SCIENCE CHINA Information Sciences, Volume 62 , Issue 2 : 022301(2019) https://doi.org/10.1007/s11432-017-9388-1

Lifetime maximization via joint channel and power assignment for incremental-relay multi-channel systems

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  • ReceivedOct 4, 2017
  • AcceptedFeb 27, 2018
  • PublishedOct 15, 2018



This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61401321, 61701392, 91538105), Fundamental Research Funds for the Central Universities (Grant No. JB180107), National Basic Research Program of China (Grant No. 2014CB340206), Open Research Fund of National Mobile Communications Research Laboratory (Grant No. 2015D01), Scientific Research Plan Projects of Shaanxi Provincial Department of Education (Grant Nos. 16JK1498, 16JK1501), China Postdoctoral Science Foundation (Grant No. 2015M5826), and Natural Science Foundation of Xi'an University of Science and Technology (Grant No. 2018YQ3-07).


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  • Figure 1

    Illustration of incremental AF-OFDM multi-relay system.

  • Figure 2

    Convergence properties of the inner and the outer searching loops. (a) Dual problem with fixed $m$; (b) bisection searching method

  • Figure 3

    Network lifetime performance with respect to different schemes.

  • Figure 4

    Network lifetime vs. number of relays.

  • Figure 5

    Network lifetime vs. number of subcarriers.

  • Figure 6

    The comparison of the residual energy when the network lifetime is achieved.


    Algorithm 1 Executive procedures for the determination of binary indicators

    for $t=1\rightarrow~m$

    STEP 1 Preparation: require $H_\mathrm{s}^{i,(1)}(t)$, $H_\mathrm{s}^{j,(2)}(t)$, and $H_l^{i,j}(t)$;

    for $i=1\rightarrow~N$

    Calculate $P_\mathrm{s}^{i,(\mathrm{NC},1)}(t)$, $H_\mathrm{s}^{i,(1)}(t)$;

    end for

    for $j=1\rightarrow~N$

    Calculate $P_\mathrm{s}^{j,(\mathrm{NC},2)}(t)$, $H_\mathrm{s}^{j,(2)}(t)$;

    end for

    for $l=1\rightarrow~L$

    for $i=1\rightarrow~N$

    for $j=1\rightarrow~N$

    Calculate $P_\mathrm{s}^{i,(\mathrm{C},1)}(t)$, $P_l^{j,(\mathrm{C},2)}(t)$, $H_l^{i,j}(t)$;

    end for

    end for

    end for

    STEP 2 Determine incremental policy and relay selection strategy for each channel pair;

    for $i=1\rightarrow~N$

    for $j=1\rightarrow~N$

    for $l=1\rightarrow~L$

    Denote ${\boldsymbol~A}=a(i,j)=\max\{H_l^{i,j}(t),H_\mathrm{s}^{i,(1)}(t)+H_\mathrm{s}^{j,(2)}(t)\}$;

    end for

    end for

    end for

    STEP 3 Channel pairing;

    Apply Hungarian method on matrix ${\boldsymbol~A}$;

    end for


    Algorithm 2 Executive procedures of the proposed network lifetime optimization scheme

    Initialize $m_{\rm~min}$, $m_{\rm~max}$, ${\rm~flag}=1$;

    while ${\rm~flag}=1$ do


    Initialize $\boldsymbol{\mu}$, $\boldsymbol{\nu}$, $\kappa$;

    Call Algorithm 1;

    Update $\boldsymbol{\mu}$, $\boldsymbol{\nu}$, and $\kappa$ based on subgradient algorithm and repeat above steps in Algorithm 1 until convergence;

    if c1, c2, and c3 in (7) are satisfied then




    end if

    if $m_{\rm~max}-m_{\rm~min}\leq1$ then



    end if

    end while