This　paper　investigates　the　resource　allocation　problem　in　heterogeneous　cognitive　radio　networks　(HCRNs).　In　this　paper,　two　types　of　users,　i.e.,　multi-homing　and　single-network　cognitive　radio　users　(CRUs),　are　considered　to　coexist　in　HCRNs.　Multi-homing　CRUs　can　access　multiple　networks　simultaneously,　while　single-network　CRUs　can　be　served　by　only　one　network　at　a　time.　With　the　aim　of　maximizing　the　system　capacity　of　HCRNs,　the　resource　allocation　problem　is　formulated　as　a　joint　multi-dimension　optimization　problem　which　includes　network　selection,　bandwidth　and　power　allocation　for　both　multi-homing　and　single-network　CRUs.　However,　the　joint　multi-dimension　optimization　leads　the　problem　to　be　non-convex　and　NP-hard.　To　solve　the　problem　efficiently,　continuous　relaxation　is　performed　firstly,　and　next　a　near-optimal　solution　using　Lagrangian　dual　decomposition　and　Karush-Kuhn-Tucker　(KKT)　conditions　is　proposed　in　this　paper.　Numerical　results　show　the　proposed　algorithm　improves　the　system　capacity　significantly　compared　to　the　traditional　ones.　©　2017　IEEE.