Читать книгу Spatial Multidimensional Cooperative Transmission Theories And Key Technologies - Lin Bai - Страница 20

We will introduce the basic principles of spatial multiplexing gain obtained by the space-based cooperative transmission system. Based on the active antenna array, we take the downlink between a ground receiver consisting of M_E receiving antennas and a cooperative satellite group consisting of M_S satellites, as shown in Fig. 1.3. Among them, each satellite is equipped with M_L transmitting antenna arrays.

The frequency-selective MIMO satellite communication channel can be described by its channel matrix H(f). Due to the characteristics of the satellite communication system, the link is actually a non-fading and shadowless LOS channel. In groundwireless communication systems, we have demonstrated that orthogonal channels in the LOS channel can provide optimal channel capacity,³⁴ which requires that the channel response between the transmitting and receiving antennas meets special requirements and is quasi-static. Since groundwireless system terminals are almost mobile, the assumption of quasi-static channels is not true in groundcellular mobile systems.

Fortunately, in the satellite communication system, the ground station has a very low movement speed relative to the satellite in most cases. The geometric arrangement of the receiving and transmitting antenna arrays is almost constant in a short time, and thus, the LOS channel can be approximated as static. Therefore, the satellite channel has unique advantages in realizing channel capacity optimization. Through the cooperative multi-beam transmission technology of constellation, we can achieve theoretically optimal antenna configuration, thereby increasing the capacity gain of the satellite communication system.

Fig. 1.3. Downlink of space-based cooperative transmission system.

Regardless of the noise generated during signal propagation, the propagation process of a frequency stationary signal from constellation in MIMO channel can be expressed as

where the groundreceiving signal vector is y = [y₁, . . . , y_mE]^T, the transmitting signal vector of constellation is x = [x₁, . . . , x_ms]^T, and the channel matrix is . The number of transmitting antennas is M_T = M_SM_L and the number of receiving antennas is M_R = M_E.

For a MIMO system, the highest spectral efficiency of the channel can be calculated by Telatar’s famous formula.³⁵

where (·)^H is the transpose of matrix and ρ is the linear signal-to-noise ratio of the channel. The signal-to-noise ratio of the channel is defined as SNR = 10 lg(ρ) = EIRP + (G − T)−κ − β [dB], where EIRP, (G−T), κ, and β are the effective isotropic radiated power, the quality factor, the Boltzmann constant, and the logarithm of downlink bandwidth, respectively. Since the distance between the satellite and the ground is much larger than the distance between array antennas, each element in the transfer matrix H can be considered to be of the same magnitude. Therefore, the transfer matrix H of the MIMO channel satisfying the maximum multiplexing gain is an orthogonal matrix. The theoretically optimal channel capacity can be achieved by adjusting the distance between the antennas and the distance between the constellations. The accessibility and conditions of the optimal channel capacity will be discussed in detail in Chapter 8.