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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

Abstract

A comprehensive resource optimization framework is designed for incremental amplify-and-forward orthogonal frequency division multiplexing (AF-OFDM) relaying systems to maximize the network lifetime. Specifically, joint channel and power assignment, i.e., all degrees of freedom such as incremental policy, channel pairing, relay selection, and power allocation, are optimized with quality of service (QoS) constraints. The lifetime maximization problem is formulated as a mixed-integer nonlinear programming which at first glance seems mathematically intractable. However, a two-nested search loop, in which the outer loop varies the lifetime based on bisection criterion until finding the optimum while the inner loop attempts to derive the corresponding feasible solution set for that given lifetime by employing dual decomposition and subgradient techniques, is then presented to solve it. Numerical results are shown to verify the near-optimality and the effectiveness of our proposal.


Acknowledgment

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).


References

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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

    $m=\lfloor\frac{m_{\rm~min}+m_{\rm~max}}{2}\rfloor$;

    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

    $m_{\rm~min}=m$;

    else

    $m_{\rm~max}=m$;

    end if

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

    $m=m_{\rm~min}$;

    ${\rm~flag}=0$;

    end if

    end while

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