## 2 Channel State Information Reference Signals  
One of the key design principles of NR is to avoid, as far as possible, \"always-on\" signals [21; 33]. In release 8 of the LTE standard, channel sounding for downlink transmissions is performed by means of device measurements on cell-specific reference signals (CRS) [34], which are transmitted over the whole transmission bandwidth in each subframe. From release 10 on [35], these reference signals are complemented by another type of reference signal called CSI-RS, which, in contrast to the first, is not expected to be continuously transmitted. The main reason for this upgrade lays in the necessity to support spatial multiplexing with more than four layers; however, as [21] points out, CSI-RS introduction has opened the way to further technological extensions, such as coordinated multi-point (CoMP) [36] operations and interference estimation.  
In 3 GPP specifications [37], the channel quality indicator (CQI), rank indicator (RI), precoding matrix indicator (PMI), and several other quantities, are jointly referred to as channel state information (CSI). The precoding matrix indicator is reported by the user equipment (UE) to the base station (BS); it represents an indication of what the user considers to be a suitable precoding matrix to be applied on downlink transmissions. In particular, the PMI is no more than a set of indexes or a single index pointing to a specific entry in the precoding codebook, which contains a list of all the possible precoding matrices \(\mathbf{W}\) that the device can select and report to the network. There exists at least one codebook for each permitted combination of \(N_{T}\) (number of antenna ports) and \(N_{L}\) (number of layers) associated with the configured CSI-RS.  
It is important to stress that precoding codebooks play a role only in the context of PMI reporting and do not impose any restriction in the choice of the precoding matrix to be applied by the network [21]. In some cases, it is convenient for the network to select the precoding matrix suggested by the device, but, when, for example, the network is in possession of additional information, the precoding computation may lead to a different choice.  
As [21] reports, the typical use case of multi-antenna precoding is multi-user MIMO (MU-MIMO) [38; 39; 40]. In this case, the main purposes are to direct the energy towards the device and simultaneously limit the interference towards the other users scheduled on the same time-frequency resource. In this kind of scenario, it is clear that the network needs more detailed information about the channel experienced by different UEs so that it can take into account the PMI reported by all simultaneously scheduled devices when selecting the precoding matrix [21].  
The NR standard defines two types of CSI reporting, each characterized by a different size and structure of the codebook [37]:  
* Type I CSI codebooks: designed for single user-MIMO (SU-MIMO) scenarios, where a single user is scheduled within a certain time-frequency resource, transmitting on a potentially large number of layers in parallel;
* Type II CSI codebooks: designed for MU-MIMO scenarios, where many users are scheduled within the same time-frequency resource, each transmitting on a limited number of layers in parallel (two at most).  
For fast time-varying wireless channels, the adoption of delayed CSI at the transmitter can help reduce the feedback frequency of the channel estimates [41].