The　restricted　isometry　property　(RIP)　of　the　sensing　matrix　has　recently　received　a　lot　of　attention　under　the　rubric　of　compressive　sensing.　Most　studies　have　shown　that　a　Gaussian　random　sensing　matrix　satisfies　the　RIP　in　theory.　However,　due　to　its　high　cost　of　storage　and　complex　physical　implementation,　the　Toeplitz　sensing　matrix　is　more　in　favored　than　the　Gauss　sensing　matrix　in　actual.　Because　it　can　be　implemented　by　the　fast　discrete　Fourier　transform.　Proof　of　the　RIP　for　the　sensing　matrix　exploiting　graph　theory　and　the　Geršgorin＇s　disc　theorem　is　given.　The　results　show　that　the　Toeplitz　random　matrix　satisfies　the　RIP　with　high　probability.　And　the　least　square　(LS),　linear　minimum　mean　square　error　(LMMSE),　compressive　sensing　algorithm　with　the　Gauss　sensing　matrix　and　compressive　sensing　algorithm　with　Toeplitz　sensing　matrix　channel　estimation　algorithm　are　compared.　The　simulation　results　show　that　the　Toeplitz　sensing　matrix　has　a　superiority　over　the　Gauss　sensing　matrix　on　computation　complexity　and　the　traditional　channel　estimation　method　on　performance　and　computation　complexity.　It　provides　a　theoretical　and　realistic　foundation　for　reconstructing　the　original　signal　losslessly.　©,　2015,　Chinese　Institute　of　Electronics.　All　right　reserved.