hybrid 16 FDMA 60 Interval with useful signal (3,3) hybrid 16 FDMA 70 70 Interference level (db) 80 90 100 Interference level (db) 80 90 100 110 110 120 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 time (sec) 120 0.8 1 1.2 1.4 1.6 1.8 2 time (sec) Fig. 2.5: Downlink interference level at three points of a cell. The first column shows an entire period, and the second is a detail of the receiving interval. The packets for outer nodes should be sent during the first half of the interval (first half of the detail) while those for nodes close to the center of the cell (first row) should be sent during the second. 2.4.2 Choosing the parameters The cell radius is usually limited by the number of base stations or the user density, but it should be chosen as small as possible to maximize the capacity per square meter. The carrier frequency, on the contrary, must be as high as possible to increase the absorption of the interferences, but without forgetting that the useful signal will also be attenuated. Once the SIR threshold for correct reception, cell radius and carrier frequency are set, the first step is to find the cluster size that FDMA would require, namely N F DMA. This will give an idea of the nearest layer whose interference can be tolerated. Once this is done, the direct approach would be to choose N hybrid and k 0 such that N hybrid k 0 N F DMA. In most cases the interference level will be low enough but there are some unlucky combinations where interferences from layers between N F DMA and 3N F DMA add up causing unexpected interference peaks during 17

50 60 whole period hybrid 16 FDMA 50 60 Interval with useful signal (3,3) hybrid 16 FDMA Interfering power (db) 70 80 90 100 Interference level (db) 70 80 90 100 110 110 120 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 time (sec) 120 0.8 1 1.2 1.4 1.6 1.8 2 time (sec) Fig. 2.6: Interference level at the base station when it acts as a sink. Entire period (left) and detail of the receiving interval (right). During the first half of the interval, while the interference is weak, it will receive packets from outer nodes. the receiving interval. In such a case, a different combination of N hybrid and k 0 must be chosen. Just as there are unlucky combinations there are lucky ones that achieve high SIR levels with low N hybrid and k 0. Table 1 presents the combination which gives the best efficiency while keeping the SIR for outer nodes over the one achieved by N F DMA -FDMA. Cell radius of 1 km and carrier frequency of 30 khz are assumed. N fdma η F DMA N hybrid k η hybrid 3 4 7 We need X>2 9 0.111 3 1 0.133 12 0.083 4 1 0.115 13 0.077 3 3 0.093 16 0.063 3 3 0.093 19 0.053 3 4 0.083 21 0.048 4 3 0.082 >21 We do not need dividing the interval (X=1) Table 2.1: Optimal N hybrid and k 0. For very small values of N F DMA (under 7), it is impossible to protect all the nodes in the outer half of the cell from interference while keeping a higher efficiency than FDMA. X should then be increased to 3 ( 1 of the active period is free from 3 interference) or higher. If more than 21 cells per cluster are needed in FDMA (very likely if the cells are small), X can be reduced to 1. The efficiency will be lower but the base station no longer has to make any distinction between the nodes. Additionally it would be 18

50 60 whole period (3,3) hybrid 16 FDMA 50 60 Uplink interval with useful signal (3,3) hybrid 16 FDMA 70 70 Interference level (db) 80 90 100 Interference level (db) 80 90 100 110 110 120 120 130 0 1 2 3 4 5 6 7 8 9 time (sec) 130 4.8 5 5.2 5.4 5.6 5.8 6 time (sec) 50 60 whole period (3,3) hybrid 16 FDMA 50 60 Downlink Interval with useful signal (3,3) hybrid 16 FDMA 70 70 Interference level (db) 80 90 100 Interference level (db) 80 90 100 110 110 120 120 130 0 1 2 3 4 5 6 7 8 9 time (sec) 130 0.8 1 1.2 1.4 1.6 1.8 2 time (sec) Fig. 2.7: Interfering power at the base station (top) and on the edge of the cell (bottom) during an entire period (left) and during the receiving interval (right). possible to implement power control because the protocol no longer assumes higher power received over short links. In plain FDMA, the second layer of interference is usually neglected because it is always 3 1.73 times farther than the first. In our scheme, on the contrary, both can be very close and not all layers have the same number of cells. Consequently, several layers have to be taken into account and there are too many variables to give a general formula for the optimal N hybrid and k 0. For example, (N hybrid, k 0 ) = (3, 3) has the closest layer of co-channel interference at a distance of 6R (12-FDMA), and the second at a distance of 8R (21-FDMA). However, this second layer has 12 cells, while the first one only has 6. If the frequency is low or the cell radius short, the interference from the second layer can be stronger than the one from the first. Hence, the best option for a practical implementation different from our example would be to calculate all the different combinations and pick the best one. 19

2.4.3 Parameter sensitivity The SIR in an underwater channel has two components corresponding to the two types of signal attenuation mentioned in the introduction: spreading and absorption. The one due to spreading is approximately given by: SIR spread = 3 2 log( d I d T ) where d I and d T stand for the distances to the interfering and transmitting nodes, respectively. From the above formula it is clear that the spreading does not depend on the absolute value of the distances, but on their ratio. In cellular networks, particularly, it only depends on the number of cells between the receiver s and the interfering one. On the other hand, the second component is given by: SIR absorp = A(f) (d I d T ) where A(f) is the frequency-dependent absorption given by Eq.1.1. In this case the cell radius and the carrier frequency determine the order of magnitude of the SIR. SIR absorp predominates when the distances are long, while SIR spread is much higher when the distances are short. Interference arriving during the first half of the interval has its origin in distant cells, while the one heard during the second half comes from closer ones. The resulting SIR is obtained as SIR spread + SIR absorp in both cases but SIR absorp is much higher than SIR spread during the first half, while it is the other way around during the second one. Consequently, increasing the carrier frequency or cell radius reduces considerably the interference during the first half of the interval but only decreases slightly during the second half. FDMA lies between the two cases, with interference caused by the cells at an intermediate distance. 35 40 (4,1) hybrid 12 FDMA Interval with useful signal 35 40 Interval with useful signal (4,1) hybrid 12 FDMA 35 40 Interval with useful signal (4,1) hybrid 12 FDMA Interference level (db) 45 50 Interference level (db) 45 50 Interference level (db) 45 50 55 55 55 60 60 60 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 time (sec) time (sec) time (sec) (a) (b) (c) Fig. 2.8: Interference level during the base station s receiving interval (uplink). (N hybrid, k 0 ) = (4,1) in all cases but the radii and carrier frequencies are different: (a) Radius=250m freq=20khz, (b) Radius=250m freq=30khz, (c) Radius=400m freq=30khz. 20

Fig.2.8 shows the interfering power at the base station in an uplink scheme for (N hybrid, k 0 )=(4,1) with different cell radii and carrier frequencies. The first two have a cell radius of 250m but the carrier frequency has been increased from 20kHz in the first to 30kHz in the second. This has caused an 8dB decrease in the interference level during the first half, 5dB for 12-FDMA and only 3dB during the second half. Similarly, when the cell radius is increased from 250m in the second plot to 400m in the third, the interference falls 11dB during the first half, 9 for 12-FDMA, and 6dB during the second half. Further cell expansions would report similar results to those found in Fig.2.6, where the gap between both halves is much longer. Fig. 2.8 also shows how the interference with 12-FDMA can be higher, equal or lower than that with the (4,1) hybrid scheme depending on the frequency and cell radius. Therefore, Table 2.1 is not always valid. 2.4.4 Error sensitivity At this point, it might seem that our scheme relies on the geometry of the hexagonal tessellation. Real networks do not have perfect hexagonal cells nor symmetric delays or deterministic signal attenuation. We will model this imperfections by means of a gaussian random error in the position of the base station. The cell radius will be 1km and the carrier frequency 30 khz. 50 60 Uplink interval with useful signal (3,4) hybrid 12 FDMA 50 60 Downlink Interval with useful signal (3,4) hybrid 12 FDMA Interference level (db) 70 80 90 100 Interference level (db) 70 80 90 100 110 110 120 5.4 5.6 5.8 6 6.2 6.4 6.6 time (sec) 120 0.8 1 1.2 1.4 1.6 1.8 2 time (sec) Fig. 2.9: Average interference at the base station during the uplink receiving interval (left) and at the edge of the cell during the downlink receiving interval (right). Both (3,4)-hybrid and 12-FDMA have the same efficiency. radius We fixed a standard deviation of (250m), simulated the bidirectional 4 scheme and took for each instant the average interference in 1000 runs. The effect was double: on the one hand, some interference components grew stronger because the distance had decreased, and on the other, some arrived at the wrong time. When N hybrid is small and k 0 large, as in Fig. 2.9, the interference from the first co-channel layer can arrive early, creating an unexpectedly high interference at the end of the first half. The invaded portion depends on the distance from the 21

base station to the transmitting and interfering nodes, but as long as the transmitter is closer than the interferer, the beginning will have a low interference level. When N hybrid is large, as in Fig.2.10, the effect is reversed. The long distance to the first co-channel layer reduces the chances of an early interference, but the small k 0 reduces the waiting time, making the beginning of the first half vulnerable to late interferences. 70 75 Uplink interval with useful signal (7,1) hybrid 13 FDMA 70 75 Downlink Interval with useful signal (7,1) hybrid 13 FDMA 80 80 85 85 Interference level (db) 90 95 100 105 Interference level (db) 90 95 100 105 110 110 115 115 120 120 125 6.5 7 7.5 8 8.5 9 9.5 time (sec) 125 1 1.5 2 2.5 3 3.5 4 time (sec) Fig. 2.10: Average interference level at the base station during the uplink receiving interval (left) and at the edge of the cell during the downlink receiving interval (right). (7,1)-hybrid and 13-FDMA have similar efficiency. In a bidirectional communication, the waiting time before the downlink is longer than that before the uplink, and is therefore better protected from late interferences. Besides, we are taking the worst case for the uplink, so Fig.2.10 shows low interference in the downlink. 2.5 Small cells When distances are short, the absorption is nearly negligible. The network must then rely on spreading to attenuate the interference. However, spreading in the underwater environment is slow, and big clusters are usually required. Repeating an example from Section 2.3, FDMA requires over 25 cells per cluster to achieve SIR>10dB with a cell radius of 50 meters and carrier at 30kHz. Our protocol can provide considerable improvements in such cases. Firstly, the number of different sub-channels can be as small as necessary: A 25-FDMA scheme can be emulated with only 3 sub-bands, by establishing a schedule to avoid the interference from the first 4 layers of co-channel cells: (N hybrid, k 0 )=(3,7). Secondly, the efficiency is higher: (4,4)-hybrid has the nearest interfering layer farther than 25- FDMA and achieves higher efficiency: 0.0743 with X=2 and 0.0436 without dividing the interval (X=1). 22

Figs.2.11 and 2.12 show a couple of examples. The cell radius is 50 m and the carrier frequency is 30 khz. If the interference level needs to be under -38 db (approximately SIR=12dB in the worst case), FDMA requires at least 48 cells per cluster (efficiency=0.0208). Theoretically, a hybrid scheme with N hybrid = 7 and k 0 = 4 should provide lower interference because the closest layer of co-channel interfering cells is 350 3 meters away (as in 49-FDMA), but it does not. The reason is that, although the closest layer is equivalent to a 49-FDMA, there are others equivalent to 63,84,91,...-FDMA whose interference adds up over the one in 48-FDMA. Consequently, k 0 will be increased to 13 for the case with X=2 and to 9 for the case without division of the interval. 25 Interval with useful signal (7,13) hybrid 48 FDMA 25 Interval with useful signal (7,13) hybrid 48 FDMA 30 30 Interference level (db) 35 Interference level (db) 35 40 40 45 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 time (sec) 45 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 time (sec) Fig. 2.11: Interference levels of 48-FDMA and (7,13)-hybrid for a network with small cells (50m in radius) On the left, worst case of an uplink receiving interval at the base station, on the right, downlink receiving interval at the edge of the cell. Fig.2.11 shows that the interference level for peripheral nodes with our scheme is lower than with 48-FDMA for both downlink (left) and uplink (right). Despite the long idle period (k 0 = 13), the efficiency is 70% higher than that of FDMA. When the position of the nodes is not known, the whole interval must be received without interference. In such cases we use the scheme that was initially proposed (X=1). Fig.2.12 shows that the interference level of (7,9)-hybrid with X=1 is lower than that of 48-FDMA most of the time. k 0 can be smaller because by reducing the length of the transmitting interval, the overall interference created has also decreased. 2.6 Further work This section briefly describes some aspects of the protocol that could be object of further study: When the cell radius is long or k 0 large, the idle periods can be on the order of seconds. To avoid the consequent latency, each cell could have two sub- 23

25 Interval with useful signal (7,9) hybrid 48 FDMA 25 Uplink Interval with useful signal (7,9) hybrid 48 FDMA 30 30 Interference level (db) 35 Interference level (db) 35 40 40 45 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 time (sec) 45 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 time (sec) Fig. 2.12: Example of the hybrid protocol without dividing the cell in different areas. Interference level of 48-FDMA and (7,9)-hybrid with a cell radius of 50m. Receiving interval at the base station on the left and at the edge of the cell on the right. channels so as to insert a second active interval in the idle time following the first. This can be done only if the idle period is longer than the transmitting interval, but in most cases it is. The efficiency remains the same because even though the node transmits twice longer, it is only using one of the two channels at any given time. k 0 was chosen among a finite set of whole numbers (solutions to Eq.2.1) It denoted the farthest layer whose interference was to be avoided, so that when, for example, k 0 =7, the idle period lasts until the interference from the fourth layer has passed the cell completely. However, k 0 represents time, and thus it does not have to be discrete. If the waiting time is slightly decreased, some of the interference that was to be avoided will be heard by the outer nodes on the far side of the cell, but not by those closest to the source. This provides a way of finely adjusting the interference level instead of using discrete steps as in FDMA. It might also be useful to avoid early or late interference as described in Section 2.4.4. It has been assumed that signals propagate only along the direct path, but this is not usually true in underwater networks. As a matter of fact, multipath tends to be very strong. If this becomes a problem, the schedule and cell radius should be designed such that the strongest multipath components of the interference arrive during the idle period. The same concept could be extended to a 3D network of rhombic dodecahedrons, which can tessellate a volume in a similar way as hexagons tessellate a surface. 24

2.7 Conclusion We have proposed a channel-allocation and scheduling protocol for cellular networks which exploits the long delays and attenuation in the underwater channel. By grouping the cells into small clusters and scheduling their transmissions to avoid strong interference, it achieves higher SIR and efficiency than plain FDMA or CDMA. Additionally, it can achieve any SIR level without dividing the narrow available bandwidth into many sub-bands. If the cells are small, FDMA or CDMA require many cells per cluster, which limits the maximum number of users per square meter. By reducing the size of the cluster or the cell radius and compensating for the SIR loss by means of the schedule, our protocol increases the capacity of the network. The base stations located at the center of each cell must all be synchronized to a common time base but in a very loose way, as the slot length is on the order of seconds. If they cannot know the approximate distance to each node in their cell, the achievable efficiency is reduced by a 0.75 factor so that it is only worth for networks with specially high SIR needs (more than 19-FDMA). 25

Chapter 3 Ad-hoc network 3.1 Introduction Ad-hoc is a Latin term for to a specific end or purpose in opposition to arranged in advance. In the case of communication networks it means that the nodes are deployed without previous organization concerning the communication protocol. Instead of sending their packets through a centralizing access point, nodes send them directly to each other, usually using some collision avoidance protocol. Low traffic networks can spare some time in each transmission to avoid collisions. When the traffic is low enough, a sleep schedule can be established to reduce the energy wasted on listening and overhearing ([10],[11]). Heavily loaded networks, on the contrary, require short transmissions in order to send as many packets as possible. The protocol described in this chapter focuses on this last group of networks. Current Medium Access Control (MAC) protocols designed for ad-hoc wireless sensor networks (WSN) can be classified into allocation and contention-based protocols. The first group includes all those protocols that rely on dividing the channel into sub-channels, either by using time (TDMA), frequency (FDMA) or code division multiple access (CDMA). An example for the underwater channel can be found in [1]. These protocols are usually preferred when it comes to saving energy in radio networks, but in the underwater environment synchronization for TDMA is not easy, and the available bandwidth is too narrow for efficient FDMA. As for CDMA, its effectiveness against multipath, noise, and interference has encouraged its application ([1],[5],[6],[7]) but it has some drawbacks such as lengthening of the packets. In contention based protocols all the nodes can transmit at any time contending to acquire the channel. Whichever wins the contention transmits using the whole available bandwidth. Some examples for the underwater channel are PCAP (Propagation-delay-tolerant Collision Avoidance Protocol [2]), Slotted FAMA (Floor Acquisition Multiple Access [3]) and the one here proposed. Collisions are most commonly avoided by hand-shaking. Hand-shaking was introduced by Karn in [8] with a protocol named MACA (Multiple Access with Collision Avoidance). It consists of an exchange of short 26