This　work,　for　the　first　time,　tackles　channel　estimation　design　with　pilots　in　the　context　of　covert　wireless　communication.　We　consider　Rayleigh　fading　for　the　communication　channel　from　a　transmitter　to　a　receiver,　both　additive　white　Gaussian　noise　(AWGN)　and　Rayleigh　fading　for　the　detection　channel　from　the　transmitter　to　a　warden.　Before　transmitting　information　signals,　the　transmitter　has　to　send　pilots　to　enable　channel　estimation　at　the　receiver.　For　the　case　with　AWGN　detection　channel,　we　first　analytically　prove　that　transmitting　pilot　and　information　signals　with　equal　power　minimizes　the　warden＇s　detection　performance.　This　motivates　us　to　consider　the　equal　transmit　power　and　then　optimize　channel　use　allocation　between　pilot　and　information　signals　under　this　case.　Our　analysis　shows　that　the　optimal　number　of　the　channel　uses　allocated　to　pilots　increases　as　the　covertness　constraint　becomes　tighter.　For　the　case　with　Rayleigh　fading　detection　channel,　we　present　a　general　framework　to　optimally　allocate　transmit　power　and　channel　uses　between　pilot　and　information　signals.　Our　examination　shows　that　the　covert　communication　performance　gain　achieved　by　this　general　framework　is　not　remarkable　relative　to　the　scheme　with　equal　transmit　power　and　this　gain　diminishes　as　the　covertness　constraint　becomes　stricter.　©　1972-2012　IEEE.