# Research on Tbps and Kilometer-Range Transmission of Terahertz Signals
## 3 Enabling Technologies for THz Communication Systems
### Adopting MIMO Architecture Combining Polarization Multiplexing and MRC
For a MIMO system with t transmit antennas and r receive antennas, the received signal Y can be expressed as  
\[\mathbf{Y}=\mathbf{H}\mathbf{X}+\mathbf{n}. \tag{6}\]  
where \(\mathbf{X}\) is the \(N_{t}\times 1\) transmit vector, \(\mathbf{H}\) is the \(N_{r}\times N_{t}\) THz channel matrix, and \(\mathbf{n}\) is the \(N_{r}\times 1\) additive white Gaussian noise (AWGN) vector satisfying \(\mathrm{E}[\mathbf{n}\mathbf{n}^{\mathrm{H}}]=N_{0}\mathrm{I}\). At the receiver, the MRC algorithm is employed, and the receiver applies a complex weight vector \(\mathbf{W}=\left[w_{1},w_{2},\ldots,w_{N_{t}}\right]^{T}(N_{r}\times 1)\) to the received signals and combines them:  
\[\mathbf{W}^{H}\mathbf{Y}=\mathbf{W}^{H}\mathbf{H}\mathbf{X}+\mathbf{W}^{H}n. \tag{7}\]  
The SNR after MRC combining is derived as  
\[SNR=\frac{\left|\mathbf{W}^{H}\mathbf{H}\right|^{2}E_{s}}{\|\mathbf{W}\|N_{0}}. \tag{8}\]  
where \(E_{s}\) is symbol energy, and \(N_{0}\) is noise power spectral density. Under this constraint, maximizing SNR becomes equivalent to minimizing the effective noise power \(\|\mathbf{W}\|N_{0}\). The SNR maximization under unit-norm constraint \(\|\mathbf{W}\|=1\) is formulated as  
\[\underset{\mathbf{W}}{\max}\gamma=\frac{\left|\mathbf{W}^{H}\mathbf{H}\right| ^{2}E_{s}}{N_{0}},\text{ s.t.}\ \|\mathbf{W}\|^{2}=1. \tag{9}\]  
Using the Lagrange multiplier \(\lambda\),  
\[\mathbf{L}=\mathbf{W}^{H}\mathbf{H}\mathbf{H}\mathbf{W}^{H}\mathbf{W}-\lambda( \mathbf{W}^{H}\mathbf{W}-1). \tag{10}\]  
Taking gradient w.r.t. \(\mathbf{W}\),  
\[\
abla\mathbf{w}\mathbf{L}=2\mathbf{H}\mathbf{H}^{H}\mathbf{W}-2\lambda \mathbf{W}=0. \tag{11}\]  
Thus, the maximum received SNR is denoted as  
\[SNR=\frac{\|\mathbf{H}\|E_{s}}{N_{0}}. \tag{12}\]  
Figure 8: MIMO-PDM-based long-distance radio-over-fiber (RoF) terahertz transmission system; HA: horn antenna [88]. where the channel gain is \(g=\|\mathbf{H}\|\). We compared systems transmitting identical symbols across all paths to exploit diversity gain through signal combining at the receiver. As shown in Figure 9, in a single-transmitter antenna system, MRC provides superior gain compared to Selection Combining (SC) and Equal Gain Combining (EGC). In our commonly deployed 2 \(\times\) 2 MIMO systems, employing MRC technology can achieve up to 9 dB of diversity gain [89; 90]. By combining PDM with a MIMO architecture, signals transmitted on two orthogonal polarizations preserve inter-channel incoherence. When identical signals are transmitted over both channels, MRC can be applied at the receiver to achieve diversity gain. This approach not only prevents the disruption of coherence caused by phase differences induced by wavelength discrepancies during transmission but also simultaneously obtains diversity gain. In reference [91], we effectively resolved coherence disruption and enhanced performance in a 300 GHz terahertz wireless link over 200 m using a MIMO-PDM transmitter architecture combined with a MIMO-MRC receiver architecture. The system configuration is depicted in Figure 10. At the transmitter, PDM generates two orthogonally polarized 300 GHz terahertz signals (via a PDM module and dual UTC-PD opto-terahertz conversion), emitted by a high-gain cylindrical lens antenna array. At the receiver, dual antennas capture these independent polarization signals, with the MRC algorithm applied for optimal signal combining. This architecture innovatively leverages orthogonal polarization to ensure signal incoherence between paths, fundamentally preventing coherence disruption caused by phase differences in same-frequency/same-polarization signals, while enabling effective MRC implementation. Experimental results demonstrate successful achievement of a total data rate of 100 Gbit/s (50 Gbaud PDM-QPSK) over a 200 m wireless distance.