System Level Modeling and Optimization of the LTE Downlink

B. Correlation Matrices for Shadow Fading GenerationB. Correlation Matrices for ShadowFading GenerationThis appendix details the correlation matrix employed for the generation of theshadow fading traces, which is explained in Section 3.1.1.5. The LTE L2S modelpresented in Chapter 3 extends the model in [87] to twelve neighbors, employing thecorrelation matrix detailed below.The distance matrix (in pixels) between the current pixel, denoted as s n , and its 12neighbors s n−1 . . . s n−12 , is depicted in Figure 3.8:⎡ √ √ √ √ √ √ √ √ ⎤0 2 1 5 5 1 2 8 2 10 5 13 1√ √ √ √ √ √ 2 0 1 1 1 5 2 2 2 2 5 5 1√ √ √ √ √ √ 1 1 0 2 2 2 1 5 1 3 2 10 2√ √ √ √ √ √ √ 5 1 2 0 2 10 5 1 3 1 10 2 2√ √ √ √ √ √ 5 1 2 2 0 8 1 1 5 5 2 2 2√ √ √ √ √ √ √ √ 1 5 2 10 8 0 5 13 1 17 2 20 2√ √ √ √ √ √ X s =2 2 1 5 1 5 0 2 2 10 1 3 5√ √ √ √ √ √ √ .8 2 5 1 1 13 2 0 10 2 3 1 5√ √ √ √ √ √ 2 2 1 3 5 1 2 10 0 4 1 17 5√ √ √ √ √ √ √ 10 2 3 1 5 17 10 2 4 0 17 1 5√ √ √ √ √ √ 5 5 2 10 2 2 1 3 1 17 0 4 8⎢√ √ √ √ √ √ √ ⎥⎣ 13 5 10 2 2 20 3 1 17 1 4 0 8 ⎦√ √ √ √ √ √ √ √1 1 2 2 2 2 5 5 5 5 8 8 0(B.1)Assuming α = 1/20, as stated in Section 3.1.1.5, and a pixel resolution d of 5 m, the91