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SCIENCE CHINA Information Sciences, Volume 63 , Issue 12 : 223301(2020) https://doi.org/10.1007/s11432-020-2875-7

Stochastic geometry based analysis for heterogeneous networks: a perspective on meta distribution

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  • ReceivedMar 6, 2020
  • AcceptedApr 14, 2020
  • PublishedOct 23, 2020

Abstract


Acknowledgment

The work was supported by National Natural Science Foundation of China (Grant Nos. 61941114, 61941105, 61971066), Beijing Natural Science Foundation (Grant No. L182038), and National Youth Top-notch Talent Support Program.


References

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  • Figure 1

    (Color online) Heterogeneous cellular network and its stochastic geometry based model. (a) Illustration of an HCN and (b) a realization of 3-tier PPP model [8]@Copyright 2012 IEEE.

  • Figure 2

    (Color online) The relationship among the success probability, the conditional success probability, and the meta distribution.

  • Figure 3

    (Color online) The empirical probability density function (PDF) of link success probability of networks A and B [45]@Copyright 2018 IEEE.

  • Figure 4

    (Color online) Comparison of the meta distributions for the general user and the worst-case user with DPB, DPS/DPB, and JT (including non-coherent, enhanced non-coherent, and coherent JT [93]), where the cardinality of the cooperation set $n=3$, the path loss exponent $\alpha=4$, and the SIR threshold $\theta=0$ dB [51]@Copyright 2018 IEEE.

  • Figure 5

    (Color online) Comparison of the beta approximation, the generalized beta approximation and the exact results (Gil-Pelaez approach) for the SINR meta distribution in the D2D mmWave scenario, where the density of D2D transmitters $\lambda=0.1,0.001$, and the square antenna array of a D2D transmitter has $N=4,64$ elements [44]@Copyright 2017 IEEE.

  • Table 1  

    Table 1Comparison of the computational complexity among the approaches according to the moments $M_j$ used in the calculation and the existence of the imaginary moments and the integral

    Approach Integral Imaginary $M_j$ $M_j$ used in calculation
    Gil-Pelaez $\surd$ $\surd$ $j={{\mathrm~i}t}$, $t\in[0,+\infty)$
    Beta approximation (or generalized) $\surd$ $j=1,2$ (or $j=1,2,3$)
    Binomial mixtures $j=1,2,\ldots,n$ (e.g., $n=25$ [38,84])
    Fourier-Jacobi $\surd$ $j=1,2,\ldots,n$
    Euler sum $\surd$ $j=-\frac{A+2\pi~k~{\mathrm~i}}{2\ln(x)}$, $k={1,2,\ldots,N+Q}$, $x\in[0,1)$
    (e.g., $(A,N,Q)=(24,10,20)$ [85])