The present disclosure relates to train communication technologies, and in particular, to a method and a device for wireless typology discovery for train backbone networks.
The international standard IEC61375 divides a train communication network (TCN) into two hierarchical networks, namely a train backbone network at a higher level and consist networks (CNs) at a lower level. Currently, the train backbone network is mainly based on bus technology, and consists, for example, of wire train bus (WTB) and multifunction vehicle bus (MVB). WTB is primarily used in vehicles such as locomotives and EMU trains having requirements for dynamic car configuration, and MVB is primarily used in vehicles such as EMU trains with fixed car configuration.
The process for initiation and dynamic configuration of TCN is called train inauguration. The inauguration process is a precondition for normal operation of TCN and is performed when power supply or car configuration in a train changes. This process involves assignment of identifiers (IDs) to train backbone nodes (TBNs) and CNs, construction of physical topology for the network, determination of direction of cars with relation to a reference direction of the backbone network, and construction of logical typology for the network, etc.
Because a train backbone network consists of linear networks, completion of communications in such a network critically depends on topology discovery or train inauguration. Topology discovery or train inauguration is, however, achieved through learning and exchange of messages among BNs in the network. According to current standard for inauguration of wired train backbone networks, only neighboring BNs are connected via physical wires (as shown in
To summarize, the implementation of topology discovery over a wired network is capable of realizing train inauguration, but is restricted in its application by electrical connections between cars, high wiring cost, difficulty in detecting of a line fault and in maintaining of lines, limited wiring space for which it has to contend with power lines, and by the need to manually cut off or reconnect the cables between different consist networks for car reconfiguration, which is complex to operate and time-consuming, and may result in wrong and unstable cable connection. Besides, connectors used become easily aged and may also cause faults in the lines.
Backbone communications based on a wireless network can avoid all the above problems. However, the implementation of wireless topology discovery is made difficult by the broadcast nature of the wireless medium, and by fading and interference.
It is therefore desirable to provide a method and a system for simple and effective topology discovery for a wireless train backbone network, for example, in the process of train inauguration.
The objective of the present disclosure is to address the technical problem of the incapability of the existing technologies in providing simple and effective topology discovery for a wireless train backbone network.
In order to achieve the above objective, the present disclosure provides a method for wireless typology discovery for train backbone networks. The method comprises steps of: receiving, by a BN in a train backbone network, data from a neighbor of the BN, through one directional antenna of at least one pair of directional antennas provided thereon; recording a receiving direction of said data, and determining said data to be a hello frame or a typology frame; performing neighbor discovery or topology discovery based on the type of said data; performing, in neighbor discovery phase, a pair consistency check on the data received by the BN along a same direction, so as to identify a neighbor of the BN, and at the same time, stopping receiving hello frames along said direction, updating, in typology discovery phase, a local typology table of the current BN based on the received typology frames; and performing a topology convergence check to determine whether any change occurs to the local typology table of the current BN during a period of time, and reporting the status of the typology discovery phase to a high-level application if no change occurs.
According to one embodiment of the present disclosure, the frequency at receiving channel of each BN is different from that at transmission channel, and each antenna of the directional antenna pair has a different frequency band.
According to another embodiment of the present disclosure, in the neighbor discovery phase, a neighbor discovery counter is provided for counting hello frames received from a same BN, and the BN is identified as a neighbor of the current BN if the neighbor discovery counter reaches or exceeds a first pre-defined threshold value.
According to another embodiment of the present disclosure, after identifying the neighbor of the current BN, typology frames along said direction from the neighbor are received, and wherein if the destination address of the received typology frames is the address of the current BN, a pair consistency check on said currently received typology frames and previously saved typology frames is performed so as to determine whether the current BN and the neighbor are pairwise consistent or not, and in the meantime, receiving any hello frames along said direction from the neighbor is stopped.
According to another embodiment of the present disclosure, after identifying the neighbor of the current BN, it starts to receive typology frames along said direction from the neighbor node, and wherein if the destination address of the received typology frames is not an address of the current BN and the neighbor discovery counter exceeds a pre-defined threshold value, a notice of a neighbor discovery failure is issued.
According to another embodiment of the present disclosure, a typology convergency check on local typology frames received by the current BN is performed, and wherein if any change occurs to the local typology frames, the current BN fails the typology convergency check, and then updating the local typology table based on changed typology frames and initializing the typology counter to zero; and if no change occurs to the local typology frames, the typology counter is increased by one, and if the typology counter reaches or exceeds a pre-defined threshold, the typology convergency check is passed and typology discovery at the current BN is completed.
According to another embodiment of the present disclosure, the typology frame contains a list of ordered MAC addresses in a current typology table of a sender BN.
According to another embodiment of the present disclosure, a topology frame sent by a BN to a right neighbor contains all the currently known MAC address of BNs on the left of the BN in the discovered physical order, and a topology frame sent by the BN to a left neighbor contains all the currently known MAC address of BNs on the right of the BN in the discovered physical order.
According to another aspect of the present disclosure, a device for wireless typology discovery for train backbone networks is provided.
The device comprises: a receiving unit, for receiving, by a backbone node in a train backbone network data from a neighbor BN of the backbone node, through one directional antenna of at least one pair of directional antennas provided thereon, a recording unit, for recording a receiving direction of said data, and determining said data to be a hello frame or a typology frame, a neighbor discovery unit, for performing neighbor discovery or topology discovery based on the type of said data, and in neighbor discovery phase, performing a pair consistency check on the data received by the BN along a same direction, so as to identify a neighbor of the BN, and at the same time, stopping receiving hello frames along said direction by the BN, a topology discovery unit, for updating a local typology table of the current BN based on the received typology frames in typology discovery phase, and a typology generation unit, for performing a topology convergence check to determine whether any change occurs to the local typology table of the current BN during a period of time, and, reporting the status of the typology discovery phase to a high-level application if no changes occurs.
According to one embodiment of the present disclosure, the frequency at receiving channel of each BN is different from that at transmission channel, and each antenna of the directional antenna pair has different frequency band.
According to another embodiment of the present disclosure, in the neighbor discovery phase, a neighbor discovery counter is used for counting hello frames received from a same BN, and the BN is identified as a neighbor of the current BN if the neighbor discovery counter reaches or exceeds a first pre-defined threshold value.
According to another embodiment of the present disclosure, after identifying the neighbor of the current BN, the current BN starts to receive typology frames sent along said direction from the neighbor, and wherein if the destination address of the received typology frames is the address of the current BN, a pair consistency check on said currently received typology frames and previously saved typology frames is performed so as to determine whether the current BN and the neighbor are pairwise consistent or not, and in the meantime, the current BN stops receiving any hello frames along said direction from the neighbor.
According to another embodiment of the present disclosure, after identifying the neighbor of the current BN, the BN starts to receive typology frames along said direction from the neighbor node, and wherein if the destination address of the received typology frames is not an address of the current BN and the neighbor discovery counter exceeds a pre-defined threshold value, a notice of a neighbor discovery failure is issued.
According to another embodiment of the present disclosure, a typology convergency check is performed with respect to local typology frames received by the current BN. If any change occurs to the local typology frames, it signals that the current BN fails the typology convergency check, and then the local typology table is updated based on changed typology frames and a typology counter is initialized to zero; and if no change occurs to the local typology frames, the typology counter is increased by one, and if the typology counter reaches or exceeds a pre-defined threshold, it signals that the typology convergency check is passed and typology discovery at the current BN is completed.
According to another embodiment of the present disclosure, the typology frame contains a list of ordered MAC addresses in a current typology table of a sender BN.
According to another embodiment of the present disclosure, a topology frame sent by a BN to a right neighbor contains all the currently known MAC address of BNs on the left of the BN in the discovered physical order, and a topology frame sent by the BN to a left neighbor contains all the currently known MAC address of BNs on the right of the BN in the discovered physical order.
Other features and advantages of the present disclosure will be further explained in the following description, and will partly become self-evident therefrom, or be understood through the implementation of the present disclosure. The objectives and advantages of the present disclosure will be achieved through the structures specifically pointed out in the description, claims, and the accompanying drawings.
The accompanying drawings, together with the embodiments, are provided for a further understanding of the present disclosure, and constitute a part of the description, and are not intended to limit the present disclosure.
and
The present disclosure will be explained in detail below with reference to the accompanying drawings, so that the objective, technical solutions and advantages thereof can be understood more clearly.
The basic task of typology discovery is to enable each BN to learn the physical topology of a train backbone network. The physical topology consists of an ordered list of media access control (MAC) addresses of the BNs in the network, where the order reflects the physical location of the BNs in the linear topology. According to current standard IEC61375-2-5, the process operates via the exchange of MAC-level messages among the BNs in a distributive fashion. To illustrate the concept of a physical topology, an example is provided in
The typology discovery protocol (TDP) that is currently being standardized for train backbone communications applies to wired train backbone networks, in which the BNs are connected to their neighbors via dedicated wires. The TDP usually consists of two phases, namely neighbor discovery and topology discovery.
In the neighbor discovery phase, each BN finds the MAC address of its neighboring BNs. In the topology discovery phase, the physical topology is detected via message exchange at the MAC layer. The standard also considers the discovery of the “logical” topology of the train. To implement TDP, the BNs transmit two types of MAC frames: hello frames, which carry only the MAC address of the sender BN and are used for neighbor discovery; and topology frames which carry information about the MAC addresses of the BNs currently “discovered” by the sender BN and are used for topology discovery.
While the standard IEC61375-2-5 applies to wired backbone networks, there is high interest in the industry to develop a fully wireless solution. The implementation of TDP over a wireless network is made difficult by the broadcast nature of the wireless medium, and by fading and interference. Consider for instance the neighbor discovery phase. In wired TDP, hello frames are transmitted only to the neighbor(s) of a BN as shown in
This effect is compounded by the fact that, due to fading and interference, there is a non-zero probability that decoding errors impair the transmission from physical neighbors more significantly than the transmission from further BNs. Unlike the wired case, simultaneous transmissions in the same frequency band may lead to interference, which may cause the loss of a packet. For instance, with reference to
In studies on wireless network topology discovery, the key underlying assumption is that two BNs are considered to be neighbors if they are within their respective transmission ranges such that it is possible to establish a direct link between them. The topology discovery protocol hence aims at identifying connectivity, or reachability, properties of the network. This is typically done either by checking if a hello message is successfully received or by measuring received signal strengths. The design of specific topology discovery algorithms has been conducted in the context of different protocols such as IEEE802.11, or ZigBee. However, train backbone networks have their own features, and hence design of topology discovery algorithms for them is unique, too.
In classical topology discovery, as discussed above, a BN is considered to be a neighbor as long as it is reached with a significantly large power. This goal is completely different from the requirements of train backbone inauguration, in which instead a neighbor is defined by its physical location and not by the strength of the received power. To see the difference, note that each BN has only two neighbors, one that should be specified as left-neighbor and one as right-neighbor. In contrast, a classical topology discovery scheme may identify an arbitrary number of neighbors that happen to receive the transmitted signal with sufficient power without consideration of their physical location.
The following is a brief review about the standard wired TDP. Before the inauguration process, each BN knows its own MAC address and also the unique identifier (ID) of the consist networks (CNs) that are connected to the BN. A CN represents a subnetwork on the train. BNs may belong to multiple CNs, as illustrated in
After inauguration, a BN ID is assigned to each BN according to the identified physical topology, and a subnet ID is assigned to each CN following the logical topology that is discovered. Taking the backbone network in
Each BN, except the two at the beginning and end of the train, has two outgoing links, one toward its neighbor to the “right” and one towards the “left”. Note that the notions of “left” and “right” are common to all BNs on the backbone and are set by construction. Similarly, each BN has also two incoming links, one from the neighbor on the left and one from the neighbor on the right.
Neighbor discovery is achieved as follows. Each BN sends a hello frame to its neighboring BNs in the network via the MAC layer. When another BN receives the hello frame, it learns the MAC address of the sending neighbor, and identifies the sending neighbor as a right-neighbor or a left-neighbor by the incoming link thereof through which the hello frame is received. When the BN receives both the hello frames from the right neighbor and the left neighbor, the neighbor discovery phase is completed (An end BN can learn that a BN is not provided on its right side or on its left side).
After neighbor discovery, topology discovery is performed. Each BN sends a topology frame carrying topology information (see Table I) to its neighboring BNs. All the BNs and CNs has a unique ID. Each BN maintains a physical and topology table and updates its physical and logical topology table upon reception of a topology frame, and transmits information about the updated topology table via a topology frame. Topology discovery is completed when the topology information of each BN no longer changes.
To prevent effect on the wireless communication caused by frequency interference, each BN operates on a pair of two different frequencies in each direction, one for transmission and the other for reception, and operates on two different pairs of frequencies in both directions. As shown in
All the BNs have two directional antennas and share the notion of a “left” and a “right” direction, so that the BNs can distinguish between the signals received from the right and left directions, thus providing a physical basis for the BN's identification for right and left neighbors in neighbor discovery. In addition, the use of directional antenna can define the direction and scope of wireless signal coverage. This can reduce interference on a target train by a neighboring train on a parallel track, thus avoiding topology discovery failure caused by an error of identifying a BN in the neighboring train as a neighboring BN in the target train.
To summarize, in order to ensure accuracy of typology discovery, the following conditions must be satisfied before the typology discovery algorithm provided by the present disclosure is performed. Each BN should be assigned with a unique MAC address. A right end BN and a left end BN should be specified. A wireless network should be configured to make wireless communications possible. Wireless communication protocol is not restricted in present disclosure, and it can be ZigBee, WiFi, etc.
In addition, the algorithm provided by the present disclosure makes use of communications at the MAC layer, and determines a source BN and a destination BN through the MAC address of the BN.
Neighbor Discovery:
As discussed above, neighbor discovery in a wireless train backbone is significantly more complex than in the wired counterpart system. This is due to the broadcast properties of the wireless channel, which cause the hello frame transmitted by a BN to be received not only by the actual neighbor BN but generally also by further away BNs. As a result, unlike in the wired system, reception of the hello frame does not, per se, establish that the sender BN is a neighbor.
In order to achieve neighbor discovery, the proposed scheme leverages the fact that, on the average, the power received from an actual neighboring BN is larger than that received from any other BN. This is due to the lower path loss between closer BNs. Therefore, for instance, it is more likely that a hello frame is received correctly from an actual neighbor than from farther BNs. It is critical to note, however, that, due to fading, it cannot be excluded that a hello frame from a non-neighboring BN is received successfully, while that of the actual neighbor is not.
For each hello frame correctly decoded in either direction, if the MAC of the sender BN is already in the list of neighbor discovery (ND) counters, then the corresponding counter is increased by one; else, a new counter is created, initialized to zero and associated to the MAC address at hand. A BN is identified to be a neighbor if it is the first whose ND counter reaches a pre-defined threshold MH. In this event, this BN is defined as the identified neighbor of the receiving BN. The described operations are within in the “neighbor discovery” block of
Specifically, in the process of neighbor discovery, a BN transmits a same hello frame to the right and left directions, and at the same time receives hello frames from BNs on its right and left. Taking a BN named BNi for instance, when BNi receives a hello frame from BNj on its left, if this is the first time that BNi receives a hello frame from BNj, then an ND counter corresponding to BNj is created, and is initialized to zero (NDC(j)=0); if BNi has received a hello frame from BNj, then the ND counter corresponding to BNj is increased by one. In this case, if NDC(j)≧MND (MND represents a pre-defined threshold), BNj will be defined as the left-neighbor of BNi. After that, BNi starts pair consistency check (PCC) in the left direction. If topology frames from other BNs are received during neighbor discovery phase, said topology frames are saved.
The algorithm proposed above makes exclusive use of information available at the MAC layer. This choice has been made in order to allow for a simpler implementation, and is in line with the wired counterpart standard.
Pair Consistency Check (FCC):
If a BN starts PCC in a certain direction, it stops receiving hello frames coming from said direction, but still sends hello frames periodically. In the meanwhile, the BN starts to send a typology frame to the identified neighbor in said direction, receives typology frames transmitted from said direction, and performs PCC and neighbor discovery failure check (NDFC) with respect to typology frames received from said direction and previously saved typology frames.
If a BN receives typology frames addressed to a BN other than itself, neighbor discovery failure check (NDFC) is performed. If the number of typology frames addressed to other BNs reaches a pre-defined threshold MNDF, it indicates failure of NDFC and incorrect neighbor discovery, and an error is reported for further processing.
In order to reduce the probability of incorrect neighbor discovery, the present disclosure proposes to perform a pairwise consistency check (PCC) upon the reception of a topology frame. The key observation is that the topology frame is addressed to the currently identified neighbor. Note that the hello frames in the present disclosure are instead broadcast. Therefore, based on the reception of topology frames, each BN can verify whether the neighbor discovery is pairwise consistent with respect to its neighbor in either direction. Pairwise consistency means that two BNs consider each other as neighbors, one on the left and the other on the right. If a topology frame is received from a BN that is not considered as a neighbor, then the receiving BN can conclude that neighbor discovery is not pairwise consistent in the direction of the received packet.
To be specific, if the topology frame is received from a currently identified neighbor, this identified neighbor passes the PCC and is upgraded to the status of locked neighbor. Once a locked neighbor is established for a BN, any received topology frame from other BNs is discarded. Instead, if a BN receives a topology frame from a BN different from the identified neighbor, its identified neighbor fails the PCC and all ND counters are reinitialized to zero in order to restart the neighbor discovery phase for the receiving BN. Note that, if a topology frame is received before any identified neighbor is established, the frame is saved for a PCC later. The detailed procedure for PCC is described within the “pairwise consistency check” block of
As shown in
Neighbor Discovery Failure Check (NDFC):
PCC helps improve the accuracy of neighbor discovery, but it does not rectify errors that occur when two neighboring BNs identify their neighbors incorrectly. This type of failure is defined as neighbor identification failure. An example is shown in
In order to identify the neighbor discovery failure described above, the present disclosure proposes to perform neighbor discovery failure check. The idea is that, after a neighbor has been identified but not locked, if a BN receives too many topology frames addressed to a BN other than itself, it is probable that its actual neighbor had identified some other BN as its neighbor. In this case, this BN cannot successfully complete neighbor discovery and a red flag is raised. Specifically, each BN maintains an NDF counter, which counts the number of topology frames addressed to other BNs that are received after a neighbor has been identified. When the NDF counter reaches a pre-defined threshold MNDF, the BN raises a red flag warning the train operator of a neighbor discovery failure.
The other possible neighbor discovery failure happens when a BN is established as the locked neighbors by more than one BN. This causes the problem that certain BNs do not receive topology frame from their locked neighbors and thus topology discovery will never be completed. This type of failure is defined as neighbor locking failure. An example is shown in
Due to the introduction of the PCC phase and NDFC phase, the protocol proposed in the present disclosure is a bidirectional protocol. Hence, these phases can also be used to counteract hello flooding attacks based on wormhole (tunneling), or compromised nodes. In a hello flooding attack, hello messages/frames are transmitted or tunneled with a very abnormal high power convincing many surrounding nodes that the malicious node is their neighbor.
Specifically, in one embodiment, when a BN starts NDFC, if it receives a typology frame addressed to a BN other than itself, it performs NDFC with respect to said received typology frame. If NDFC is passed, it indicates a success of typology discovery; otherwise, it indicates a failure of typology discovery, and an error is reported for further processing. If the BN receives a typology frame addressed to itself, it starts typology discovery.
Topology Discovery:
As described above, multicasting a topology frame is impractical in WTDP. To solve this issue, the present disclosure proposes that, in WTDP, the topology frame contains an ordered, rather than an unordered as in wired TDP, list of MAC addresses in the current topology table of the sender BN. Specifically, the topology frame sent to the neighbor on the right contains all the currently known MAC address of the BNs on the left of the BN in the discovered physical order, and vice versa for the topology frame sent to the neighbor on the left. The topology frame also includes the CN IDs that are connected to, rather than only the sender BN as in wired TDP, all BNs currently discovered. Taking the wireless backbone network in
After a successful neighbor discovery has been resolved for all BNs, it is necessary and sufficient to have a “right-ward” and a “left-ward” pass in order to complete topology discovery. For instance, in
The WTDP proposed by the present disclosure differs from the standard wired TDP in that the latter prescribes multicasting of topology frames and the inclusion of an unordered list of discovered BNs and the CN IDs that are connected to the sender BN only in the topology frames.
In typology discovery phase, if the BN receives a typology frame addressed to a BN other than itself, it performs NDFC with respect to said received typology frame. If NDFC is not passed, it indicates a failure of typology discovery, and an error is reported for further processing. If the BN receives a typology frame addressed to itself, it updates its typology table based on the received typology frames, and starts topology convergency check (TCC) phase.
Topology Convergency Check (TCC):
In order for the operator to make a decision about the completion of the inauguration process, the BNs must report on the status of their topology discovery phase. To this end, each BN runs a topology convergence check as shown in the “topology convergency check” block of
To be specific, in one embodiment, in the TCC phase, TCC is performed with respect to the local typology frames. If any change occurs to any of the local typology frames, TCC is not passed, and the local typology table is updated based on the local typology frames and the typology counter is initialized to zero; otherwise, the typology counter is increased by one. If the typology counter reaches a pre-defined threshold MTC, the topology discovery completion for the BN is claimed, and the BN completes typology discovery. After completion of the typology discovery, the BN still has to send typology frames to other BNs periodically to ensure completion of typology discovery by other BNs. The BN, in the meanwhile, reports on the status of its typology discovery phase to an up-level application.
The data structure in the present disclosure can be normalized as required. An example is provided herein for a better understanding. According to one embodiment of the present disclosure, a hello frame can be described as shown in Table II.
A typology frame can be described as shown in Table III.
WTDP is based on a physical implementation of the system that leverages directional antennas and frequency planning.
Directional Antenna:
All the BNs have two directional antennas and share the notion of a “left” and a “right” direction. Each BN hence can transmit and receive on both its right-pointing and left-pointing antennas. Note that the assumption concerning the common notion of the left and right directions is consistent with the model considered in the wired standard. Directional antennas enable a BN to distinguish between the signals received from the left and right directions.
Frequency Planning:
To cope with interference, two sets of frequencies are used, one for the right-pointing antennas and one for the left-pointing antennas. Each directional antenna operates on two different frequencies, one for transmission and one for reception. Moreover, the same frequency is reused every F hops. Therefore, if F=1, full frequency reuse in each direction occurs; instead, if F>1, there are F−1 BNs transmitting in the same direction but using different frequencies between two transmitters using the same frequency.
In order to get some insights into the performance of the proposed WTDP, the implementation of WTDP with a slotted ALOHA MAC protocol is considered. Note that the protocol does not depend on the adoption of a specific MAC layer protocol and that slotted ALOHA is assumed here to enable analysis. According to slotted ALOHA, time is slotted, a transmitted frame takes one slot, and each BN transmits a frame in a slot with probability p. Specifically, at each time slot, a BN transmits a hello frame with probability pH, and transmits a topology frame with probability pT. Hence, the transmission probability p is the sum of pH and pT, i.e., p=pH+pT.
Flat Rayleigh fading channels are assumed such that the instantaneous channel gain between two BNs k hops away can be written as SNR0|h|2/(1+(k−1)F)η, where the average signal to noise ratio (SNR) for two BNs one hop away is defined as SNR0, |h|2 is exponentially distributed with mean one, and η denotes the path loss exponent. Furthermore, the channels across different time slots are assumed to be independent, while the channel is a constant within the period of a frame transmission. It is noted that a more general channel model, such as Rician or Nakagami fading, could also be accommodated in the analysis but at the cost of a more cumbersome notation due to the lack of some closed-form expressions that are available for Rayleigh fading as discussed below. Experiments with Rician fading will be presented later.
In the following, an analysis is provided for the neighbor discovery phase in terms of the probability of correct neighbor discovery and of the average time required to complete neighbor discovery. There two conflicting criteria will also be combined to yield the average time needed to achieve successful neighbor discovery. The goal of the analysis is to obtain insights into the selection of the critical threshold parameter MH. The performance of the overall WTDP will be evaluated in the next section via numerical results.
In this subsection, the neighbor discovery for a single receiving BN on any given side is considered. The probability QC,ND of correct neighbor discovery and the cumulative distribution function (CDF) FTND(t) of the time TND that it takes to complete neighbor discovery are computed. To elaborate, assume that the furthest BN from which hello frames can be received is K hops away. The signal-to-interference-and-noise ratio (SINR) for the signal transmitted by a BN k hops away is given by
where ik′=1 if the BN k′ hops away is transmitting and ik′=0 otherwise. Moreover, the instantaneous channel capacity for the link between the two BNs, which are k hops away from each other, is given by [34]
C
k=log(1+SINRk) (2)
Whenever the transmission rate R [bits/sec/Hz] is not larger than the instantaneous capacity Ck, the packet transmitted by the BN k hops away is correctly received, and an outage is declared otherwise [35].
Define the vector i=[i1, . . . , iK]T that defines the set of currently transmitting BNs. At any time slot, the probability of a successful frame reception from a BN k hops away conditioned on i can be expressed as
Substituting (2) into (3) leads to
Using the result in [36] leads to
Averaging over all possible transmission states i, the probability of a successful frame transmission from a BN k hops away can be written as
where I denotes the set that contains all possible 2K transmission state vectors and Pi(i) is the probability mass function of vector i.
Due to the independence of the fading channels across the time slots, the time TK that it takes to receive MH hello frames from a BN k hops away is distributed as Tk˜NB(MH,QS(k)), where the notation NB(M,p) is used to denote a negative binomial distribution (in a sequence of independent Bernoulli (p) trials, let the random variable N denote the trial at which the Mth success occurs, where M is a fixed integer. Then N has a negative binomial distribution [37] with parameter (M, p), i.e. N˜NB(M,p)) with parameter (M,p). Accordingly, the probability mass function of TK is given by [37]
for t≧MH; and the complementary cumulative distribution function (CCDF) of TK, which for t≧MH; and the complementary cumulative distribution function (CCDF) of TK, which equals to the probability that hello frames sent by a BN k hops away are received successfully MH times after the tth time slot, can be expressed as [37]
T
(t)=1−IQ
where Ix(z,w) denotes the regularized incomplete beta function with parameters (x, z, w).
So far, the distribution of the time needed to receive MH hello frames from a given transmitting BN has been considered. Now interest is given in deriving the probability QC,ND of correct neighbor discovery. This calculation is complicated by the fact that the receptions of frames from different BNs are correlated with each other due to the mutual interference among BNs. To address this issue, an approximation is made here that the decoding outcomes for the packets sent by different BNs are independent. The validity of this approximation will be evaluated in later section by numerical results. Recall that, if the first BN from which hello frames are received successfully MH times is the BN one hop away, neighbor discovery is correct. Hence, using the said independence assumption, the probability of correct neighbor discovery for a single receiving BN is
Finally, regardless of whether it is correct or not, neighbor discovery is considered to be complete when a BN decodes MH hello frames successfully from at least one of other transmitting BNs. The CDF of the time it takes to complete neighbor discovery for the BN TND can be expressed, under the independence assumption, as
In this subsection, the performance metrics of neighbor discovery across the entire network is derived. Specifically, the probability QC,ND* of correct neighbor discovery, the average time E[TND*] required to complete neighbor discovery for all BNs and the average time E[TND,suc*] needed to achieve a successful neighbor discovery are derived.
Because the neighbor discovery outcomes for different BNs are not independent, the analytical derivation of statistical quantities associated with neighbor discovery performance is challenging. For this reason, the approximation mentioned above will be made that the neighbor discovery outcomes for different BNs are independent. With this approximation, probability of correct left and right neighbor discovery for all BNs in the network can be expressed as
Q
C,ND*=(QC,ND)2D (11)
where D denotes the total number of receiving BNs and the factor 2 stems from the fact that different frequencies are used for transmission and reception and hence, the left neighbor discovery is independent from the right neighbor discovery. Similarly, the CDF of the time it takes to achieve a successful neighbor discovery on both left and right sides is given by
F
T
*(t)=(FT
The average time needed to achieve a successful neighbor discovery E[TND] is then given by
Next, the two statistical quantities QC,ND* and E[TND*] are combined to yield the average time it takes to achieve a successful neighbor discovery E[TND,suc*]. Using Wald's equality [38] (If {xn; n≧1} is a sequence of independent identically distributed random variables with mean
In this section, a scenario of practical interest is provided. In this scenario, two trains located on parallel tracks perform separate inauguration processes. As shown in
The following section deals with the evaluation of the performance of the proposed WTDP as applied to a wireless network that runs the ALOHA MAC protocol. Unless stated otherwise, the following conditions are assumed: i) a flat Rayleigh fading channels; ii) a path loss exponent η=3.5; iii) an average SNR of 15 dB for two BNs one hop away, i.e., SNR0=15 dB; iv) a total of six BNs in the network; v) at any time slot, a hello frame is transmitted with probability, pH=0.15, and a topology frame is transmitted with probability, pT=0.15; vi) a data rate R 1.5 [bits/sec/Hz] for the hello frames, and vii) full frequency reuse is adopted, i.e., F=1. A more conservative frequency reuse would alleviate interference and therefore improve the performance.
The effect of the threshold parameter MH on the neighbor discovery performance is first investigated. In
B. Effects of the Threshold MNDF and MT
The effects of two thresholds MNDF and MT on the performance of WTDP are now discussed. The value of threshold MH is set to 3 based on the discussion above.
Neighbor discovery over flat-fading Rician channels is now considered. The defining parameter of Rician fading is the K-factor, which is defined as the power ratio of the line-of-sight component and diffuse components.
In this subsection, the neighbor discovery performance is evaluated with two trains located on parallel tracks as described in the former section. The BNs of both trains transmit by using the slotted ALOHA protocol. Note that while this assumes synchronization between the trains, it is expected that the effect of inter-train interference is qualitatively the same even under asynchronous MACs. The neighbor discovery performance for train 1 is evaluated with train 2 serving as interference. Each train is equipped with six BNs. The beam width θ is selected as θ=π/3. Rayleigh fading is assumed.
In contrast to the probability of correct neighbor discovery, the average time required to complete neighbor discovery is shown in
It should be noted that the above embodiments are described only for better understanding, rather than restricting the present disclosure. Anyone skilled in the art can make any amendments to improvements on the implementing forms or details without departing from the scope of the present disclosure. The protection scope of the present disclosure shall still be determined by the claims.
Number | Date | Country | |
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62300193 | Feb 2016 | US |