S1. constructing a model of a coordinated multiple access system for multi-cell ground-to-air data transmission, including constructing a scenario model and constructing a channel model; wherein

the constructing a scenario model includes that:

each cell consists of a cell-center area and a cell-edge area; a ground station is located at a center of a corresponding cell, and the ground station implements backhaul transmission through optical fibers; an aircraft located in the cell-center area is served by a ground station to which the aircraft belongs, and an aircraft located in the cell-edge area is served by a plurality of ground stations to implement data transmission simultaneously using a CoMP technology;

three adjacent ground stations form a consideration range of a regular hexagon as three non-adjacent vertices of the regular hexagon;

the constructing the channel model includes that:

each ground station sends signals to a single-antenna aircraft using a horizontally placed uniform planar array antenna, wherein a count of available subcarriers is denoted as X, a total count of planar array antennas is denoted as N, and a transmission bandwidth is denoted as B; wherein

the channel model for aeronautical broadband communication is constructed based on a Saleh-Valenzuela channel model; a channel of an x-th subcarrier between the ground station and the aircraft is expressed as:

wherein L denotes a count of multipaths, a_i denotes a gain of an l-th path, j denotes an imaginary unit, f_x denotes a frequency selective fading coefficient on a subcarrier x, τ_l denotes an arrival delay of the l-th path, a(θ₁, φ_l) denotes an array steering vector, θ₁ denotes a pitch angle of the aircraft relative to a planar array, φ_l denotes an azimuth angle of the aircraft relative to the planar array, and H denotes conjugate transpose of a matrix;

S2. calculating a transmission rate of the aircraft within the consideration range, and constructing a multi-cell airspace and power domain resource allocation optimization problem by taking maximizing a system transmission rate as an optimization objective;

S3. constructing a Markov decision process model based on the optimization objective and constraints;

S4, solving the optimization problem using a multi-agent deep reinforcement learning algorithm; wherein

i, n, and z denote different aircrafts;

in S1, the three ground stations simultaneously serve a cell-edge aircraft k through CoMP transmission, let α∈1,2,3 denote a ground station index, h_a,k[x] denotes a channel response matrix between a ground station a and the cell-edge aircraft k on the subcarrier x, m_a,k denotes a cluster of the cell-edge aircraft k in the ground station a, m_a′ denotes other clusters in the ground station a, _ma,k and _ma′ denote a set of aircrafts in the clusters m_a,k and m_a′, respectively, w_a,ma,k[x] and w_a,ma′[x] denote hybrid beamforming vectors of the ground station a for the clusters m_a,k and m_a′ on the subcarrier x respectively, p_a,k[x], p_a,i[x], and p_a,n[x] denote power allocation variables of the ground station a for aircrafts k, i, n on the subcarrier x, respectively, s_k[x], s_i[x], and s_n[x] denote signals received by the aircrafts k, i, n on the subcarrier x, respectively, and n_k[x] denotes noise of the cell-edge aircraft k on the subcarrier x;

the signal received by the cell-edge aircraft k on the subcarrier x is expressed as:

assuming considering a scenario of coherent joint transmission (CJT) based on an ideal backhaul capacity, real-time channel state information is shared among the ground stations, a capacity gain is obtained by coherent merging of multipath signals at the cell-edge aircraft k, and power P_desired of a received useful signal is a power of a sum of the useful signals from all the ground stations, which is expressed as:

a signal interference received by a cell-center aircraft k′ served by a ground station a′ includes a signal interference from the cell-edge aircraft, a signal interference from the cell-center aircraft of a current cell and neighboring cells, K^C denotes a set of the cell-edge aircrafts, K_a′^N and K_a^N denote a set of cell-center aircrafts served by the ground station a′ and a set of cell-center aircrafts served by the ground station a, respectively, h_a′,k′[x] and h_a,k′[x] denote channels from the ground station a′ and the ground station a to the cell-center aircraft k′ on the subcarrier x, respectively, p_a′,k′[x] and p_a,k′[x] denote power allocation variables of the ground station a′ to the aircrafts k′ and i on the subcarrier x, respectively, s_k′[x] denotes a signal received by the cell-center aircraft k′ on the subcarrier x, m_a′,k′ and m_a′,i denote clusters of the aircrafts k′ and i in the ground station a′, respectively, m_a,k and m_a,n denote the clusters of the aircrafts k and n in the ground station a, respectively, w_{a′,ma′,k′}[x] and w_a′,ma′,i[x] respectively denote hybrid beamforming vectors of the ground station a′ on subcarrier x for the clusters m_a′,k′ and m_a′,i; w_a,ma,k[x] and w_a,ma,n[x] denote the hybrid beamforming vectors of the ground station a on the subcarrier x for the clusters m_a,k and m_a,n, respectively; n_k′[x] denotes noise of the cell-center aircraft k′ on the subcarrier x, and the signal received by the cell-center aircraft k′ served by the ground station a′ on the subcarrier x is expressed as:

in S2, the calculating a transmission rate of the aircraft within the consideration range, and constructing a multi-cell airspace and power domain resource allocation optimization problem by taking maximizing a system transmission rate as an optimization objective includes:

S21. calculating a transmission rate of the cell-edge aircraft k; wherein a_k,i^m_a,k denotes an SIC decoding order of the cell-edge aircraft k and the aircraft i of the cluster m_a,k in the ground station a, a_k,i^m_a,k=0 means that a receiver of the cell-edge aircraft k of the cluster m_a,k first decodes the signal of the aircraft i and eliminates the signal using an SIC technology; otherwise, a_k,i^m_a,k=1 means that the receiver of the cell-edge aircraft k of the cluster m_a,k first decodes the signal of the cell-edge aircraft k, accordingly, it is deduced that the transmission rate R_k[x] between the ground station a and the cell-edge aircraft k on the subcarrier x is expressed as:

wherein I_C denotes a signal interference of other cell-edge aircrafts except the cell-edge aircraft k, I_N denotes the signal interference of the cell-center aircraft, σ_k² denotes noise power; and w_a,ma,i[x] denotes a hybrid beamforming vector of the ground station a for the cluster m_a,i on the subcarrier x;

S22, calculating a transmission rate of the cell-center aircraft k′; wherein

the transmission rate R_a,k′[x] of the cell-center aircraft k′ served by the ground station a′ is expressed as:

wherein ICI_C denotes an inter-cluster interference to the cell-center aircraft k′ from the cell-edge aircraft, and ICI_C is 0 if the cell-center aircraft k′ and the cell-edge aircraft are in the same cluster; INI_N and ICI_N denote signal interferences of the cell-center aircrafts in the same cluster and different clusters as the cell-center aircraft k′ in the ground station a′, respectively; ICI_cell denotes inter-cell signal interferences caused by cell-center aircrafts served by neighboring ground stations; _ma′,k′ denotes a set of aircrafts in a cluster m_a′,k′, p_a′,z[x] denotes a power allocation variable of the ground station a′ to an aircraft z on the subcarrier x, a_k′,z^m_a′,k′ denotes an SIC decoding order of the cell-edge aircraft k′ and the aircraft z of the cluster m_a′,k′ in the ground station a′; and σ_k′² denotes noise power of the aircraft k′;

S23. constructing a multi-cell joint transmission resource allocation optimization problem; wherein

the optimization variables are transmission power of each ground station to each aircraft and a hybrid analog and digital beamforming vector for each cluster, P denotes total power that each ground station can allocate to the aircraft on each subcarrier, W_a,A denotes an analog beamforming matrix of the ground station a, F denotes all elements in W_a,A, W_a,A(c_x, c_y) denotes elements at coordinates (c_x, c_y) in the matrix W_a,A, w_a,D,ma,n[x] denotes a digital beamforming vector of the ground station a for a cluster m_a,n on the subcarrier x, which satisfies w_a,ma,n[x]=W_a,A×w_a,D,ma,n[x], R_n[x] denotes a transmission rate of an aircraft n on the subcarrier x, R_n^thr[x] denotes a minimum transmission rate threshold of the aircraft n, and constructing the multi-cell joint transmission resource allocation optimization problem is expressed as follows:

wherein a constraint C1 denotes a maximum transmission power limit of the ground station; a constraint C2 denotes a non-negative value constraint of power; a constraint C3 denotes a normalization constraint of the hybrid beamforming vector of the ground station; a constraint C4 denotes a constant modulus constraint of elements in an analog beamforming matrix; and a constraint C5 denotes a minimum transmission rate constraint of the aircraft n;

in order to correctly implement SIC decoding at the aircraft, a minimum value of the transmission rate of the cell-center aircraft k′ served by the ground station a′ at an aircraft of which a decoding order is later than the decoding order of the cell-center aircraft k′ is taken as the transmission rate of the cell-center aircraft k′, which is expressed as:

wherein Φ_a′,k′ denotes a set of aircrafts in the same cluster as the cell-center aircraft k′ in the ground station a′ and whose decoding orders are not earlier than that of the cell-center aircraft k′, i.e., Φ_a′,k′={i|α_i,k′^m_a′,k′[x]=0}∪{k′}, wherein α_i,k′^m_a,k′[x] denotes an SIC decoding order of the cell-center aircraft k′ and an aircraft i of a cluster m_a′,k′ in the ground station a′; and R_{ma′,k′,i→k′}[x] denotes a transmission rate of a signal of the cell-center aircraft k′ decoded at the aircraft i of the cluster m_a′,k′;

for the cell-edge aircraft k, since the signal of the cell-edge aircraft k participates in an SIC process of three ground stations, the transmission rate of the cell-edge aircraft k is less than transmission rates of aircrafts decoded later in the corresponding clusters of the all ground stations; Φ_a,k denotes a set of aircrafts in the same cluster as the cell-edge aircraft k in ground station a and whose decoding orders are not earlier than that of the cell-edge aircraft k, and R_ma,k,i→k[x] denotes a transmission rate of the signal of the cell-edge aircraft k decoded at the aircraft i in a cluster m_a,k, which is expressed as:

in S3, constructing the Markov decision process model includes a local observation state O, an action A, and a reward function R; wherein

the local observation state O: for multi-agent deep reinforcement learning, each ground station is regarded as an agent, and local observation state information o_a,t of the ground station a at a t-th step is defined as channel state information from the ground station a to each aircraft and a signal interference suffered by each aircraft; h_a,n[x] denotes a channel from the ground station a to the aircraft n on the subcarrier x, I_a,n[x] denotes a total signal interference intensity suffered by the aircraft n served by the ground station a on the subcarrier x, and the local observation state information o_a,t is expressed as:

the action A: an action a_a,t of the ground station a in the t-th step consists of an analog beamforming matrix of the ground station a and power allocation to each aircraft; since the analog beamforming matrix needs to satisfy the constant modulus constraint, a modulus value of each element in the matrix is fixed to 1/√N, so the action A only needs to contain a phase of each element in the analog beamforming matrix, which is expressed as:

the reward function R: the reward function consists of a reward for achieving a high transmission rate in the ground station a and a penalty for violating the constraint;

for the optimization problem (7), the constraints C1 and C2 are satisfied by performing softmax normalization on the power allocation, while the constraints C3 and C4 are satisfied by normalizing the beamforming; accordingly, considering the constraint C5, when the transmission rate of the aircraft n in the ground station a does not satisfy the minimum transmission rate threshold, a negative penalty is fed back to an agent represented by the ground station a;

C_a,t denotes a count of times the minimum transmission rate constraint of the ground station a is violated in the t-th step, then the reward of the ground station a in the t-th step is expressed as:

wherein constraint coefficients k₁, k₂ denote positive constant coefficients.