#### Downlink Precoding for Massive MIMO Systems Exploiting Virtual Channel Model Sparsity

##### Thomas Ketseoglou, Ender Ayanoglu

In this paper, the problem of designing a forward link linear precoder for Massive Multiple-Input Multiple-Output (MIMO) systems in conjunction with Quadrature Amplitude Modulation (QAM) is addressed. First, we employ a novel and efficient methodology that allows for a sparse representation of multiple users and groups in a fashion similar to Joint Spatial Division and Multiplexing. Then, the method is generalized to include Orthogonal Frequency Division Multiplexing (OFDM) for frequency selective channels, resulting in Combined Frequency and Spatial Division and Multiplexing, a configuration that offers high flexibility in Massive MIMO systems. A challenge in such system design is to consider finite alphabet inputs, especially with larger constellation sizes such as $M\geq 16$. The proposed methodology is next applied jointly with the complexity-reducing Per-Group Processing (PGP) technique, on a per user group basis, in conjunction with QAM modulation and in simulations, for constellation size up to $M=64$. We show by numerical results that the precoders developed offer significantly better performance than the configuration with no precoder or the plain beamformer and with $M\geq 16$.

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