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The concept of a simple correlation model for shadow fading has been widely adopted in LTE co-existence studies mostly employed in uplink case. The propagation attenuation is modelled as the product of the path loss and the shadow fading. The shadow fading is well approximated by a log-normal distribution. Let z denotes shadow fading in dB with zero mean and variance σ². Then the shadow fading of path from one UE to the i-th BS is expressed as

                                  z_i=a*x + b*y_i ,                                                                                 (Eq. 64)

where a²+b²=1 and xand y_iare independent Gaussian distributed variables, both with zero mean and variance σ².y_i and y_jfor are independent as well.

Figure 209 presents how to set-up the pathloss correlation in SEAMCAT (only available for OFDMA). The panel is similar for the OFDMA DL and UL.

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Figure 209: Illustration of the pathloss correlation – input parameters

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Figure 210: Illustration of the pathloss correlation principle

Thus, the correlation coefficient of the shadow fading from one UE to two different BSs, i.e., the i-th and j-th BS, is

                                                                              Image Added         (Eq. 65)

 In most LTE studies, Image Added  is assumed ‎[10]. For cellular systems with three-sector antennas, the shadowing correlation between sites (equivalent to BS in Omni antenna system) is of 0.5 and correlation between sectors of the same site is consequently of 1.