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Symbol Level Precoding (SLP) has attracted significant research interest due to its ability to exploit interference for energy-efficient transmission. This paper proposes an unsupervised deep-neural network (DNN) based SLP framework. Instead of naively training a DNN architecture for SLP without considering the specifics of the optimization objective of the SLP domain, our proposal unfolds a power minimization SLP formulation based on the interior point method (IPM) proximal ‘log’ barrier function. Furthermore, we extend our proposal to a robust precoding design under channel state information (CSI) uncertainty. The results show that our proposed learning framework provides near-optimal performance while reducing the computational cost from $\mathcal{O}(n^{7.5})$ to $\mathcal{O}(n^{3})$ for the symmetrical system case where $n=\text {number of transmit antennas}=\text {number of users}$ . This significant complexity reduction is also reflected in a proportional decrease in the proposed approach’s execution time compared to the SLP optimization-based solution.

Linear and symbol-level precoding in satellite communications have received increasing research attention thanks to their ability to tackle inter-beam interference, allowing the use of spectral resources more efficiently. However, there are still challenges and open questions regarding the implementation of practical precoding systems taking the phase uncertainties in estimating the channel state information into account. This work assesses the impact of phase variations and uncertainties inherent to the satellite communication system operating a precoded forward link. Specifically, we address the inability to measure at the user terminal, the absolute phase rotation introduced by the channel, and the transponder local oscillator phase noise effects on the precoding operations considering the use of frequency division multiplexing in the forward-uplink transmission. We formally demonstrate that the system performance for linear and non-linear precoding operations is not affected by the uncertainty in the phase measurements at the user terminal. Additionally, we show that using a single frequency reference for all the local oscillators at the transponder does not avoid the phase variations related to the frequency division multiplexing in the forward-uplink. This work demonstrates that these phase variations would not affect the system performance for an ideal zero-delay precoding loop. However, this is not feasible in practical scenarios, where the phase noise of the frequency reference at the transponder and the loop delay determine the impact on the system performance. We validate our results by simulations considering three frequency references with different stability levels in a typical geosynchronous orbit (GEO) satellite system. Our results suggest that practical implementations of multiuser-MISO precoding systems must include a differential phase synchronization loop to compensate for this performance degradation.

In Constant Envelope Symbol Level Precoding (CESLP), the transmitted signals by the antennas have constant amplitude regardless of the channel realization and the conveyed information symbols. Such solutions enable the use of power-efficient components, i.e. non-linear power amplifiers and thus, are suitable for systems based on large-scale antenna arrays. In the latter systems, the hardware complexity and power consumption can be limiting factors since each antenna element requires dedicated hardware components. These components include the Digital-to-Analog Converters (DACs) that have exponential complexity and power consumption with the number of the supported resolution. To that end, in this paper, a CESLP precoding technique is presented for Multi-User Multiple Input-Multiple Output (MU-MIMO) systems with low resolution DACs. The case of a multi-carrier system employing the well-known Orthogonal Frequency Division Multiplexing (OFDM) technique is considered. The precoding design problem is formulated as a mixed discrete-continuous least-squares optimization one which is NP-hard. An efficient low complexity solution is developed based on the Cyclic Coordinate Descent (CCD) optimization framework. Simulations show that the proposed solution is able to achieve very close performance to the one of the infinite resolution CESLP precoding counterpart even though, it is based on DACs that have resolution of only a few bits.