# 9.11 Pathloss Correlation

The concept of a simple correlation model for shadow fading has been widely adopted in <span data-highlighted="true" data-vc="highlighted-text"><span class="_kqswh2mm"><span class="_5pioz8co _189e1dm9 _1il9buyh _19lc184f _d0altlke" data-testid="definition-highlighter">LTE</span></span></span> 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 σ<sup data-renderer-mark="true">2</sup>. Then the shadow fading of path from one <span data-highlighted="true" data-vc="highlighted-text"><span class="_kqswh2mm"><span class="_5pioz8co _189e1dm9 _1il9buyh _19lc184f _d0altlke" data-testid="definition-highlighter">UE</span></span></span> to the *i-th* <span data-highlighted="true" data-vc="highlighted-text"><span class="_kqswh2mm"><span class="_5pioz8co _189e1dm9 _1il9buyh _19lc184f _d0altlke" data-testid="definition-highlighter">BS</span></span></span> is expressed as

[![image.png](https://wiki.cept.org/uploads/images/gallery/2026-04/scaled-1680-/XMGfKQ6ynQYnMePO-image.png)](https://wiki.cept.org/uploads/images/gallery/2026-04/XMGfKQ6ynQYnMePO-image.png) (Eq. 64)

where *a<sup data-renderer-mark="true">2</sup>+b<sup data-renderer-mark="true">2</sup>=1* and *x* and *y<sub data-renderer-mark="true">i</sub>* are independent Gaussian distributed variables, both with zero mean and variance *σ<sup data-renderer-mark="true">2</sup>* . *y<sub data-renderer-mark="true">i</sub>* and *y<sub data-renderer-mark="true">j</sub>* for are independent as well.

Figure 207 presents how to set-up the pathloss correlation in SEAMCAT (only available for <span data-highlighted="true" data-vc="highlighted-text"><span class="_kqswh2mm"><span class="_5pioz8co _189e1dm9 _1il9buyh _19lc184f _d0altlke" data-testid="definition-highlighter">OFDMA</span></span></span>). The panel is similar for the <span data-highlighted="true" data-vc="highlighted-text">OFDMA</span> DL and <span data-highlighted="true" data-vc="highlighted-text"><span class="_kqswh2mm"><span class="_5pioz8co _189e1dm9 _1il9buyh _19lc184f _d0altlke" data-testid="definition-highlighter">UL</span></span></span>.

[![image.png](https://wiki.cept.org/uploads/images/gallery/2026-04/scaled-1680-/3LCbelyUy1QEEkj5-image.png)](https://wiki.cept.org/uploads/images/gallery/2026-04/3LCbelyUy1QEEkj5-image.png)

<div class="highlighter-context page view" data-inline-comments-target="true" data-testid="page-content-only" id="bkmrk--1"><div class="_19itglyw _vchhusvi _r06hglyw _19pkidpf _2hwx1wug _otyr1epz _18u01wug _1bsb1osq"><div class="wiki-content css-th923b e5xcnr80" data-test-appearance="max" data-testid="pageContentRendererTestId" data-vc="pageContentRendererTestId"><div class="renderer-overrides"><div class="css-3qfej8"><div class="ak-renderer-wrapper is-max css-pw7jst"><div class="css-1g3hymi" role="none"><div class="ak-renderer-document"><div class="rich-media-item mediaSingleView-content-wrap image-align-start css-1eg2hv5" data-layout="align-start" data-media-vc-wrapper="true" data-node-type="mediaSingle" data-renderer-start-pos="801" data-vc="media-single" data-width="403" data-width-type="pixel"><div class="css-11ftnp8"><div data-alt="" data-collection="contentId-493467" data-context-id="493467" data-file-mime-type="image/png" data-file-name="image2016-8-9 9:54:42.png" data-file-size="15224" data-height="133" data-id="7816acac-164e-4e45-a9f6-2ffd21ef6891" data-node-type="media" data-renderer-start-pos="802" data-type="file" data-width="403"><div class="_2rko18qm _vchhusvi _kqswh2mm _ect4ttxp _p12f1osq _c71l1osq _1bsb1qmm _4t3ine4n _1hlmd0i9 _1rquusvi _eg541i5c _mts3kb7n _1ntskb7n _yfmhtlke _5sb1v00u new-file-experience-wrapper" data-media-vc-wrapper="true" data-testid="media-card-view" id="bkmrk--2"><div class="_1reo15vq _18m915vq _2rko18qm _1e0c1txw _kqswh2mm _p12f1osq _1bsb1osq _4t3i1osq _c71l1osq media-file-card-view" data-cursor="pointer" data-test-media-name="image2016-8-9 9:54:42.png" data-test-progress="1" data-test-source="remote" data-test-status="complete" data-testid="media-file-card-view"></div></div></div></div></div></div></div></div></div></div></div></div></div>**Figure 207: Illustration of the pathloss correlation – input parameters**

<div class="highlighter-context page view" data-inline-comments-target="true" data-testid="page-content-only" id="bkmrk--3"><div class="_19itglyw _vchhusvi _r06hglyw _19pkidpf _2hwx1wug _otyr1epz _18u01wug _1bsb1osq"><div><div class="wiki-content css-th923b e5xcnr80" data-test-appearance="max" data-testid="pageContentRendererTestId" data-vc="pageContentRendererTestId"><div class="renderer-overrides"><div class="css-3qfej8"><div class="ak-renderer-wrapper is-max css-pw7jst"><div class="css-1g3hymi" role="none"><div class="ak-renderer-document"><div class="fabric-editor-block-mark fabric-editor-alignment" data-align="center">  
</div><div class="rich-media-item mediaSingleView-content-wrap image-align-start css-1p6fm5h" data-layout="align-start" data-media-vc-wrapper="true" data-node-type="mediaSingle" data-renderer-start-pos="880" data-vc="media-single" data-width="320" data-width-type="pixel"><div class="css-n4gizo">  
</div></div></div></div></div></div></div></div></div></div></div>[![image.png](https://wiki.cept.org/uploads/images/gallery/2026-04/scaled-1680-/EjQMZ7L6nZNbaelU-image.png)](https://wiki.cept.org/uploads/images/gallery/2026-04/EjQMZ7L6nZNbaelU-image.png)

<div class="highlighter-context page view" data-inline-comments-target="true" data-testid="page-content-only" id="bkmrk-figure-208%3A-illustra"><div class="_19itglyw _vchhusvi _r06hglyw _19pkidpf _2hwx1wug _otyr1epz _18u01wug _1bsb1osq"><div><div class="wiki-content css-th923b e5xcnr80" data-test-appearance="max" data-testid="pageContentRendererTestId" data-vc="pageContentRendererTestId"><div class="renderer-overrides"><div class="css-3qfej8"><div class="ak-renderer-wrapper is-max css-pw7jst"><div class="css-1g3hymi" role="none"><div class="ak-renderer-document"><div class="rich-media-item mediaSingleView-content-wrap image-align-start css-1p6fm5h" data-layout="align-start" data-media-vc-wrapper="true" data-node-type="mediaSingle" data-renderer-start-pos="880" data-vc="media-single" data-width="320" data-width-type="pixel"><div class="css-n4gizo"><div data-alt="" data-collection="contentId-493467" data-context-id="493467" data-file-mime-type="image/png" data-file-name="image2016-8-9 9:54:49.png" data-file-size="37379" data-height="235" data-id="9a6509ba-8173-4771-94e1-103aa9fa329a" data-node-type="media" data-renderer-start-pos="881" data-type="file" data-width="320"><div class="_2rko18qm _vchhusvi _kqswh2mm _ect4ttxp _p12f1osq _c71l1osq _1bsb1qmm _4t3ine4n _1hlmd0i9 _1rquusvi _eg541i5c _mts3kb7n _1ntskb7n _yfmhtlke _5sb1v00u new-file-experience-wrapper" data-media-vc-wrapper="true" data-testid="media-card-view" id="bkmrk-figure-208%3A-illustra-1"><div class="_1reo15vq _18m915vq _2rko18qm _1e0c1txw _kqswh2mm _p12f1osq _1bsb1osq _4t3i1osq _c71l1osq media-file-card-view" data-cursor="pointer" data-test-media-name="image2016-8-9 9:54:49.png" data-test-progress="1" data-test-source="remote" data-test-status="complete" data-testid="media-file-card-view"><div class="_kqswstnw _1bsb1osq _4t3i1osq _1e0c1txw _2lx21bp4 _1bah1h6o _4cvr1h6o align-center" data-testid="ImageRendererWrapper">![](blob:https://ecowiki.atlassian.net/9c46dc60-412f-4a20-9b00-8e770cfee245#media-blob-url=true&id=9a6509ba-8173-4771-94e1-103aa9fa329a&collection=contentId-493467&contextId=493467&width=320&height=235&alt=&clientId=113268fe-fe5b-4bc3-8ff3-07965dbf1d18)**Figure 208: Illustration of the pathloss correlation principle**</div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>Thus, the correlation coefficient of the shadow fading from one <span data-highlighted="true" data-vc="highlighted-text">UE</span> to two different BSs, i.e., the *i-th* and *j-th* <span data-highlighted="true" data-vc="highlighted-text">BS</span>, is

[![image.png](https://wiki.cept.org/uploads/images/gallery/2026-04/scaled-1680-/oC86pU9lhJUl0TzJ-image.png)](https://wiki.cept.org/uploads/images/gallery/2026-04/oC86pU9lhJUl0TzJ-image.png)(Eq. 65)

<div class="highlighter-context page view" data-inline-comments-target="true" data-testid="page-content-only" id="bkmrk--5"><div class="_19itglyw _vchhusvi _r06hglyw _19pkidpf _2hwx1wug _otyr1epz _18u01wug _1bsb1osq"><div class="wiki-content css-th923b e5xcnr80" data-test-appearance="max" data-testid="pageContentRendererTestId" data-vc="pageContentRendererTestId"><div class="renderer-overrides"><div class="css-3qfej8"><div class="ak-renderer-wrapper is-max css-pw7jst"><div class="css-1g3hymi" role="none"><div class="ak-renderer-document"><div class="fabric-editor-block-mark fabric-editor-alignment" data-align="end"><div data-testid="inline-image"></div>  
</div></div></div></div></div></div></div></div></div> In most <span data-highlighted="true" data-vc="highlighted-text">LTE</span> studies,[![image.png](https://wiki.cept.org/uploads/images/gallery/2026-04/scaled-1680-/NuUAhgQK3FkXRFvm-image.png)](https://wiki.cept.org/uploads/images/gallery/2026-04/NuUAhgQK3FkXRFvm-image.png) is assumed ‎\[10\]. For cellurar systems with three-sector antennas, the shadowing correlation between sites (equivalent to <span data-highlighted="true" data-vc="highlighted-text">BS</span> in Omni antenna system) is of 0.5 and correlation between sectors of the same site is consequently of 1.

[![image.png](https://wiki.cept.org/uploads/images/gallery/2026-04/scaled-1680-/ZHwQ9wcfq6YrHHr0-image.png)](https://wiki.cept.org/uploads/images/gallery/2026-04/ZHwQ9wcfq6YrHHr0-image.png)

<div class="highlighter-context page view" data-inline-comments-target="true" data-testid="page-content-only" id="bkmrk--7"><div class="_19itglyw _vchhusvi _r06hglyw _19pkidpf _2hwx1wug _otyr1epz _18u01wug _1bsb1osq"><div><div class="wiki-content css-th923b e5xcnr80" data-test-appearance="max" data-testid="pageContentRendererTestId" data-vc="pageContentRendererTestId" id="bkmrk--8"><div class="renderer-overrides"><div class="css-3qfej8"><div class="ak-renderer-wrapper is-max css-pw7jst"><div class="css-1g3hymi" role="none"><div class="ak-renderer-document"><div class="rich-media-item mediaSingleView-content-wrap image-align-end css-q9btkw" data-layout="align-end" data-media-vc-wrapper="true" data-node-type="mediaSingle" data-renderer-start-pos="1418" data-vc="media-single" data-width="270" data-width-type="pixel"><div class="css-18cpusc"><div class="css-vhfmu2" contenteditable="false" data-media-badges="true" data-testid="media-badges">  
</div><div data-alt="" data-collection="contentId-493467" data-context-id="493467" data-file-mime-type="image/png" data-file-name="image2016-8-9 9:56:59.png" data-file-size="52772" data-height="270" data-id="fcb03aa6-0fd3-4b21-b1a0-18d6d8491ede" data-node-type="media" data-renderer-start-pos="1419" data-type="file" data-width="292"><div class="_2rko18qm _vchhusvi _kqswh2mm _ect4ttxp _p12f1osq _c71l1osq _1bsb1qmm _4t3ine4n _1hlmd0i9 _1rquusvi _eg541i5c _mts3kb7n _1ntskb7n _yfmhtlke _5sb1v00u new-file-experience-wrapper" data-media-vc-wrapper="true" data-testid="media-card-view" id="bkmrk--9"><div class="_1reo15vq _18m915vq _2rko18qm _1e0c1txw _kqswh2mm _p12f1osq _1bsb1osq _4t3i1osq _c71l1osq media-file-card-view" data-cursor="pointer" data-test-media-name="image2016-8-9 9:56:59.png" data-test-progress="1" data-test-source="remote" data-test-status="complete" data-testid="media-file-card-view"><div class="_kqswstnw _1bsb1osq _4t3i1osq _1e0c1txw _2lx21bp4 _1bah1h6o _4cvr1h6o" data-testid="ImageRendererWrapper">![](blob:https://ecowiki.atlassian.net/83997b9d-0bff-4c28-8bd6-b61bc0f11384#media-blob-url=true&id=fcb03aa6-0fd3-4b21-b1a0-18d6d8491ede&collection=contentId-493467&contextId=493467&mimeType=image%2Fpng&name=image2016-8-9%209%3A56%3A59.png&size=52772&width=292&height=270&alt=&clientId=113268fe-fe5b-4bc3-8ff3-07965dbf1d18)</div></div></div></div></div></div></div></div></div></div><div class="_kqswstnw _lcxvglyw _c71l12am" data-testid="comment-container" id="bkmrk--10"></div></div></div></div></div></div><div class="_1reoewfl _18m9ewfl _kqswh2mm _1pby1o8a" id="bkmrk--11"></div>