## 3 Link Level Parameters and Channel Coefficient Generation
### Large Scale Parameters  
In this step, we generate the Large Scale Parameters (LSPs), e.g., all the per-link parameters useful to describe the link behavior between transmitter and receiver. We have seven LSPs for \(LOS\) link and six for \(NLOS\) case: Delay Spread (DS), angular spreads of departure and arrival in both directions azimuth and zenith (ASA, ASD, ZSA, and ZSD), Ricean \(K\)-factor (only of \(LOS\) links, \(K_{R}\)), and shadow fading \(\sigma_{SF}\). Table 7.5-6 of [21] provides the means and the variances in logarithmic scale of all these parameters, i.e., all the LSPs are lognormal random variables. The LSPs are generally correlated among them with different kinds of correlations: intra-UT correlation (parameters correlation in the same link) and inter-UT correlation (for different links and can be intra-cell and inter-cell). If we have \(M\) LSPs (\(M=7\) for a \(LOS\) link and \(M=6\) in the \(NLOS\) case) and a total of \(K\) users, and if we assume to take into account both intra- and inter-user correlations, there is a total of \(M\cdot K\) parameters to generate and the total correlation matrix has size \(MK\times MK\). Undoubtedly, if hundreds of links in system level simulation are considered, the computation of LSPs will be extremely large. WINNER II [23] proposes to calculate inter-UT correlation first and then the intra-UT correlation.
* The inter-UT correlation is calculated by generating a 2-D rectangular mesh based on the UT location for each of the \(M\) LSPs. For each mesh grid, \(M\) standard normally distributed random variables, which correspond to \(M\) LSPs, are assigned and filtered by their corresponding 2-D FIR filter separately. In the following formula, we can see the general expression of the impulse response \(h^{m}(d)\) of the filter for the \(m\)-th LSP \[h^{m}(d)=\exp\biggl{(}-\frac{d}{d_{corr}^{m}}\biggr{)}\] (35) where \(d\) is the distance and \(d_{corr}^{m}\) represents the correlation distance of the \(m\)-th parameter. If a dense 2-D spatial sampling is applied to each mesh grid, this filtering operation becomes computationally very expensive. Given also that, according to [21], links of UTs on different floors are uncorrelated, we decided not to take into account inter-user correlation.
* Intra-UT correlation is taken into account as follows: for each UT, the \(M\) correlated parameters can be obtained by the linear transformation \[\mathbf{\bar{s}}=\sqrt{C_{xx}(0)}\,\mathbf{\zeta}\] (36) where \(C_{xx}(0)\) is the \(M\times M\) intra-user inter-parameter correlation matrix (which can be obtained from Table 7.5-6 of [21]), \(\mathbf{\zeta}\sim\mathcal{N}(\mathbf{0},\mathbf{I})\) is a standard normal random vector (all elements are independent zero-mean random variables with unitary variance), and \(\mathbf{\bar{s}}\) is the vector of correlated normal random variables. The final LSPs can be obtained as [41]: \[\begin{array}{ll}10^{\mathcal{N}(\mu_{x},\,\sigma_{x}\bar{s}_{m})}&\text{ for DS, ASA, ASD, ZSA, and ZSD}\\ 10^{\mathcal{N}\left(\mu_{x},\,\frac{\sigma_{x}\bar{s}_{m}}{10}\right)}&\text{ for SF and K}\end{array}\] (37) where \(\mu_{x}\) and \(\sigma_{x}\) are proper mean and standard deviation, respectively, of the parameter \(x\) from Table 7.5-6 of [21].  
Finally, in this LSP step, we generate the number of cluster \(N_{cl}\) per link and the total number of rays per cluster \(M_{ray}\). Both parameters are listed in Table 7.5-6 of [21] for LOS, NLOS, and O2I cases. For UMi, \(N_{cl}=12\) for \(LOS\) and O2I, while \(N_{cl}=19\) for \(NLOS\); \(M_{ray}=20\) for all three case.