CN114826986A - Performance analysis method for ALOHA protocol of priority frameless structure - Google Patents

Performance analysis method for ALOHA protocol of priority frameless structure Download PDF

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CN114826986A
CN114826986A CN202210332470.2A CN202210332470A CN114826986A CN 114826986 A CN114826986 A CN 114826986A CN 202210332470 A CN202210332470 A CN 202210332470A CN 114826986 A CN114826986 A CN 114826986A
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priority
users
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time slot
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CN114826986B (en
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蔡雪莲
范逸馨
樊聪
郑静
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Xidian University
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W74/00Wireless channel access
    • H04W74/08Non-scheduled access, e.g. ALOHA
    • H04W74/0833Random access procedures, e.g. with 4-step access
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L43/00Arrangements for monitoring or testing data switching networks
    • H04L43/18Protocol analysers
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04WWIRELESS COMMUNICATION NETWORKS
    • H04W28/00Network traffic management; Network resource management
    • H04W28/02Traffic management, e.g. flow control or congestion control
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Abstract

The invention discloses a performance analysis method for an ALOHA protocol with a priority frameless structure, which divides users into different priorities according to the requirement degree of the users on time delay, and the users with higher time delay requirements preferentially transmit packets so as to meet the access time delay requirements of different users and reduce the average time delay of a performance analysis system; further, the optimal time slot allocation scheme of the priority frameless ALOHA protocol is solved by utilizing a particle swarm optimization; the protocol divides users into different priorities according to the requirement degree of the users for time delay, and the users with higher time delay requirements can transmit packets preferentially. Further, the optimal time slot allocation scheme of the priority frameless ALOHA protocol is solved by utilizing a particle swarm optimization. The simulation verifies the proposed theoretical analysis, and simultaneously proves that compared with the frameless ALOHA protocol, the average time delay of the priority frameless ALOHA protocol can be reduced by about 50%, and different requirements of users on the time delay are met.

Description

Performance analysis method for ALOHA protocol of priority frameless structure
Technical Field
The invention relates to the technical field of communication, in particular to a performance analysis method for an ALOHA protocol of a priority frameless structure.
Background
The random multiple access protocol is a technique that solves how efficiently access users share a common channel. The ALOHA protocol is a network protocol developed by the university of hawaii, usa. ALOHA uses a random access channel access method, which is at the data link layer in the OSI model. It belongs to one of the Random Access protocols (Random Access protocols). Slotted ALOHA protocol is an improvement over pure ALOHA protocol, the idea being to use a clock to unify the data transmission of users. The improvement is that it segments the channel in time, each transmission point being able to transmit only at the beginning of a segment. The user must wait until the next time slice each time to begin transmitting data, and the data transmitted each time must be less than or equal to one time segment of a channel. This greatly reduces collisions of the transmission channels. Therefore, the randomness of data transmission of users is avoided, the possibility of data collision is reduced, and the utilization rate of the channel is improved. Slotted ALOHA is one of typical random multiple access protocols and is widely used in satellite networks and cellular mobile communication networks. However, since the user randomly transmits the packet, when the number of the access users is high, the probability of packet collision in the time slot is high, the packet with collision cannot be decoded and is discarded, and the packet with collision is retransmitted in the subsequent time slot, which may cause performance degradation such as throughput delay of the system. In 1983, Choudhury et al proposed a dsa (diversity Slotted aloha) protocol, which can reduce the number of packet retransmissions, reduce the user delay, and improve the system throughput by transmitting the same packet twice in different time slots. However, although the number of packet retransmissions can be reduced by transmitting the same packet 2 times, the probability of packet collisions in a slot is increased, and the Successive Interference Cancellation (SIC) technique queues the received signal from large to small in strength, and then the users are despread sequentially. Once a signal is detected, the receiver reconstructs the signal and eliminates the signal from the received signal, thereby reducing the interference to the residual signal, effectively solving the problem that a plurality of packets in the time slot of the slotted ALOHA can not be decoded due to collision and improving the system capacity. In 2007, Casini et al propose a CRDSA protocol, firstly apply the SIC technology in S-ALOHA, through the sending end repeatedly sending 2 times of packets in the transmission period, the receiving end uses the SIC technology to decode the received packets, effectively solving the problem that the packets in the time slot collide and can not be decoded, reducing the time delay caused by packet retransmission, and greatly improving the system performance. The application of the SIC technology in the S-ALOHA protocol greatly changes the performance of the random multiple access protocol and promotes the development and research of the SIC-based S-ALOHA protocol, which is collectively called the frame structure ALOHA protocol. Compared with the DSA protocol, the frame structure ALOHA protocol can greatly improve the system throughput, but due to the introduction of the serial interference technology, the decoding complexity of a receiving end is increased. In 2013, Stefanovic et al firstly apply the rate code-free idea to the research of an S-ALOHA protocol, and propose the frame structure-free ALOHA protocol on the basis of the frame structure ALOHA. In the frameless ALOHA protocol, the transmission period changes according to the decoding condition fed back immediately by the base station, and compared with the framed ALOHA protocol, the frameless ALOHA protocol can reduce the waste of time slot resources and improve the channel utilization rate. Based on the flexibility of the frameless ALOHA transmission period, a large number of system performance analyses based on the frameless ALOHA protocol are successively proposed, and most of the researches focus on improving the system throughput, and the research analysis about the ductility of the frameless ALOHA protocol is fresh.
Disclosure of Invention
Aiming at the defects of the prior art, the embodiment of the invention provides a performance analysis method for a priority frameless ALOHA protocol, which provides the priority frameless ALOHA protocol on the basis of the frameless ALOHA protocol, can meet the access delay requirements of different users in a mode of prioritizing the users, and simultaneously reduces the average delay of a system. The invention provides theoretical analysis of the performance of the priority frameless ALOHA protocol and simulation verification. Meanwhile, in order to obtain a time slot allocation scheme which meets the time delay requirement of a high-priority user and ensures that the system performance is better, the invention provides a time slot allocation method based on Particle Swarm Optimization (PSO).
In order to achieve the purpose, the invention provides the following technical scheme: a performance analysis method for an ALOHA protocol with a priority frameless structure divides users into different priorities according to the degree of the requirements of the users on time delay, the users with higher time delay requirements preferentially transmit packets, so as to meet the access time delay requirements of different users and reduce the average time delay of a performance analysis system; further, the optimal time slot allocation scheme of the priority frameless ALOHA protocol is solved by utilizing a particle swarm optimization; the method specifically comprises the following steps:
step 1: u users randomly compete with the access base station according to the probability p to send a packet, and the access users have different requirements on time delay; according to different requirements of users on time delay, the users are divided into c priorities, corresponding time slots divided into c levels are allocated to the users with different priorities, the time slot number in the ALOHA with a different frame structure is a fixed frame length, and the time slot number s in the ALOHA without the frame structure is instantly changed according to the decoding condition of the users until the decoding of the packets transmitted by most of the users is successful;
step 2: to simplify the theoretical analysis of the subsequent system, assume that the system: 1) time synchronization of a base station and a user; 2) the time for transmitting the packet by the user is not more than the time of the time slot; the base station decodes the received packet by using the serial interference elimination technology and feeds back the decoded packet to the user;
in order to analyze the system performance, a degree distribution is introduced to describe the conditions of a user sending packet and a time slot receiving packet; the degree distribution of the ith priority user and the time slot is expressed by formula (1), wherein i (x) Is the degree distribution of the users and is,
Figure BDA0003573550700000031
representing the probability that a user transmits the same packet for l times in the allocated time slot; wherein omega i (x) For the distribution of the degrees of the time slots,
Figure BDA0003573550700000032
represents the probability of the number of packets received in a time slot being l; with U ═ U 1 ,u 2 ,...,u c Denotes a set of users, where u i Represents the number of ith priority users; corresponding to S ═ S 1 ,s 2 ,...,s c Denotes the set of slots, where s i The number of time slots representing the ith grade is changed instantly according to the decoding condition of the user; the distribution of the slot degree of the ith level can be subject to a binomial distribution
Figure BDA0003573550700000033
The approximation is Poisson distribution as formula (2), where
Figure BDA0003573550700000034
The number of users competing for access to the base station for the ith priority;
x l is that a time slot node receives l packets or a user transmits a packet l times, k represents the value of the variable, k and e Is the quantity, Pe, within the Poisson distribution equation i-1 Representing the probability of packet error Pe for the i-1 th slot; k! Is a factorial of k;
Figure BDA0003573550700000041
Figure BDA0003573550700000042
and step 3: modeling a grouping decoding process based on serial interference elimination when a feedback process user is used as a receiving end, and dividing all time slots of the ith level into different sets according to definition 1, definition 2 and definition 3:
definition 1 as set Z i : the set element is the slot in which all the packets received were decoded successfully, i.e. the slot with degree 0, set Z i The number of elements in (1) is represented by z i Represents;
definition 2 as the set R i The set element is a time slot in which one packet in all the received packets is not decoded successfully, and the set R i The number of elements in (1) is represented by r i Represents;
definition 3 as set C i : the set element being two or more of all the packets receivedTime slots with undecoded success, set C i The number of elements in (1) is represented by c i Represents;
the base station starts to decode the received packets one by one after the ith grade time slot is finished, and defines one time slot to finish decoding into one iteration; after each iteration is completed, according to the number of groups which are not decoded successfully in the time slots before and after the time slot iteration, the transfer conditions of the set to which all the time slot states of the ith level belong are four: from the set C i Transfer to set C i (ii) a From the set C i Transfer to set R i (ii) a From the set R i Transfer to set R i (ii) a From the set R i Transfer to set Z i (ii) a The requirement that each iteration be able to decode successfully is the set R i The element in (1) is not 0, namely, only one time slot in which the packet is not decoded successfully exists, and the decoding based on the serial interference elimination can be continued;
for the subsequent numerical analysis of the performance of the ith priority user, the following notation is introduced and explained:
Figure BDA0003573550700000043
after each iteration is finished, the data is collected by a set C i Transfer to set R i The number of time slots of (a);
Figure BDA0003573550700000051
from the set R after each iteration is complete i Transfer to set Z i The number of time slots of (a);
Figure BDA0003573550700000052
time slot formed by set C i Transfer to set R i The probability of (d);
Pe i : packet drop rate for ith priority user;
T i : system throughput of the ith priority user;
D i : average time delay of ith priority user;
introducing subscript n to indicate the number of packets which are not decoded successfully in the packet decoding process; focusing on the state transition from n to n-1, a slot is represented from the set R i Transfer to set Z i (ii) a The introduced state is as formula (3) and lemma 1 to analyze the decoding process of the ith priority user packet:
Figure BDA0003573550700000053
introduction 1: the current state of a decoder for a known decoding process is
Figure BDA0003573550700000054
When in use
Figure BDA0003573550700000055
The time decoder is in state
Figure BDA0003573550700000056
The probability of (2) is calculated by formula (4);
Figure BDA0003573550700000057
wherein
Figure BDA0003573550700000058
In equation (4): pr is the probability of the signal,
Figure BDA0003573550700000059
in the former state, the state of the mobile phone is changed,
Figure BDA00035735507000000510
for the number of slots in which two or more packets are successfully un-decoded in all packets received after each iteration is completed,
Figure BDA00035735507000000511
for the number of slots in which one packet is still successfully un-decoded in all packets received after each iteration is completed,
Figure BDA00035735507000000512
for the number of successfully decoded slots, s, in all packets received after each iteration i Is the number of all slots;
Figure BDA0003573550700000061
in equation (5): omega d A distribution of the number d of undecoded packets in a time slot,
Figure BDA0003573550700000062
all time slot sets with the number of the un-decoded packets being 1, and y is the current time slot;
when set R i When the number of elements of (2) is 0
Figure BDA0003573550700000063
At this time, when two or more packets in all time slots of the ith level are not decoded successfully, based on the end of the serial interference elimination process, the packet discarding rate of the ith priority user is derived according to the state machine of the decoder and is expressed as a formula (6), the throughput is expressed as a formula (7), and the average time delay is expressed as a formula (8), wherein
Figure BDA0003573550700000064
The time slot position of the j-th user access with the priority i is represented;
Figure BDA0003573550700000065
Figure BDA0003573550700000066
Figure BDA0003573550700000067
because the base station will send the packet information of decoding failure to the user after the ith level time slot is finished, the packet of decoding failure can be retransmitted with probability p in the following (i + 1) level time slot, so the system packet discarding rate is only related to the packet discarding rate of the lowest priority, and is deduced as formula (9); the system throughput is deduced to be formula (10), and the weighted average of the system average delay and the delay of each priority is expressed as formula (11);
Figure BDA0003573550700000071
wherein ,
Figure BDA0003573550700000072
Figure BDA0003573550700000073
in the above formula: pe is the system packet drop rate, Pe c The packet drop rate for the c-th priority user,
Figure BDA0003573550700000074
the number of users competing for accessing the base station for the c-th priority, and T is the system throughput;
and 4, step 4: the priority frameless ALOHA effectively reduces the access delay of the users by allocating time slots of different levels to the users with different requirements on the delay, and meets different requirements of different users on the delay; however, if the time slot allocation scheme is not reasonable, for example, a large amount of time slot resources are allocated to a high-priority user, a high packet discarding rate of a low-priority user is caused, and thus system performance is greatly affected; therefore, a reasonable time slot allocation scheme needs to be found to ensure that the stability of the system performance is ensured while the requirement of the high-priority user on the time delay is met;
suppose that among c priority users, there is c r Each priority user has a requirement on time delay; the delay requirement of the user with the priority i is d r Indicating, i.e. average delay of ith priority user
Figure BDA0003573550700000075
While the requirement of priority on time delay is met, the system performance can be optimized, namely the system throughput can be maximized, and meanwhile, the packet discarding rate of the system meets the condition that Pe is less than or equal to Pe r Then the problem of the system is modeled as equation (12):
Figure BDA0003573550700000081
since the packet discard rate of the ith priority in equations (4) to (6) is a function of the number of users competing for the intervention, the number of assigned slots and the packet transmission probability
Figure BDA0003573550700000082
Carrying out representation;
solving a formula (12) as an optimal solution by a traversal method to obtain a time slot allocation scheme for optimizing the system performance; due to the function
Figure BDA0003573550700000083
The complexity of (2) and the traversing mode can greatly increase the cost of computing time; to reduce computation time cost, a function is computed
Figure BDA0003573550700000084
The formula (12) is solved by the particle PSO algorithm, so that a time slot allocation scheme is obtained, and the system performance is maximized while the time delay requirements of priority users are ensured; in the slot allocation scheme based on the particle PSO, the number of slots allocated to different priorities represents a particle, and the system throughput is an evaluation function.
Preferably, in step 1, the ith priority user may transmit its packet multiple times in the assigned ith level time slot, and the packet that the user fails to transmit successfully is retransmitted with probability p in the following (i + 1) th level time slot.
Preferably, for the user with priority i in step 2, the base station sends the packet information with decoding failure to the user after the ith level time slot is finished, and the packet with decoding failure is retransmitted with probability p in the following (i + 1) th level time slot.
Has the advantages that:
the invention provides a performance analysis method for an ALOHA protocol of a priority frameless structure, which has the following beneficial effects:
(1) different time delay requirements of users in a random multiple access system are met;
(2) the particle swarm algorithm can obtain a time slot allocation scheme which enables a system to be better with lower calculation cost.
Drawings
FIG. 1 is a schematic diagram of a system model of the present invention;
FIG. 2 is a graph of theoretical analysis and simulation fit for packet drop rate of the present invention;
FIG. 3 is a graph of throughput theory analysis and simulation versus fit of the present invention;
fig. 4 is a schematic diagram of an iteration result of the time slot allocation scheme based on the particle swarm algorithm.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Embodiment-a method for analyzing the performance of the ALOHA protocol for the priority frameless structure according to the present invention is shown in fig. 1-4, and the specific steps are shown in table 1.
TABLE 1 PSO-based Slot Allocation scheme
Figure BDA0003573550700000091
Figure BDA0003573550700000101
Performance analysis:
a. simulation verification
To evaluate the effectiveness of the 3.1 user and system performance theory derivation, first a fit graph of the priority user and system performance theory analysis and simulation results is given as in fig. 2 and 3. Analyzing the user number U to 8, the user access probability p to 0.5, the time slot number S to 32, and the user and time slot sets to U to {4,4} S to { S,31-S, respectively 1 }={9~28,31-s 1 The performance of the system. As can be seen from fig. 2, in a given timeslot resource allocation range, when the timeslot resources allocated to the high priority users are gradually increased, the packet dropping rate of the high priority users is gradually decreased, but then the packet dropping rate of the whole system is gradually increased due to the gradual decrease of the timeslot resources acquired by the low priority users. Also, as can be seen from FIG. 3, when the slot allocation is within a certain range, s 1 9-28, the throughputs of the high priority users and the low priority users are in complementary states, namely, the number of packets which can be decoded by a decoder is in a relatively stable state, so the throughput of the whole system is in a relatively stable state, and when s is the number of packets 1 When the time slot resource is not reasonably allocated for more than 20 hours, the time slot resource is wasted for the high priority users, and the packets which can be successfully decoded are reduced for the low priority users due to less time slot resources, so the throughput of the whole system is gradually reduced.
b. Comparison of Performance
Firstly, according to the parameter settings in table 2, an exhaustive method is used to find out the time slot allocation scheme which makes the system throughput optimal under the condition of satisfying the time delay and the packet discarding rate, as shown in table 2. The performance of the frameless ALOHA and priority frameless ALOHA systems are then analyzed given the same users and the same timeslot resources, as shown in table 3. It can be seen from table 3 that although the priority frameless ALOHA has a reduction in system throughput and packet drop rate compared to the frameless ALOHA, the priority frameless ALOHA can meet the delay requirements of high priority users while the average delay of the system is relatively low.
TABLE 2 Framless ALOHA vs. priority Framless ALOHA Performance
Figure BDA0003573550700000111
TABLE 3 comparison of time slot allocation schemes based on particle swarm and exhaustive methods
Figure BDA0003573550700000112
And according to the parameter setting of the table 2, determining an optimal time slot allocation scheme by using a particle swarm algorithm and comparing the optimal time slot allocation scheme with the time slot allocation scheme determined by an exhaustion method. Fig. 4 shows the iteration results of the particle swarm algorithm, where the size N of the particle swarm is 10 and the maximum number of iterations is 10, and table 3 shows the comparison results of the two schemes, where the calculation costs (calculation functions) of the two schemes are represented
Figure BDA0003573550700000113
Number of times) of the calculation, the calculation cost C of the exhaustion method can be derived from the equations (6), (10) and (12) Is exhaustive (s-1) × C, the calculation cost of the time slot allocation method based on the particle swarm is C PSO =c*N*I max . As can be seen from table 3, compared with the slot allocation method of the exhaustive method, the slot allocation mechanism based on the PSO can obtain a better slot allocation scheme at a lower calculation cost.
In order to meet different time delay requirements of users in a random multiple access system, a priority-level frameless ALOHA protocol is provided. The protocol divides users into different priorities according to the requirement degree of the users for time delay, and the users with higher time delay requirements can transmit packets preferentially. Further, the optimal time slot allocation scheme of the priority frameless ALOHA protocol is solved by utilizing a particle swarm optimization. The simulation verifies the proposed theoretical analysis, and simultaneously proves that compared with the frameless ALOHA protocol, the average time delay of the priority frameless ALOHA protocol can be reduced by about 50%, and different requirements of users on the time delay are met. Further, simulation data proves that the particle swarm algorithm can obtain a time slot allocation scheme which enables the system to be better with lower calculation cost.
It should be noted that, in this document, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (3)

1. A performance analysis method for an ALOHA protocol of a priority frameless structure is characterized in that users are divided into different priorities according to the requirement degree of the users for time delay, the users with higher time delay requirements preferentially transmit packets, so that the access time delay requirements of different users are met, and the average time delay of a performance analysis system is reduced; further, the optimal time slot allocation scheme of the priority frameless ALOHA protocol is solved by utilizing a particle swarm optimization; the method specifically comprises the following steps:
step 1: u users randomly compete with the access base station according to the probability p to send a packet, and the access users have different requirements on time delay; according to different requirements of users on time delay, the users are divided into c priorities, corresponding time slots divided into c levels are allocated to the users with different priorities, the time slot number in the ALOHA with a frame structure is different from the fixed frame length, and the time slot number s in the ALOHA with a frame-free structure is instantly changed according to the decoding conditions of the users until the decoding of the packets transmitted by most of the users is successful;
step 2: to simplify the theoretical analysis of the subsequent system, assume that the system: 1) time synchronization of a base station and a user; 2) the time for transmitting the packet by the user is not more than the time of the time slot; the base station decodes the received packet by using the serial interference elimination technology and feeds back the decoded packet to the user;
in order to analyze the system performance, a degree distribution is introduced to describe the conditions of a user sending packet and a time slot receiving packet; the degree distribution of the ith priority user and the time slot is expressed by formula (1), wherein i (x) Is the degree distribution of the users and is,
Figure FDA0003573550690000014
representing the probability that a user transmits the same packet for l times in the allocated time slot; wherein omega i (x) For the distribution of the degrees of the time slots,
Figure FDA0003573550690000011
represents the probability of the number of packets received in a time slot being l; by U ═ U 1 ,u 2 ,...,u c Denotes a set of users, where u i Represents the number of ith priority users; corresponding to S ═ S 1 ,s 2 ,...,s c Denotes the set of slots, where s i The number of time slots representing the ith grade is changed instantly according to the decoding condition of the user; the distribution of the slot degree of the ith level can be subject to a binomial distribution
Figure FDA0003573550690000012
The approximation is Poisson distribution as formula (2), where
Figure FDA0003573550690000013
The number of users competing for access to the base station for the ith priority;
x l is that a time slot node receives l packets or a user transmits a packet l times, k represents the value of the variable, k and e Is the quantity, Pe, within the Poisson distribution equation i-1 Representing the probability of packet error Pe for the i-1 th slot; k! Is a factorial of k;
Figure FDA0003573550690000021
Figure FDA0003573550690000022
and step 3: modeling a grouping decoding process based on serial interference elimination when a feedback process user is used as a receiving end, and dividing all time slots of the ith level into different sets according to definition 1, definition 2 and definition 3:
definition 1 as set Z i : the set element is the slot in which all the packets received were decoded successfully, i.e. the slot with degree 0, set Z i The number of elements in (1) is represented by z i Represents;
definition 2 as set R i The set element is a time slot in which one packet in all the received packets is not decoded successfully, and the set R i The number of elements in (1) is represented by r i Represents;
definition 3 as set C i : the set element is two or more than two time slots with successfully undecoded packets in all the received packets, and the set C i The number of elements in (1) is represented by c i Represents;
the base station starts to decode the received packets one by one after the ith grade time slot is finished, and defines that one time slot is decoded into one iteration; each iteration is completed according to the undecodability in the time slot before and after the time slot iterationThe packet number and the transition condition of the set to which all slot states of the ith level belong are four types: from the set C i Transfer to set C i (ii) a From the set C i Transfer to set R i (ii) a From the set R i Transfer to set R i (ii) a From the set R i Transfer to set Z i (ii) a The requirement that each iteration be able to decode successfully is the set R i The element in (1) is not 0, namely, only one time slot in which the packet is not decoded successfully exists, and the decoding based on the serial interference elimination can be continued;
for the subsequent numerical analysis of the performance of the ith priority user, the following notation is introduced and explained:
Figure FDA0003573550690000031
after each iteration is completed, the data is collected by a set C i Transfer to set R i The number of time slots of (a);
Figure FDA0003573550690000032
from the set R after each iteration is complete i Transfer to set Z i The number of time slots of (a);
Figure FDA0003573550690000033
time slot formed by set C i Transfer to set R i The probability of (d);
Pe i : packet drop rate for ith priority user;
T i : system throughput of the ith priority user;
D i : average time delay of ith priority user;
introducing subscript n to indicate the number of packets which are not decoded successfully in the packet decoding process; focusing on the state transition from n to n-1, a slot is represented from the set R i Transfer to set Z i (ii) a The introduction state analyzes the decoding process of the ith priority user packet according to the formula (3) and the theorem 1:
Figure FDA0003573550690000034
introduction 1: the current state of a decoder for a known decoding process is
Figure FDA0003573550690000035
When in use
Figure FDA0003573550690000036
The time decoder is in state
Figure FDA0003573550690000037
The probability of (2) is calculated by formula (4);
Figure FDA0003573550690000038
wherein
Figure FDA0003573550690000039
In equation (4): pr is the probability of the signal,
Figure FDA00035735506900000310
in the former state, the state of the mobile phone is changed,
Figure FDA00035735506900000311
for the number of slots in which two or more packets are successfully un-decoded in all packets received after each iteration is completed,
Figure FDA00035735506900000312
for the number of slots in which one packet is still successfully un-decoded in all packets received after each iteration is completed,
Figure FDA00035735506900000313
for the number of successfully decoded slots, s, in all packets received after each iteration i Is the number of all slots;
Figure FDA0003573550690000041
in equation (5): omega d A distribution of the number d of undecoded packets in a time slot,
Figure FDA0003573550690000042
all time slot sets with the number of the un-decoded packets being 1, and y is the current time slot;
when set R i When the number of elements of (2) is 0
Figure FDA0003573550690000043
At this time, when two or more packets in all time slots of the ith level are not decoded successfully, based on the end of the serial interference elimination process, the packet discarding rate of the ith priority user is derived according to the state machine of the decoder and is expressed as a formula (6), the throughput is expressed as a formula (7), and the average time delay is expressed as a formula (8), wherein
Figure FDA0003573550690000044
The time slot position of the j-th user access with the priority i is represented;
Figure FDA0003573550690000045
Figure FDA0003573550690000046
Figure FDA0003573550690000047
because the base station will send the packet information of decoding failure to the user after the ith level time slot is finished, the packet of decoding failure can be retransmitted with probability p in the following (i + 1) level time slot, so the system packet discarding rate is only related to the packet discarding rate of the lowest priority, and is deduced as formula (9); the system throughput is deduced to be formula (10), and the weighted average of the system average delay and the delay of each priority is expressed as formula (11);
Figure FDA0003573550690000051
wherein ,
Figure FDA0003573550690000052
Figure FDA0003573550690000053
Figure FDA0003573550690000054
in the above formula: pe is the system packet drop rate, Pe c The packet drop rate for the c-th priority user,
Figure FDA0003573550690000055
the number of users competing for accessing the base station for the c-th priority, and T is the system throughput;
and 4, step 4: the priority frameless ALOHA allocates the time slots of different levels to users with different time delay requirements, thereby effectively reducing the access time delay of the users and meeting the different time delay requirements of the different users; however, if the time slot allocation scheme is not reasonable, for example, a large amount of time slot resources are allocated to a high-priority user, a high packet discarding rate of a low-priority user is caused, and thus system performance is greatly affected; therefore, a reasonable time slot allocation scheme needs to be found to ensure that the stability of the system performance is ensured while the requirement of the high-priority user on the time delay is met;
suppose that among c priority users, there is c r Each priority user has a requirement on time delay; the delay requirement of the user with the priority i is d r Indicating, i.e. average delay of ith priority user
Figure FDA0003573550690000056
While the requirement of priority on time delay is met, the system performance can be optimized, namely the system throughput can be maximized, and meanwhile, the packet discarding rate of the system meets the condition that Pe is less than or equal to Pe r Then the problem of the system is modeled as equation (12):
Figure FDA0003573550690000061
since the packet discard rate of the ith priority in equations (4) to (6) is a function of the number of contending intervening users, the number of allocated slots and the packet transmission probability
Figure FDA0003573550690000062
Carrying out representation;
solving a formula (12) as an optimal solution by a traversal method to obtain a time slot allocation scheme for optimizing the system performance; due to the function
Figure FDA0003573550690000063
The complexity of (2) and the traversing mode can greatly increase the cost of computing time; to reduce computation time cost, a function is computed
Figure FDA0003573550690000064
The particle PSO algorithm is used for solving the formula (12) to obtain a time slot allocation scheme, and the time slot allocation scheme can meet the time delay requirement of priority users to the maximum extentChanging the system performance; in the slot allocation scheme based on the particle PSO, the number of slots allocated to different priorities represents a particle, and the system throughput is an evaluation function.
2. The method as claimed in claim 1, wherein the ith priority user can transmit its packet multiple times in the assigned ith class slot, and the packet that the user fails to transmit successfully is retransmitted with probability p in the following (i + 1) th class slot.
3. The method as claimed in claim 1, wherein in step 2, for the user with priority i, the base station sends the information of the packet with decoding failure to the user after the ith class slot is ended, and the packet with decoding failure is retransmitted with probability p in the following (i + 1) th class slot.
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