Collaborative Spectrum Sensing Optimisation Algorithms for Cognitive Radio Networks

<table>Receiver operating characteristics for <svg height="10.925" id="M266" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.2875004 10.925" width="8.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.65)"><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
l-26 -65h-233z" id="x35"></path></g>
</svg> collaborating users in shadow fading (<svg height="15.2375" id="M267" style="vertical-align:-3.39069pt" version="1.1" viewbox="0 0 51.212502 15.2375" width="51.212502" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.963)"><path d="M548 455q-32 -77 -74 -77q-37 0 -103 10l-3 -2q36 -30 48.5 -62t12.5 -80q0 -103 -75 -179.5t-175 -76.5q-70 0 -113 45t-43 128q0 115 83.5 200.5t209.5 85.5q31 0 77.5 -4t67.5 -4q36 0 62 30zM350 274q0 54 -17 86q-19 35 -57 35q-50 0 -90 -37.5t-59 -91.5t-19 -109
q0 -61 24.5 -96.5t65.5 -35.5q51 0 87.5 46.5t50.5 100.5t14 102z" id="x1D70E"></path></g>
<g transform="matrix(.012,-0,0,-.012,9.663,15.038)"><path d="M517 51v-25q-101 -18 -155 -38v65l-61 -36q-50 -29 -78 -29q-68 0 -126.5 58t-58.5 155q0 103 77 175.5t180 72.5q36 0 67 -12v143q0 48 -11.5 58.5t-65.5 14.5v25q79 9 156 34v-597q0 -38 7.5 -48t36.5 -13zM362 85v275q-35 51 -103 51q-20 0 -40.5 -8.5t-42 -28
t-35 -57.5t-13.5 -89q0 -83 42 -130t96 -47q51 0 96 34z" id="x64"></path></g><g transform="matrix(.012,-0,0,-.012,15.945,15.038)"><path d="M372 352v-2q176 -27 176 -159q0 -99 -95 -151q-73 -40 -196 -40h-221v28q65 5 78.5 19t13.5 76v404q0 63 -12 77t-72 18v28h257q102 0 150 -34q26 -18 41 -48.5t15 -65.5q0 -111 -135 -150zM213 362h47q80 0 117.5 32t37.5 96q0 56 -33 92t-100 36q-41 0 -56 -10
q-13 -8 -13 -50v-196zM213 328v-203q0 -54 17 -72.5t66 -18.5q67 1 110.5 37t43.5 110q0 147 -192 147h-45z" id="x42"></path></g>
<g transform="matrix(.017,-0,0,-.017,28.288,10.963)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,42.974,10.963)"><path d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5
t96 -62.5q53 0 78 45.5t25 105.5q0 68 -35 116t-99 48z" id="x36"></path></g>
</svg>) in <svg height="11.125" id="M268" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.2875004 11.125" width="8.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg> cases: Case <svg height="10.9125" id="M269" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 8.2875004 10.9125" width="8.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><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>
</svg> (all users have similar SNR), Case <svg height="10.9125" id="M270" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 8.2875004 10.9125" width="8.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><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> (half of the users have high SNR), and Case <svg height="11.125" id="M271" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.2875004 11.125" width="8.2875004" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5
q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" id="x33"></path></g>
</svg> (only one user has high SNR).</table>

International Journal of Digital Multimedia Broadcasting

fig9

Figure 9

Figure 9: Collaborative Spectrum Sensing Optimisation Algorithms for Cognitive Radio Networks 