LDM-Based Communication and Computation Co-Design in Integrated Satellite and Aerial Networks

This paper investigates a highly spectrally efficient transmission scheme in an integrated satellite and aerial network (ISAN). Specifically, we first propose a novel uplink access framework, where the co-design of communication and over-the-air computation (AirComp) is implemented through layer division multiplexing (LDM) in the aerial network, while the cognitive radio-inspired non-orthogonal multiple access (CR-NOMA) technology is employed in the satellite network. Then, according to the proposed framework, we mathematically formulate a joint optimization problem that aims at maximizing the system achievable sum rate, subject to the constraints of minimal accuracy requirement of AirComp and minimal quality-of-service requirements of communication service. Next, by introducing the inter-network interference-related auxiliary variable, we divide the original optimization problem into two subproblems associated with the optimization of the satellite and aerial networks. To tackle the first subproblem, we propose a beamspace-inspired analog beamforming (BF) method, and derive closed-form expressions for BF vectors and transmit powers to implement the CR-NOMA scheme in the satellite network. Meanwhile, to address the second subproblem, we propose a beamspace-inspired digital BF together with successive convex approximation and alternating optimization approaches, to obtain the BF matrices, transmit power coefficients and AirComp scaling factor, so that the LDM-based communication and computation co-design (CCCD) can be realized in the aerial network. Moreover, for complexity reduction, we propose a beamspace-inspired zero-forcing BF method to calculate the communication BF matrices, and then leverage the orthogonal beam superposition approach to obtain the computation BF matrix, thereby presenting another CCCD scheme. Finally, our simulation results confirm that since the proposed schemes can realize spectrum multiplexing for communication and AirComp services, we achieve higher system spectral efficiency and lower computation error than the benchmarks.