where the groundreceiving signal vector is y = [y1, . . . , ymE]T, the transmitting signal vector of constellation is x = [x1, . . . , xms]T, and the channel matrix is
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.
1.4Summary
Traditional wireless communication mainly uses ground-based wireless communication systems. However, with the rapid development of wireless communication systems, it is increasingly requiring higher spectrum utilization, greater system capacity, more flexible network coverage, and lower construction costs. With the continuous improvement of aerospace technology and the rapid growth of the types and quantities of space-based and air-based platforms, the space–air–ground integrated information network consisting of satellites, stratospheric balloons, and various aerospace vehicles is developed. This chapter mainly summarizes the characteristics and development process of the ground-based, air-based, and space-based wireless communication systems. In the following chapters, we will elaborate on the space–air–ground integrated cooperative transmission theories and key technologies.
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