ROD-based hybrid TH precoding and combining for mmWave large-scale MIMO systems

Hybrid TH precoding with subarray connection for multi‐user mmWave MIMO systems

“…For the convenience of analysis, the system described in the previous section assumes that perfect channel state information (CSI) can be gained. The signal transmission channel of multi‐user millimeter‐wave system is considered to be made up of LOS channel and NLOS channel, and the channel type belongs to Rice channel 14,21,22 $$$$ {\boldsymbol{H}}_k=\sqrt{\frac{p_k}{p_k+1}}{\boldsymbol{H}}_{\mathrm{LOS},k}+\sqrt{\frac{1}{p_k+1}}{\boldsymbol{H}}_{\mathrm{NLOS},k}, $$$$ where $$$ {p}_k $$$ represents the Rice channel factor in the communication system. $$$ {\boldsymbol{H}}_{\mathrm{LOS},k} $$$ and $$$ {\boldsymbol{H}}_{\mathrm{NLOS},k} $$$ are the LOS channel and the NLOS channel separately.…”

“…$$$ {\boldsymbol{H}}_{\mathrm{LOS},k} $$$ and $$$ {\boldsymbol{H}}_{\mathrm{NLOS},k} $$$ are the LOS channel and the NLOS channel separately. It is supposed that $$$ {\boldsymbol{H}}_{\mathrm{NLOS},k} $$$ is composed of $$$ {N}_{c,k} $$$ clusters, in sequence each cluster corresponds to $$$ {N}_{l,k} $$$ paths, in quick succession, the $$$ {\boldsymbol{H}}_{\mathrm{LOS},k} $$$ and $$$ {\boldsymbol{H}}_{\mathrm{NLOS},k} $$$ can be expressed as 14,21 …”

“…Here, the system also considers the nonlinear module at the user receiver. Let $$$ {\boldsymbol{H}}_e={\boldsymbol{W}}_{RF}^{\mathrm{H}}{\boldsymbol{H}}_k{\boldsymbol{F}}_{RF} $$$ be an effective channel, according to References 14 and 20, it is pretty simple to learn about that the lower triangular feedback matrix $$$ \boldsymbol{B} $$$ of nonlinear element, the digital precoding matrix at the transmitter $$$ {\boldsymbol{F}}_{BB} $$$ and the digital combining matrix at the receiver $$$ {\boldsymbol{W}}_{BB} $$$ can be obtained by 15 $$$$ \kern0.5em \boldsymbol{B}={\boldsymbol{G}}_e^{-1}{\boldsymbol{R}}_e^{\mathrm{H}}-\boldsymbol{I}, $$$$ $$$$ \kern0.5em {\boldsymbol{F}}_{BB}=\gamma {\boldsymbol{Q}}_e, $$$$ $$$$ \kern0.5em {\boldsymbol{W}}_{BB}={\boldsymbol{G}}_e^{-1}, $$$$…”

“…The $$$ {N}_{RF} $$$ steps correspond to $$$ K $$$ submatrices respectively, and the value of $$$ \boldsymbol{T} $$$ is further updated to obtain the final optimal or suboptimal solution. Specifically, according to References 9 and 14, the optimization subproblem (12) can be expressed as $$$$ R=\sum \limits_{N=1}^{{\boldsymbol{N}}_{RF}}{\log}_2\left(\left|\boldsymbol{I}+\frac{P_t}{{\sigma_n}^2}{\boldsymbol{P}}_{\mathrm{N}}^{\mathrm{H}}{\boldsymbol{G}}_{N-1}{\boldsymbol{P}}_{\mathrm{N}}\right|\right), $$$$ where $$$ {\boldsymbol{G}}_{N-1}={\boldsymbol{H}}_W^{\mathrm{H}}{\boldsymbol{T}}_{\mathrm{N}\hbox{-} 1}^{-1}{\boldsymbol{H}}_W,\kern0.3em {\boldsymbol{T}}_{\mathrm{N}\hbox{-} 1}=\boldsymbol{I}+\frac{P_t}{{\sigma_n}^2}{\boldsymbol{H}}_W{\boldsymbol{P}}_{\ma...$…”

“…As a suboptimal nonlinear VP, the original signal vector is added to the additional disturbance vector to form the disturbance signal vector, which reduces the total transmitted power and has better performance than linear precoding 12 . Compared with DPC and VP, TH precoding has certain advantages 14 . The modular operator in TH model's nonlinear elements can effectively improve its anti‐interference performance by disturbing the data stream 15 .…”