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SCIENCE CHINA Information Sciences, Volume 63 , Issue 12 : 220304(2020) https://doi.org/10.1007/s11432-019-2836-0

Secure transmission for heterogeneous cellular network with limited feedback

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  • ReceivedNov 30, 2019
  • AcceptedMar 16, 2020
  • PublishedNov 11, 2020

Abstract


Acknowledgment

This work was supported in part by National Key Research and Development Program of China (Grant No. 2017YFB0801900).


Supplement

Appendixes A–C.


References

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  • Figure 1

    (Color online) An illustration of 3-tier HCN down-link transmission with feedback coexist with eavesdroppers.

  • Figure 2

    (Color online) Scheduling period partition of a specific time slot in proposed transmission protocol.

  • Figure 3

    (Color online) Coverage probability in a 2 tier HCN vs. feedback length in tier-1 $B_1$.

  • Figure 4

    (Color online) Coverage probability in a 2 tier HCN vs. different estimation error $\sigma~_m^2$.

  • Figure 5

    (Color online) The secrecy throughput vs. $R_b$ and $R_e$.

  • Figure 6

    (Color online) The max average secrecy throughput vs. different feedback lengths.

  • Figure 7

    (Color online) The optimal feedback length vs. antenna numbers.

  • Figure 8

    (Color online) Maximization average secrecy throughput vs. antenna numbers.

  •   

    Algorithm 1 Sub-algorithm for solving problem (25)

    Require:Current $R_b$ and $R_e$;

    Initial $B_{i,{\rm~max}}$, $\Omega~_{\rm~opt}^i=0$, $B_{i,{\rm~opt}}=1$;

    for $B_i=1,2,~\ldots,~B_{i,{\rm~max}}$

    Compute $\Omega_u^i$ using Eq. (25);

    if ${{~\Omega_u^i~}}~>~{\Omega~_{\rm~opt}^i}$ then

    update ${\Omega~_{\rm~opt}^i}~=~\Omega~_u^i,{B_{i,{\rm~opt}}}~=~{B_i}$;

    end if

    end for

    Output: Optimal $B_{i,{\rm~opt}}$.

  •   

    Algorithm 2 Iterative algorithm for solving the problem (24)

    Initial $\Delta~{{R}_{\rm{b}}}~>~0$, $\varepsilon~~>~0$, ${\Omega~_{\rm~opt}}~=~0$, ${{R}_{{b}}}[0]~=~2$, ${{R}_{{e}}}[0]~=~1$, ${\boldsymbol{B}}[0]~=~\{~1,~\ldots,~1\}~$, $n~=~1;$

    while $\Omega~({\boldsymbol{B}}{{[n]}},{{R}_{{b}}}[n],{{R}_{{e}}}[n])~-~\Omega~({\boldsymbol{B}}{\rm{[}}n~-~1{\rm{]}},{{R}_{{b}}}[n~-~1],{{R}_{{e}}}[n~-~1])~>~\varepsilon$ do

    $n=n+1$;

    Find ${\boldsymbol~B}{{[n]}}$ using sub-algorithm for each tier;

    while ${{R}_{{b}}}~=~{{R}_{{b}}}+\Delta~{{R}_{{b}}}$ and $p_c^i({R_b})~>~\kappa$ do

    Get the $R_e$ by solving (31);

    Calculate $\Omega$ using (22);

    if ${\rm{\Omega~}}~>~{\Omega~_{\rm~opt}}$ then

    Update ${\Omega~_{\rm~opt}}~=~\Omega~$, ${B_{i,{\rm~opt}}}~=~{B_i}$, ${{R}_{{b,{\rm~opt}}}}~=~{{R}_{{b}}}$, ${{R}_{{{e,{\rm~opt}}}}}~=~{{R}_e}$;

    end if

    end while

    end while

    Output: Optimal ${\boldsymbol~B}[n],~{{R}_{{b}}}[n],{{R}_{{e}}}[n]$.