# Beam Grouping Based RS Resource Reuse and De-Contamination in Large Scale MIMO Systems
## 3 Analysis of RS Overhead  
The current 3 GPP LTE system, which is considered as a reference model, uses five kinds of RS, i.e., common reference signal (CRS), channel state information reference signal (CSI-RS), demodulation reference signal (DM-RS), multicast-broadcast single-frequency network (MBSFN) reference signal, positioning reference signal (PRS). In this paper, we only consider CRS, CSI-RS, and DM-RS because these three signals take most of the resources for RS. The CRS is usually called a cell specific reference signal and has been in the LTE system from release 8. The role of CRS is cell search and initial acquisition, downlink channel estimation for coherent demodulation/detection at the UE, and downlink channel quality measurements. The CSI-RS has been introduced from release 10 and used by the UE to estimate the channel and report channel quality information (CQI) to the BS. The DM-RS is usually called a UE specific reference signal, and its role is for the demodulation of the signal. The analysis in this paper is from the BS point of view, since the proposed scheme is for LS-MIMO systems, which can be installed in the BS. Although it is difficult to estimate how technology will be evolved especially for the BS point of view, it is quite obvious that the overhead of RS will be increased as the number of TX antennas is increased. In this section, we present analysis of RS overhead based on several assumptions. In current 3 GPP LTE-A systems, the available number of resource elements is 168 (12 (frequency tones) \(\times\) 14 (time symbols)) and there are 24 CRSs in two resource blocks (1 ms). This means that CRS itself takes14.8% of available resource elements, which is not a small portion. In this paper, we use the following model for the analysis of RS overhead:  
\[\chi_{WCR}(\%) = (\eta_{CRS}+K+K\cdot\chi_{DM-RS})/\eta_{RB_{tot}}\times 100, \tag{7}\] \[\chi_{WOCK}(\%) = (\eta_{CRS}+N_{t}+K\cdot\chi_{DM-RS})/\eta_{RB_{tot}}\times 100, \tag{8}\]  
where \(\chi_{WCR}(\%)\) and \(\chi_{WOCK}(\%)\) are the overhead of RS, which are represented in percentage for \"with channel reciprocity (WCR)\" and \"without channel reciprocity (WOCR)\" in a given resource, respectively. The WCR means that BS estimates the channel for downlink precoding by using an uplink signal from UE. That is to say, BS measures the channel by using an uplink signal. It indicates that the number of CSI-RS is proportional to the number of UEs, \(K\). This kind of mechanism usually can be used for a TDD system. Uplink/downlink channel calibration is necessary to use an uplink signal for downlink precoding. The WOCR means that BS estimates the channel for precoding by using a feedback signal from UE. That is to say, UE measures the channel by using the downlink RS. It indicates that the number of CSI-RS is proportional to the number of TX antennas, \(N_{t}\). This kind of mechanism can be applicable for both TDD and FDD systems. \(\eta_{CRS}\) is the number of CRS, and \(\chi_{DM-RS}\) is the DM-RS proportional factor of \(K\) in a given resource \(\eta_{RB_{tot}}\). The second term \(K\) in Label (7) and \(N_{t}\) in Label (8) indicate the number of CSI-RS in a given resource \(\eta_{RB_{tot}}\). We assume channel measurement is performed by using CRS and CSI-RS, while demodulation is performed by using DM-RS. Figure 2 shows the RS overhead (%) versus the number of TX antennas, \(N_{t}\), for 5 ms coherence time, which means nomadic or static channel. Here, we assume \(K\) also is increased as \(N_{t}\) is increased, while maintaining \(K=0.1N_{t}\). If we increase the number of TX antennas \(N_{t}\), there is an opportunity to increase the co-scheduled number of UEs, \(K\), with minimum channel hardening effect of LS-MIMO, \(N_{t}=10K\). We also assume that the fundamental limit of overhead of RS is 50%, which is corresponding to \(N_{t}=273\) in the case of WCR, and \(N_{t}=150\) in the case of WOCR.