To　improve　the　spectrum　efficiency　and　alleviate　scarcity,　ultra-narrow　band　(UNB)　technique　is　proposed　with　high　bandwidth　efficiency　and　low　bit　error　rate　(BER).　In　this　paper,　the　waveform　design　schemes,　which　are　sine　amplitude　modulation　(AM-sine),　dual-frequency　amplitude　modulation　(DFAM)　and　constant　modulus　dual-frequency　(CMDF)　modulation　for　wireless　communication　networks　employing　UNB　technique,　are　proposed.　We　investigate　the　Euclidean　distance　of　binary　modulated　signals　for　UNB　communication　under　the　bandwidth　restriction　compared　to　very-minimum　waveform　difference　keying　(VWDK).　We　derive　the　simplicity　to　optimize　our　proposed　schemes　by　introducing　sine-like　signal.　By　applying　the　concavity　optimization　theory,　we　get　more　smooth　phase　waveform　than　VWDK.　We　formulate　the　optimization　problem　to　minimize　the　average　BER　subject　to　these　conditions,　one　is　the　Euclidean　distance　between　modulated　signals　and　carrier　signal,　the　other　one　is　the　signal　energy.　Simulation　results　are　provided　to　show　the　superiority　of　our　proposed　schemes　as　compared　to　VWDK.　©　ICST　Institute　for　Computer　Sciences,　Social　Informatics　and　Telecommunications　Engineering　2018.