## 2 System Description
### RS Overhead Model  
As a reference model, the current 3 GPP LTE systems use following types of RSs; 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 the three signals take most of resources for RS [36; 37]. PRS are only transmitted in resource blocks over downlink subframes that are configured for PRS transmission, and The MBSFN reference signals are only transmitted in the MBSFN region of MBSFN subframes [36; 37], thus PRS and MBSFN are not included in general operation mode and we disregard both cases for simplicity.  
CRS is called as a cell specific reference signal, and has been in the LTE system from Release 8. The role of CRS can be defined as the cell search and initial acquisition, the downlink channel estimation for coherent demodulation/detection at the UE, and the downlink channel quality measurements. CSI-RS has been introduced from Release 10, and used by UE to estimate the channel and report channel quality information (CQI) to BS. DM-RS is usually called as an UE specific reference signal, and the role of it is for the demodulation of the signal.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Precoder** & **MF** & **ZF** & **RZF** \\ \hline
**F** & \(\mathbf{H}^{H}\) & \(\mathbf{H}^{H}(\mathbf{H}\mathbf{H}^{H})^{-1}\) & \(\mathbf{H}^{H}(\mathbf{H}\mathbf{H}^{H}+\
u\mathbf{I}_{K})^{-1}\) \\ \hline Where superscript “\(H\)” denotes conjugate transpose, \((\cdot)^{-1}\) is the inverse operator, and \(\mathbf{I}_{K}\) is the \(K\times K\) identity matrix. & \\ \end{tabular}
\end{table}
Table 1: The precoding matrices of MF (matched filtering), ZF (zero-forcing), and RZF.  
In this paper, assuming frequency division multiplexing (FDD) mode, we use the following RS overhead factor for analysis [20]:  
\[\chi(\%) = (\eta_{CRS}+N_{t}+K\cdot\psi_{DM-RS})/\eta_{RB_{tot}}\times 100, \tag{9}\]  
where \(\chi(\%)\) is expressed as a percentage of RS overhead in a given total resources, \(\eta_{CRS}\) is the number of CRS in a given resource, \(\psi_{DM-RS}\) is the DM-RS proportional factor of \(K\) which we use 10, and \(\eta_{RB_{tot}}\) is the total resource elements for a given resource block for a coherence time. In the current 3 GPP LTE-A systems, the number of resource elements available in two resource blocks (1 ms ) is 168 (12 (frequency tones) \(\times\) 14 (time symbols)). Then, \(\eta_{RB_{tot}}=840\) resource elements assuming 5 ms coherence time. The CRS takes 14.8% of available resource elements, which is not a small portion. We do not know how technology will be evolved from an RS perspective. However it is quite obvious that RS overhead increases as the number of TX antennas increases. In this respect, (9) is reliable enough to use. The expected RS overhead reduction factor can be written as follows [20]:  
\[\chi_{r}(\%) = (\eta_{CRS}+(N_{t}+K\cdot\psi_{DM-RS})/N_{g})/\eta_{RB_{tot}} \times 100, \tag{10}\]  
where \(N_{g}\) is the RS overhead reduction factor to represent the number of antennas in each group, and the performance of RS overhead reduction scheme. Here we assume that the CRS is irreducible for cell search and initial acquisition, downlink channel estimation for coherent demodulation/detection at the UE, and downlink channel quality measurements, while all of the other RSs are ideally reducible by the RS overhead reduction scheme. Since resources of the CSI-RS and DM-RS are shared in the same group of antenna elements, it is divided by \(N_{g}\). In other word, \(N_{g}\) number of antenna elements share the same CSI-RS and DM-RS resources, and they are not orthogonal in each group, thus in each group, CSI-RS and DM-RS resources are reduced by factor of \(N_{g}\), but CRS is irreducible and not divided by \(N_{g}\), because it requires high accuracy. Reducing RS resources causes channel estimation error.