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0 R /P 850 0 R /ID (434) >> endobj 860 0 obj << /K [ 861 0 R 30 ] /S /Link /Pg 41 0 R /P 859 0 R /ID (433) >> endobj 861 0 obj << /Obj 46 0 R /Type /OBJR >> endobj 862 0 obj << /K [ 33 863 0 R ] /Alt (\\begin{equation} h_{\\mathrm{FSO}} = h_{p}^{\\mathrm{FSO}}h_{a}^{\\mathrm{FSO}} h_{pg}^{ \\mathrm{FSO}} h_{pa}^{\\mathrm{FSO}}, \\label{eq2} \\end{equation}) /S /DISPLAYMATH /Pg 41 0 R /ID (335) /P 460 0 R /A 864 0 R >> endobj 863 0 obj << /K 34 /S /EQNUM /Pg 41 0 R /P 862 0 R /ID (334) >> endobj 864 0 obj << /O /Layout /BBox [ 0 0 252 11.94 ] /Placement /Block >> endobj 865 0 obj << /K [ 36 866 0 R 38 868 0 R 40 870 0 R 42 872 0 R 44 874 0 R 46 876 0 R 48 877 0 R 52 ] /S /P /Pg 41 0 R /P 460 0 R /ID (435) >> endobj 866 0 obj << /K 37 /Alt ($h_{p}^{\\mathrm{FSO}}=\\exp{\\left \(-D_{\\mathrm{FSO}}\\xi \\right \)}$) /S /MATH /Pg 41 0 R /ID (336) /P 865 0 R /A 867 0 R >> endobj 867 0 obj << /O /Layout /BBox [ 0 0 41.72 39.67 ] >> endobj 868 0 obj << /K 39 /Alt ($\\xi $) /S /MATH /Pg 41 0 R 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\\bar{\\gamma}_{FSO} &=& \\frac{\\eta ^{2} {\\left \(\\mathbb{E}[h_{FSO}] \\right\)^{2}}E_{\\mathrm{FSO}}} { N_{FSO} } \\nonumber\\\\ &=& \\frac{ \\eta ^{2} A_{0}^{2} \\tau ^{2} \(h_{p}^{FSO}\)^{2} E_{\\mathrm{FSO}} }{ \(1+\\tau \)^{2} N_{FSO} }, \\label{eq3} \\end{eqnarray}) /S /DISPLAYALIGN /Pg 41 0 R /ID (343) /P 460 0 R /A 882 0 R >> endobj 881 0 obj << /K 56 /S /EQNUM /Pg 41 0 R /P 880 0 R /ID (342) >> endobj 882 0 obj << /O /Layout /BBox [ 0 0 510 25.31 ] /Placement /Block >> endobj 883 0 obj << /K [ 58 884 0 R 60 886 0 R 62 ] /S /P /Pg 41 0 R /P 460 0 R /ID (438) >> endobj 884 0 obj << /K 59 /Alt ($A_{0} = \(\\mathrm{erf}\(v\)\)^{2}$) /S /MATH /Pg 41 0 R /ID (344) /P 883 0 R /A 885 0 R >> endobj 885 0 obj << /O /Layout /BBox [ 0 0 49.4 9.56 ] >> endobj 886 0 obj << /K 61 /Alt ($\\tau $) /S /MATH /Pg 41 0 R /ID (345) /P 883 0 R /A 887 0 R >> endobj 887 0 obj << /O /Layout /BBox [ 0 0 4.44 3.85 ] >> endobj 888 0 obj << /K [ 63 64 889 0 R ] /Alt (\\begin{equation} \\tau = \\frac{w^{2}_{zeq}}{4\\left \(D_{\\mathrm{FSO}}^{2}\\sigma _{to}^{2}+\\sigma_{tp}^{2}+\\sigma _{rp}^{2}\\right \)}. \\label{eq:tau} \\end{equation}) /S /DISPLAYMATH /Pg 41 0 R /ID (347) /P 460 0 R /A 890 0 R >> endobj 889 0 obj << /K 65 /S /EQNUM /Pg 41 0 R /P 888 0 R /ID (346) >> endobj 890 0 obj << /O /Layout /BBox [ 0 0 252 31.12 ] /Placement /Block >> endobj 891 0 obj << /K [ 67 892 0 R 73 896 0 R 75 898 0 R 77 ] /S /P /Pg 41 0 R /P 460 0 R /ID (439) >> endobj 892 0 obj << /K [ 68 893 0 R 72 ] /S /EQNUM /Pg 41 0 R /P 891 0 R /ID (348) >> endobj 893 0 obj << /K 894 0 R /S /Reference /Pg 41 0 R /P 892 0 R /ID (441) >> endobj 894 0 obj << /K [ 895 0 R 70 ] /S /Link /Pg 41 0 R /P 893 0 R /ID (440) >> endobj 895 0 obj << /Obj 48 0 R /Type /OBJR >> endobj 896 0 obj << /K 74 /Alt ($w^{2}_{zeq}$) /S /MATH /Pg 41 0 R /ID (349) /P 891 0 R /A 897 0 R >> endobj 897 0 obj << /O /Layout /BBox [ 0 0 16.34 11.51 ] >> endobj 898 0 obj << /K 76 /Alt ($w_{z}$) /S /MATH /Pg 41 0 R /ID (350) /P 891 0 R /A 899 0 R >> endobj 899 0 obj << /O /Layout /BBox [ 0 0 10.35 6.21 ] >> endobj 900 0 obj << /K [ 78 79 80 901 0 R ] /Alt (\\begin{equation} w^{2}_{zeq}=w^{2}_{z} \\frac{\\sqrt{\\pi}\\mathrm{erf}\(v\)}{2v\\exp \\left\(-v^{2}\\right \)}, \\label{eq5} \\end{equation}) /S /DISPLAYMATH /Pg 41 0 R /ID (352) /P 460 0 R /A 902 0 R >> endobj 901 0 obj << /K 81 /S /EQNUM /Pg 41 0 R /P 900 0 R /ID (351) >> endobj 902 0 obj << /O /Layout /BBox [ 0 0 252 25.36 ] /Placement /Block >> endobj 903 0 obj << /K [ 83 904 0 R 88 906 0 R 90 908 0 R 92 910 0 R 94 912 0 R 96 914 0 R 98 ] /S /P /Pg 41 0 R /P 460 0 R /ID (442) >> endobj 904 0 obj << /K [ 84 85 86 87 ] /Alt ($v=\\frac{\\sqrt{\\pi}}{\\sqrt{2}w_{z}}r_{a}$) /S /MATH /Pg 41 0 R /ID (353) /P 903 0 R /A 905 0 R >> endobj 905 0 obj << /O /Layout /BBox [ 0 0 40.44 18.58 ] >> endobj 906 0 obj << /K 89 /Alt ($r_{a}$) /S /MATH /Pg 41 0 R /ID (354) /P 903 0 R /A 907 0 R >> endobj 907 0 obj << /O /Layout /BBox [ 0 0 7.25 5.94 ] >> endobj 908 0 obj << /K 91 /Alt ($\\mathrm{erf}\(\\cdot \)$) /S /MATH /Pg 41 0 R /ID (355) /P 903 0 R /A 909 0 R >> endobj 909 0 obj << /O /Layout /BBox [ 0 0 19.1 7.39 ] >> endobj 910 0 obj << /K 93 /Alt ($\\sigma _{tp}^{2}$) /S /MATH /Pg 41 0 R /ID (356) /P 903 0 R /A 911 0 R >> endobj 911 0 obj << /O /Layout /BBox [ 0 0 10.25 11.52 ] >> endobj 912 0 obj << /K 95 /Alt ($\\sigma _{rp}^{2}$) /S /MATH /Pg 41 0 R /ID (357) /P 903 0 R /A 913 0 R >> endobj 913 0 obj << /O /Layout /BBox [ 0 0 10.86 11.51 ] >> endobj 914 0 obj << /K 97 /Alt ($\\sigma _{to}^{2}$) /S /MATH /Pg 41 0 R /ID (358) /P 903 0 R /A 915 0 R >> endobj 915 0 obj << /O /Layout /BBox [ 0 0 10.06 10.41 ] >> endobj 916 0 obj << /K [ 99 100 101 917 0 R ] /Alt (\\begin{eqnarray} \\gamma _{\\mathrm{FSO}}&=& \\frac{\\eta ^{2} h_{\\mathrm{FSO}}^{2} E_{\\mathrm{FSO}}}{N_{\\mathrm{FSO}}} \\nonumber\\\\ &=& \\left \( \\frac{ \(1+\\tau \) h_{a}^{\\mathrm{FSO}} h_{pg}^{\\mathrm{FSO}} h_{pa}^{\\mathrm{FSO}} }{ A_{0} \\tau } \\right \)^{2} \\bar{\\gamma}_{\\mathrm{FSO}} \\label{eq6} \\end{eqnarray}) /S /DISPLAYALIGN /Pg 41 0 R /ID (360) /P 460 0 R /A 918 0 R >> endobj 917 0 obj << /K 102 /S /EQNUM /Pg 41 0 R /P 916 0 R /ID (359) >> endobj 918 0 obj << /O /Layout /BBox [ 0 0 510 28.53 ] /Placement /Block >> endobj 919 0 obj << /K [ 104 920 0 R 108 ] /S /P /Pg 41 0 R /P 460 0 R /ID (443) >> endobj 920 0 obj << /K 921 0 R /S /Reference /Pg 41 0 R /P 919 0 R /ID (445) >> endobj 921 0 obj << /K [ 922 0 R 106 ] /S /Link /Pg 41 0 R /P 920 0 R /ID (444) >> endobj 922 0 obj << /Obj 49 0 R /Type /OBJR >> endobj 923 0 obj << /K [ 109 110 924 0 R ] /Alt (\\begin{align} f_{\\gamma _{\\mathrm{FSO}}}\(\\gamma _{\\mathrm{FSO}}\) &\\simeq a_{1} \\delta \(\\gamma _{\\mathrm{FSO}}\) + C_{1} \\gamma _{\\textrm{FSO}}^{-1/2} \\nonumber\\\\ & \\quad \\times \\left . G_{1,3}^{3,0} \\left \( C_{2} \\sqrt{\\gamma _{\\textrm{FSO}}} \\left | \\begin{array}{c} \\tau\\\\ \\tau -1, \\alpha -1, \\beta -1 \\end{array} \\right . \\right \) \\right ], \\label{eq:f_FSO} \\end{align}) /S /DISPLAYALIGN /Pg 41 0 R /ID (363) /P 460 0 R /A 925 0 R >> endobj 924 0 obj << /K 111 /S /EQNUM /Pg 41 0 R /P 923 0 R /ID (362) >> endobj 925 0 obj << /O /Layout /BBox [ 0 0 511.32 26.08 ] /Placement /Block >> endobj 926 0 obj << /K 113 /S /P /Pg 41 0 R /P 460 0 R /ID (446) >> endobj 927 0 obj << /K [ 114 115 116 117 118 119 928 0 R ] /Alt (\\begin{eqnarray} \\nonumber C_{1} &=& \\frac{\(1-a_{1}\)\\alpha \\beta \\tau ^{2} }{ 2\(1+\\tau \) \\Gamma \(\\alpha \)\\Gamma \(\\beta \) \\sqrt{\\bar{\\gamma}_{FSO}} } , \\nonumber\\\\ C_{2} &=& \\frac{ \\alpha \\beta \\tau }{ \(1+\\tau \)\\sqrt{\\bar{\\gamma}_{FSO}} } , \\label{eq8} \\end{eqnarray}) /S /DISPLAYALIGN /Pg 41 0 R /ID (365) /P 460 0 R /A 929 0 R >> endobj 928 0 obj << /K 120 /S /EQNUM /Pg 41 0 R /P 927 0 R /ID (364) >> endobj 929 0 obj << /O /Layout /BBox [ 0 0 508.31 24.41 ] /Placement /Block >> endobj 930 0 obj << /K [ 122 931 0 R 124 933 0 R 126 ] /S /P /Pg 41 0 R /P 460 0 R /ID (447) >> endobj 931 0 obj << /K 123 /Alt ($\\Gamma \(\\cdot \)$) /S /MATH /Pg 41 0 R /ID (366) /P 930 0 R /A 932 0 R >> endobj 932 0 obj << /O /Layout /BBox [ 0 0 23.19 7.39 ] >> endobj 933 0 obj << /K 125 /Alt ($\\delta \(.\)$) /S /MATH /Pg 41 0 R /ID (367) /P 930 0 R /A 934 0 R >> endobj 934 0 obj << /O /Layout /BBox [ 0 0 21.93 7.39 ] >> endobj 935 0 obj << /K [ 127 128 936 0 R ] /Alt (\\begin{equation} a_{1} = \\exp \\left \(- \\frac{\\theta ^{2}_{\\mathrm{FOV}}}{2\\left \(\\sigma^{2}_{to} + \\sigma ^{2}_{ro}\\right \)} \\right \) \\label{eq9} \\end{equation}) /S /DISPLAYMATH /Pg 41 0 R /ID (369) /P 460 0 R /A 937 0 R >> endobj 936 0 obj << /K 129 /S /EQNUM /Pg 41 0 R /P 935 0 R /ID (368) >> endobj 937 0 obj << /O /Layout /BBox [ 0 0 252 26.11 ] /Placement /Block >> endobj 938 0 obj << /K [ 131 939 0 R 133 941 0 R 135 943 0 R 137 945 0 R 139 947 0 R 141 ] /S /P /Pg 41 0 R /P 460 0 R /ID (448) >> endobj 939 0 obj << /K 132 /Alt ($\\theta _{\\mathrm{FOV}}$) /S /MATH /Pg 41 0 R /ID (370) /P 938 0 R /A 940 0 R >> endobj 940 0 obj << /O /Layout /BBox [ 0 0 10.32 13.02 ] >> endobj 941 0 obj << /K 134 /Alt ($\\sigma _{ro}^{2}$) /S /MATH /Pg 41 0 R /ID (371) /P 938 0 R /A 942 0 R >> endobj 942 0 obj << /O /Layout /BBox [ 0 0 14.36 6.72 ] >> endobj 943 0 obj << /K 136 /Alt ($\\sigma _{R}^{2}$) /S /MATH /Pg 41 0 R /ID (372) /P 938 0 R /A 944 0 R >> endobj 944 0 obj << /O /Layout /BBox [ 0 0 14.84 7.19 ] >> endobj 945 0 obj << /K 138 /Alt ($\\alpha $) /S /MATH /Pg 41 0 R /ID (373) /P 938 0 R /A 946 0 R >> endobj 946 0 obj << /O /Layout /BBox [ 0 0 4.28 3.85 ] >> endobj 947 0 obj << /K 140 /Alt ($\\beta $) /S /MATH /Pg 41 0 R /ID (374) /P 938 0 R /A 948 0 R >> endobj 948 0 obj << /O /Layout /BBox [ 0 0 7.88 7.22 ] >> endobj 949 0 obj << /K [ 142 143 950 0 R ] /Alt (\\begin{equation} \\alpha = \\left [ \\exp \\left \( \\frac{ 0.49 \\sigma _{R}^{2} }{ \(1+1.11\\sigma_{R}^{12/5}\)^{7/6} } \\right \) -1 \\right ]^{-1} \\label{eq10} \\end{equation}) /S /DISPLAYMATH /Pg 41 0 R /ID (376) /P 460 0 R /A 951 0 R >> endobj 950 0 obj << /K 144 /S /EQNUM /Pg 41 0 R /P 949 0 R /ID (375) >> endobj 951 0 obj << /O /Layout /BBox [ 0 0 252 29.3 ] /Placement /Block >> endobj 952 0 obj << /K 146 /S /P /Pg 41 0 R /P 460 0 R /ID (449) >> endobj 953 0 obj << /K [ 147 148 954 0 R ] /Alt (\\begin{equation} \\beta = \\left [ \\exp \\left \( \\frac{ 0.51 \\sigma _{R}^{2} }{ \(1+0.69\\sigma_{R}^{12/5}\)^{5/6} } \\right \) -1 \\right ]^{-1}, \\label{eq11} \\end{equation}) /S /DISPLAYMATH /Pg 41 0 R /ID (378) /P 460 0 R /A 951 0 R >> endobj 954 0 obj << /K 149 /S /EQNUM /Pg 41 0 R /P 953 0 R /ID (377) >> endobj 955 0 obj << /K 151 /S /P /Pg 41 0 R /P 460 0 R /ID (450) >> endobj 956 0 obj << /K 152 /S /H3 /Pg 41 0 R /P 460 0 R /ID (451) >> endobj 957 0 obj << /K [ 153 958 0 R 155 960 0 R 157 ] /S /P /Pg 41 0 R /P 460 0 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0 R 167 972 0 R 169 974 0 R 171 976 0 R 173 978 0 R 175 980 0 R 177 982 0 R 179 984 0 R 181 986 0 R 183 988 0 R 185 990 0 R 187 992 0 R 189 994 0 R 191 996 0 R 193 998 0 R 195 1000 0 R 197 ] /S /P /Pg 41 0 R /P 460 0 R /ID (453) >> endobj 966 0 obj << /K 162 /Alt ($h_{k}=\\alpha _{k}e^{-j\\varphi _{k}}$) /S /MATH /Pg 41 0 R /ID (384) /P 965 0 R /A 967 0 R >> endobj 967 0 obj << /O /Layout /BBox [ 0 0 45.77 9.06 ] >> endobj 968 0 obj << /K 164 /Alt ($g_{k}=\\beta _{k} e^{-j\\psi _{k}}$) /S /MATH /Pg 41 0 R /ID (385) /P 965 0 R /A 969 0 R >> endobj 969 0 obj << /O /Layout /BBox [ 0 0 44.75 9.06 ] >> endobj 970 0 obj << /K 166 /Alt ($v_{k}=e^{j\\phi _{k}}$) /S /MATH /Pg 41 0 R /ID (386) /P 965 0 R /A 971 0 R >> endobj 971 0 obj << /O /Layout /BBox [ 0 0 32.28 9.4 ] >> endobj 972 0 obj << /K 168 /Alt ($k$) /S /MATH /Pg 41 0 R /ID (387) /P 965 0 R /A 973 0 R >> endobj 973 0 obj << /O /Layout /BBox [ 0 0 4.7 5.75 ] >> endobj 974 0 obj << /K 170 /Alt ($\\varphi _{k}$) /S /MATH /Pg 41 0 R /ID 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($\\delta _{k}$) /S /MATH /Pg 41 0 R /ID (410) /P 1014 0 R /A 1019 0 R >> endobj 1019 0 obj << /O /Layout /BBox [ 0 0 7.97 7.85 ] >> endobj 1020 0 obj << /K [ 217 218 219 220 1021 0 R ] /Alt (\\begin{equation} f_{\\delta _{k}}\(r\) = \\frac{4m_{I}^{\\frac{m_{I}+1}{2}} r^{m_{I}} }{\\Gamma \(m_{I}\)}K_{m_{I}-1}\(2 \\sqrt{m_{I}}r\), \\label{eq15} \\end{equation}) /S /DISPLAYMATH /Pg 41 0 R /ID (412) /P 460 0 R /A 1022 0 R >> endobj 1021 0 obj << /K 221 /S /EQNUM /Pg 41 0 R /P 1020 0 R /ID (411) >> endobj 1022 0 obj << /O /Layout /BBox [ 0 0 252 29.2 ] /Placement /Block >> endobj 1023 0 obj << /K [ 223 1024 0 R 225 1026 0 R 227 ] /S /P /Pg 41 0 R /P 460 0 R /ID (457) >> endobj 1024 0 obj << /K 224 /Alt ($K_{v}\(\\cdot \)$) /S /MATH /Pg 41 0 R /ID (413) /P 1023 0 R /A 1025 0 R >> endobj 1025 0 obj << /O /Layout /BBox [ 0 0 18.35 8.06 ] >> endobj 1026 0 obj << /K 226 /Alt ($v$) /S /MATH /Pg 41 0 R /ID (414) /P 1023 0 R /A 1027 0 R >> endobj 1027 0 obj << /O /Layout /BBox [ 0 0 4.39 3.85 ] >> endobj 1028 0 obj << /K [ 228 1029 0 R ] /Alt (\\begin{equation} \\gamma _{RIS} =\\mathcal{H}^{2}\\bar{\\gamma}_{\\textrm{RIS}} \\xch{,}{.} \\label{eq16} \\end{equation}) /S /DISPLAYMATH /Pg 41 0 R /ID (416) /P 460 0 R /A 1030 0 R >> endobj 1029 0 obj << /K 229 /S /EQNUM /Pg 41 0 R /P 1028 0 R /ID (415) >> endobj 1030 0 obj << /O /Layout /BBox [ 0 0 252 10 ] /Placement /Block >> endobj 1031 0 obj << /K [ 0 1032 0 R 3 1034 0 R 7 1037 0 R 11 1040 0 R 13 1042 0 R 16 1044 0 R 18 1046 0 R 20 ] /S /P /Pg 50 0 R /P 460 0 R /ID (549) >> endobj 1032 0 obj << /K [ 1 2 ] /Alt ($\\bar{\\gamma}_{\\textrm{RIS}}=\\frac{E_{\\mathrm{RIS}}}{N_{\\mathrm{RIS}}}$) /S /MATH /Pg 50 0 R /ID (418) /P 1031 0 R /A 1033 0 R >> endobj 1033 0 obj << /O /Layout /BBox [ 0 0 29 16.56 ] >> endobj 1034 0 obj << /K 1035 0 R /S /Reference /Pg 50 0 R /P 1031 0 R /ID (551) >> endobj 1035 0 obj << /K [ 1036 0 R 5 ] /S /Link /Pg 50 0 R /P 1034 0 R /ID (550) >> endobj 1036 0 obj << /Obj 54 0 R /Type /OBJR >> endobj 1037 0 obj 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f_{\\mathcal{H}_{RIS}}\(r|k_{w},m_{w},\\Omega _{w}\) \\approx \\frac{ 4 \\Xi ^{\\zeta_{w}^{+}} r^{\\zeta _{w}^{+}-1} }{ \\Gamma \(k_{w}\)\\Gamma \(m_{w}\) } K_{\\zeta_{w}^{-}}\(2\\Xi _{w} r\), \\label{eq17} \\end{eqnarray}) /S /DISPLAYALIGN /Pg 50 0 R /ID (459) /P 460 0 R /A 1050 0 R >> endobj 1049 0 obj << /K 23 /S /EQNUM /Pg 50 0 R /P 1048 0 R /ID (458) >> endobj 1050 0 obj << /O /Layout /BBox [ 0 0 254 21.42 ] /Placement /Block >> endobj 1051 0 obj << /K [ 25 1052 0 R 27 1054 0 R 29 1056 0 R 33 1058 0 R 37 1060 0 R 40 1062 0 R 42 1064 0 R 44 1066 0 R 46 1068 0 R 48 ] /S /P /Pg 50 0 R /P 460 0 R /ID (554) >> endobj 1052 0 obj << /K 26 /Alt ($\\zeta _{w}^{-} = k_{w}-m_{w}$) /S /MATH /Pg 50 0 R /ID (460) /P 1051 0 R /A 1053 0 R >> endobj 1053 0 obj << /O /Layout /BBox [ 0 0 49.42 8.7 ] >> endobj 1054 0 obj << /K 28 /Alt ($\\zeta _{w}^{+} = k_{w}+m_{w}$) /S /MATH /Pg 50 0 R /ID (461) /P 1051 0 R /A 1055 0 R >> endobj 1055 0 obj << /O /Layout /BBox [ 0 0 49.42 9.5 ] >> endobj 1056 0 obj << /K [ 30 31 32 ] /Alt ($k_{w} = \\frac{-b+\\sqrt{b^{2}-4ac}}{2a}$) /S /MATH /Pg 50 0 R /ID (462) /P 1051 0 R /A 1057 0 R >> endobj 1057 0 obj << /O /Layout /BBox [ 0 0 59.3 15.69 ] >> endobj 1058 0 obj << /K [ 34 35 36 ] /Alt ($m_{w}=\\frac{-b - \\sqrt{b^{2}-4ac}}{2a}$) /S /MATH /Pg 50 0 R /ID (463) /P 1051 0 R /A 1059 0 R >> endobj 1059 0 obj << /O /Layout /BBox [ 0 0 60.72 15.69 ] >> endobj 1060 0 obj << /K [ 38 39 ] /Alt ($\\Xi _{w} = \\sqrt{k_{w}m_{w}/\\Omega _{w}}$) /S /MATH /Pg 50 0 R /ID (464) /P 1051 0 R /A 1061 0 R >> endobj 1061 0 obj << /O /Layout /BBox [ 0 0 65.84 11 ] >> endobj 1062 0 obj << /K 41 /Alt ($\\Omega _{w}=\\mu _{\\mathcal{H}}\(2\)$) /S /MATH /Pg 50 0 R /ID (465) /P 1051 0 R /A 1063 0 R >> endobj 1063 0 obj << /O /Layout /BBox [ 0 0 42.14 8.12 ] >> endobj 1064 0 obj << /K 43 /Alt ($\\mathcal{H}_{RIS}$) /S /MATH /Pg 50 0 R /ID (466) /P 1051 0 R /A 1065 0 R >> endobj 1065 0 obj << /O /Layout /BBox [ 0 0 20.56 7.9 ] >> endobj 1066 0 obj << /K 45 /Alt ($a,b$) /S /MATH /Pg 50 0 R /ID (467) /P 1051 0 R /A 1067 0 R >> endobj 1067 0 obj << /O /Layout /BBox [ 0 0 11.64 6.91 ] >> endobj 1068 0 obj << /K 47 /Alt ($c$) /S /MATH /Pg 50 0 R /ID (468) /P 1051 0 R /A 1069 0 R >> endobj 1069 0 obj << /O /Layout /BBox [ 0 0 4.04 3.85 ] >> endobj 1070 0 obj << /K 49 /Alt (\\begin{eqnarray*} a &=& \\mu _{\\mathcal{H}} \(6\)\\mu _{\\mathcal{H}} \(2\) + \\mu _{ \\mathcal{H}}^{2} \(2\) \\mu _{\\mathcal{H}} \(4\) - 2 \\mu _{\\mathcal{H}}^{2} \(4\) \\\\ b &=& \\mu _{\\mathcal{H}} \(6\)\\mu _{\\mathcal{H}} \(2\) - 4 \\mu _{ \\mathcal{H}}^{2} \(4\) + 3\\mu _{\\mathcal{H}}^{2} \(2\) \\mu _{\\mathcal{H}} \(4\) \\\\ c &=& 2\\mu _{\\mathcal{H}}^{2} \(2\) \\mu _{\\mathcal{H}} \(4\), \\end{eqnarray*}) /S /DISPLAYALIGN /Pg 50 0 R /ID (469) /P 460 0 R /A 1071 0 R >> endobj 1071 0 obj << /O /Layout /BBox [ 0 0 769.89 11.06 ] /Placement /Block >> endobj 1072 0 obj << /K 50 /S /P /Pg 50 0 R /P 460 0 R /ID (555) >> endobj 1073 0 obj << /K 51 /Alt (\\begin{eqnarray*} \\mu _{\\mathcal{H}}\(n\) &=& \\sum _{n_{1}=0}^{n}\\sum _{n_{2}=0}^{n_{1}} \\cdots \\sum _{n_{N-1}=0}^{n_{N-2}} {\\binom{n}{n_{1}}}{\\binom{n_{1}}{n_{2}}} ... {\\binom{n_{N-2}}{n_{N-1}}} \\\\ && \\times M_{\\delta _{1}} \(n-n_{1}\) M_{\\delta _{2}} \(n_{1}-n_{2}\) \\\\ && \\cdots \\times M_{\\delta _{N-1}} \(n_{N-2}-n_{N-1}\) M_{\\delta _{N}} \(n_{N-1}\) \\end{eqnarray*}) /S /DISPLAYALIGN /Pg 50 0 R /ID (470) /P 460 0 R /A 1074 0 R >> endobj 1074 0 obj << /O /Layout /BBox [ 0 0 768.41 26.99 ] /Placement /Block >> endobj 1075 0 obj << /K 52 /S /P /Pg 50 0 R /P 460 0 R /ID (556) >> endobj 1076 0 obj << /K [ 53 54 55 ] /Alt (\\begin{equation*} M_{\\delta _{i}}\(n\)=\\frac{m_{I}^{-\\frac{n}{2}}}{\\Gamma \(m_{I}\)}\\Gamma \(1+n/2\) \\Gamma \(m_{I}+n/2\) \\end{equation*}) /S /DISPLAYMATH /Pg 50 0 R /ID (471) /P 460 0 R /A 1077 0 R >> endobj 1077 0 obj << /O /Layout /BBox [ 0 0 252 27.08 ] /Placement /Block >> endobj 1078 0 obj << /K [ 56 1079 0 R 58 1081 0 R 60 1083 0 R 62 1085 0 R 64 1087 0 R 66 1089 0 R 68 1091 0 R 70 1093 0 R 72 ] /S /P /Pg 50 0 R /P 460 0 R /ID (557) >> endobj 1079 0 obj << /K 57 /Alt ($n$) /S /MATH /Pg 50 0 R /ID (472) /P 1078 0 R /A 1080 0 R >> endobj 1080 0 obj << /O /Layout /BBox [ 0 0 4.31 3.85 ] >> endobj 1081 0 obj << /K 59 /Alt ($\\delta _{i}$) /S /MATH /Pg 50 0 R /ID (473) /P 1078 0 R /A 1082 0 R >> endobj 1082 0 obj << /O /Layout /BBox [ 0 0 6.5 7.85 ] >> endobj 1083 0 obj << /K 61 /Alt ($b^{2}-4ac \\leq 0$) /S /MATH /Pg 50 0 R /ID (474) /P 1078 0 R /A 1084 0 R >> endobj 1084 0 obj << /O /Layout /BBox [ 0 0 42.89 8.22 ] >> endobj 1085 0 obj << /K 63 /Alt ($k_{w}$) /S /MATH /Pg 50 0 R /ID (475) /P 1078 0 R /A 1086 0 R >> endobj 1086 0 obj << /O /Layout /BBox [ 0 0 10.13 7.85 ] >> endobj 1087 0 obj << /K 65 /Alt ($m_{w}$) /S /MATH /Pg 50 0 R /ID (476) /P 1078 0 R /A 1088 0 R >> endobj 1088 0 obj << /O /Layout /BBox [ 0 0 11.55 5.94 ] >> endobj 1089 0 obj << /K 67 /Alt ($\\mathcal{H}_{d}$) /S /MATH /Pg 50 0 R /ID (477) /P 1078 0 R /A 1090 0 R >> endobj 1090 0 obj << /O /Layout /BBox [ 0 0 11.41 7.9 ] >> endobj 1091 0 obj << /K 69 /Alt ($h_{d}$) /S /MATH /Pg 50 0 R /ID (478) /P 1078 0 R /A 1092 0 R >> endobj 1092 0 obj << /O /Layout /BBox [ 0 0 9.26 7.85 ] >> endobj 1093 0 obj << /K 71 /Alt ($K_{G}$) /S /MATH /Pg 50 0 R /ID (479) /P 1078 0 R /A 1017 0 R >> endobj 1094 0 obj << /K [ 73 1095 0 R ] /Alt (\\begin{equation} f_{\\mathcal{H}_{d}}\(r|k_{d},m_{d},\\Omega _{d}\) \\label{eq18} \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (481) /P 460 0 R /A 1096 0 R >> endobj 1095 0 obj << /K 74 /S /EQNUM /Pg 50 0 R /P 1094 0 R /ID (480) >> endobj 1096 0 obj << /O /Layout /BBox [ 0 0 252 9.64 ] /Placement /Block >> endobj 1097 0 obj << /K [ 76 1098 0 R 78 1100 0 R 80 1102 0 R 82 1104 0 R 84 1105 0 R 86 1107 0 R 90 1110 0 R 92 1111 0 R 94 1113 0 R 96 ] /S /P /Pg 50 0 R /P 460 0 R /ID (558) >> endobj 1098 0 obj << /K 77 /Alt ($k_{d}$) /S /MATH /Pg 50 0 R /ID (482) /P 1097 0 R /A 1099 0 R >> endobj 1099 0 obj << /O /Layout /BBox [ 0 0 8.96 7.85 ] >> endobj 1100 0 obj << /K 79 /Alt ($m_{d}$) /S /MATH /Pg 50 0 R /ID (483) /P 1097 0 R /A 1101 0 R >> endobj 1101 0 obj << /O /Layout /BBox [ 0 0 10.39 5.94 ] >> endobj 1102 0 obj << /K 81 /Alt ($\\Omega _{d}$) /S /MATH /Pg 50 0 R /ID (484) /P 1097 0 R /A 1103 0 R >> endobj 1103 0 obj << /O /Layout /BBox [ 0 0 10.67 8.06 ] >> endobj 1104 0 obj << /K 83 /Alt ($\\mathcal{H}_{d}$) /S /MATH /Pg 50 0 R /ID (485) /P 1097 0 R /A 1090 0 R >> endobj 1105 0 obj << /K 85 /Alt ($\\mathcal{H}$) /S /MATH /Pg 50 0 R /ID (486) /P 1097 0 R /A 1106 0 R >> endobj 1106 0 obj << /O /Layout /BBox [ 0 0 7.65 5.89 ] >> endobj 1107 0 obj << /K 1108 0 R /S /Reference /Pg 50 0 R /P 1097 0 R /ID (560) >> endobj 1108 0 obj << /K [ 1109 0 R 88 ] /S /Link /Pg 50 0 R /P 1107 0 R /ID (559) >> endobj 1109 0 obj << /Obj 56 0 R /Type /OBJR >> endobj 1110 0 obj << /K 91 /Alt ($K_{G}$) /S /MATH /Pg 50 0 R /ID (487) /P 1097 0 R /A 1017 0 R >> endobj 1111 0 obj << /K 93 /Alt ($\\mathcal{H}_{RIS}+\\mathcal{H}_{d}$) /S /MATH /Pg 50 0 R /ID (488) /P 1097 0 R /A 1112 0 R >> endobj 1112 0 obj << /O /Layout /BBox [ 0 0 40.98 7.9 ] >> endobj 1113 0 obj << /K 95 /Alt ($K_{G}$) /S /MATH /Pg 50 0 R /ID (489) /P 1097 0 R /A 1017 0 R >> endobj 1114 0 obj << /K [ 97 1115 0 R ] /Alt (\\begin{equation} m=k= \\left [ 2\\Omega ^{2} + \\Omega \(4\\Omega ^{2}+8 \\mathcal{S}\)^{-1/2} \\right ] /\\mathcal{S}, \\label{eq19} \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (491) /P 460 0 R /A 1116 0 R >> endobj 1115 0 obj << /K 98 /S /EQNUM /Pg 50 0 R /P 1114 0 R /ID (490) >> endobj 1116 0 obj << /O /Layout /BBox [ 0 0 252 10.9 ] /Placement /Block >> endobj 1117 0 obj << /K [ 1118 0 R 102 1120 0 R 104 1122 0 R 109 1124 0 R 111 ] /S /P /Pg 50 0 R /P 460 0 R /ID (561) >> endobj 1118 0 obj << /K 101 /Alt ($\\Omega = \\sum _{i}\\Omega _{i}$) /S /MATH /Pg 50 0 R /ID (492) /P 1117 0 R /A 1119 0 R >> endobj 1119 0 obj << /O /Layout /BBox [ 0 0 35.94 9.08 ] >> endobj 1120 0 obj << /K 103 /Alt ($\\mathcal{S}=\\sum _{i} \\textit{AF}_{i}\\Omega _{i}$) /S /MATH /Pg 50 0 R /ID (493) /P 1117 0 R /A 1121 0 R >> endobj 1121 0 obj << /O /Layout /BBox [ 0 0 47.68 9.08 ] >> endobj 1122 0 obj << /K [ 105 106 107 108 ] /Alt ($\\textit{AF}_{i}=\\frac{1}{m_{i}}+\\frac{1}{k_{i}}+\\frac{1}{m_{i}k_{i}}$) /S /MATH /Pg 50 0 R /ID (494) /P 1117 0 R /A 1123 0 R >> endobj 1123 0 obj << /O /Layout /BBox [ 0 0 71.35 14.19 ] >> endobj 1124 0 obj << /K 110 /Alt ($i\\in [w,d]$) /S /MATH /Pg 50 0 R /ID (495) /P 1117 0 R /A 1125 0 R >> endobj 1125 0 obj << /O /Layout /BBox [ 0 0 32.62 6.98 ] >> endobj 1126 0 obj << /K [ 112 113 114 115 116 117 1127 0 R ] /Alt (\\begin{equation} \\label{eq:f_RIS} f_{\\gamma _{\\mathrm{RIS}}}\(\\gamma _{\\mathrm{RIS}}\) \\approx \\frac{ 2 \\Xi^{\\zeta ^{+}} \\gamma _{\\mathrm{RIS}}^{\\frac{\\zeta ^{+}}{2}-1} K_{\\zeta^{-}}\(2\\Xi \\sqrt{\\frac{\\gamma _{\\mathrm{RIS}} }{\\bar{\\gamma}_{\\mathrm{RIS}}}}\) }{ \\Gamma \(k\)\\Gamma \(m\) \(\\bar{\\gamma}_{\\mathrm{RIS}}\)^{\\frac{\\zeta ^{+}}{2}} }, \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (497) /P 460 0 R /A 1128 0 R >> endobj 1127 0 obj << /K 118 /S /EQNUM /Pg 50 0 R /P 1126 0 R /ID (496) >> endobj 1128 0 obj << /O /Layout /BBox [ 0 0 252 38.11 ] /Placement /Block >> endobj 1129 0 obj << /K [ 120 1130 0 R 123 1132 0 R 125 1134 0 R 127 ] /S /P /Pg 50 0 R /P 460 0 R /ID (562) >> endobj 1130 0 obj << /K [ 121 122 ] /Alt ($\\Xi = \\sqrt{km/\\Omega}$) /S /MATH /Pg 50 0 R /ID (498) /P 1129 0 R /A 1131 0 R >> endobj 1131 0 obj << /O /Layout /BBox [ 0 0 23.59 29.23 ] >> endobj 1132 0 obj << /K 124 /Alt ($\\zeta ^{-} = k-m$) /S /MATH /Pg 50 0 R /ID (499) /P 1129 0 R /A 1133 0 R >> endobj 1133 0 obj << /O /Layout /BBox [ 0 0 32.41 9.38 ] >> endobj 1134 0 obj << /K 126 /Alt ($\\zeta ^{+} = k+m$) /S /MATH /Pg 50 0 R /ID (500) /P 1129 0 R /A 1135 0 R >> endobj 1135 0 obj << /O /Layout /BBox [ 0 0 36.82 9.38 ] >> endobj 1136 0 obj << /K 128 /S /H2 /Pg 50 0 R /P 460 0 R /ID (563) >> endobj 1137 0 obj << /K 129 /S /P /Pg 50 0 R /P 460 0 R /ID (564) >> endobj 1138 0 obj << /K 130 /S /H3 /Pg 50 0 R /P 460 0 R /ID (565) >> endobj 1139 0 obj << /K 131 /S /P /Pg 50 0 R /P 460 0 R /ID (566) >> endobj 1140 0 obj << /K [ 132 1141 0 R ] /Alt (\\begin{equation} P_{\\mathrm{out}} = \\Pr \( \\textrm{min} \\{ \\gamma _{\\mathrm{FSO}} , \\gamma _{\\mathrm{RIS}} \\} \\leq \\gamma _{th} \), \\label{eq21} \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (502) /P 460 0 R /A 1142 0 R >> endobj 1141 0 obj << /K 133 /S /EQNUM /Pg 50 0 R /P 1140 0 R /ID (501) >> endobj 1142 0 obj << /O /Layout /BBox [ 0 0 252 8.06 ] /Placement /Block >> endobj 1143 0 obj << /K 135 /S /P /Pg 50 0 R /P 460 0 R /ID (567) >> endobj 1144 0 obj << /K [ 136 1145 0 R ] /Alt (\\begin{equation} P_{\\mathrm{out}} = P_{\\mathrm{out, FSO}} + P_{\\mathrm{out, RIS}} - P_{ \\mathrm{out, FSO}}P_{\\mathrm{out, RIS}}. \\label{eq22} \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (504) /P 460 0 R /A 1146 0 R >> endobj 1145 0 obj << /K 137 /S /EQNUM /Pg 50 0 R /P 1144 0 R /ID (503) >> endobj 1146 0 obj << /O /Layout /BBox [ 0 0 252 8.72 ] /Placement /Block >> endobj 1147 0 obj << /K [ 139 1148 0 R 145 1152 0 R 149 1155 0 R 151 1157 0 R 153 1159 0 R 155 1161 0 R 157 1163 0 R 159 1165 0 R 161 1167 0 R 163 ] /S /P /Pg 50 0 R /P 460 0 R /ID (568) >> endobj 1148 0 obj << /K [ 140 1149 0 R 144 ] /S /EQNUM /Pg 50 0 R /P 1147 0 R /ID (505) >> endobj 1149 0 obj << /K 1150 0 R /S /Reference /Pg 50 0 R /P 1148 0 R /ID (570) >> endobj 1150 0 obj << /K [ 1151 0 R 142 ] /S /Link /Pg 50 0 R /P 1149 0 R /ID (569) >> endobj 1151 0 obj << /Obj 57 0 R /Type /OBJR >> endobj 1152 0 obj << /K 1153 0 R /S /Reference /Pg 50 0 R /P 1147 0 R /ID (572) >> endobj 1153 0 obj << /K [ 1154 0 R 147 ] /S /Link /Pg 50 0 R /P 1152 0 R /ID (571) >> endobj 1154 0 obj << /Obj 58 0 R /Type /OBJR >> endobj 1155 0 obj << /K 150 /Alt ($\\tau =\\gamma _{FSO}$) /S /MATH /Pg 50 0 R /ID (506) /P 1147 0 R /A 1156 0 R >> endobj 1156 0 obj << /O /Layout /BBox [ 0 0 32.13 5.94 ] >> endobj 1157 0 obj << /K 152 /Alt ($\\alpha =1/2$) /S /MATH /Pg 50 0 R /ID (507) /P 1147 0 R /A 1158 0 R >> endobj 1158 0 obj << /O /Layout /BBox [ 0 0 27.14 7.73 ] >> endobj 1159 0 obj << /K 154 /Alt ($\\beta =1$) /S /MATH /Pg 50 0 R /ID (508) /P 1147 0 R /A 1160 0 R >> endobj 1160 0 obj << /O /Layout /BBox [ 0 0 18.41 7.44 ] >> endobj 1161 0 obj << /K 156 /Alt ($l=1$) /S /MATH /Pg 50 0 R /ID (509) /P 1147 0 R /A 1162 0 R >> endobj 1162 0 obj << /O /Layout /BBox [ 0 0 16.55 5.97 ] >> endobj 1163 0 obj << /K 158 /Alt ($k=2$) /S /MATH /Pg 50 0 R /ID (510) /P 1147 0 R /A 1164 0 R >> endobj 1164 0 obj << /O /Layout /BBox [ 0 0 18.28 5.97 ] >> endobj 1165 0 obj << /K 160 /Alt ($a=\\gamma _{th}$) /S /MATH /Pg 50 0 R /ID (511) /P 1147 0 R /A 1166 0 R >> endobj 1166 0 obj << /O /Layout /BBox [ 0 0 23.49 5.94 ] >> endobj 1167 0 obj << /K 162 /Alt ($P_{\\mathrm{out, FSO}}$) /S /MATH /Pg 50 0 R /ID (512) /P 1147 0 R /A 1168 0 R >> endobj 1168 0 obj << /O /Layout /BBox [ 0 0 27.4 8.72 ] >> endobj 1169 0 obj << /K [ 164 165 166 167 1170 0 R ] /Alt (\\begin{eqnarray} {eq:P_out_FSO} P_{\\mathrm{out,FSO}} = a_{1}+ \\frac{ C_{1} 2^{\\alpha +\\beta -3} \\sqrt{\\gamma_{th}} }{ 2 \\pi } G_{3,7}^{6,1} \\left \( \\left . \\frac{ C_{2}^{2} \\gamma _{th} }{ 2^{4} } \\right | \\begin{array}{c} \\kappa _{1} \\\\ \\kappa _{2} \\end{array} \\right \), \\end{eqnarray}) /S /DISPLAYALIGN /Pg 50 0 R /ID (514) /P 460 0 R /A 1171 0 R >> endobj 1170 0 obj << /K 168 /S /EQNUM /Pg 50 0 R /P 1169 0 R /ID (513) >> endobj 1171 0 obj << /O /Layout /BBox [ 0 0 254 27.98 ] /Placement /Block >> endobj 1172 0 obj << /K [ 170 1173 0 R 175 1175 0 R 184 ] /S /P /Pg 50 0 R /P 460 0 R /ID (573) >> endobj 1173 0 obj << /K [ 171 172 173 174 ] /Alt ($\\kappa _{1} = \\frac{1}{2}, \\frac{\\tau}{2}, \\frac{\\tau +1}{2}$) /S /MATH /Pg 50 0 R /ID (515) /P 1172 0 R /A 1174 0 R >> endobj 1174 0 obj << /O /Layout /BBox [ 0 0 57.79 15.31 ] >> endobj 1175 0 obj << /K [ 176 177 178 179 180 181 182 183 ] /Alt ($\\kappa _{2}=\\frac{\\tau -1}{2}, \\frac{\\tau}{2}, \\frac{\\alpha -1}{2}, \\frac{\\alpha}{2}, \\frac{\\beta -1}{2}, \\frac{\\beta}{2}, - \\frac{1}{2}$) /S /MATH /Pg 50 0 R /ID (516) /P 1172 0 R /A 1176 0 R >> endobj 1176 0 obj << /O /Layout /BBox [ 0 0 121.99 15.64 ] >> endobj 1177 0 obj << /K [ 185 1178 0 R 189 1181 0 R 195 ] /S /P /Pg 50 0 R /P 460 0 R /ID (574) >> endobj 1178 0 obj << /K 1179 0 R /S /Reference /Pg 50 0 R /P 1177 0 R /ID (576) >> endobj 1179 0 obj << /K [ 1180 0 R 187 ] /S /Link /Pg 50 0 R /P 1178 0 R /ID (575) >> endobj 1180 0 obj << /Obj 59 0 R /Type /OBJR >> endobj 1181 0 obj << /K [ 190 1182 0 R 194 ] /S /EQNUM /Pg 50 0 R /P 1177 0 R /ID (517) >> endobj 1182 0 obj << /K 1183 0 R /S /Reference /Pg 50 0 R /P 1181 0 R /ID (578) >> endobj 1183 0 obj << /K [ 1184 0 R 192 ] /S /Link /Pg 50 0 R /P 1182 0 R /ID (577) >> endobj 1184 0 obj << /Obj 60 0 R /Type /OBJR >> endobj 1185 0 obj << /K [ 196 197 198 1186 0 R ] /Alt (\\begin{equation} \\label{eq:P_out_RIS} P_{\\mathrm{out, RIS}} \\simeq \\frac{1}{\\Gamma \(k\)\\Gamma \(m\)}G_{1,3}^{2,1} \\left [ \\left . \\frac{\\Xi ^{2}\\gamma _{th}}{\\bar{\\gamma}_{\\mathrm{RIS}}} \\right | \\begin{array}{c} 1 \\\\ k, m, 0 \\end{array} \\right ]. \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (519) /P 460 0 R /A 1187 0 R >> endobj 1186 0 obj << /K 199 /S /EQNUM /Pg 50 0 R /P 1185 0 R /ID (518) >> endobj 1187 0 obj << /O /Layout /BBox [ 0 0 252 26.08 ] /Placement /Block >> endobj 1188 0 obj << /K [ 201 1189 0 R 203 1191 0 R 209 1195 0 R 211 ] /S /P /Pg 50 0 R /P 460 0 R /ID (579) >> endobj 1189 0 obj << /K 202 /Alt ($ P_{\\mathrm{out}} \\rightarrow P_{\\mathrm{out,FSO}}^{A} + P_{ \\mathrm{out,RIS}}^{A}$) /S /MATH /Pg 50 0 R /ID (520) /P 1188 0 R /A 1190 0 R >> endobj 1190 0 obj << /O /Layout /BBox [ 0 0 87.47 11.83 ] >> endobj 1191 0 obj << /K [ 204 1192 0 R 208 ] /S /EQNUM /Pg 50 0 R /P 1188 0 R /ID (521) >> endobj 1192 0 obj << /K 1193 0 R /S /Reference /Pg 50 0 R /P 1191 0 R /ID (581) >> endobj 1193 0 obj << /K [ 1194 0 R 206 ] /S /Link /Pg 50 0 R /P 1192 0 R /ID (580) >> endobj 1194 0 obj << /Obj 61 0 R /Type /OBJR >> endobj 1195 0 obj << /K 210 /Alt ($P_{\\mathrm{out,FSO}}$) /S /MATH /Pg 50 0 R /ID (522) /P 1188 0 R /A 1168 0 R >> endobj 1196 0 obj << /K [ 212 213 1197 0 R ] /Alt (\\begin{equation} P_{\\mathrm{out,FSO}}^{A} \\approx a_{1} = \\exp \\left \(- \\frac{\\theta^{2}_{\\mathrm{FOV}}}{2\\left \(\\sigma ^{2}_{to} + \\sigma ^{2}_{ro}\\right \)} \\right \). \\label{eq25} \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (524) /P 460 0 R /A 937 0 R >> endobj 1197 0 obj << /K 214 /S /EQNUM /Pg 50 0 R /P 1196 0 R /ID (523) >> endobj 1198 0 obj << /K [ 216 1199 0 R 220 1202 0 R 223 1204 0 R 225 ] /S /P /Pg 50 0 R /P 460 0 R /ID (582) >> endobj 1199 0 obj << /K 1200 0 R /S /Reference /Pg 50 0 R /P 1198 0 R /ID (584) >> endobj 1200 0 obj << /K [ 1201 0 R 218 ] /S /Link /Pg 50 0 R /P 1199 0 R /ID (583) >> endobj 1201 0 obj << /Obj 62 0 R /Type /OBJR >> endobj 1202 0 obj << /K [ 221 222 ] /Alt ($z=\\frac{ \\Xi^{2}\\gamma _{th} }{ \\bar{\\gamma}_{\\mathrm{RIS}} }$) /S /MATH /Pg 50 0 R /ID (526) /P 1198 0 R /A 1203 0 R >> endobj 1203 0 obj << /O /Layout /BBox [ 0 0 31.25 16.21 ] >> endobj 1204 0 obj << /K 224 /Alt ($P_{\\mathrm{out,RIS}}$) /S /MATH /Pg 50 0 R /ID (527) /P 1198 0 R /A 1205 0 R >> endobj 1205 0 obj << /O /Layout /BBox [ 0 0 25.63 8.72 ] >> endobj 1206 0 obj << /K [ 226 227 228 1207 0 R ] /Alt (\\begin{equation} P_{\\mathrm{out,RIS}}^{A} \\approx \\frac{ \\Gamma \(m-k\) }{ \\Gamma \(1+k\) \\Gamma\(m\) } \\left \( \\frac{ \\Xi ^{2}\\gamma _{th} }{ \\bar{\\gamma}_{\\mathrm{RIS}} } \\right \)^{k} . \\label{eq:P_out_RIS_saturated} \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (529) /P 460 0 R /A 1208 0 R >> endobj 1207 0 obj << /K 229 /S /EQNUM /Pg 50 0 R /P 1206 0 R /ID (528) >> endobj 1208 0 obj << /O /Layout /BBox [ 0 0 252 23.81 ] /Placement /Block >> endobj 1209 0 obj << /K [ 231 1210 0 R 233 1211 0 R 235 ] /S /P /Pg 50 0 R /P 460 0 R /ID (585) >> endobj 1210 0 obj << /K 232 /Alt ($k$) /S /MATH /Pg 50 0 R /ID (530) /P 1209 0 R /A 973 0 R >> endobj 1211 0 obj << /K 234 /Alt ($1$) /S /MATH /Pg 50 0 R /ID (531) /P 1209 0 R /A 997 0 R >> endobj 1212 0 obj << /K [ 236 237 1213 0 R ] /Alt (\\begin{equation} P_{\\mathrm{out}} \\rightarrow \\exp \\left \(- \\frac{\\theta^{2}_{\\mathrm{FOV}}}{2\\left \(\\sigma ^{2}_{to} + \\sigma ^{2}_{ro}\\right \)} \\right \). \\label{eq:p_out_saturated} \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (533) /P 460 0 R /A 937 0 R >> endobj 1213 0 obj << /K 238 /S /EQNUM /Pg 50 0 R /P 1212 0 R /ID (532) >> endobj 1214 0 obj << /K [ 240 1215 0 R 246 1219 0 R 252 1223 0 R 256 ] /S /P /Pg 50 0 R /P 460 0 R /ID (586) >> endobj 1215 0 obj << /K [ 241 1216 0 R 245 ] /S /EQNUM /Pg 50 0 R /P 1214 0 R /ID (534) >> endobj 1216 0 obj << /K 1217 0 R /S /Reference /Pg 50 0 R /P 1215 0 R /ID (588) >> endobj 1217 0 obj << /K [ 1218 0 R 243 ] /S /Link /Pg 50 0 R /P 1216 0 R /ID (587) >> endobj 1218 0 obj << /Obj 63 0 R /Type /OBJR >> endobj 1219 0 obj << /K [ 247 1220 0 R 251 ] /S /EQNUM /Pg 50 0 R /P 1214 0 R /ID (535) >> endobj 1220 0 obj << /K 1221 0 R /S /Reference /Pg 50 0 R /P 1219 0 R /ID (590) >> endobj 1221 0 obj << /K [ 1222 0 R 249 ] /S /Link /Pg 50 0 R /P 1220 0 R /ID (589) >> endobj 1222 0 obj << /Obj 64 0 R /Type /OBJR >> endobj 1223 0 obj << /K 1224 0 R /S /Reference /Pg 50 0 R /P 1214 0 R /ID (592) >> endobj 1224 0 obj << /K [ 1225 0 R 254 ] /S /Link /Pg 50 0 R /P 1223 0 R /ID (591) >> endobj 1225 0 obj << /Obj 65 0 R /Type /OBJR >> endobj 1226 0 obj << /K [ 257 258 259 260 ] /Alt (\\begin{equation} G_{d} = \\min \\left \( 0, \\frac{\\tau}{2}, \\frac{\\alpha}{2}, \\frac{\\beta}{2}, k \\right \). \\nonumber\\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (536) /P 460 0 R /A 1227 0 R >> endobj 1227 0 obj << /O /Layout /BBox [ 0 0 252 20.86 ] /Placement /Block >> endobj 1228 0 obj << /K 261 /S /P /Pg 50 0 R /P 460 0 R /ID (593) >> endobj 1229 0 obj << /K [ 262 263 264 265 ] /Alt (\\begin{equation} G_{d,prac} = \\min \\left \( \\frac{\\tau}{2}, \\frac{\\alpha}{2}, \\frac{\\beta}{2}, k \\right \). \\nonumber\\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (537) /P 460 0 R /A 1227 0 R >> endobj 1230 0 obj << /K 266 /S /H3 /Pg 50 0 R /P 460 0 R /ID (594) >> endobj 1231 0 obj << /K [ 267 1232 0 R 271 ] /S /P /Pg 50 0 R /P 460 0 R /ID (595) >> endobj 1232 0 obj << /K 1233 0 R /S /Reference /Pg 50 0 R /P 1231 0 R /ID (597) >> endobj 1233 0 obj << /K [ 1234 0 R 269 ] /S /Link /Pg 50 0 R /P 1232 0 R /ID (596) >> endobj 1234 0 obj << /Obj 66 0 R /Type /OBJR >> endobj 1235 0 obj << /K [ 272 1236 0 R ] /Alt (\\begin{equation} P_{\\mathrm{BER}} = P_{\\mathrm{e,FSO}} + P_{\\mathrm{e,RIS}} - 2 P_{ \\mathrm{e,FSO}} P_{\\mathrm{e,RIS}}, \\label{eq28} \\end{equation}) /S /DISPLAYMATH /Pg 50 0 R /ID (539) /P 460 0 R /A 1237 0 R >> endobj 1236 0 obj << /K 273 /S /EQNUM /Pg 50 0 R /P 1235 0 R /ID (538) >> endobj 1237 0 obj << /O /Layout /BBox [ 0 0 252 8.93 ] /Placement /Block >> endobj 1238 0 obj << /K [ 275 1239 0 R 277 1241 0 R 279 1243 0 R 283 ] /S /P /Pg 50 0 R /P 460 0 R /ID (598) >> endobj 1239 0 obj << /K 276 /Alt ($P_{\\mathrm{e,FSO}}$) /S /MATH /Pg 50 0 R /ID (540) /P 1238 0 R /A 1240 0 R >> endobj 1240 0 obj << /O /Layout /BBox [ 0 0 21.72 8.72 ] >> endobj 1241 0 obj << /K 278 /Alt ($P_{\\mathrm{e,RIS}}$) /S /MATH /Pg 50 0 R /ID (541) /P 1238 0 R /A 1242 0 R >> endobj 1242 0 obj << /O /Layout /BBox [ 0 0 19.95 8.72 ] >> endobj 1243 0 obj << /K 1244 0 R /S /Reference /Pg 50 0 R /P 1238 0 R /ID (600) >> endobj 1244 0 obj << /K [ 1245 0 R 281 ] /S /Link /Pg 50 0 R /P 1243 0 R /ID (599) >> endobj 1245 0 obj << /Obj 67 0 R /Type /OBJR >> endobj 1246 0 obj << /K [ 284 1247 0 R 1248 0 R 1249 0 R 1250 0 R 1251 0 R 1252 0 R 1253 0 R ] /Alt (\\begin{eqnarray} P_{\\mathrm{e}} &=& - \\int _{0}^{\\infty} F_{\\gamma}\\left \( x\\right \)dP_{b} \\left \( x\\right \) \\nonumber\\\\ &\\approx & \\frac{m_{1}m_{2}}{2\\sqrt{2\\pi}}\\int _{0}^{\\infty} \\frac{1}{\\sqrt{x}}\\exp{\\left \(-\\frac{m_{2}^{2}x}{2}\\right \)} F_{ \\gamma}\\left \( x\\right \)dx, \\label{eq:P_e_in_CDF} \\end{eqnarray}) /S /DISPLAYALIGN /Pg 50 0 R /ID (543) /P 460 0 R /A 1254 0 R >> endobj 1247 0 obj << /MCID 0 /Pg 68 0 R /Type /MCR >> endobj 1248 0 obj << /MCID 1 /Pg 68 0 R /Type /MCR >> endobj 1249 0 obj << /MCID 2 /Pg 68 0 R /Type /MCR >> endobj 1250 0 obj << /MCID 3 /Pg 68 0 R /Type /MCR >> endobj 1251 0 obj << /MCID 4 /Pg 68 0 R /Type /MCR >> endobj 1252 0 obj << /MCID 5 /Pg 68 0 R /Type /MCR >> endobj 1253 0 obj << /K 6 /S /EQNUM /Pg 68 0 R /P 1246 0 R /ID (542) >> endobj 1254 0 obj << /O /Layout /BBox [ 0 0 510 32.05 ] /Placement /Block >> endobj 1255 0 obj << /K [ 8 1256 0 R 10 1258 0 R 13 1260 0 R 16 1262 0 R 20 1264 0 R 22 1266 0 R 26 ] /S /P /Pg 68 0 R /P 460 0 R /ID (679) >> endobj 1256 0 obj << /K 9 /Alt ($m_{1} = 1$) /S /MATH /Pg 68 0 R /ID (601) /P 1255 0 R /A 1257 0 R >> endobj 1257 0 obj << /O /Layout /BBox [ 0 0 21.15 6.97 ] >> endobj 1258 0 obj << /K [ 11 12 ] /Alt ($m_{2} = \\sqrt{2}$) /S /MATH /Pg 68 0 R /ID (602) /P 1255 0 R /A 1259 0 R >> endobj 1259 0 obj << /O /Layout /BBox [ 0 0 26.27 12.11 ] >> endobj 1260 0 obj << /K [ 14 15 ] /Alt ($m_{1} = \\frac{4}{\\log _{2}{\\mathrm{M}}}$) /S /MATH /Pg 68 0 R /ID (603) /P 1255 0 R /A 1261 0 R >> endobj 1261 0 obj << /O /Layout /BBox [ 0 0 29.48 20.22 ] >> endobj 1262 0 obj << /K [ 17 18 19 ] /Alt ($m_{2} = \\sqrt{\\frac{3}{\\mathrm{M}-1}}$) /S /MATH /Pg 68 0 R /ID (604) /P 1255 0 R /A 1263 0 R >> endobj 1263 0 obj << /O /Layout /BBox [ 0 0 31.52 24.55 ] >> endobj 1264 0 obj << /K 21 /Alt ($M$) /S /MATH /Pg 68 0 R /ID (605) /P 1255 0 R /A 1265 0 R >> endobj 1265 0 obj << /O /Layout /BBox [ 0 0 6.53 8.52 ] >> endobj 1266 0 obj << /K 1267 0 R /S /Reference /Pg 68 0 R /P 1255 0 R /ID (681) >> endobj 1267 0 obj << /K [ 1268 0 R 24 ] /S /Link /Pg 68 0 R /P 1266 0 R /ID (680) >> endobj 1268 0 obj << /Obj 76 0 R /Type /OBJR >> endobj 1269 0 obj << /K [ 27 1270 0 R 31 ] /S /P /Pg 68 0 R /P 460 0 R /ID (682) >> endobj 1270 0 obj << /K 1271 0 R /S /Reference /Pg 68 0 R /P 1269 0 R /ID (684) >> endobj 1271 0 obj << /K [ 1272 0 R 29 ] /S /Link /Pg 68 0 R /P 1270 0 R /ID (683) >> endobj 1272 0 obj << /Obj 77 0 R /Type /OBJR >> endobj 1273 0 obj << /K [ 32 33 34 35 1274 0 R ] /Alt (\\begin{eqnarray} P_{\\mathrm{e,FSO}} = \\frac{a_{1}}{2} + \\frac{ C_{1}2^{\\alpha +\\beta -2} m_{1} }{ \(2 \\pi \)^{3/2} m_{2} } G_{4,7}^{6,2} \\left \( \\left . \\frac{ C_{2}^{2} }{ 2^{3}m_{2}^{2} } \\right | \\begin{array}{c} \\kappa _{1}' \\\\ \\kappa _{2} \\end{array} \\right \), \\label{eq30} \\end{eqnarray}) /S /DISPLAYALIGN /Pg 68 0 R /ID (607) /P 460 0 R /A 1171 0 R >> endobj 1274 0 obj << /K 36 /S /EQNUM /Pg 68 0 R /P 1273 0 R /ID (606) >> endobj 1275 0 obj << /K [ 38 1276 0 R 40 1278 0 R 44 ] /S /P /Pg 68 0 R /P 460 0 R /ID (685) >> endobj 1276 0 obj << /K 39 /Alt ($\\kappa '_{1} = \(0, \\kappa _{1}\)$) /S /MATH /Pg 68 0 R /ID (608) /P 1275 0 R /A 1277 0 R >> endobj 1277 0 obj << /O /Layout /BBox [ 0 0 39.04 10.15 ] >> endobj 1278 0 obj << /K 1279 0 R /S /Reference /Pg 68 0 R /P 1275 0 R /ID (687) >> endobj 1279 0 obj << /K [ 1280 0 R 42 ] /S /Link /Pg 68 0 R /P 1278 0 R /ID (686) >> endobj 1280 0 obj << /Obj 78 0 R /Type /OBJR >> endobj 1281 0 obj << /K [ 45 46 47 48 49 50 1282 0 R ] /Alt (\\begin{equation} P_{\\mathrm{e,RIS}} = \\frac{1}{\\Gamma \(k\)\\Gamma \(m\)} \\frac{m_{1}}{2\\sqrt{\\pi}} G_{2,3}^{2,2} \\left [ \\left . \\frac{\\Xi ^{2}}{\\bar{\\gamma}_{\\mathrm{RIS}}} \\frac{2}{m_{2}^{2}} \\right | \\begin{array}{c} 1/2, 1 \\\\ k, m, 0 \\end{array} \\right ]. \\label{eq31} \\end{equation}) /S /DISPLAYMATH /Pg 68 0 R /ID (610) /P 460 0 R /A 1283 0 R >> endobj 1282 0 obj << /K 51 /S /EQNUM /Pg 68 0 R /P 1281 0 R /ID (609) >> endobj 1283 0 obj << /O /Layout /BBox [ 0 0 252 27.98 ] /Placement /Block >> endobj 1284 0 obj << /K [ 53 1285 0 R 55 1287 0 R 59 ] /S /P /Pg 68 0 R /P 460 0 R /ID (688) >> endobj 1285 0 obj << /K 54 /Alt ($ P_{\\mathrm{BER}} \\rightarrow P_{\\mathrm{e,FSO}}^{A} + P_{ \\mathrm{e,RIS}}^{A}$) /S /MATH /Pg 68 0 R /ID (611) /P 1284 0 R /A 1286 0 R >> endobj 1286 0 obj << /O /Layout /BBox [ 0 0 60.67 16.58 ] >> endobj 1287 0 obj << /K 1288 0 R /S /Reference /Pg 68 0 R /P 1284 0 R /ID (690) >> endobj 1288 0 obj << /K [ 1289 0 R 57 ] /S /Link /Pg 68 0 R /P 1287 0 R /ID (689) >> endobj 1289 0 obj << /Obj 79 0 R /Type /OBJR >> endobj 1290 0 obj << /K [ 60 61 62 63 1291 0 R ] /Alt (\\begin{equation} P_{\\mathrm{e,FSO}}^{A} \\approx \\frac{a_{1}}{2} = \\frac{1}{2}\\exp \\left \(- \\frac{\\theta ^{2}_{\\mathrm{FOV}}}{2\\left \(\\sigma ^{2}_{to} + \\sigma^{2}_{ro}\\right \)} \\right \). \\label{eq32} \\end{equation}) /S /DISPLAYMATH /Pg 68 0 R /ID (613) /P 460 0 R /A 937 0 R >> endobj 1291 0 obj << /K 64 /S /EQNUM /Pg 68 0 R /P 1290 0 R /ID (612) >> endobj 1292 0 obj << /K [ 66 1293 0 R 70 1296 0 R 72 ] /S /P /Pg 68 0 R /P 460 0 R /ID (691) >> endobj 1293 0 obj << /K 1294 0 R /S /Reference /Pg 68 0 R /P 1292 0 R /ID (693) >> endobj 1294 0 obj << /K [ 1295 0 R 68 ] /S /Link /Pg 68 0 R /P 1293 0 R /ID (692) >> endobj 1295 0 obj << /Obj 80 0 R /Type /OBJR >> endobj 1296 0 obj << /K 71 /Alt ($P_{\\mathrm{e,RIS}}$) /S /MATH /Pg 68 0 R /ID (614) /P 1292 0 R /A 1242 0 R >> endobj 1297 0 obj << /K [ 73 74 75 1298 0 R ] /Alt (\\begin{equation} P_{\\mathrm{e,RIS}} \\approx \\frac{ \\Gamma \(m-k\) }{ 2\\Gamma \(k\) } \\left \( \\frac{ \\Xi ^{2} \\gamma _{th} }{ \\bar{\\gamma}_{\\mathrm{RIS}} } \\right \)^{k} . \\label{eq33} \\end{equation}) /S /DISPLAYMATH /Pg 68 0 R /ID (616) /P 460 0 R /A 1208 0 R >> endobj 1298 0 obj << /K 76 /S /EQNUM /Pg 68 0 R /P 1297 0 R /ID (615) >> endobj 1299 0 obj << /K [ 78 1300 0 R 80 1302 0 R 82 ] /S /P /Pg 68 0 R /P 460 0 R /ID (694) >> endobj 1300 0 obj << /K 79 /Alt ($k$) /S /MATH /Pg 68 0 R /ID (617) /P 1299 0 R /A 1301 0 R >> endobj 1301 0 obj << /O /Layout /BBox [ 0 0 5.85 5.75 ] >> endobj 1302 0 obj << /K 81 /Alt ($1$) /S /MATH /Pg 68 0 R /ID (618) /P 1299 0 R /A 1303 0 R >> endobj 1303 0 obj << /O /Layout /BBox [ 0 0 5.98 5.88 ] >> endobj 1304 0 obj << /K [ 83 84 85 1305 0 R ] /Alt (\\begin{equation} P_{\\mathrm{BER}} \\rightarrow \\frac{1}{2}\\exp \\left \(- \\frac{\\theta^{2}_{\\mathrm{FOV}}}{2\\left \(\\sigma ^{2}_{to} + \\sigma ^{2}_{ro}\\right \)} \\right \). \\label{eq34} \\end{equation}) /S /DISPLAYMATH /Pg 68 0 R /ID (620) /P 460 0 R /A 937 0 R >> endobj 1305 0 obj << /K 86 /S /EQNUM /Pg 68 0 R /P 1304 0 R /ID (619) >> endobj 1306 0 obj << /K 88 /S /H3 /Pg 68 0 R /P 460 0 R /ID (695) >> endobj 1307 0 obj << /K 89 /S /P /Pg 68 0 R /P 460 0 R /ID (696) >> endobj 1308 0 obj << /K [ 90 91 1309 0 R ] /Alt (\\begin{eqnarray} C_{avg} = \\frac{1}{2} \\mathbb{E}\\{\\log _{2} \( 1+ \\textrm{min} \( \\gamma _{\\mathrm{FSO}} , \\gamma _{\\mathrm{RIS}}\)\) \\} . \\label{eq35} \\end{eqnarray}) /S /DISPLAYALIGN /Pg 68 0 R /ID (622) /P 460 0 R /A 1310 0 R >> endobj 1309 0 obj << /K 92 /S /EQNUM /Pg 68 0 R /P 1308 0 R /ID (621) >> endobj 1310 0 obj << /O /Layout /BBox [ 0 0 253.37 16.73 ] /Placement /Block >> endobj 1311 0 obj << /K [ 94 1312 0 R 96 1314 0 R 98 1315 0 R 100 1317 0 R 102 ] /S /P /Pg 68 0 R /P 460 0 R /ID (697) >> endobj 1312 0 obj << /K 95 /Alt ($C_{\\mathrm{FSO}}=\\log _{2} \(1+ \\gamma _{\\mathrm{FSO}}\)$) /S /MATH /Pg 68 0 R /ID (623) /P 1311 0 R /A 1313 0 R >> endobj 1313 0 obj << /O /Layout /BBox [ 0 0 68.17 13.01 ] >> endobj 1314 0 obj << /K 97 /Alt ($C_{\\mathrm{RIS}}=\\log _{2} \(1+ \\gamma _{\\mathrm{RIS}}\)$) /S /MATH /Pg 68 0 R /ID (624) /P 1311 0 R /A 1313 0 R >> endobj 1315 0 obj << /K 99 /Alt ($\\mathbb{E}\\{\\log _{2} \( 1+ \\textrm{min} \( \\gamma_{\\mathrm{FSO}} , \\gamma _{\\mathrm{RIS}}\)\) \\} = \\mathbb{E}\\{ \\textrm{min} \( C_{ \\mathrm{FSO}} , C_{\\mathrm{RIS}}\) \\} = \\textrm{min} \( \\mathbb{E}\\{ \\textrm{min} \( C_{\\mathrm{FSO}} , C_{ \\mathrm{RIS}}\) \\} \) \\leq \\textrm{min} \( \\mathbb{E}\\{ C_{\\mathrm{FSO}} \\} , \\mathbb{E}\\{ C_{\\mathrm{RIS}}\\} \)$) /S /MATH /Pg 68 0 R /ID (625) /P 1311 0 R /A 1316 0 R >> endobj 1316 0 obj << /O /Layout /BBox [ 0 0 363.06 15.93 ] >> endobj 1317 0 obj << /K 101 /Alt ($C_{avg}$) /S /MATH /Pg 68 0 R /ID (626) /P 1311 0 R /A 1318 0 R >> endobj 1318 0 obj << /O /Layout /BBox [ 0 0 9.84 10.29 ] >> endobj 1319 0 obj << /K [ 103 104 1320 0 R ] /Alt (\\begin{eqnarray} C_{avg} \\leq \\frac{1}{2} \\min \( \\mathbb{E}\\{ C_{\\mathrm{FSO}} \\} , \\mathbb{E}\\{ C_{\\mathrm{RIS}} \\}\), \\label{eq36} \\end{eqnarray}) /S /DISPLAYALIGN /Pg 68 0 R /ID (628) /P 460 0 R /A 1310 0 R >> endobj 1320 0 obj << /K 105 /S /EQNUM /Pg 68 0 R /P 1319 0 R /ID (627) >> endobj 1321 0 obj << /K 107 /S /P /Pg 68 0 R /P 460 0 R /ID (698) >> endobj 1322 0 obj << /K [ 108 109 1323 0 R ] /Alt (\\begin{equation} \\mathbb{E}\\{ C_{\\mathrm{FSO}} \\} = \\frac{1}{\\ln \(2\)} \\int _{0}^{ \\infty} \\ln \(1+\\gamma _{\\mathrm{FSO}}\) f_{\\gamma _{\\mathrm{FSO}}}\( \\gamma _{\\mathrm{FSO}}\) \\label{eq37} \\end{equation}) /S /DISPLAYMATH /Pg 68 0 R /ID (630) /P 460 0 R /A 1324 0 R >> endobj 1323 0 obj << /K 110 /S /EQNUM /Pg 68 0 R /P 1322 0 R /ID (629) >> endobj 1324 0 obj << /O /Layout /BBox [ 0 0 252 32.05 ] /Placement /Block >> endobj 1325 0 obj << /K 112 /S /P /Pg 68 0 R /P 460 0 R /ID (699) >> endobj 1326 0 obj << /K [ 113 114 1327 0 R ] /Alt (\\begin{equation} \\mathbb{E}\\{ C_{\\mathrm{RIS}} \\} = \\frac{1}{\\ln \(2\)} \\int _{0}^{ \\infty} \\ln \(1+\\gamma _{\\mathrm{RIS}}\) f_{\\gamma _{\\mathrm{RIS}}}\( \\gamma _{\\mathrm{RIS}}\) , \\label{eq38} \\end{equation}) /S /DISPLAYMATH /Pg 68 0 R /ID (632) /P 460 0 R /A 1324 0 R >> endobj 1327 0 obj << /K 115 /S /EQNUM /Pg 68 0 R /P 1326 0 R /ID (631) >> endobj 1328 0 obj << /K [ 117 1329 0 R 121 1332 0 R 123 1334 0 R 125 1336 0 R 127 1338 0 R 129 1340 0 R 131 1342 0 R 133 1344 0 R 137 ] /S /P /Pg 68 0 R /P 460 0 R /ID (700) >> endobj 1329 0 obj << /K 1330 0 R /S /Reference /Pg 68 0 R /P 1328 0 R /ID (702) >> endobj 1330 0 obj << /K [ 1331 0 R 119 ] /S /Link /Pg 68 0 R /P 1329 0 R /ID (701) >> endobj 1331 0 obj << /Obj 81 0 R /Type /OBJR >> endobj 1332 0 obj << /K 122 /Alt ($\\ln\(1+\\gamma \) = G_{2,2}^{1,2} \\left [ \\gamma |_{1,0}^{1,1} \\right ]$) /S /MATH /Pg 68 0 R /ID (633) /P 1328 0 R /A 1333 0 R >> endobj 1333 0 obj << /O /Layout /BBox [ 0 0 83.44 26.85 ] >> endobj 1334 0 obj << /K 124 /Alt ($\\alpha =1/2$) /S /MATH /Pg 68 0 R /ID (634) /P 1328 0 R /A 1335 0 R >> endobj 1335 0 obj << /O /Layout /BBox [ 0 0 30.69 7.73 ] >> endobj 1336 0 obj << /K 126 /Alt ($\\sigma =1$) /S /MATH /Pg 68 0 R /ID (635) /P 1328 0 R /A 1337 0 R >> endobj 1337 0 obj << /O /Layout /BBox [ 0 0 17.17 5.97 ] >> endobj 1338 0 obj << /K 128 /Alt ($\\omega =C_{2}$) /S /MATH /Pg 68 0 R /ID (636) /P 1328 0 R /A 1339 0 R >> endobj 1339 0 obj << /O /Layout /BBox [ 0 0 21.03 7.78 ] >> endobj 1340 0 obj << /K 130 /Alt ($l=1$) /S /MATH /Pg 68 0 R /ID (637) /P 1328 0 R /A 1341 0 R >> endobj 1341 0 obj << /O /Layout /BBox [ 0 0 18.82 5.97 ] >> endobj 1342 0 obj << /K 132 /Alt ($k=2$) /S /MATH /Pg 68 0 R /ID (638) /P 1328 0 R /A 1343 0 R >> endobj 1343 0 obj << /O /Layout /BBox [ 0 0 18.65 5.97 ] >> endobj 1344 0 obj << /K 1345 0 R /S /Reference /Pg 68 0 R /P 1328 0 R /ID (704) >> endobj 1345 0 obj << /K [ 1346 0 R 135 ] /S /Link /Pg 68 0 R /P 1344 0 R /ID (703) >> endobj 1346 0 obj << /Obj 82 0 R /Type /OBJR >> endobj 1347 0 obj << /K [ 1348 0 R 1350 0 R ] /S /FigureEnv /Pg 68 0 R /P 460 0 R /ID (654) >> endobj 1348 0 obj << /K 139 /Alt (Image of Fig. 2) /S /Figure /Pg 68 0 R /ID (648) /P 1347 0 R /A 1349 0 R >> endobj 1349 0 obj << /O /Layout /BBox [ 0 0 250 201 ] >> endobj 1350 0 obj << /K [ 1351 0 R 1352 0 R ] /S /Caption /Pg 68 0 R /P 1347 0 R /ID (649) >> endobj 1351 0 obj << /K 142 /S /CaptionLbl /Pg 68 0 R /P 1350 0 R /ID (651) >> endobj 1352 0 obj << /K [ 144 1353 0 R 146 ] /S /CaptionBody /Pg 68 0 R /P 1350 0 R /ID (652) >> endobj 1353 0 obj << /K 145 /Alt (MATH) /S /MATH /Pg 68 0 R /ID (653) /P 1352 0 R /A 1354 0 R >> endobj 1354 0 obj << /O /Layout /BBox [ 0 0 39.86 6.41 ] >> endobj 1355 0 obj << /K [ 149 150 151 152 1356 0 R ] /Alt (\\begin{equation} \\mathbb{E}\\{ C_{\\mathrm{FSO}} \\} = \\frac{2^{\\alpha +\\beta -3} }{2\\pi} \\frac{C_{1}}{\\ln \(2\)} G_{4,8}^{8,1} \\left \( \\frac{C_{2}^{2} }{2^{4}} \\left | \\begin{array}{c} \\kappa _{1}'' \\\\ \\kappa _{2}' \\end{array} \\right . \\right \), \\label{eq39} \\end{equation}) /S /DISPLAYMATH /Pg 68 0 R /ID (640) /P 460 0 R /A 1187 0 R >> endobj 1356 0 obj << /K 153 /S /EQNUM /Pg 68 0 R /P 1355 0 R /ID (639) >> endobj 1357 0 obj << /K [ 155 1358 0 R 158 1360 0 R 161 ] /S /P /Pg 68 0 R /P 460 0 R /ID (706) >> endobj 1358 0 obj << /K [ 156 157 ] /Alt ($\\kappa ''_{1} = \(-\\frac{1}{2}, \\kappa _{1}\)$) /S /MATH /Pg 68 0 R /ID (641) /P 1357 0 R /A 1359 0 R >> endobj 1359 0 obj << /O /Layout /BBox [ 0 0 47.85 12.55 ] >> endobj 1360 0 obj << /K [ 159 160 ] /Alt ($\\kappa _{2}'=\(\\kappa _{2}, -\\frac{1}{2}\)$) /S /MATH /Pg 68 0 R /ID (642) /P 1357 0 R /A 1361 0 R >> endobj 1361 0 obj << /O /Layout /BBox [ 0 0 46.19 12.55 ] >> endobj 1362 0 obj << /K [ 162 1363 0 R 166 1366 0 R 173 1368 0 R 177 ] /S /P /Pg 68 0 R /P 460 0 R /ID (707) >> endobj 1363 0 obj << /K 1364 0 R /S /Reference /Pg 68 0 R /P 1362 0 R /ID (709) >> endobj 1364 0 obj << /K [ 1365 0 R 164 ] /S /Link /Pg 68 0 R /P 1363 0 R /ID (708) >> endobj 1365 0 obj << /Obj 83 0 R /Type /OBJR >> endobj 1366 0 obj << /K [ 167 168 169 170 171 172 ] /Alt ($K_{\\nu} \(\\sqrt{z} \) = \\frac{1}{2}G_{0,2}^{2,0} \\left [ \\frac{z}{4}| \\frac{\\nu}{2}, -\\frac{\\nu}{2} \\right ] $) /S /MATH /Pg 68 0 R /ID (643) /P 1362 0 R /A 1367 0 R >> endobj 1367 0 obj << /O /Layout /BBox [ 0 0 89.44 39.96 ] >> endobj 1368 0 obj << /K 1369 0 R /S /Reference /Pg 68 0 R /P 1362 0 R /ID (711) >> endobj 1369 0 obj << /K [ 1370 0 R 175 ] /S /Link /Pg 68 0 R /P 1368 0 R /ID (710) >> endobj 1370 0 obj << /Obj 84 0 R /Type /OBJR >> endobj 1371 0 obj << /K [ 178 179 180 181 1372 0 R ] /Alt (\\begin{eqnarray} \\mathbb{E}\\{ C_{\\mathrm{RIS}} \\} = 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/Length 6265 /Subtype /XML /Type /Metadata >> stream http://creativecommons.org/licenses/by-nc-nd/4.0/ elsevier.com sciencedirect.com true 10.1016/j.dcan.2025.02.001 2010-04-23 application/pdf 10.1016/j.dcan.2025.02.001 Chongqing University of Posts and Telecommunications Digital Communications and Networks, 11 (2025) 1271-1279. doi:10.1016/j.dcan.2025.02.001 Unmanned aerial vehicle Free-space optics Reconfigurable intelligent surface Mixed RF/FSO channel Outage probability Bit-error rate Performance analysis of RIS-assisted dual-hop mixed FSO-RF UAV communication systems Donghyun Kim Hwi Sung Park Bang Chul Jung VoR 1st September 2025 Acrobat Distiller 8.1.0 (Windows) Unmanned aerial vehicle,Free-space optics,Reconfigurable intelligent surface,Mixed RF/FSO channel,Outage probability,Bit-error rate 1st September 2025 sciencedirect.com elsevier.com true 2010-04-23 10.1016/j.dcan.2025.02.001 noindex journal © 2025 Chongqing University of Posts and Telecommunications. 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