Providing the evolution from current wireless systems to fifth generation (5G) network is to support massive Machine-to-Machine (M2M) wireless communications in radio access network. Performance analysis of the random access channel (RACH) is a top issue within the M2M-connection in LTE networks, because prior the data transmitting, the session initiation procedure, which perform the connection initiation for user equipment, could overload the channel dealing with burst arrival of connection requests. The purpose of this paper is to continue the analysis of RACH initiation procedure using discrete Markov chain model, and to investigate the dependence of average delay time from preamble processing time. The simulation model is obtained, which allows for estimating the influence of preamble collision on the success access connection initiation in radio access network.
The basic concept of the transition from modern wireless systems to 5G-technologies
is to support the massive machine-to-machine(M2M)and Internet-of-things (IoT)
devices’ connections and still provide a number of promising highly demanded services.
According to ETSI [
At the same time, the main tasks for observing the required performance indicators
are the ability to scale the network, improve energy eficiency and reduce the cost
of sensory user devices. Such technologies as Radio Frequency Identification, Zigbee,
Bluetooth Low Energy and Low-Power WiFi, which typically implement unlicensed
frequency bands, and operate on low power consumption and short transmission range,
are designed to support M2M applications. The disadvantage of using such technologies
are excessive interference between devices in the coverage of the unlicensed spectrum,
which reduces the reliability of these systems, and complicating of initiating access to
the radio environment increases the connection delays [
To address these issues in the development of IoT, the application of low-power
technologies, such as Low Power Wide Area (LPWA), Sigfox, Long Range (LoRa),
Weightless and Long Term Evolution (LTE), is recommended, and LTE cellular
technology is the most suitable solution due to the wide coverage in the existing infrastructure,
security, licensed spectrum and easier maintenance [
In paper [
The purpose of the current work is to continue an analytical model’s development for evaluating performance measures, provided possible retransmission of three messages (Msg1, Msg3, Msg4), which we describe in Section 3. To verify the obtain results we build the simulation model of session initiation procedure, and in Section 4 present the part of simulated programme code. Section 5 is provided with numerical analysis of the dependence of diferent preambles processing time on average RA procedure delay and comparison of analytical and simulation methods.
2.
The basic Random Access (RA) procedure, which initiate the connection between UE and eNB, consists of four steps and can be divided into two stages: a link synchronization step (Msg1, Msg2) and a service transfer (Msg3, Msg4). UE
eNB RA Resource selection TRA_REP (k1) 5 TRAR 2
WRAR 5 Completion RA procedure 6 ms
Msg 1 Msg 2
Msg 3 HARQ ACK
Msg 4 HARQ ACK
Preamble successful transmitted UE monitors RAR during interval t 0 t WRAR
The HARQ
Retransmission of Msg 3 TM 4, GAP 1 and Msg 4 can be up NHARQ times
It begins with transfer from UE to eNB the Msg1 (Preamble Transmission), and
selection one from the set of 64 preambles [
By exceeding the Msg1 transmission counter the connection initiation procedure is considered unsuccessful. In case of exceeding number of Msg3/Msg4 transmission, the procedure starts from the new Msg1 preamble transmission, in case the maximum number of preamble transmission preambleTransMax is not reached. The example of complete successful connection initiation is presented on Fig. 1.
3.
In this work we extend the previous results, presented in [
Let us introduce probabilistic events ={Msg(i) is successfully transmitted}, inverse events ={Msg(i) is unsuccessfully transmitted}, and denote the corresponding probabilities P({})=1 − and P({})=, ∈ {1, 3, 4}. We consider discrete-time Z3 ⋃︀(0, 0, 0)}, so that: {(x, y, z) =
1 is total number of transmitted Msg1, 0, 4, 4 ≤ 3 ≤ 34, 5 ∈ {0, 1}, 2 ∈ {0, 1}, 2 ∈ {0, 1}, }, where: 1 Markov chain { , = 0, 1, . . . , (1 + 3 + 4)1} over the state space = {(x, y, z) ∈ where () is Heaviside function. The multipliers with the Heaviside function in the exponents allow to ignore redundant retransmissions that arise if the connection initiation procedure is not successful. initiation procedure states.
We denote the set of states = {(x, y, z) : 5 = 2 = 2 = 1}, leading to successful session initiation and the set = {(x, y, z) : 1 = 1, 3 + 4 = 2, 2 = 0} of failed
Then access success probability and access failure probability are derived with (2) and (3) respectively: = = ∑︁ ∑︁ (x,y,z)∈ (x,y,z)∈ (x, y, z) , (x, y, z) .
(2) (3) Statement 2. For 1 ∈ {1, 2, 3} expression (2) can be obtained in closed form (4): = 1 −
41 − 6 [︂( 1(1 − 3) 1 + (1 − 1) 33 + (1 − 3)44 )︁ )︂ 1 −
︁( − 3 1 + 3− 1(1 − 1) 3 + (1 − 3)4 )︁ )︂ 1 ]︂ ︂(
︁( 3 4
Since the normalization condition ∑︀(x,y,z)∈ (x, y, z) = 1, the access failure probability could be obtained as = 1 − .
On Fig. 2 the scheme of transitions between events of procedure with instructions of corresponding time intervals is presented. Total delay of the transition from the initial state (0, 0, 0) to the state (x, y, z) is the sum of the time intervals of the transmission corresponding messages, and described by formula (5): = (x, y, z) = 3(△1 + + + △2 + 3( + 3 ) + + 4(△1 + + + △2 + + 4 + 4( + 4 )) + (3 − 4)( + 3 ) + 5(2)(△1 + + + △2) + (1 − 2) × × (△1 + + + ) + 2(22)( + 4 ) + (1 − 2)(22) × × ( + 3 ) + (1 − 2)(2)( + 4 ) + 2. (5) To find average access delay the formula (6) is presented.
= ∑︀(x,y,z)∈ (x, y, z) (x, y, z) .
(6) 4.
This section presents the simulation model of RA procedure. To verify the results obtained using the formulas from Section 2, the code for the simulation model was written, which is a simulated attempt of initiation connection between UE and the BS.
The main part of the code is the imfn function. The input values for this function are as follows: 1. the maximum number of retransmissons 1, 3, 4; 2. collision probability 1; 3. probability of unsuccessful transmissions of Msg3 and Msg4; 4. time intervals vector.
After setting the value to variables using given time interval vector, we build the
matrix, which contain the final state that the system transit to after the connection
attempt is completed, and the time it takes for one attempt to initiate a connection.
imfn=function(N1,N3,N4,p,p34,app,time){
del1=time[
Next is the for loop, which execute set number of iterations. The more iterations are set, the better simulation is obtained. The body of the for loop starts with another while loop, which iterates until the connection is initiated or the counter 1 is exceeded. The body of the for loop begins with the adding to the matrix element value △1, which corresponds to the duration, required for the current attempt – the time interval determined for RA Resource seletion before sending the message Msg1. Next, the sample function returns one value (0 is the collision of the Msg1, 1 is the successful transmission of the Msg1), which is then added to the value of the matrix element, corresponding to the given total number of Msg1 retransmission. Appropriate time intervals are added to the total duration (, ). for(i in 1:app){ while(m[i,1]<N1 && m[i,10]!=1){ m[i,11]=m[i,11]+del1 m[i,12]=m[i,12]+1 res1=sample(c(0,1), size=1, replace=T, prob=c(p,(1-p))) m[i,1]=m[i,1]+1 m[i,11]=m[i,11]+Trar+Wrar m[i,12]=m[i,12]+1 5.
In this section probabilistic characteristics of the procedure are analyzed. The results of calculations using analytical and simulation models are compared.
We define three scenarios, which difers on the allowed numbers of retransmissions 1, 3 and 4: first scenario stands for 1 = 3 = 4 = 2 number of attempts, second presents 1 = 4, 3 = 4 = 2 and third is 1 = 10, 3 = 4 = 5. Furthermore, each scenario presents two diferent sets of time intervals, needed for preamble processing time: set "a" define △1 = 1 ms, △2 = 1 ms, = 1 ms, = 1 ms, and set "b" define △1 = 5 ms, △2 = 2 ms, = 2 ms, = 5 ms.
The results of simulation model are statistics, collected with 500000 iterations, and presented on Fig. 3 and Fig. 4. Fig. 3 depicts the number of successful and unsuccessful states of the system at the end of the procedure in dependence of collision probability. The state at the end of procedure is considered final if the last message – Msg4 – is transmitted successfully or if the number of attempts 1 is reached. The light gray block consists of all attempts, needed for system to obtain the state, which belongs to , and dark gray block counts all attempts, at the end of which the system falls into a state of the set . In Fig. 4 we obtain the total number of preamble retransmission due to reaching 3 or 4.
We use the same scenarios to obtain the analytical results using formula (6) for average access delay. As it could be seen on Fig. 5, with increasing of preamble’ and HARQ’s retransmission attempts, average access delay expectedly increases. Specifically, assuming conditions with long-term preamble processing time (all b scenarios), the longest delay is 40.4 ms, but in scenario 3-b it increases more than 4 times and reaches value 172.3 ms. Significantly reducing average delay is possible by assuming scenario a, thereby characteristics becomes 25.9 ms and 121.9 ms respectively.
Another numerical result was obtained using analytical formulas (1) and (2) to find the access success probability in the dependence of preamble collision in case of limiting attempts 1 = 10, 3 = 4 = 5. As it could be seen on Fig. 6 for diferent low values of Msg3/Msg4 retransmission probabilities 3 = 4 = {0.1, 0.3, 0.5}, graphs almost match: for 3 = 4 = 0.1 probability = 0.6513, for 3 = 4 = 0.3 probability = 0.6494, for 3 = 4 = 0.5 probability = 0.6267. But for higher values of 3 and 4 even under condition of minimum value of collision probability 1 = 0.001, access success probability does not exceed value 0.8402.
The main results obtained within this study can be implemented in the concepts of smart parking in big cities or flame detector in remote industrial. The average delay for transmitting data from UE is important in the performance of the technical conditions: information on the status of each sensors must be provided in real time. Our results indicate the exponentiate growth of access delay in case of longer longer preamble processing time’ assignment, and according to the collected statistical data, the probability of successful connection with the increase in the probability of collision decreases slowly.
The model is planned to be used in simulating adaptive radio access schemes for
LTE networks as a development of previous research [
The publication has been prepared with the support of the “RUDN University Program 5-100” and funded by RFBR according to the research projects No. 17-0700845, 19-07-00933. The authors thank Elvira Zaripova for fruitful discussions.