Uplink Transmit Design for Massive MIMO LEO Satellite Communications

This paper investigates the uplink (UL) transmit design for massive multiple-input multiple-output (MIMO) low-earth-orbit (LEO) satellite communication (SATCOM), where the long-term statistical channel state information is utilized at the user terminals (UTs). We consider that the uniform planar arrays are deployed at both the satellite and UTs, and derive the UL massive MIMO LEO satellite channel model. With the aim to achieve the ergodic sum rate capacity, we show that the rank of each UT's optimal transmit covariance matrix does not exceed that of its channel correlation matrix at the UT sides. This reveals the maximum number of independent data streams that can be transmitted from each UT to the satellite. We further show that the design of the transmit covariance matrices can be reduced into that of lower-dimensional matrices, for which a stochastic programming based algorithm is developed by exploiting the optimal lower-dimensional matrices' structure. To reduce the computational complexity, we invoke the asymptotic programming and develop a computationally efficient algorithm to compute the transmit covariance matrices. Simulations show that the proposed UL transmit strategies are superior to the conventional schemes, and the low-complexity asymptotic programming based UL transmit design can attain near-optimal performance in massive MIMO LEO SATCOM.