Optimization of Power Allocation for Multiusers in Multi-Spot-Beam Satellite Communication Systems

<table class="table-group" id="tab8"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td align="left">Adopted coding and<br/>modulation mode of each user</td><td align="center"><span style="width: 82.387497px;"><svg height="20.0625" id="M117" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 82.387497 20.0625" width="82.387497" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,32.85,19.863)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
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<g transform="matrix(.017,-0,0,-.017,40.5,15.775)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,-0,0,-.017,54.235,15.775)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
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<g transform="matrix(.012,-0,0,-.012,75.988,7.613)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg></span></td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td align="left">Mode 1</td><td align="center"><span style="width: 63.700001px;"><svg height="11.375" id="M118" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 63.700001 11.375" width="63.700001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,8.222,11.112)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,12.098,11.112)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
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</svg></span></td></tr><tr><td align="left">Mode 2</td><td align="center"><span style="width: 63.700001px;"><svg height="11.375" id="M119" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 63.700001 11.375" width="63.700001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td></tr><tr><td align="left">Mode 3</td><td align="center"><span style="width: 63.700001px;"><svg height="11.425" id="M120" style="vertical-align:-0.20474pt" version="1.1" viewbox="0 0 63.700001 11.425" width="63.700001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Sum of <svg height="20.0625" id="M116" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 66.800003 20.0625" width="66.800003" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.017,-0,0,-.017,24.912,15.775)"><path d="M535 230h-483v50h483v-50z" id="x2212"></path></g><g transform="matrix(.017,-0,0,-.017,38.664,15.775)"><path d="M682 629q-1 -16 -1.5 -72t-2.5 -86l-31 -4q-5 92 -51 129t-139 37q-100 0 -177 -49t-116 -125t-39 -162q0 -122 66 -201t182 -79q83 0 137 42.5t112 128.5l26 -15q-12 -31 -42.5 -88t-45.5 -75q-139 -27 -199 -27q-148 0 -243 81.5t-95 226.5q0 173 129.5 274.5
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<g transform="matrix(.012,-0,0,-.012,50.65,19.863)"><path d="M244 607q0 -25 -15.5 -43t-37.5 -18q-19 0 -32 13t-13 35q0 21 15 41t39 20q20 0 32 -14t12 -34zM222 91q-29 -33 -79 -68t-75 -35q-13 0 -19 7.5t-6 31t10 65.5l62 253q5 26 -1 26q-21 0 -72 -43l-13 24q43 40 91 68t71 28q30 0 10 -78l-71 -274q-8 -30 3 -30
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<g transform="matrix(.017,-0,0,-.017,54.525,15.775)"><path d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" id="x29"></path></g>
<g transform="matrix(.012,-0,0,-.012,60.4,7.613)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
</svg> of the three different spot beams bandwidths.

Mathematical Problems in Engineering

tab8

Table 8

Table 8: Optimization of Power Allocation for Multiusers in Multi-Spot-Beam Satellite Communication Systems 