In　cognitive　radio　(CR),　power　allocation　plays　an　important　role　in　protecting　primary　user　from　disturbance　of　secondary　user.　Some　existing　studies　about　power　allocation　in　CR　utilize　＇interference　temperature＇　to　achieve　this　protection,　which　might　not　be　suitable　for　the　OFDM-based　CR.　Thus　in　this　paper,　power　allocation　problem　in　multi-user　orthogonal　frequency　division　multiplexing　(OFDM)　and　distributed　antenna　cognitive　radio　with　radio　over　fiber　(RoF)　is　firstly　modeled　as　an　optimization　problem,　where　the　limitation　on　secondary　user　is　not　＇interference　temperature＇,　but　that　total　throughput　of　primary　user　in　all　the　resource　units　(RUs)　must　be　beyond　the　given　threshold.　Moreover,　based　on　the　theorem　about　maximizing　the　total　throughput　of　secondary　user,　equal　power　allocation　algorithm　is　introduced.　Furthermore,　as　the　optimization　problem　for　power　allocation　is　not　convex,　it　is　transformed　to　be　a　convex　one　with　geometric　programming,　where　the　solution　can　be　obtained　using　duality　and　Karush-Kuhn-Tucker　(KKT)　conditions　to　form　the　optimal　power　allocation　algorithm.　Finally,　extensive　simulation　results　illustrate　the　significant　performance　improvement　of　the　optimal　algorithm　compared　to　the　existing　algorithm　and　equal　power　allocation　algorithm.　©　2010　The　Journal　of　China　Universities　of　Posts　and　Telecommunications.