- Research Article
- Open Access
Biologically Inspired Intercellular Slot Synchronization
© A. Tyrrell and G. Auer. 2009
- Received: 30 June 2008
- Accepted: 21 January 2009
- Published: 2 March 2009
The present article develops a decentralized interbase station slot synchronization algorithm suitable for cellular mobile communication systems. The proposed cellular firefly synchronization (CelFSync) algorithm is derived from the theory of pulse-coupled oscillators, common to describe synchronization phenomena in biological systems, such as the spontaneous synchronization of fireflies. In order to maintain synchronization among base stations (BSs), even when there is no direct link between adjacent BSs, some selected user terminals (UTs) participate in the network synchronization process. Synchronization emerges by exchanging two distinct synchronization words, one transmitted by BSs and the other by active UTs, without any a priori assumption on the initial timing misalignments of BSs and UTs. In large-scale networks with inter-BS site distances up to a few kilometers, propagation delays severely affect the attainable timing accuracy of CelFSync. We show that by an appropriate combination of CelFSync with the timing advance procedure, which aligns uplink transmission of UTs to arrive simultaneously at the BS, a timing accuracy within a fraction of the inter-BS propagation delay is retained.
- Global Position System
- Propagation Delay
- Timing Advance
- Phase Response Curve
- Frequency Division Duplex
Slot synchronization is an enabling component for cellular systems. It is a prerequisite for advanced intercellular cooperation schemes, such as interference suppression between neighboring cells, as well as multicast and broadcasting services. The problem of intercell slot synchronization is to align the internal timing references of all nodes, so that base stations (BSs) and user terminals (UTs) agree on a common reference instant that marks the start of a transmission slot. In the context of cellular systems a slot is composed of a number of successive uplink and downlink frames, referred to as superframe.
Network synchronization in cellular systems is commonly performed in a master-slave manner: BSs synchronize to an external timing reference, known as the primary reference clock, and transfer this timing to UTs. This reference clock can be acquired through the global positioning system (GPS) or through the backbone connection. The first method requires the installation of a GPS receiver at each BS, which increases costs and, more importantly, does not work in environments where GPS signals cannot be received. For high accuracy, the second method requires precise delay compensation, and the accuracy severely decreases when clocks are chained .
Over-the-air decentralized intercell slot synchronization that avoids the need for an external timing reference was pioneered in , and further elaborated in [3, 4]. Its basic principle is summarized as follows: a BS emits a pulse indicating its own timing reference and is receptive to pulses from surrounding BSs; internal timing references are adjusted based on the power-weighted average of received pulses. Conditions for convergence were derived in , which reveals that convergence and stability are tightly linked to the intersite propagation delays between neighboring BSs. This is a critical issue, as inter-BS propagation delays are not known a priori. Furthermore, in , direct communication between BSs is required, and for the exchange of synchronization pulses, a separate frequency band is assumed to be available.
In the present paper a different approach is taken based on the theory of pulse-coupled oscillators (PCOs), which is commonly used to describe self-organized synchronization of biological systems such as swarms of fireflies, heart cells, or neurons. Mirollo and Strogatz  derived a theoretical framework for the convergence to synchrony. Various aspects regarding the application of the PCO model to wireless networks are addressed in literature: radio effects such as propagation delays , channel attenuation, and noise [8, 9], and allowing for long synchronization words . The rules that govern the PCO synchronization model are intriguingly simple and serve as a basis for inter-BS synchronization.
The proposed cellular firefly synchronization (CelFSync) algorithm adapts the PCO model to account for constraints of cellular networks. CelFSync operates over-the-air, in a decentralized manner; no constraints are imposed on the availability of an external timing reference. As BSs and UTs typically transmit on successive downlink and uplink frames, two groups need to be distinguished; the BS group transmitting on the downlink and the UT group transmitting on the uplink. To facilitate the formation of two groups, two synchronization words are specified, one associated to BSs and the other to UTs. UTs transmit an uplink sync word based on their internal timing reference, which is received by BSs to update their own timing; in return UTs adjust their timing reference upon reception of downlink sync words from neighboring BSs. Thus, unlike , no separate frequency band is required as sync words are transmitted in-band with data. Moreover direct communication among BSs is not mandatory as synchronization is performed by hopping over UTs. As the downlink sync word is mandatory for conventional cellular systems to align the timing of UTs with the BS, the only overhead for inter-BS synchronization is the insertion of the uplink sync word. Thanks to the proposed strategy, the network is able to synchronize starting from an arbitrary misalignment, and propagation delays only affect the achieved accuracy but do not compromise the convergence to synchrony.
When considering a scenario where BSs are separated by several hundred meters up to a few kilometers, propagation delays severely affect the attainable timing accuracy. We propose to combine CelFSync with the timing advance procedure, which ensures that UT uplink transmissions arrive simultaneously at the BS. Compensating intracell propagation delays with the timing advance procedure, as well as selecting cell edge users to participate in CelFSync, are effective means to substantially improve the achieved interbase station timing accuracy.
The remainder of the paper is structured as follows. In Section 2 the PCO model and its achieved synchronization accuracy in the presence of delays are presented. In Section 3 CelFSync is developed by adopting the rules that govern the synchronization of PCOs to cellular networks, and Section 4 combines CelFSync with timing advance to compensate the effects of propagation delays. Practical constraints regarding the implementation in cellular networks are addressed in Section 5, and simulation results are presented in Section 6 that investigate the time to convergence and the achieved accuracy for an indoor office environment as well as an urban macrocell deployment composed of hexagonal cells.
Pulse-coupled oscillators (PCOs) describe systems where individual nodes periodically emit pulses and adjust their internal time reference upon reception of pulses from neighboring oscillators. In this section the rules that govern the PCO model  are summarized, and the achieved accuracy in the stable state is elaborated.
2.1. Phase Function
2.2. Synchronization Rules
where the coupling parameters and determine the coupling between oscillators. Figure 1(b) plots the time evolution of the phase when receiving a pulse at . The received pulse causes the oscillator to fire early.
Provided that and , a system of identical oscillators coupled all-to-all is always able to synchronize, so that all PCOs agree on a common reference instant, independent of initial timing misalignments .
As nodes have the same internal dynamics and if they are coupled all-to-all, absorptions remain permanently (see Figure 2). Therefore nodes following the PCO rules first gather into groups that gradually absorb one another, and after some time, always coalesce into one synchronized group.
In  Lucarelli and Wang extended the demonstration of  to remove the all-to-all assumption. Under weak coupling assumptions, that is, close to and close to in (3) (no proof for strong coupling exists), equivalent phase deviation variables are derived for each node (each variable represents the mean local interactions over one period) and are shown to asymptotically converge to the same value .
Unfortunately the analysis in  is not applicable when delays are introduced. Izhikevich showed that there is no equivalent phase deviation variable when interactions are delayed . As the proposed inter-BS synchronization scheme always delays interactions (see Section 3), an analytical convergence study appears infeasible. Convergence is consequently studied through simulations in Section 6.
2.4. Impact of Delays
Because of delays nodes are no longer able to perfectly align their reference instants . Nevertheless nodes converge to a stable state where reference instants are spread within an interval limited only by the coupling delays , as detailed for networks of two and three nodes in the remainder of this section. Further discussion on the achieved accuracy of the PCO scheme in the presence of delays is available in .
2.4.1. Two Nodes
The introduction of a refractory period thus may result in a state where one node imposes its timing onto the other, in a similar way to a master-slave synchronization scheme. However, the achieved state is random: it depends on the initial condition and on interactions with other nodes in the network. Therefore the role of the forcing node is arbitrary, and PCO synchronization is still considered decentralized.
2.4.2. Three Nodes
The forcing node is directly connected with all nodes.
The forcing node is the edge node of a line topology and imposes its timing to the other edge node by hopping over the center node.
Considering (i), suppose that node is the forcing node that imposes its delayed timing onto nodes and . This state is shown in Figure 3: node fires at instant , which causes nodes and to increment their phases at instants and , respectively. Assuming that their phase exceeds the absorption limit (4), nodes and fire at instants and , and subsequently enter refractory. No further phase increments occur because the pulses from nodes and are received when nodes are in refractory (5). Therefore the network is in a stable state, and the achieved accuracies of node relative to node and amount to and , respectively. Interestingly, the accuracy between nodes and is equal to the difference in delays with forcing node , that is, . Thus this achieved accuracy does not depend on the direct delay but on the delay difference with the forcing node .
In case (ii) the considered nodes form a line topology, where the edge nodes and , cannot communicate directly. Suppose that node is the forcing node that imposes its timing onto node via the center node . As the accuracy between adjacent nodes is bounded by (7), that is, and , the resulting accuracy interval over two hops between edge nodes and amounts to the sum of delays: .
This section presents an adaptation of the PCO model to perform intercell synchronization. To facilitate reliable exchange of reference instants in the presence of signal fading, interference, and noise, long synchronization sequences that are transmitted in-band with data are considered instead of pulses. Furthermore, half-duplex transmission is considered, which implies that nodes cannot receive whilst transmitting. To this end, when two nodes transmit sync words that partially overlap, both nodes are unable to detect the sync word sent by the other node, referred to as deafness between nodes. Hence both nodes are effectively uncoupled, an effect which may severely disrupt intercell synchronization. Further accounting for constraints in cellular systems, the frame structure does not allow for overlapping downlink and uplink slots. Thus synchronized BSs and UTs should not transmit simultaneously.
The proposed cellular firefly synchronization (CelFSync) scheme takes into account these fundamental constraints, by resorting to an out-of-phase synchronization regime, introduced in Section 3.1. CelFSync relies on two synchronization sequences, one transmitted by BSs to adjust timing references of UTs, and a second one transmitted by UTs to adjust timing references of BSs, based on rules that are established in Section 3.2. The detection of the two distinct synchronization sequences in an asynchronous environment is discussed in Section 3.3. For ease of explanation, propagation delays are neglected in this section and are treated specifically in Section 4.
3.1. Synchronization Regimes
The in-phase regime is the most common form of synchronization; pacemaker cells pulse simultaneously to pump the heart, fireflies emit light at the same time. Antiphase synchronization is also familiar; when walking, our legs are antiphase synchronized: the left foot touches the ground half a period after the right one, and vice versa.
Following the frame structure of cellular systems composed of successive downlink and uplink frames, BSs are to be synchronized out-of-phase with UTs. Out-of-phase synchronization ensures that uplink and downlink transmissions in the steady state do not overlap, so that detrimental effects of deafness between nodes, inherent to half-duplex transmission, are mitigated.
3.2. Cellular Firefly Synchronization
The coupling parameters are chosen in accordance to the PCO synchronization model: and .
Thanks to this strategy, the formation of two groups is controlled. Starting from an arbitrary initial misalignment, where all reference instants , are randomly distributed within , by following simple coupling rules, reference instants of UTs and BSs separate over time into two groups; all BS fire after UTs, and all UTs fire after BSs. This state corresponds to the synchronized state shown in Figure 6. Convergence is verified through simulations in Section 6; by appropriately selecting the coupling parameters, it is shown that synchronization is always accomplished.
To speed up the convergence of CelFSync, two enhancements are possible, namely BS-BS and UT-UT couplings and the selection of active UTs.
BS-BS and UT-UT Coupling
In case BSs can communicate directly or UTs are placed close to one another, convergence may be accelerated by allowing coupling between nodes of the same group. Moreover, the occurrence of deafness between nodes decreases because the number of nodes that are potentially coupled is increased. As half-duplex transmission is considered, BS-BS and UT-UT couplings are useful only during the coarse synchronization phase, that is, among nodes whose reference instants are misaligned by more than the sync word length.
Phase adjustments are made similarly to (8) and (11) for BSs and UTs; however decoding delays are different, as nodes need to align in time with other nodes from their own group. Therefore the interaction delay upon detection of and needs to be equal to one period , giving a decoding delay of for BSs and for UTs.
Active UT Selection
Since uplink sync words should be heard by multiple BSs, it is reasonable to select a subset of UTs close to the cell boundary to participate in intercell synchronization. Therefore, in each cell, the base station selects the UTs with the largest propagation delay among total UTs in the cell. The remaining UTs are not active in CelFSync and follow the timing reference dictated by their closest BS, by aligning their local clocks based on .
3.3. Synchronization Word Detection
CelFSync relies on the detection of transmitted and sequences. In the following, we assume that uplink and downlink sync words are two different random sequences, each composed of symbols. Sync word detection is carried out by the link-level synchronization unit, which cross-correlates the received signal stream with the sync word , where if uplink sync words are to be detected, and otherwise. The output of the link-level synchronization unit is denoted by . The correlator output produces a series of peaks, in a similar way to the emission of pulses in the PCO model, and detection of a sync word is declared when exceeds the detection threshold .
where , the hypothesis that no sync word is present at the receiver, is the complement of .
The Neyman-Pearson criterion is used to design the sync word detector : the detection threshold is set according to the desired false alarm rate ; once is set, the detection rate is determined. The impact of false alarm and detection rates on an adaptation of the PCO model to ad hoc networks was studied for a multicarrier system in . It was shown that false alarms have a higher impact on the convergence than missed detections . Hence, it is necessary to maintain a sufficiently low false alarm rate .
The reliability of the link-level synchronization unit can be enhanced by increasing the length of the sync word . Increasing improves the detection rate for a given false alarm rate, at the expense of higher overhead .
The accuracy of CelFSync is limited by propagation delays, similarly to the PCO model discussed in Section 2. In an indoor environment where distances between nodes are typically small, propagation delays are negligible. However, for cellular systems where the inter-BS distance is up to a few kilometers, Section 4.1 reveals that propagation delays cannot be ignored. A common procedure to align uplink transmissions is the timing advance procedure, described in Section 4.2. Timing advance is combined with CelFSync in Section 4.3 to achieve a timing accuracy within a fraction of the inter-BS propagation delays.
4.1. Achieved Accuracy in the Stable State
where is the propagation delay between and . When the upper bound in (16) is approached, then , is the forcing node that imposes its timing onto . Likewise, (16) approaches the lower bound, , when is the forcing node that imposes its timing onto .
Given that in cellular networks the inter-BS distance is up to a few kilometers, propagation delays have a major impact on the achieved accuracy in the stable state.
4.2. Timing Advance Procedure
The propagation delay may be determined by estimating the round trip delay between and . Upon reception of from , responds with the transmission of a random access preamble (RAP) at . Since is a constant known to , the round trip delay is determined by detecting the received timing of the RAP at . In addition, the RAP identifies , so that can distribute the estimate of to .
4.3. CelFSync with Timing Advance
In order to combat propagation delays, we propose to combine CelFSync with the timing advance procedure. If knows the propagation delay to its serving base station , the corresponding round trip delay of can be compensated. Owing to the multi-point-to-point topology specific to cellular networks, of cell typically serves several mobiles , , each with a specific propagation delay . Hence, all timing inaccuracies, the propagation delays from to and back from to , must be compensated for at the mobile . This is accomplished by advancing both, the transmitted and the coupling of the received at , by the BS-UT propagation delay .
For the following discussion, suppose that has carried out the timing advance procedure with , but its transmission is received by .
Figure 7 summarizes the proposed combination of CelFSync with timing advance: starts transmision at , so that the coupling at occurs exactly at ; in return, starts transmission of its sync word, whose decoding time is reduced at by so that fires exactly after . Hence, all entities within one cell are perfectly timing aligned, and thus, the only remaining source of timing inaccuracies is between entities of neighboring cells.
Therefore combining timing advance with CelFSync always achieves an accuracy, that is, bounded by the difference of UT-BS propagation delays.
Provided that is located near the cell boundary, its propagation delays to and are similar, so that the difference is much smaller than the individual delays and . This is in sharp contrast to the achieved accuracy without timing advance in (17), which is bounded by the sum of propagation delays. Increasing the UT density per cell increases the probability of selected UTs to be close to the cell edge, which has the appealing effect that the inter-BS accuracy (22) improves. The accuracy bound is extended to multiple UTs in the Appendix.
connects to the BS with the strongest received signal strength, assumed to be .
aligns its timing to by carrying out a timing advance procedure, as described in Section 4.2.
If identified as active, emits at reference instants in (18) and adjusts its phase upon reception of according to (20).
In order to integrate CelFSync into a cellular mobile radio standard, several practical constraints need to be taken into consideration. Constraints regarding the frame structure and the chosen duplexing scheme are addressed in this section.
5.1. Frame Structure
CelFSync is implemented and verified based on the frame structure taken from the specifications of the Wireless World Initiative New Radio (WINNER, URL: http://www.ist-winner.org.) system concept . Consecutive downlink and uplink slots constitute one frame, and a number of successive frames form one super-frame of duration . One uplink and one downlink sync words and are placed into the superframe with a relative spacing of , as illustrated in Figure 4.
The downlink sync word allows UTs to synchronize to its BS and is therefore essential for cellular networks. Unlike , the insertion of the uplink sync word adds overhead, as is typically not required in current cellular networks. Fortunately, this overhead is modest as is typically transmitted with low rate. For the WINNER system the respective durations for superframe and are 5.8 ms and 45 s. Hence the resulting overhead is less than .
5.2. Acquisition and Tracking Modes
An intrinsic property of PCO synchronization is that coupling between nodes effectively shortens period . However, cellular systems typically rely on a fixed frame structure, which specifies the way uplink and downlink slots are arranged to exchange payload data. To this end, whilst the reception of payload data is still ongoing, CelFSync may shorten the period of two successive reference instants to , which effectively shortens the duration of the superframe.
As long as the effective period is only slightly shortened, such that , insertion of a guard time with duration ensures that reception of payload data is completed before a sync word is transmitted. The condition corresponds to the tracking mode in the steady synchronization state, where small offsets due to clock skews, leading to deviations of the natural oscillation period between nodes, are compensated.
suspending payload data transmission while intercell synchronization is in progress;
shortening the superframe duration to .
Scheme (i) does not allow for exchange of payload data before CelFSync has reached a steady state. Given that a steady state is likely to be maintained for hours or even days, while CelFSync typically converges within a fraction of a second or so, the loss in system throughput due to suspended data transmissions may be acceptable. For instance, scheme (i) is applied to facilitate the synchronization procedure in the wireless LAN standard 802.11 [23, 24]: periodically, data transfer is preempted, and the access point transfers its clock value, known as timing synchronization function (TSF), to the networks participants.
Scheme (ii) avoids conflicts by forcing the effective period to be at least as long as . By doing so, continuous exchange of payload data is maintained, at the expense of reducing the throughput during acquisition by about .
5.3. Duplexing Scheme
CelFSync is applicable to both time division duplex (TDD) and frequency division duplex (FDD). Nodes adjust their internal clocks based on received sync words; whether the uplink and downlink sync words are transmitted on different frequency bands or not is irrelevant. The discussion in this paper targets half-duplex transmission, where nodes cannot receive and transmit at the same time, applicable to TDD and half-duplex FDD. Full-duplex FDD benefits CelFSync, since nodes can transmit and receive simultaneously, which eliminates deafness due to missed sync words whilst transmitting.
5.4. Imposing a Global Timing Reference
An inherent problem of any distributed synchronization procedure is that nodes agree on a relative time reference, that is, valid only among the considered nodes and has no external tie. Such a relative reference is opposed to a global time reference such as the Coordinated Universal Time, which is provided by GPS for example. Furthermore, as the size of the network increases, it becomes increasingly difficult to synchronize the entire network in a completely decentralized manner. To avoid this difficulty, in  a scenario was considered where only a few nodes have access to a global time reference. The PCO model was extended such that these master nodes impose a global time reference to the entire network, even though the number of master nodes was only a small fraction of the total number of nodes in the network. Furthermore, the behavior of normal nodes that do not have access to a global time reference is not modified at all.
Applied to CelFSync a subset of BSs get access to a global time reference. These master BS emit downlink sync words with a slightly shortened period , and are not receptive to sync words from other nodes . Neighboring cells then align their reference instants following the synchronization rules outlined in Section 3.2. It was demonstrated in  that for , arbitrarily large networks are reliably synchronized. By doing so the problem of synchronizing large networks with a distributed algorithm is reduced to synchronizing a number of cells (typically up to or tiers) around a master BS.
Default simulation parameters.
False alarm rate
Sync word length
Number of BSs
Number of active UTs
Both environments impose different strains on CelFSync. In the indoor environment, sync words are subject to a high level of interference from other transmitting UTs. In the outdoor environment, the large distance between UTs and BSs results in higher channel attenuations, creating a more sparsely connected network, which implies that network synchronization is to be carried out over multiple hops.
In both scenarios, Monte-Carlo simulations are conducted for 5000 sets of initial conditions: all BSs initially commence with uniformly distributed internal timing references, while UTs are locally synchronized to their closest BS. Synchronization is declared when two groups have formed, so that reference instants of UTs are aligned and out-of-phase synchronized with reference instants of BSs, with a relative timing difference of .
6.1. Indoor Office Environment
The performance of the proposed inter-BS synchronization scheme can be controlled by the coupling factor . For a high coupling value, , synchronization is reached quickly, but convergence to a synchronized stable state is not always achieved. The fraction of initial conditions that do not converge to this state is due to deafness among nodes: some part of the network transmits partially overlapping and sequences, and due to the half-duplex assumption, some nodes are thus not able to synchronize. The deafness probability increases with the coupling factor , and for , it is approximately . If the coupling is low, , synchronization is always reached within periods, and for , of initial conditions lead to synchrony within periods. This is encouraging given the fact that deafness among nodes does not occur when , even though nodes start with a random initial timing reference. Setting sufficiently low reduces the absorption limit (4), which allows nodes to receive more sync words in the synchronization phase. This lowers the deafness probability, and enables the network to synchronize starting from any initial timing misalignment.
6.2. Macrocell Deployment
6.2.1. Time to Synchrony
As expected, networks of BSs converge less rapidly than smaller networks of BSs. This degradation is due to the increase in network diameter from hops to hops. Moreover, the number of UTs per cell participating in CelFSync, , does not significantly change the time to synchrony, and a synchrony rate of is achieved within when BSs and within when BSs. In all cases, a synchronization rate of is achieved within periods, which means that deafness between nodes, due to partially overlapping sync words, does not corrupt the convergence of CelFSync.
6.2.2. Achieved Inter-BS Accuracy
As the accuracy bound (22) suggests, the inter-BS accuracy is significantly improved as the node density increases. Augmenting increases the probability for selected UTs to be close to the cell edge, which decreases the delay difference in (22). For a UT density equal or higher than UTs per cell, the achieved accuracy is bounded by s. This is a significant achievement as the propagation delay for an inter-BS distance of is s.
This paper studied the application of self-organized synchronization inspired from the theory of pulse-coupled oscillators to cellular systems. The original algorithm was modified to align the timing references of base stations to simultaneously transmit on downlink frames, and of user terminals to simultaneously transmit on uplink frames. With the proposed decentralized cellular firefly synchronization (CelFSync) algorithm, a local area wireless network composed of base stations and user terminals is always able to synchronize within periods. In large-scale networks where propagation delays are typically non-negligible, the timing advance procedure, common in current cellular networks, was combined with CelFSync to combat the effect of propagation delays. By compensating intra-cell propagation delays with timing advance together with selecting cell edge users to participate in CelFSync, the detrimental effects of large propagation delays are substantially reduced. Simulation results demonstrated that the achieved inter-BS timing accuracy is always below s when at least users are randomly distributed per cell, which corresponds to approximately of the direct propagation delay for an inter-BS spacing of .
Achieved Accuracy for Multiple UTs
In the following the inter-BS accuracy bound (22) is extended to multiple UTs. Active UTs that are timing aligned to and are associated to cells and , respectively. Entities within cells and are perfect timing aligned, such that , , and , . In line with the discussion in Section 4.3, timing misalignments between entities belonging to different cells are bounded by four extreme cases: either UTs in cell or are forcing by imposing their timing reference to neighboring BS; alternatively either or force UTs in neighboring cells.
If UTs are timing aligned to the BSs with the shortest distance, the difference , for and , for , will always be positive. Hence, the bound (A.3) improves with growing numbers of UTs per cell and . Asymptotically, when , the accuracy approaches zero, so that the effect of propagation delays is perfectly compensated. This trend is confirmed by the simulation results presented in Section 6.2.2, which show that the achieved inter-BS accuracy significantly improves as the number of users per cell increases.
This work has been performed in the framework of the IST project IST-4-027756 World Wireless Initiative New Radio (WINNER), which is partly funded by the European Union. This paper was presented in part at the IEEE Vehicular Technology Conference (VTC 2008 Fall), Calgary, Canada, September 2008.
- Bregni S: Synchronization of Digital Telecommunications Networks. 1st edition. John Wiley & Sons, New York, NY, USA; 2002.View ArticleGoogle Scholar
- Akaiwa Y, Andoh H, Kohama T: Autonomous decentralized inter-base-station synchronization for TDMA microcellular systems. Proceedings of the 41st IEEE Vehicular Technology Conference (VTC '91), May 1991, St. Louis, Mo, USA 257-262.View ArticleGoogle Scholar
- Lagrange X, Godlewski P: Autonomous inter base station synchronisation via a common broadcast control channel. Proceedings of the 44th IEEE Vehicular Technology Conference (VTC '94), June 1994, Stockholm, Sweden 2: 1050-1054.View ArticleGoogle Scholar
- Izumi S, Hirukawa A, Takanashi H: PHS inter-base-station frame synchronization technique using UW with experimental results. Proceedings of the 6th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC '95), September 1995, Toronto, Canada 3: 1128-1132.View ArticleGoogle Scholar
- Tong F, Akaiwa Y: Theoretical analysis of interbase-station synchronization systems. IEEE Transactions on Communications 1998, 46(5):590-594. 10.1109/26.668726View ArticleGoogle Scholar
- Mirollo RE, Strogatz SH: Synchronization of pulse-coupled biological oscillators. SIAM Journal on Applied Mathematics 1990, 50(6):1645-1662. 10.1137/0150098MathSciNetView ArticleMATHGoogle Scholar
- Mathar R, Mattfeldt J: Pulse-coupled decentral synchronization. SIAM Journal on Applied Mathematics 1996, 56(4):1094-1106. 10.1137/S0036139994278135MathSciNetView ArticleMATHGoogle Scholar
- Hong Y-W, Scaglione A: A scalable synchronization protocol for large scale sensor networks and its applications. IEEE Journal on Selected Areas in Communications 2005, 23(5):1085-1099.View ArticleGoogle Scholar
- Simeone O, Spagnolini U, Bar-Ness Y, Strogatz SH: Distributed synchronization in wireless networks: global synchronization via local connections. IEEE Signal Processing Magazine 2008, 25(5):81-97.View ArticleGoogle Scholar
- Tyrrell A, Auer G, Bettstetter C: Biologically inspired synchronization for wireless networks. In Advances in Biologically Inspired Information Systems. Springer, New York, NY, USA; 2007:47-62.View ArticleGoogle Scholar
- Lucarelli D, Wang I-J: Decentralized synchronization protocols with nearest neighbor communication. Proceedings of the 2nd International Conference on Embedded Networked Sensor Systems (SenSys '04), November 2004, Baltimore, Md, USA 62-68.View ArticleGoogle Scholar
- Izhikevich EM: Phase models with explicit time delays. Physical Review E 1998, 58(1):905-908. 10.1103/PhysRevE.58.905View ArticleGoogle Scholar
- Ernst U, Pawelzik K, Geisel T: Synchronization induced by temporal delays in pulse-coupled oscillators. Physical Review Letters 1995, 74(9):1570-1573. 10.1103/PhysRevLett.74.1570View ArticleGoogle Scholar
- Tyrrell A, Auer G, Bettstetter C: On the accuracy of firefly synchronization with delays. Proceedings of the 1st International Symposium on Applied Sciences on Biomedical and Communication Technologies (ISABEL '08), October 2008, Aalborg, Denmark 1-5.Google Scholar
- Izhikevich EM: Weakly pulse-coupled oscillators, FM interactions, synchronization, and oscillatory associative memory. IEEE Transactions on Neural Networks 1999, 10(3):508-526. 10.1109/72.761708View ArticleGoogle Scholar
- Sourour E, Nakagawa M: Mutual decentralized synchronization for intervehicle communications. IEEE Transactions on Vehicular Technology 1999, 48(6):2015-2027. 10.1109/25.806794View ArticleGoogle Scholar
- Van Trees HL: Detection, Estimation, and Modulation Theory—Part I. 2nd edition. John Wiley & Sons, New York, NY, USA; 2001.View ArticleMATHGoogle Scholar
- Sanguinetti L, Tyrrell A, Morelli M, Auer G: On the performance of biologically-inspired slot synchronization in multicarrier ad hoc networks. Proceedings of the 67th IEEE Vehicular Technology Conference (VTC '08), May 2008, Marina Bay, Singapore 21-25.Google Scholar
- 3GPP TS 05.10 : Radio subsystem synchronization. 3GPP Std. 3GPP TS 05.10, 1995Google Scholar
- Lindsey WC, Ghazvinian F, Hagmann WC, Dessouky K: Network synchronization. Proceedings of the IEEE 1985, 73(10):1445-1467.View ArticleGoogle Scholar
- 3GPP : Evolved Universal Terrestrial Radio Access (E UTRA); physical channels and modulation. 3GPP Std. 3GPP TS 36.211, 2008Google Scholar
- IST-4-027756 WINNER II : D6.13.14: WINNER II System Concept Description. December 2007Google Scholar
- IEEE Std. 802.11a : Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications. 1999Google Scholar
- Zhou D, Lai T-H: Analysis and implementation of scalable clock synchronization protocols in IEEE 802.11 ad hoc networks. Proceedings of IEEE International Conference on Mobile Ad-Hoc and Sensor Systems, October 2004, Fort Lauderdale, Fla, USA 255-263.Google Scholar
- Tyrrell A, Auer G: Imposing a reference timing onto firefly synchronization in wireless networks. Proceedings of the 65th IEEE Vehicular Technology Conference (VTC '07), April 2007, Dublin, Ireland 222-226.Google Scholar
- IST-4-027756 WINNER II : D1.1.2: WINNER II Channel Models. December 2007Google Scholar
- IST-4-027756 WINNER II : D6.13.7: Test Scenarios and Calibration Cases Issue 2. December 2006Google Scholar
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