System Level Modeling and Optimization of the LTE Downlink

B. Correlation Matrices for Shadow Fading Generationcorrelation matrix R s can be expressed element-wise as()[R s ] i,j= exp −α · [X s ] i,j · d , (B.2)resulting in a correlation matrix R s⎡⎤1 0.7 0.78 0.57 0.57 0.78 0.61 0.49 0.7 0.45 0.57 0.41 0.780.7 1 0.78 0.78 0.78 0.57 0.7 0.7 0.61 0.61 0.57 0.57 0.780.78 0.78 1 0.61 0.7 0.7 0.78 0.57 0.78 0.47 0.7 0.45 0.70.57 0.78 0.61 1 0.7 0.45 0.57 0.78 0.47 0.78 0.45 0.7 0.70.57 0.78 0.7 0.7 1 0.49 0.78 0.78 0.57 0.57 0.61 0.61 0.610.78 0.57 0.7 0.45 0.49 1 0.57 0.41 0.78 0.36 0.61 0.33 0.61R s =0.61 0.7 0.78 0.57 0.78 0.57 1 0.61 0.7 0.45 0.78 0.47 0.57,0.49 0.7 0.57 0.78 0.78 0.41 0.61 1 0.45 0.7 0.47 0.78 0.570.7 0.61 0.78 0.47 0.57 0.78 0.7 0.45 1 0.37 0.78 0.36 0.570.45 0.61 0.47 0.78 0.57 0.36 0.45 0.7 0.37 1 0.36 0.78 0.570.57 0.57 0.7 0.45 0.61 0.61 0.78 0.47 0.78 0.36 1 0.37 0.49⎢⎥⎣0.41 0.57 0.45 0.7 0.61 0.33 0.47 0.78 0.36 0.78 0.37 1 0.49⎦0.78 0.78 0.7 0.7 0.61 0.61 0.57 0.57 0.57 0.57 0.49 0.49 1(B.3)where L s L H s = R s , and ˜L s can be obtained by removing the last row and column ofL s .92