A random access protocol for massive mimo the adaptive acb based collision resolution

A Random Access Protocol for Massive MIMO The Adaptive ACB Based Collision Resolution XXX X XXXX XXXX X/XX/$XX 00 ©20XX IEEE A Random Access Protocol for Massive MIMO The Adaptive ACB based Collision[.]

A Random Access Protocol for Massive MIMO: The Adaptive ACB based Collision Resolution

Ha Tran Huu

Wireless Communications Department

VNU-UET

Hanoi, Vietnam

huuha.tran306@gmail.com

Hung Gia Hoang

Computer Engineering Department

VNU-UET

Hanoi, Vietnam

hunghg@vnu.edu.vn

Duong Chu Huy

VNPT Hung Yen

Hung Yen, Vietnam duongch.hyn@gmail.com Thang Xuan Vu

Interdisciplinary Centre for SnT University of Luxembourg

Luxembourg thang.vu85@gmail.com

Vu Trinh Anh*

Wireless Communications Department

VNU-UET

Hanoi, Vietnam Corresponding author: vuta@vnu.edu.vn

Abstract— mMTC (massive Machine Type

Communications) is one of the key components in beyond 5G

networks for smart manufacturing and the Fourth Industrial

Revolution Due to the massive connectivity in mMTC, it is vital

to have an efficient random access (RA) protocol In the paper,

we propose a new random access technique called the Adaptive

ACB (A-ACB) to minimize collisions We show that, in terms of

successfully resolved probability, the proposed A-ACB always

outperforms the ACBPC protocol while surpassing the SUCRe

protocol when the number of collisions per preamble is large In

addition, the proposed protocol achieves better fairness than the

SUCRe but less than the ACBPC Finally, numerical results are

provided to demonstrate the effectiveness of the proposed

random access protocol

Keywords— random access protocol, massive MIMO,

SUCRe, ACBPC, collision resolution

I INTRODUCTION

The success of massive MIMO techniques [4] in the Fifth

Generation (5G) communications for eMBB applications [3]

has opened up a new research direction for massive machine

type communications (mMTC) and ultra-reliable low-latency

communications (URLLC) [5,6] A common approach in

developing RA techniques for mMTC applications is to adapt

from a reference LTE RA method [9] According to

LTE-based protocols, an active user equipment (UE) randomly

selects a preamble from a common list and then send it to the

base station (BS) to request a connection When two or more

UEs collide on the same preamble, the connection requests are

dropped and the preamble is not used This leads to a waste of

resources because LTE does not resolve but detects collisions

only To improve resource utilization, several attempts have

been made to address random access collision, especially for

mMTC [8,10]

Massive MIMO techniques bring a number of great

benefits such as bandwidth and energy savings, as well as

creating good transmission conditions, namely channel

hardening and favorable propagation [5] These properties

also facilitate the study of collision resolution problems for

mMTC random access, resulting in two prominent schemes:

strongest-user collision resolution (SUCRe) [2] and access

class barring with power control (ACBPC) [1]

In the SUCRe protocol, collisions are completely resolved

in a distributed manner on the UE side Specifically, each UE will estimate the ratio of its channel gain to the total channel gain of the UEs that have selected the same preamble If a UE has this ratio greater than 1/2, all other UEs’ ratios will be less than 1/2 This protocol allows only one UE with a ratio greater than 1/2 to retransmit the request while other UEs whose ratios are less than 1/2 must wait for the next turn Note that this collision avoidance policy is handled at the UEs, not at the BS, hence is fully distributed It was shown that the SUCRe protocol achieves good collision resolution when managing less than 104 UEs One drawback of this protocol, however, is that it always gives priority to UEs with large channel gain In addition, when managing a larger machine set (e.g., more than

104 UEs), the protocol’s collision resolution success rate quickly deteriorates because the average number of UEs choosing the same preamble increases significantly

The ACBPC protocol, first proposed in [1], aims to overcome the unfairness disadvantage of SUCRe In the first phase of this protocol, the UEs send preambles to the BS with the power inversely proportional to their channel gain Thus, the BS will receive signals with the same power from all active UEs Consequently, the BS can only detect the number of UEs which have chosen the same preamble without detecting the total channel gain The number of UE per preamble is reported back to the UEs, enabling each UE sets an appropriate ACB level to reduce the probability of collision during the retransmission phase When the number of active UEs is reasonably small, ACBPC does not perform as well as SUCRe However, ACBPC outperforms SUCRe when the number of active UEs are large

In this paper, we propose a new random access protocol, advisedly referred to as the Adaptive - ACB (A-ACB), which

is capable of exploiting the advantages of both ACBPC and SUCRe protocols The key idea behind A-ACB is that rather than using a uniform ACB level for all of the collided UEs, each UE in the collision list will be assigned a theoretically- different individual ACB value based on its location (and thus large-scale channel fading) We show that in comparison with ACBPC, the proposed A-ACB protocol improves the successful resolution probability considerably at the expense

the proposed A-ACB scheme achieves better fairness as well

as higher successful resolution probability when handling a

high number of active UEs

The paper is organized as follows Section II provides

background on SUCRe and ACBPC protocols Section III

presents the proposed protocol with analytical proof

Simulation results are presented in Section IV Finally,

Section V concludes the paper

II SUCRE AND ACBPCPROTOCOLS

Fig 1 and Fig 2 summarize the four phases of random

access in SUCRe [2] and ACBPC [1] protocols Both

protocols have been built on Massive MIMO technology, in

which uplink signals are processed by the maximal ratio

combining (MRC) technique while downlink signals are

processed by the maximal ratio transmission (MRT) method

The SUCRe protocol consists of four phases as follows:

• At the initial request phase (uplink): Active UEs

randomly select 1 preamble from the available set and

send it to the BS The BS uses the available preamble

set to correlate the received signal For each preamble

used, the BS will separate the total channel gain of the

UEs which have selected it

• In the second phase (downlink), the sum of these

channel gains is inverted by the precoding and is

beamed back to the requested UEs The BS also

encloses information about resource block (RB) of the

connection to the future winner Due to the separation

of the downlink, each UE will be able to estimate the

ratio of its channel gain to the total channel gain of all

UEs that have the preamble in common (Massive

MIMO uses TDD protocol with the assumption that the channel is reciprocity)

• In the third phase, if a UE has the ratio greater than 1/2 (which means all the remaining UEs have their ratios less than 1/2), it will be the obvious winner and retransmit over the allocated RB resources The remaining UEs must wait for the next step, so there is

no collision Notice that collision has been resolved in

a distributed manner and by hard decisions If only one UE chooses one preamble, its ratio is approximately 1, which makes it always be the winner If, however, no UE has a ratio greater than 1/2 then this preamble will be waste

• In the fourth phase, upon receiving retransmission from the winning UE, the BS sends a signal to officially allocate RB of the connection to the UE, completing the random access protocol

The main advantage of the SUCRe protocol is that it is fully distributed and can achieve a high resolution probability because the probability of two UEs choosing the same preamble is large A drawback of this technique is low degree

of fairness: UEs near the BS with strong channel gain are always preferred In addition, the collision resolution of SUCRe decreases sharply when the number of UEs choosing

a preamble is large

In order to improve fairness, the ACBPC protocol is proposed in [1] and summarized in Fig 2

• At the initial request phase, the UEs, after randomly selecting a preamble, will transmit to the BS with a power equal to the inverse of its channel gain (the gain

is detected from phase 0 when the BS is broadcasting) such that the BS will receive signals with the same

Fig 1 Four phases of random access in SUCRe protocol

Fig 2 Four phases of random access in ACBPC protocol

magnitude Therefore, the BS will not detect the total

channel gain as it does in SUCRe protocol, but the

number of UEs sharing a preamble that we designate

as 𝑘

• In the second phase, the value of 𝑘 is reported back

to the relevant UEs by the BS along with RB

information

• In the third phase, each UE will generate a random

number evenly distributed from 0 to 1 If the random

number is less than 1/𝑘 , the UE will retransmit the

request; otherwise, it will not retransmit According

to this protocol, there may still be unexpected

situations: no UE has a random number less than 1/𝑘

or there are two or more UEs with a random number

less than 1/𝑘 However, equal access is guaranteed,

and the collision probability is reduced since each UE

is setting up an ACB

• In the fourth phase, the collision is resolved at the BS

If there is no ID collision from UEs, it means that only

one UE retransmits The BS will officially allocate

resources to this UE

The ACBPC protocol is not as efficient as the SUCRe

protocol when the average number of UE collisions per

preamble is not too large (< 104) When the average number

of UE collisions per preamble becomes larger (> 104), the

ACBPC protocol will gradually be more efficient

III PROPOSED PROTOCOL

The proposed protocol is similar to SUCRe in phase 1 and

phase 2 Therefore, after the first two phases, each UE knows

the ratio of its channel gain to the total channel gain of all the

UEs that share the same preamble The main difference in the

proposed A-ACB protocol lies in a novel collision resolution

method in phase 3 Note in passing that the sum of ratios of

the involved UEs always equals to 1 This simple observation,

nonetheless, enables the basis of the proposed method to be

formed

• In the third phase: Each UE sets its ACB value equal

to the ratio it has estimated The collision resolution

method is similar to ACBPC, but the ACB for each UE

is different in that it varies depending on the UE

location (or equivalently, channel gain) rather than

being a constant Subsequently, each UE generates a

random number uniformly distributed from 0 to 1 If

this random number is less than the ACB, it will

retransmit Otherwise, it will wait for the next access

step The proposed name for this method, adaptive

ACB (A-ACB), emphasizes the innovative use of

adaptive values for each UE’s ACB

• In the fourth phase: BS behaves like the fourth phase

of ACBPC protocol If there is no collision ID for UEs,

BS will officially allocate connection resources to the

winner

Next, we will analyze the performance of the proposed

A-ACB protocol In particular, we present a concrete analytical

proof showing that A-ACB always achieves a higher

resolution probability than the celebrated ACBPC protocol

Recall that after phase 2 in ACBPC, each UE was notified

by the BS on the downlink that there are 𝑘 UEs with the same preamble To reduce the chance of collision, the ACB are set equally to a value 𝑝 (0 < 𝑝 < 1) seeding a random number (uniformly distributed from 0 to 1), if its value less than 𝑝,

UE will retransmit the request together with ID and if the random number is larger than 𝑝, it will silent and wait the next random access The probability that there is a retransmission UE without collision when 𝑘 UEs choose the same 𝑝 value is:

𝑃𝑝(1 UE repeat) = (𝑘

1) 𝑝(1 − 𝑝)

𝑘−1 (1) The expression represents the combination of case where only one UE retransmits and k − 1 the remain UEs are silent Since 𝑃𝑝 is a function of 𝑝, take the first derivative respect to

𝑝 yields:

𝑑𝑃𝑝

𝑑𝑝 = 𝑘(1 − 𝑘𝑝) (1 − 𝑝)(𝑘−2)= 0 (2) Clearly, the solution of (2) is 𝑝 =1

𝑘 Substituting 𝑝 =1

𝑘

into (1), we obtain the maximum collision resolution probability as:

𝑃𝑝,max= 𝑘1

𝑘(1 −1

𝑘)𝑘−1= (1 −1

𝑘)𝑘−1, (3) which is the maximum achievable collision resolution probability of the ACBPC protocol [1]

For the proposed protocol (A-ACB), the ACBs of the UEs are different because the channel gain to each UE is different Suppose that the values of the ACBs are 𝑝1, 𝑝2, , 𝑝𝑘, they must adhere to the constraint: ∑𝑘𝑖=1𝑝𝑖= 1

The collision resolution probability in which only 1 UE retransmits while 𝑘 − 1 remaining UEs are silent is given by:

𝑃𝑝𝑘(1 UE repeat) = 𝑝1(1 − 𝑝2)(1 − 𝑝3) … (1 −

𝑝𝑘) + 𝑝2(1 − 𝑝1)(1 − 𝑝3) … (1 −

𝑝𝑘−1)+ +𝑝𝑘(1 − 𝑝1)(1 − 𝑝2) … (1 − 𝑝𝑘−1) (4)

We are going to prove that min

𝑝1,𝑝2, ,𝑝𝑘𝑃𝑝𝑘= 𝑃𝑝,max, subject

to the constraints

𝑝𝑖 > 0 and ∑𝑘 𝑝𝑖

𝑖=1 = 1, (5) where 𝑃𝑝𝑘 is assumed to be a convex function Using the Lagrange multiplier method, let

Ω = 𝑃𝑝𝑘+ 𝜆(𝑝1+ 𝑝2+ +𝑝𝑘) (6.0)

be the Lagrange objective function, the optimal solutions of the optimization problem min

𝑝1,𝑝2, ,𝑝𝑘𝑃𝑝𝑘 subject to (5) must satisfy the following conditions:

𝛿Ω/𝛿𝑝1= (1 − 𝑝2)(1 − 𝑝3) … (1 − 𝑝𝑘) −

𝑝2(1 − 𝑝3) … (1 − 𝑝𝑘) − − 𝑝𝑘(1 − 𝑝2)(1 −

𝑝3) … (1 − 𝑝𝑘−1) + 𝜆 (6.1)

𝛿Ω/𝛿𝑝2= (1 − 𝑝1)(1 − 𝑝3) … (1 − 𝑝𝑘) −

𝑝1(1 − 𝑝3) … (1 − 𝑝𝑘) − − 𝑝𝑘(1 − 𝑝1)(1 −

𝑝3) … (1 − 𝑝𝑘−1) + 𝜆 (6.2)

…

𝛿Ω/𝛿𝑝𝑘= (1 − 𝑝1)(1 − 𝑝3) … (1 − 𝑝𝑘−1) −

𝑝1(1 − 𝑝2) … (1 − 𝑝𝑘−1) − − 𝑝𝑘−1(1 −

𝑝1)(1 − 𝑝2) … (1 − 𝑝𝑘−2) + 𝜆 (6.k)

𝑝1+ 𝑝2+ ⋯ + 𝑝𝑘 = 1 (6.k+1)

Subtracting (6.2) from (6.1), we obtain

(𝑝1− 𝑝2)(1 − 𝑝3) … (1 − 𝑝𝑘) + (𝑝1− 𝑝2)(1 − 𝑝3) … (1 −

𝑝𝑘)+ −(𝑝1− 𝑝2)𝑝𝑘(1 − 𝑝3) … (1 − 𝑝𝑘−1) = 0

⟺ (𝑝1− 𝑝2)[(2(1 − 𝑝3) … (1 − 𝑝𝑘) − 𝑝3(1 − 𝑝4) … (1 −

𝑝𝑘)− −𝑝𝑘(1 − 𝑝3) … (1 − 𝑝𝑘−1)] = 0,

which yields 𝑝1= 𝑝2

Similarly, by subtracting (6.3) from (6.2), we have

(𝑝2− 𝑝3)(1 − 𝑝1)(1 − 𝑝4) … (1 − 𝑝𝑘) + (𝑝2− 𝑝3)(1 −

𝑝1)(1 − 𝑝4) … (1 − 𝑝𝑘)− −(𝑝1− 𝑝2)𝑝𝑘(1 − 𝑝3) … (1 −

𝑝𝑘−1) = 0

⟺ (𝑝2− 𝑝3)[(2(1 − 𝑝1) … (1 − 𝑝𝑘) − 𝑝1(1 − 𝑝4) … (1 −

𝑝𝑘)− −𝑝𝑘(1 − 𝑝3) … (1 − 𝑝𝑘−1)] = 0,

which yields 𝑝2= 𝑝3

It is obvious that the equations (6.i) are circularly

symmetric: substituting 𝑝𝑗 for 𝑝𝑖(𝑖 ≠ 𝑗) into equation (6.i),

we get the equation (6.j) Therefore, the optimal solutions

obey 𝑝1= 𝑝2= = 𝑝𝑘, which allows us to solve equation

(6.k+1) for:

𝑝1= 𝑝2= = 𝑝𝑘 =1

𝑘 (7) Substituting equation (7) into equation (4), we obtain:

𝑃𝑝𝑘,min= 𝑘1

𝑘(1 −1

𝑘)𝑘−1= (1 −1

𝑘)𝑘−1= 𝑃𝑝,max (8) From equation (8), it is obvious that 𝑃𝑝𝑘 ≥ 𝑃𝑝,max

In the following section, we will perform numerical

evaluation for the analytical results derived above

IV SIMULATION RESULTS

In our simulation, we adopt the numerical examples and

part of the Matlab code presented in [2] to demonstrate the

performance of the proposed A-ACB in cellular networks,

whose parameters are summarized in Table 1

TABLE I S IMULATION P ARAMETERS

Number of inactive UEs 2.104

Number of BS antenna M 100

UEs are uniform distributions

in hexagonal cells, R = 25 – 250m

Power loss exponent ki = 3.2; 3.8

Deviation of shadow fading 10 dB

Probability of active UEs 0.001

Probability in next access 0.5

The simulation is carried out on a standard personal

computer using Matlab for two scenarios Firstly, we

compare the success collision resolution rate of the A-ACB protocol to those of the SUCRe and ACBPC for different numbers of active UEs choosing the same preamble Secondly, we investigate the average number of access attempts made by each UE through A-ACB and SUCRe protocols in a crowded network

A Success resolution probability for varying number of active UEs per preamble

Remarks: Fig 3 shows that the A-ACB protocol always

outperforms the ACBPC by about 12%, regardless of the number of UEs/preamble As compared to the SUCRe protocol, the success resolution rate of the A-ACB is initially lower, but levels up quickly when the number of UEs per preamble reaches 30, and becomes far more superior when the number of UEs/preamble keeps increasing above 30, where the success resolution rate of the SUCRe degrades sharply When the power loss exponent value increases from 3.2

to 3.8 in Fig 4, it is observed that the cut-off point between the A-ACB and SUCRe performances moves to the right, from 30 (in Fig 3) to 40 This is because the gain difference

Fig 3 Comparison of the probability of successful collision resolution

by the number of UEs choosing the same preamble with the power loss exponent 𝑘i= 3.2.

Fig 4 Comparison of the probability of successful collision resolution

by the number of UEs choosing the same preamble with the power loss exponent 𝑘𝑖= 3.8

of the UEs becomes bigger when the power loss exponent

increases, making the collision resolution probability of

SUCRe increases

B Average number of RA attempts in a crowded network

In this scenario, at each access step there is a random

number of UE activated with probability 0.001 UEs that are

not accepted on the first attempt will participate in the next

attempt with the probability being 0.5 Each UE can access up

to 10 subsequent attempts After 10 attempts, if it is still

unable to access, it will be eliminated Because the A-ACB

always outperforms the ACBPC, we only compare the

A-ACB and the SUCRe performances in this simulation, with

the conventional LTE protocol serves as a reference

(Baseline)

The simulation results, presented in Fig 5, clearly show

that the average number of successful RA attempts of the

A-ACB is higher than that of the SUCRe when the number of

inactive UEs ranges from 0 to 1.20 × 104 When the number

of inactive UEs increases, the average number of successful

access attempts of A-ACB becomes smaller than the

SUCRe’s

When the power loss exponent changes from 3.2 to 3.8, the curve of the SUCRe shifts to the right while the curve of A-ACB barely changes (please refer to Fig 6) The cutoff point of the two curves now moves to 1.25 × 104 This represents a better resolution probability of the SUCRe as the power loss exponent increases

V CONCLUSIONS

This paper proposes a novel random access protocol that enables adaptive ACB values for massive MIMO-aided mMTC systems We demonstrated analytically that the proposed protocol outperforms the ACBPC protocol in terms

of successful resolution probability as well as surpassing the SUCRe performance when the number of active users is large

In terms of user fairness, although the proposed A-ACB does not perform as well as the ACBPC protocol, it achieves a higher fairness than the SUCRe Simulation results confirm the theoretical analysis while showing the dependence of collision resolution on the loss exponent of the environment Future direction for the research in this paper is to develop a method capable of combining the advantages of both SUCRe and A-ACB protocols

ACKNOWLEDGMENT

This work has been partly supported by VNU University

of Engineering and Technology under project number CN21.05

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Fig 5 Comparison of the average number of the successful attempts

between SUCRe and A-ACB with the power loss exponent 𝑘𝑖= 3.2

Fig 6 Comparison of the average number of the successful attempts

between SUCRe and A-ACB with the power loss exponent 𝑘𝑖= 3.8