Just to recap, building an LTE fading simulator with the desired temporal and spatial correlation is a three step procedure.
1. Generate Rayleigh fading sequences using Smith’s method which is based on Clarke and Gan’s fading model.
2. Introduce spatial correlation based upon the spatial correlation matrices defined in 3GPP 36.101.
3. Use these spatially and temporally correlated sequences as the filter taps for the LTE channel models.
We have already discussed step 1 and 3 in our previous posts. We now focus on step 2, generating spatially correlated channels coefficients.
3GPP has defined spatial correlation matrices for the Node-B and the UE. These are defined for 1,2 and 4 transmit and receive antennas. These are reproduced below.
- Spatial Correlation Matrix
The parameters ‘alpha’ and ‘beta’ are defined as:
The combined effect of antenna correlation at the transmitter and receiver is obtained by taking the Kronecker product of individual correlation matrices e.g. for a 2×2 case the correlation matrix is given as:
- Correlation Matrix for 2×2 MIMO
Multiplying the square root of the correlation matrix with the vector of channel coefficients is equivalent to taking a weighted average e.g. for the channel between transmit antenna 1 and receive antenna 1 the correlated channel coefficient h11corr is given as:
where w1=1 and w2, w3 and w4 are less than one and greater than zero. For the high correlation case described above the channel coefficient is calculated as:
From a practical point of antenna correlation is dependent on the antenna separation. Greater the antenna spacing lower is the antenna correlation and better the system performance. However, a base station requires much higher antenna spacing than a UE to achieve the same level of antenna correlation. This is due to the fact the base station antennas are placed much higher than a UE. Therefore the signals arriving at the base station are usually confined to smaller angles and experience similar fading. A UE on the other hand has a lot of obstacles in the surrounding areas which results in higher angle spread and uncorrelated fading between the different paths.