A Tutorial on Downlink Precoder Selection Strategies for 3GPP MIMO Codebooks

This paper deals with the evolution of downlink codebook based multiple-input multiple-output (MIMO) within the third generation partnership project (3GPP) through release 15 to 17. There exist already several tutorials on this topic. However, to the authors' knowledge, the comparison in terms of complexity performance trade-off between practical precoder selection strategies in frequency or delay domain has not been tackled so far in the literature. This paper describes with matrix formalism the two main codebook types specified within 3GPP, i.e., Type-I codebook (low resolution) and Type-II codebook (high resolution). The Rel. 17 port selection is also detailed as well as the multi-user MIMO (MU-MIMO) precoding strategy to be applied relying on Type-II codebook feedback. For the enhanced Type-II codebook, two main practical precoder selection strategies are detailed at the UE side (i) based on singular value decomposition per sub-band in the frequency domain, (ii) based on wideband singular decomposition in the delay domain. Monte Carlo simulations demonstrate that the delay domain strategy performance may suffer from spatial interference for single user MIMO high rank transmissions when the channel is both spatially correlated and frequency selective. On the other hand, the frequency domain strategy complexity increases linearly with the number of sub-bands while it is not the case for the delay domain selection strategy. As a result, the delay domain selection strategy is particularly relevant for Rel. 17 Type-II codebook port selection or for a low frequency selective channel with few significant consecutive delays.