Convex optimization based downlink precoding for large-scale MIMO

In large-scale Multiple-Input-Multiple-Output (MIMO) downlink, one state-of-the-art precoder significantly reduces the Peak-to-Average Power Ratio (PAPR) of the emitted signals from the Base Station (BS) antennas through minimizing the ℓ_∞-norm of the precoded signals (generated by the precoder and transmitted by the BS RF frontends). In this paper, its computational complexity is analyzed based on the random matrix theory, and its two variants are constructed as follows. First, the ℓ_∞-norm is approximated by a high order ℓ_p-norm (e.g. ℓ₁₆), and then the downlink precoding problem is solved by classical Gradient Descent (GD) method. Second, the ℓ_∞-norm is removed directly after additional box constraints are exerted on the elements of the precoded signals. Then the precoding problem is solved by spectral GD algorithm. Simulation results show that the above three convex-optimization based precoders can reduces the PAPR by more than 11.5dB compared to conventional precoding schemes.