system model

single-cell model

$$y={\mathbf{h}}^H\mathbf{x}+n$$
where $\mathbf{h}\in {\mathbb{C}}^{N_t\times 1}$ is the downlink channel between the BS and the user, ? is the complex additive Gaussian noise (AWGN) with zero mean and variance ${\sigma }^2$, and $\mathbf{x}\in {\mathbb{C}}^{N_t\times 1}$ is the precoded signal, which is given by $\mathbf{x}=\mathbf{w}s$,and $\mathbf{h}$ can be formulated as $$\mathbf{h}=\sum _{c=1}^{N_c}\sum _{s=1}^{N_s}{g}_{c,s}\mathbf{a}({\theta }_{c,s})$$ where $N_c$ stands for the number of the scattering clusters, i.e., path number, $N_s$ in each scattering cluster, $g_{c,s}$ is the complex gain of the ?-th sub-path in ?-th scattering cluster, and ??,? is the corresponding azimuth angle-of-departure (AoD) of this sub-path. When the BS is with ULA transmit antennas, the steering vector $\mathbf{a}(\theta )\in {\mathbb{C}}^{N_t\times 1}$ can be written as $$\mathbf{a}(\theta )=[1,e^{-j2\pi d/\lambda sin(\theta )},\cdots ,e^{-j2\pi (N_t-1)d/\lambda sin(\theta )}]$$ where ? and ? are the antenna element spacing and carrier wavelength, respectively.

multi-cell model

the received signal $y_k$ of ? th user is given by
$$y_k=\sqrt{{\gamma }_{k,(d)}}{\mathbf{h}}_k^T{\mathbf{w}}_k{s}_k+\sqrt{{\gamma }_{k,(i)}}{\mathbf{g}}_{k+1}^T{\mathbf{w}}_{k+1}{s}_{k+1}+n_k$$
where $s_k$ and $s_{k+1}$ denote the symbol transmitted from the $k$th and (? + 1)th BSs, respectively, ${\mathbf{w}}_k$ and ${\mathbf{w}}_{k+1}$ are the BF vectors of the ?th and (? +1)th BSs, respectively, and $n_k$ is the zero-mean AWGN noise of the ?th user with $\mathbb{E}|n_k{|}^2=N_0$

只考虑了两个基站