Objective: In cell-free networks

access points (AP) collaborate to serve users. This coordination can break the performance bottleneck of traditional cellular network caused by inter-cell interference. However

it needs significant amounts information interaction and signal processing

which results in poor scalability. This paper studied the user association strategy that could improve the scalability of cell-free networks.

Methods:The network scalable degree was designed as a measure of scalability

and then a user association strategy to improve network scalable degree was studied by using optimization theory. 1) For modelling the optimization problem

firstly

the network coupling degree

representing the degree of association among nodes

was constructed to establish the mathematical relationship between the network scalable degree and AP group (APG).Thus

the problem of improving the network scalable degree was modeled as the problem of minimizing the network coupling degree.Then

a multi-objective optimization problem of minimum network coupling degree and maximum user rate was established to find the balance between network scalable degree and network service quality. 2) For solving the optimization problem

to avoid the high computational complexity

a heuristic user association strategy based on APG mergence and topological potential optimization was proposed.With the proposed algorithm

the number of APG could be reduced by APG mergence

and the number of APG that AP belongs to could be reduced by AP exiting APG. Thus

it can reduce the network coupling degree and improve the network scalable degree. For APG mergence

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was defined as the overlap rate between set

<math xmlns="http://www.w3.org/1998/Math/MathML"> <mi mathvariant="script">I</mi><mo>

</mo><mi mathvariant="script">J</mi></math>

and the APG whose overlap rate exceeds a certain threshold value would be merged. In terms of AP exiting APG

the relationship between network coupling degree and user rate was established by topological potential function

which was used as the performance index of AP exiting APG.

Results:1)For the rationality of problem modeling

Fig.2 and Fig.5 show that the network scalable degree is inversely proportional to the network coupling degree. Therefore

it is reasonable to model the problem of improving network scalable degree as minimizing network coupling degree

and it is feasible to improve network scalable degree by reducing network coupling degree.2)The upper limit of computational complexity of the proposed algorithm is

<math xmlns="http://www.w3.org/1998/Math/MathML"> <mi mathvariant="script">O</mi><mo stretchy="false">(</mo><mi>K</mi><mi>N</mi><msub> <mi>log</mi> <mn>2</mn> </msub> <mi>N</mi><mo>+</mo><msup> <mi>k</mi> <mn>2</mn> </msup> <mo>+</mo><mi>N</mi><mi>N</mi><msub> <mover accent="true"> <mi>N</mi> <mo>¯</mo> </mover> <mtext>p</mtext> </msub> <mo stretchy="false">)</mo></math>

while that of directly solving the optimization problem is

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.3)For theoretical analysis of the network scalable degree

take Fig.3 as an example.If AP2 changes

12 APs in Fig. 3(a)are affected and the network scalable degree is η

2

=0.51

while 4 APs in Fig.3(c)are affected and the network scalable degree is η

2

=0.79.4)Fig.5 shows the simulation results of network scalable degree.Compared with the traditi

onal strategy

the network scalable degree is improved by 9.59% with 4.43% user rate loss.Compared with the strategy in[10

]

the network scalable degree is improved by 22.15% with 4.99% user rate loss. 5) The algorithm parameters

the threshold β

0

of overlap rate and the upper limit number N

0

of AP associated

effect the performance.As shown in Fig.6

with β

0

or N

0

decreases

η increases and the total user rate decreases. With

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increases

the effect of β

0

increases and that of N

0

decreases.Take

<math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mover accent="true"> <mi>N</mi> <mo>¯</mo> </mover> <mtext>p</mtext> </msub> <mo>=</mo><mn>40</mn><mo>

</mo><mn>60</mn></math>

as an example.The η gap between β

0

=0.5 and β

0

=0.9 increases from 5.97% to 14.17%

and the user rate gap increases from 47 bit/(s·Hz) to 155 bit/(s·Hz). The η gap between N

0

=20 and N

0

=60 decreases from 1.4% to 0.4%

and the user rate gap decreases from 76 bit/(s·Hz)to 29 bit/(s·Hz).

Conclusions: The proposed user association strategy can improve the network scalable degree of cell-free networks at the cost of less rate loss. The smaller the overlap rate threshold or the upper limit of APs associated with an AP

the more the network scalable degree increases and the greater the rate loss.