CN112601200B - Low-power-consumption Bluetooth device discovery delay evaluation method based on Markov chain - Google Patents

Low-power-consumption Bluetooth device discovery delay evaluation method based on Markov chain Download PDF

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CN112601200B
CN112601200B CN202011273245.3A CN202011273245A CN112601200B CN 112601200 B CN112601200 B CN 112601200B CN 202011273245 A CN202011273245 A CN 202011273245A CN 112601200 B CN112601200 B CN 112601200B
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沈中
刘思锐
李振
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Xidian University
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/80—Services using short range communication, e.g. near-field communication [NFC], radio-frequency identification [RFID] or low energy communication
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    • H04W48/00—Access restriction; Network selection; Access point selection
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Abstract

The invention discloses a low-power-consumption Bluetooth device discovery delay evaluation method based on a Markov chain, which comprises the following steps of: obtaining operating parameters related to discovery of a BLE device; constructing a Markov chain based on the working parameters; the states in the state set of the Markov chain include: all times within three scan periods as required by the BLE specification; solving the average transfer step number of each state in the state set reaching the absorption state as the expected transfer step number of the state; the absorption state is the moment when the scanning party BLE equipment receives the advertisement sent by the advertising party BLE equipment; calculating an expected discovery delay according to the expected transition steps of all the states; determining an evaluation result according to the expected discovery delay; the evaluation result is used for determining whether to apply the operating parameter in the BLE device; the invention can accurately evaluate the discovery delay of the low-power-consumption Bluetooth equipment.

Description

Low-power-consumption Bluetooth device discovery delay evaluation method based on Markov chain
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a low-power-consumption Bluetooth device discovery delay evaluation method based on a Markov chain.
Background
BLE (Bluetooth Low Energy) is a widely used wireless communication technology and is one of the key technologies of the internet of things. Many smart devices currently support BLE. The BLE specification divides BLE devices into scanners and advertisers. Two-party BLE devices first complete device discovery before connecting, with one BLE device acting as a scanner periodically scanning 37, 38 and 39 three advertising channels, and the other BLE device acting as an advertiser periodically triggering advertising events, each specifically sending advertisements to three advertising channels. When the scanning party BLE device receives an advertisement packet sent by the advertising party BLE device on a certain advertisement channel, device discovery is completed; then, the two can establish connection and perform data transmission. It follows that how fast the device discovers is critical for BLE applications.
BLE in 4.2 and later releases provides that to avoid collisions of advertisement packets, advertisers add a pseudo-random delay of 0-10 ms before each advertisement event. While this approach improves the robustness of the system, the time of each device discovery is a random value. In order to reduce discovery delay, it is generally desirable that the delay in device discovery be as small as possible. The device discovery process for BLE devices typically involves 6 operating parameters: a scan cycle length of the scanner BLE device, a scan window length of the scanner BLE device, an advertisement cycle length of the advertiser BLE device, a pseudorandom delay, a length of time for the advertiser BLE device to send an advertisement, and a length of time for listening to a channel after sending the advertisement. It was found experimentally that the discovery delay of BLE devices is very sensitive to the 6 operating parameters mentioned above. For example, the discovery delay may vary by several times even if the advertising period length is increased or decreased by 625 microseconds, the minimum duration of variation allowed by the BLE specification. Therefore, it is necessary to evaluate the selected operating parameter to determine whether to use the operating parameter in the BLE device.
Jeon et al, in its published paper "Performance analysis of neighbor discovery process in Bluetooth low-energy networks" (2017IEEE trans. veh. technol) propose a method of evaluating the expected delay. The method takes a fixed-length time slot as a basic time unit. While the parameter values for all BLE are also approximately converted to slot numbers and then the expected delay is calculated using CRT (Chinese remainder theorem). However, in the method, the pseudo-random delays of 0-10 ms specified by the BLE specification are all approximate to the number of time slots corresponding to 5ms, that is, the pseudo-random delays become constant, a random problem is converted into a deterministic problem, and the randomness of the device discovery process is not considered, so that the method cannot accurately evaluate the discovery delay of the low-power-consumption bluetooth device.
Disclosure of Invention
In order to accurately evaluate the discovery delay of the low-power-consumption Bluetooth device, the invention provides a low-power-consumption Bluetooth device discovery delay evaluation method based on a Markov chain.
The technical problem to be solved by the invention is realized by the following technical scheme:
a low-power Bluetooth device discovery delay assessment method based on a Markov chain comprises the following steps:
acquiring working parameters related to a device discovery process of low-power-consumption Bluetooth BLE;
constructing a Markov chain based on the working parameters; wherein each state in the set of states of the Markov chain comprises: all times within three scan periods as required by the BLE specification; and the interval between adjacent moments is equal to the preset unit time;
solving the average transfer step number of each state in the state set reaching the absorption state as the expected transfer step number of the state; wherein the absorption state is: the moment when the scanning party BLE equipment receives the advertisement sent by the advertising party BLE equipment;
calculating an expected discovery delay according to the expected transition steps of all the states;
determining an evaluation result according to the expected discovery delay; wherein the evaluation result is used to determine whether to apply the operating parameter in a BLE device.
Optionally, the unit time includes: a few nanoseconds or a few microseconds.
Preferably, the state set is: {0,1,2, …,3Ts-1}；
The absorption states include all states in the following three sets:
{0，1，…，Tw-τ}、
{Ts-τ-δ，Ts-τ-δ+1，…，Ts-τ-δ+Tw-τ}、
{2(Ts-τ-δ)，2(Ts-τ-δ)+1，…，2(Ts-τ-δ)+Tw-τ}；
wherein, TsRepresenting said scanning period, TwThe length of a scanning window of the scanning party BLE device in a scanning period is τ, the time length of sending an advertisement by the advertising party BLE device is τ, and the time length of monitoring a channel after the advertising party BLE device sends the advertisement is δ.
Preferably, said states are concentrated in any state i other than said absorption state1Next state j of1Included in the following sets:
{(i1+Tl)mod3Ts，(i1+Tl+1)mod3Ts，…，(i1+Tl+r)mod3Ts}；
wherein the transition state i1Reaches the state j1State transition probability of
Figure GDA0003310720950000031
TlRepresenting an advertisement period of the advertiser BLE device, r representing a maximum value of a pseudo-random delay of an advertisement, mod representing a modulo operation.
Preferably, said solving for the average number of transition steps for each state in said set of states to reach an absorption state comprises:
constructing a state transition matrix according to the probability of each state in the state set reaching other states;
solving an average state transition order column vector according to the state transition matrix;
wherein, each element in the average state transition number sequence vector is the average transition step number of each state in the state set reaching the absorption state, and the average transition number of the absorption state reaching itself is equal to 0.
Preferably, said calculating an expected discovery delay according to the expected number of transition steps of all states comprises:
based on the desired number of transition steps for all states, the desired discovery delay is calculated using the following equation:
Figure GDA0003310720950000041
wherein, muiRepresenting the desired number of transition steps for the ith state in the state set.
In the low-power-consumption Bluetooth device discovery delay evaluation method based on the Markov chain, the expected discovery delay of the low-power-consumption Bluetooth device is calculated based on the Markov chain, so that whether the working parameters of the low-power-consumption Bluetooth device are reasonable or not is evaluated according to the expected delay, and whether the working parameters are applied to the BLE device or not is further determined. And, in the calculation process, the working parameters and discovery process of the BLE device are accurately characterized by a unit time which can be preset. By combining the two points, compared with the problem that the discovery delay error is large because the random problem is converted into the deterministic problem in the prior art, the method can accurately evaluate the discovery delay between the low-power-consumption Bluetooth devices.
The present invention will be described in further detail with reference to the accompanying drawings.
Drawings
Fig. 1 is a schematic flowchart of a method for evaluating discovery delay of a bluetooth low energy device based on a markov chain according to an embodiment of the present invention;
figure 2 is a schematic diagram of a markov chain constructed using the method of figure 1;
FIG. 3 is a simulation comparison of an embodiment of the present invention with the prior art.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
In order to accurately evaluate the discovery delay of the low-power-consumption Bluetooth device, the embodiment of the invention provides a low-power-consumption Bluetooth device discovery delay evaluation method based on a Markov chain. As shown in fig. 1, the method may include the steps of:
s10: obtaining operating parameters related to a Bluetooth Low Energy (BLE) device discovery process.
Here, the operating parameters related to the bluetooth low energy BLE device discovery procedure may include:
length T of scanning window of scanning party BLE equipment in scanning periodwThe length tau of an advertisement sent by the advertising party BLE equipment, the length delta of a monitoring channel after the advertising party BLE equipment sends the advertisement, and the scanning period T of the scanning party BLE equipmentsAdvertisement period T of advertiser BLE equipmentlPseudo-random delay Td(ii) a Wherein the pseudo-random delay T of the advertisementdHas a maximum value of r, and TdAt [0, r]It is administered orally and uniformly distributed.
S20: constructing a Markov chain based on the working parameters; wherein each state in the state set of the Markov chain comprises: all times within three scan periods as required by the BLE specification; and, the interval of adjacent time is equal to a preset unit time.
Dividing three times of scanning period required by BLE specification according to the unit time to obtain all moments of the three times of scanning period, namely, the three times of scanning period can include a set {0,1,2, …,3Ts1} which is the state set of the markov chain constructed in step S20. In this state set, any state i may be a transition state i1Or an absorption state i2。
According to the requirements of the BLE specification, the advertising party BLE device transmits advertisements on three channels 37, 38 and 39, and the device discovery is completed when the advertising party receives the advertisements on any one of the three channels; thus, from the respective phase differences of the three channels, it can be determined that the absorption states in the set of states described above can include all of the states in the following three sets:
{0，1，…，Tw-τ}、
{Ts-τ-δ，Ts-τ-δ+1，…，Ts-τ-δ+Tw-τ}、
{2(Ts-τ-δ)，2(Ts-τ-δ)+1，…，2(Ts-τ-δ)+Tw-τ}。
of these three sets, the first set is the absorption state on 37 channels, the second set is the absorption state on 38 channels, and the third set is the absorption state on 39 channels.
It will be appreciated that for any absorption state i2Say, its next state j2Necessarily itself, i.e. the absorption state i2The probability of a state transition with itself is equal to 1. Accordingly, the absorption state i2The transition probability with other states in the state set is equal to 0.
At the same time, it can also be determined that the state is concentrated except for all absorption states i2Any other transition state i1Next state j of1Specifically, the expression may be any one of the following sets:
{(i1+Tl)mod3Ts，(i1+Tl+1)mod3Ts，…，(i1+Tl+r)mod3Ts}。
wherein the transition state i1Reaches the state j1State transition probability of
Figure GDA0003310720950000061
mod represents the modulo operation. It will also be appreciated that for each transition state i1In other words, the state transition probability between it and the unreachable state is equal to 0.
S30: solving the average transfer step number of each state in the state set reaching the absorption state as the expected transfer step number of the state; wherein the absorption state is: the time when the scanning party BLE device receives the advertisement sent by the advertising party BLE device.
Specifically, the step S30 may include:
s301: and constructing a state transition matrix according to the probability of each state in the state set reaching other states.
S302: and solving the average state transition order column vector according to the state transition matrix.
Wherein, each element in the average state transition number sequence vector is the average transition step number of each state in the state set reaching the absorption state, and the average transition number of the absorption state reaching itself is equal to 0.
Specifically, if the state set includes i states, an i × i state transition matrix may be constructed. For example, assuming that the state set includes 4 states, a, b, c, and d, the constructed 4 × 4 state transition matrix is:
Paa Pab Pac Pad
Pba Pbb Pbc Pbd
Pca Pcb Pcc Pcd
Pda Pdb Pdc Pdd
where the elements in the matrix represent the state transition probabilities between the two states shown in their subscripts.
Then, based on the state transition matrix, the average state transition order column vector can be solved. The specific solving process involves mathematical operations in the markov chain technique, which will be described later in an exemplary manner.
S40: the expected discovery delay is calculated based on the expected number of transition steps for all states.
Specifically, the expected discovery delay may be calculated based on the expected number of transition steps for all states using the following equation:
Figure GDA0003310720950000071
wherein, muiRepresenting the desired number of transition steps for the ith state in the state set, and the remaining parameters have the same meaning as above.
S50: determining an evaluation result according to the expected discovery delay; wherein the evaluation result is used to determine whether to apply the operating parameter in the BLE device.
It will be appreciated that if the calculated expected discovery delay is less than the expected delay upper limit, then the evaluation passes; accordingly, the operating parameters may be applied to the BLE device. And if the calculated expected discovery delay is not less than the expected delay upper limit, the evaluation fails; accordingly, the working parameters can be discarded; then, a new set of operating parameters is obtained and the evaluation of the new set of operating parameters is continued according to the evaluation procedures of steps S10-S50.
In the low-power-consumption Bluetooth device discovery delay evaluation method based on the Markov chain, the expected discovery delay of the low-power-consumption Bluetooth device is calculated based on the Markov chain, so that whether the working parameters of the low-power-consumption Bluetooth device are reasonable or not is evaluated according to the expected delay, and whether the working parameters are applied to the BLE device or not is further determined. And, in the calculation process, the working parameters and discovery process of the BLE device are accurately characterized by a unit time which can be preset. By combining the two points, compared with the problem that the discovery delay error is large because the random problem is converted into the deterministic problem in the prior art, the method can accurately evaluate the discovery delay between the low-power-consumption Bluetooth devices.
Preferably, the unit time may include: a few nanoseconds or a few microseconds. It is understood that the terms "a" or "an" mean one or more, and the number is not limited. In addition, the length of the unit of time typically does not exceed the length of time required for the advertiser BLE device to transmit an advertisement. It will also be appreciated that different precision of the depiction may be achieved for different units of time.
For the sake of clarity, the evaluation method provided in the embodiment of the present invention is described in detail below with a specific example.
(1): obtaining a set of operating parameters related to discovery of a Bluetooth Low Energy (BLE) device:
Ts＝12，Tw＝4，τ＝1，δ＝1，Tl＝7，r＝2，Tdis 0,1 or 2; these parameters are in units of time.
(2): and (3) constructing a Markov chain based on the working parameters obtained in the step (1).
Specifically, the state set S of the markov chain is constructed as {0,1,2, …,35 }. According to the BLE specification, an advertiser sends advertisement packets on three channels of 37, 38 and 39, wherein the advertisement packets contain advertisements; the scanner receives the advertisement packet on any of these three channels and is considered to be found. The 38 channel is delayed by 10 unit times from the 37 channel and the 39 channel is delayed by 20 unit times from the 3 channel and the 7 channel. Thus, it can be determined that the set of absorption states on channel 37 is {0,1,2,3}, the set of absorption states on channel 38 is {10,11,12,13}, and the set of absorption states on channel 39 is {20,21,22,23 }.
Summarizing the states to obtain an absorption state set as follows:
{0,1,2,3,10,11,12,13,20,21,22,23}；
and, obtaining a transition state set as:
{4,5,6,7,8,9,14,15,16,17,18,19,24,25,26,27,28,29,30,31,32,33,34,35}。
figure 2 shows the markov chain constructed in this step 2; wherein, the serial number of the dark filling represents an absorption state, and the serial number without filling color represents a transfer state; each arrow connecting two states represents a transition from one of the states to the other.
As can be seen from fig. 2, the next state of each absorption state is itself, the transition probability of both states is 1, and the transition probability of each absorption state with the other states is equal to 0.
For any transition state i1Next state j1May be (i)1+7)mod36，(i1+8)mod36，(i1+9) mod 36. So when j is1＝(i1+7)mod36，j1＝(i1+8) mod36 or j1＝(i1+9) mod36, the number of bits,
Figure GDA0003310720950000091
for each transition state i1In other words, the state transition probability between it and the unreachable state is equal to 0. For example, for transition state 4 in FIG. 2, the next state can be 11,12 or 13, so the transition probabilities between transition state 4 and states 11,12 and 13, respectively, are all
Figure GDA0003310720950000092
The transition probabilities with states other than 11,12, and 13 are all 0.
(3): constructing a 36 multiplied by 36 state transition matrix according to the probability that each state in the state set S reaches other states; the state transition matrix is as follows:
Figure GDA0003310720950000101
where the state transition matrix is not shown in its entirety, limited to space.
(4): and solving the average state transition order column vector according to the state transition matrix.
Specifically, the state transition matrix is first converted into a standard form:
Figure GDA0003310720950000102
in the normalized state transition matrix, the lower right corner is a 12 × 12 identity matrix, and taking the 1 st row to the 24 th row and the 1 st column to the 24 th column of the normalized state transition matrix as a boundary, a 24 × 24 matrix Q is obtained as follows:
Figure GDA0003310720950000103
according to Q, using the formula t ═ I (I-Q)-1And c, calculating an average state transition order sequence vector t. In the formula, I is an identity matrix and c is an identity column vector. The calculated average state transition order sequence vector t is:
Figure GDA0003310720950000111
(5): the expected discovery delay is 16.77 by summing each element in t times 8 and dividing the sum by 36 according to the formula shown above for calculating the expected discovery delay.
(6): assuming that the upper delay limit is expected to be found to be 20, determining that the evaluation passes, and then setting the operating parameters acquired in step (1) into the BLE device.
It should be noted that the specific values of the parameters shown in the above embodiments are merely examples, and do not limit the present invention.
The result of the simulation based on the previous embodiment can be seen in fig. 3, where the horizontal axis represents the advertisement period and the vertical axis represents the expected discovery delay; the dotted line is the actual discovery delay based on the simulation of the operating parameters evaluated in the previous embodiment; the solid line is the expected discovery delay calculated based on the existing CRT evaluation method; the curve connected using circles is the expected discovery delay calculated based on the evaluation method of the present invention.
As can be seen from fig. 3, the actual discovery delay exactly matches the expected discovery delay calculated by the present invention, thereby demonstrating the accuracy of the evaluation method provided by the present invention. In contrast, existing CRT-based evaluation methods suffer from large errors.
In the description of the specification, reference to the description of the term "one embodiment", "some embodiments", "an example", "a specific example", or "some examples", etc., means that a particular feature or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples described in this specification can be combined and combined by those skilled in the art.
While the present application has been described in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed application, from a review of the drawings, the disclosure, and the appended claims.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (4)

1. A low-power Bluetooth device discovery delay assessment method based on a Markov chain is characterized by comprising the following steps:
acquiring working parameters related to discovery of low-power-consumption Bluetooth BLE equipment;
constructing a Markov chain based on the working parameters; wherein each state in the set of states of the Markov chain comprises: all times within three scan periods as required by the BLE specification; and the interval between adjacent moments is equal to the preset unit time;
the state set is: {0,1,2, …,3Ts-1}；TsRepresenting the scan period;
solving the average transfer step number of each state in the state set reaching the absorption state as the expected transfer step number of the state; wherein the absorption state is: the moment when the scanning party BLE equipment receives the advertisement sent by the advertising party BLE equipment;
calculating an expected discovery delay according to the expected transition steps of all the states;
determining an evaluation result according to the expected discovery delay; wherein the evaluation result is used to determine whether to apply the operating parameter in a BLE device;
the solving for the average number of transition steps for each state in the set of states to reach an absorption state comprises:
constructing a state transition matrix according to the probability of each state in the state set reaching other states;
solving an average state transition order column vector according to the state transition matrix;
wherein, each element in the average state transition number sequence vector is the average transition step number of each state in the state set reaching the absorption state, and the average transition number of the absorption state reaching itself is equal to 0;
the calculating the expected discovery delay according to the expected transition steps of all the states comprises:
based on the desired number of transition steps for all states, the desired discovery delay is calculated using the following equation:
Figure FDA0003310720940000021
wherein, muiRepresenting the expected number of transition steps, T, of the ith state in the state setlAn advertisement period on behalf of the advertiser BLE device, r a pseudo-random delay of an advertisementLate maximum.
2. The method of claim 1, wherein the unit of time comprises: a few nanoseconds or a few microseconds.
3. The method of claim 1,
the absorption states include all states in the following three sets:
{0，1，…，Tw-τ}、
{Ts-τ-δ，Ts-τ-δ+1，…，Ts-τ-δ+Tw-τ}、
{2(Ts-τ-δ)，2(Ts-τ-δ)+1，…，2(Ts-τ-δ)+Tw-τ}；
wherein, TwThe length of a scanning window of the scanning party BLE device in a scanning period is τ, the time length of sending an advertisement by the advertising party BLE device is τ, and the time length of monitoring a channel after the advertising party BLE device sends the advertisement is δ.
4. A method according to claim 3, wherein said state set is any transition state i other than said absorption state1Next state j of1Included in the following sets:
{(i1+Tl)mod 3Ts，(i1+Tl+1)mod 3Ts，…，(i1+Tl+r)mod 3Ts}；
wherein the transition state i1Reaches the state j1State transition probability of
Figure FDA0003310720940000022
mod represents the modulo operation; the probability of the absorption state to itself is 1.
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