On Capacity of Handheld to Multi-Satellite Communication

In this paper, we investigate the uplink transmission of a single-antenna handheld user to a cluster of satellites. Taking advantage of the inter-satellite links, the satellites can cooperate which each other to jointly detect the received signal. We examine a scenario in which the satellite cluster lacks access to the instantaneous channel state information (CSI). Thus, using only statistical CSI, we design the joint detection by minimizing the mean square error (MSE). We calculate the ergodic capacity using the properties of the Wishart matrix, and then for low-SNR scenarios we provide a closed-form approximation for it. Our numerical results demonstrate the effectiveness of the detection scheme, along with the proximity of the approximation to the actual ergodic capacity. Considering a mega constellation with 3168 satellites in low earth orbit (LEO), we show that a capacity of more than 10 MB/sec can be achieved even if only the statistical CSI is known to the receiver, and a capacity of up to 38 MB/sec can be achieved with perfect instantaneous CSI.