Optimized Asynchronous Multi-channel Neighbor Discovery

Transcription

1 Optimized Asynchronous Multi-channel Neighbor Discovery Niels Karowski TKN/TU-Berlin Aline Carneiro Viana INRIA and TKN/TU-Berlin Adam Wolisz TKN/TU-Berlin and UC Berkeley Abstract We consider the problem of neighbor discovery in wireless networks with nodes operating in multiple frequency bands and with asymmetric beacon intervals. This is a challenging task when considering such heterogenous operation conditions and when performed without any external assistance. We present linear programming (LP) optimization and two strategies, named OPT and SWOPT, allowing nodes performing fast, asynchronous, and passive discovery. Our optimization is slotted based and determines a listening schedule describing when to listen, for how long, and on which channel. We compare our strategies with the passive discovery of the IEEE standard. The results confirm that our optimization improves the performance in terms of first, average, and last discovery time. I. INTRODUCTION Passive neighbor discovery is the process in which devices learn about current neighbors upon listening their communication. Discovery is essential for the process of self-organization of wireless networks, where the execution of most network operations demanding nodes coordination (e.g., routing or topology control) require knowledge of neighbors. Examples are ubiquitous and social networking applications [1], [2], [3]. The neighbor discovery should proceed as quickly as possible to allow the network to begin operation. This is specially important in situations requiring emergency message propagation or where the time period for communication is very short. Hence, the fast discovery helps avoiding long listening periods, and consequently, helps improving energy efficiency. On the other hand, the heterogenous features (different duty cycles, multiple channels, mobility patterns, etc) of emerging applications require the design of efficient neighbor discovery strategies. Additionally, in the design of extensible and easy to use wireless networks, the discovery problem of asynchronous neighbors that might be operating in different channels and at different point in time can be expected to be often encountered. When considering single channel neighbor discovery, the literature offers: probabilistic and deterministic approaches. Although most commonly used, the probabilistic discovery [4], [5], [6] decreases reliability and leads to long tails on discovery probabilities as well as to unpredictable discovery latencies [7]. On the other hand, deterministic discovery helps increasing discovery speed and enhance reliability [5], [7], [8], [9], []. Such approaches, however, are not adapted to multichannel use, have to control the transmission of discovery messages, or are based on active discovery methods (i.e., request feedback of neighbors), which requires close operation with deployed MAC protocols. Providing fast discovery of non-synchronized nodes operating on multi-channel is a challenging task. If we consider the asynchronous and multi-channel passive discovery problem, the literature lacks time optimized solutions. The main issue here it to organize the listening process of nodes in discovery phase, such that the listening times are small and the neighbors can be reliably detected. This involves the design of a listening schedule determining when to listen, for how long, and on which channel. The IEEE standard [11] allows passive discovery of nodes operating in beaconed-mode in asynchronous and multi-channel networks. The discovery process is based on making nodes listening each channel for long periods. Although providing reliable discovery, it results in long discovery times. This paper presents a linear programming (LP) optimization for fast and asynchronous neighbor discovery in networks operating with different beacon intervals in the order of 2 b (e.g. used in IEEE ) and in multiple frequency bands. We formulate the general optimization problem and discuss how to transform it to a LP problem. The optimization is mainly based on the idea of re-using information gained on previous scanned slots and accelerating the discovery time of neighbors operating with smaller beacon intervals. Hence, this decreases the time to perform the first neighbor discoveries as well as allows reducing the average and last discovery time. Our LP model is slotted based and works on the organization of the schedule of listening periods of nodes only. The remainder of this paper is structured as follows. Section II presents our system model. Section III describes the LP formulation of the asynchronous and passive multi-channel neighbor discovery problem. Moreover, by varying the sustainability period of the optimized scheduled, this section also introduces two discovery strategies, named OPT and SWOPT. We compare the performance of our strategies against the passive discovery of the IEEE standard, named here PSV. Using simulation, Section IV investigates the strategies in different scenarios under varying networking parameters. The results attest the good performance of our discovery optimization on key metrics like: fast first, average, and last discovery time. Finally, Section V concludes this paper and discusses future works.

2 II. SYSTEM DESCRIPTION We consider a wireless network of n nodes uniquely identified (e.g., by MAC addresses). Each node is equipped with a single transceiver omni-directional antenna. We assume a halfduplex communication. We consider a multi-channel system, where channels are denoted by the set C = {,..., c } and C is the total number of available channels. If nodes are operating in shared frequency bands (e.g. ISM band in IEEE ), interference caused by external devices may occur on some frequencies. In this case, having the possibility to select the operating channel helps mitigating the interference. Nodes are in the communication range of each other if they are operating on the same channel c and are able to exchange messages. Each node can be in one of the following states: Communication state: Beacon signals or data can be sent. Beacons are only transmitted on the operating channel c of a node, but data can be sent on any other channel in C. Scanning state: Nodes listen for beacon signals on channels of C and are not transmitting any signal. Sleeping state: Nodes mainly turn their radio off. Each node is assumed to send a beacon signal with a period b I on its operating channel c. No jitter is considered. The period is derived by b I = 2 b z (where z is a constant), for a beacon order b. We assume a set of beacon orders B = {b min,..., b } is provided, where b is the imal allowed beacon order. By choosing B = {,..., 14} and z = 96 the resulting b I are equivalent to the IEEE standard. The deployment of nodes using different hardware, having varying purpose of use or being employed by different vendors may result in the usage of diverse beacon intervals among the nodes. Nodes are assigned to a channel c and to a beacon order b, both randomly chosen from C and B respectively, according to a uniform distribution. We assume a completely passive discovery, based exclusively on beacon listening. The listening process uses slotted time. For each node performing the discovery, we have an asynchronous discovery process, which can be completely defined by a sequence of pairs [c, number of slots]. A sequence of pairs describes a listening schedule. We define a round as the time needed for finishing one complete sequence of pairs. The minimum number of slots a node stays listening on a channel is called here as sustainability period. We assume the length of a time slot equals to the smallest beacon interval. This corresponds to the beacon order, i.e., b I = 2 z. When considering the 2.4GHz ISM band of the IEEE based radios, constant z corresponds to 96 symbols (about 16µs per symbol), resulting in the smallest beacon interval of length 15.36ms. A node i initially knows: (1) its identity ID, (2) its beacon interval b I, (3) its channel c C, (3) the set of available channels C, and (4) the set of beacon orders B possibly used in the network. A node i scanning a channel c discovers current neighbors in c whenever such neighbors are within the i s communication range and node i receives their periodically transmitted beacons. Listening schedules will be evaluated according to the metrics: first, average and last discovery time. The discovery time is the time period from when the discovery process started (i.e., the scanning state of a node started) until the first beacon of a node is received. The average is then computed among the discovery times of all the discovered nodes. III. LISTENING-BASED SCANNING SCHEDULE DESIGN This section identifies listening schedules that minimize the average discovery time. The idea of this optimization is to reuse the information gained in previously scanned slots and to accelerate the neighbor discovery for the smaller beacon intervals of set B at each channel c C. Hereafter, we provide the theoretical formulation and the linear programming model of the asynchronous neighbor discovery problem, when we define the notion of listening-based scanning schedule. Then, we discuss two resulting discovery strategies and relax the simplifying LP model assumptions to provide solutions that work in practice. A. Neighbor discovery optimizations 1) Theoretical formulation: The listening-based scanning schedule determines the periods of time that each node spends on one particular channel, listening for periodically sent beacons. Scanning nodes start listening at time slot t. The schedule involves assigning to each node in the scanning state binary variables x c,t for all c C and t T, describing whether the scanning node performs a discovery on channel c at time slot t: x c,t = { 1, if discovery is performed on channel c at time slot t, if no discovery is performed on channel c at time slot t The latency required for a node performing total discovery of neighbors operating with B and on C is defined as t = C 2 b 1, assuming no beacons losses. The set of time slot indexes can be then represented by T = {t,..., t } = {,..., C 2 b 1}. The next section considers the following assumptions: (1) no channel switching time, switching between channels is performed instantaneously; (2) no beacon transmission/reception time, the beacon length is assumed to be zero; (3) no beacon losses, no collisions are considered and channel conditions are ideal (e.g., no interference or fading). 2) Optimization model: We modeled the asynchronous multi-channel discovery problem under the following constraints: 1- Number of scanning time slots per channel: The number of time slots per channel for a scanning node to perform the total neighbor discovery can not be less than 2 b. Otherwise the discovery of nodes using the imum beacon order b can fail. t c C t=t x c,t 2 b (1)

3 (a) Optimized (OPT) (b) Switched Optimized (SWOPT) (c) IEEE Passive Disc. (PSV) Fig. 1. Distribution of scanning time slots for C = 3 and B = {1, 2} 2- Concurrent scanning: A node can not scan more than one channel at each time slot. t T x c,t 1 (2) c= 3- Allocation of time slots: The scanning time slots should be allocated in such a way that all beacon intervals b I are completely scanned at least once. Due to the periodicity and multiplicity of the beacon intervals, information gained from previous scanned slots on a channel can be reused to avoid unnecessary scans. For instance, if a scanning node is searching for neighbors with b I = 2 2 = 4 and has already performed a scan at time slots, 2, and 3 on channel c, it has only to scan one additional time slot t 4 i+1 for any i N, to detect all nodes using b I = 4. c C b B δ {,...,2b 1} x c,2b i+δ 1 (3) The formulation of the goal of minimizing the average discovery time by computing the discovery probability for any time slot results in non-linear formulation. In fact, the probability of discovering a node with beacon order b on channel c in time slot t depends on the number of previous scanned slots on channel c. Thus, x c,t would be dependent on past x c,τ with τ < t. Such a general optimization problem is known to have a high complexity. Due to the structure of the beacon interval 2 b z, it is possible to setup groups of time slots for each beacon interval b I such that, the discovery probability for nodes with a given b I is the same for all time slots. The size of a group depends on the corresponding b I and the number of channels C. However, the resulting linear formulation is specific for beacon intervals computed by 2 b z which are for example used in the IEEE standard. Finally, the linear programming (LP) model provides optimized listening schedule that minimizes the average discovery time: 2 b i C 1 min b c = b i = b min t = 2 b i C 1 i= t = 2 b (i 1) C b with u = x c,t (t +.5) u, if b i = b min u, otherwise 1 2 p C B p = b i (4) The intuitive explanation of Eq. 4 follows. The average discovery time is computed for all channels of C and beacon orders of B (cf. 1st and 2nd sum). The time slots t are grouped. The first and the last time slot of these groups depend on the current beacon order b and the number of channels C (cf. 3rd sum). The probability of discovering a node with beacon order b is the same for all time slots in one group allowing a linear formulation. In order to consider the fact that in average, nodes are discovered in the middle of each time slot, the discovery time is set to (t +.5). Finally, the probability of discovering a node in a slot depends on its beacon order, the number of channels, and the total number of beacon orders (cf. last sum). The intuition here is that lower is the beacon interval of a node, higher is the probability of finding this node in one particular slot. In this way, the optimization allows accelerating discovery of neighbors with smaller beacon interval. At the best of our knowledge, this is the first linear solution for the asynchronous multi-channel discovery problem. The modeling language ZIMPL [12] is then used to translate the mathematical model of the LP problem into the linear mathematical program which is solved by using CPLEX 9. [13]. 3) Discovery strategies: The LP model used with a sustainability period of one time slot defines a discovery strategy, named OPT. However, OPT describes a scheduling based on a high number of switches among channels. In order to reduce the number of channel switches, we increase the sustainability period to 2 bmin z. The resulting strategy as obtained from ZIMPL will be referred as SWOPT, SWitched OPTimized. In the following, we will compare OPT and SWOPT to the schedule generated by the passive discovery of the IEEE , named PSV. The PSV strategy listens for a period corresponding to the imum beacon order b on each channel of C. For this strategy, the knowledge of b is sufficient to also discover all nodes operating with a beacon order lower than b. Figure 1 depicts the scanning schedule resulted from all three strategies, when considering C = {, 1, 2} and B = {1, 2}. It is worth noting that all strategies are resulting in the same total number of discovery time slots (i.e., 12 time slots for this example), which shows OPT and SWOPT do not impose any additional overhearing energy consumption. Nevertheless, as discussed in next sections, OPT and SWOPT

4 present a significant improvement in terms of discovery time for all beacon orders smaller than b. B. Relaxing assumptions The assumptions of the LP model aide analysis but are unlikely to hold in practice. This section relaxes these assumptions and discusses their impact on the optimized strategies. 1) Imperfect knowledge of C and B: Depending on the network scenario, the complete knowledge of the required parameters (i.e., C and B) of the LP model may not be available. Using imperfect knowledge affects the discovery probability and time. If a node operates on a channel c / C, it will not be discovered. On the other hand, if there are channels in C not used by any nodes, it will not affect the discovery but will increase the discovery time of nodes operating on the used channels. If a node operates with b > b, there is a chance of not discovering this node. Otherwise, if b < b and b / B, the node will still be discovered but with increased discovery time. 2) Channel switching time: The channel switching time has an impact on the scanning schedule. In fact, a RF transceiver needs some time in order to switch from one channel to another, before it can start transmitting and receiving on the new channel. In order to avoid a time shift of the schedule the listening slots are shortened by the channel switching time in the following way. When the schedule round number is even, the slots are shortened at the end, otherwise, at the beginning. The alternation of the shortenings allows the discovery of beacon transmissions that start within the switching period. 3) Beacon transmission/reception time: Due to the limited channel bandwidth, the transmissions of beacons take time and the size of the beacons may have an impact on the scanning schedule. If a beacon is received shortly before a channel switching is scheduled and the beacon reception is not cancelled, the discovery schedule will be delayed. Therefore, we consider in this case that the next scanning slot is shortened by the delay caused by such reception. 4) Beacon losses: Due to mobility and beacon losses, the neighbors beacons may not be received, what may also delay the discovery time. Therefore, the general approach will be to repeat the listening schedules. The frequency of repetitions will depend on the current network conditions. A. Simulation Setup IV. PERFORMANCE EVALUATION The evaluation is performed using the OMNeT discrete event simulator [14] together with the Mobility Framework (MF) [15] and an OMNeT++ IEEE implementation developed at TKN. In the performance evaluation, the parameters shown in Table I are used, if not differently specified. In [] it is shown that the channel switching time of a CC24 radios take 3 µ, corresponding to about 19 symbols. The simulated scenarios consist of one scanning node and 5 neighbors placed at uniformly random locations in the communication range TABLE I PHY AND MAC LAYERS PARAMETERS Carrier frequency 2.4 GHz Thermal noise -7 dbm Transmitter power 1mW CCA threshold -77 dbm Sensitivity -85 dbm Symbol duration 16 µs Time slot duration ms (96 symbols) Channel switching time 19 symbols MAC beacon payload length bytes PHY beacon packet size 19 bytes (eq. 38 symbols) Number of channels C 8 Beacon order set B {5, 6, 7, 8} of the scanning node. The results correspond to the average among, runs with 95% confidence intervals. For each run, the channel and the beacon intervals of the communicating nodes were chosen uniformly distributed from the channel set C and beacon order set B. During the simulation, scanning nodes process the discovery schedule given by each strategy, while its neighbors periodically send beacons starting at a time uniformly distributed between [; b I [. Additionally, when neighbors are not transmitting, we consider they are in the sleeping state. The simulation stops when the scanning node discovers all neighbors or when the simulation time limit is reached. Though a rare event, this latter is required in cases where a beacon will never be received, which may happen due to two or more nodes selecting overlapping beacon transmission times on one channel. Note that this is independent of any discovery strategy scheduling. B. Performance metrics The following performance metrics were used for evaluating the discovery strategies: (1) 1st discovery time, which is the time when any first node is discovered in any channel, (2) average discovery time, which is the average time among the discovered neighbors in all channels, (3) last discovery time, which is the time when any last node is discovered. The fast discovery of the first node is motivated by emergency applications, where the transmission of a message needs to be performed as soon as possible and consequently, a next-hop has to be contacted quickly. A fast average discovery time is interesting (1) in ubiquitous monitoring applications (such as location tracking or in surveillance applications), where neighbors should be identified by a scanning or surveillance entity, and in (2) DTN scenarios, where nodes need to find a subset of good forwarders. Finally, the fast discovery of the last node is interesting in applications where the discovery of all neighbors of a node is required. In all cases, having a fast discovery will benefit the applications, improving energy efficiency, and allowing quick reaction. C. Scenarios The next sections discuss the performance of the strategies in a static scenario under varying: beacon order, channel switching time, beacon length.

5 Beacon order Channel switching time (symbols) Beacon length (bytes) (a) (b) (c) Fig. 2. Results in a static network, for varying (a) beacon orders, (b) channel switching times, (c) beacon lengths. 1) Impact on beacon order s discovery time: We show in Figure 2(a) the comparison between the first, average, and last time required to discover nodes with different beacon intervals, according to each discovery strategy. Beacon order set is B = {5, 6, 7, 8, 9, }. Results show how the OPT and SWOPT strategies accelerate the discovery times when compared to the PSV strategy. This also validates the intuition behind the LP model: to accelerate the neighbor discovery for the smaller beacon intervals of set B at each channel c C. Moreover, note that OPT and SWOPT do not add any additional delay to the discovery of nodes with the highest beacon interval (i.e., b=), which results in the same first, average, and last discovery time as PSV strategy. 2) Impact of channel switching time: Figure 2(b) proves how the approach described in Section III-B2 combined with the three strategies is able to reduce the impact on the schedule caused by channel switching time greater than zero. The first, average, and last discovery times are constant for increasing channel switching time in case of the PSV and SWOPT strategy. However, the OPT strategy shows an increasing average and last discovery time for higher channel switching time. This is caused by the high number of channel switchings required by the OPT strategy; in this scenario, OPT performs 1569 switches per round compared to 58 in SWOPT and 8 in PSV. Moreover, OPT and SWOPT presents shorter first, average, and last discovery time than the PSV. 3) Impact of beacon length: Figure 2(c) shows the first, average, and last discovery time results for PHY beacon lengths varying from to 1 bytes for the three strategies. No impact is perceived to the performance of the strategies. In particular, as discussed in Section III-B3, if a beacon is received shortly before switching to another channel, the listening time on the next slot will be decreased. Thus, in order to impact the discovery time, another node has to start transmitting its beacon on the shortened part of the scanning slot. The probability for such event happening is very low. Moreover, for any beacon length value, the OPT and SWOPT strategies present faster discovery times than PSV. Still, SWOPT presents better average and last discovery time results than OPT. This is caused by the non-zero value used for channel switching time (see Table I). V. CONCLUSIONS This paper presents a practical and optimized solution for the asynchronous passive multi-channel neighbor discovery problem, enabling efficient usage of heterogeneous hardware platforms. Our solution is based on linear programming (LP) optimization and on two discovery strategies, named OPT and SWOPT. No sending schedule is imposed by our strategies which only uses the periodic transmissions of a beaconenabled MAC. We have shown through simulation results that the OPT and SWOPT strategies achieve faster discovery than the passive discovery of IEEE standard for varying network settings. As future directions, we envision to provide discovery solutions supporting any kind of beacon intervals and to add gossip and opportunistic-based support to the strategies. REFERENCES [1] N. Eagle and A. S. Pentland, Sensor andrew: a living laboratory for infrastructure sensing techonology, sensor-andrew/, 6. [2] M. Berges, E. Goldman, H. S. Matthews, and L. 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