Table 1 Notation List.

\(\mathscr {U}\)

UAV set, \(u \in \mathscr {U}\)

\(K_i\)

Data size of IoT \(i \in \mathscr {I}\).

\(\mathscr {I}\)

IoT user set, \(i \in \mathscr {I}\).

\(D_i\)

IoT Delay Tolerance.

\(\rho _u\) , \(\mu\)

Computation resource cost of UAV , HAP.

\(H_u\)

Flight altitude of UAV u.

\(C_u\) ,C

Computing capability of UAV, HAP.

\(\sigma ^2\)

Noise Power Density.

\(q_u\) , \(q_i\)

Horizon location of UAV , IoT.

\(G_0\)

Reference Channel Gain.

\(N_u\)

The maximum number of IoT a UAV can serve.

\(\tau _0\)

Initial Step.

\(T_{iu}\)

Time cost to transmit the data of I2U.

\(\rho\)

Backtracking Factor.

\(T_{u}\)

Time cost to transmit the data to HAP by UAV u.

\(c_1\)

Armijo Parameter

\(T_u^i\)

Time cost by UAV to complete the computation.

\(\varepsilon\)

Convergence tolerance

\(T^i\)

Time cost by HAP to complete the computation.

N

Reflecting elements

\(P_i^{tr}\)

Transmission power of I2U.

\(\alpha _n\)

Amplitude Reflection Coefficients .

\(P_u^{tr}\)

Transmission power of U2H.

\(\lambda _1, \lambda _2, \lambda _3\)

Matching Weights.

\(\zeta _u\) , \(\zeta\)

Energy consumption coefficient of UAV, HAP.

\(w_1, w_2\)

Heuristic Weights .

\(E_i^c\) , \(E_u^c\) , \(E^c\)

Total energy cost of IoT, UAV, HAP.

\(f_{uh}\)

U2H Center Frequency.

\(E_i^o\) , \(E_u^o\) , \(E^o\)

Basic operation energy cost of IoT, UAV, HAP.

\(T_s\)

System Noise Temp.

\(E_i\), \(E_u\), E

Energy budget of IoT, UAV, HAP.

\(k_B\)

Boltzmann Constant.

\(E_i^{tr}\)

Energy cost for I2U data transmission.

\(BW_{iu}\)

Bandwidth of I2U channel.

\(E_u^{tr}\)

Energy cost for U2H data transmission.

\(BW_{u}\)

Bandwidth of U2H channel.

\(E_u^{co}\)

Energy cost for computation of u.

\(R_{i,u}\)

Data rate of I2U channel.

\(E^{co}\)

Energy cost of HAP for computation.

\(R_u\)

Data rate of U2H channel.

\(M_1\)

Matching in Algorithm 1.

\(A_u^i\), \(B^i\), \(\alpha _u^i\), \(\delta ^i\)

Binary Variables.