Because　traditional　subspace　algorithms　have　low　direction　of　arrival　(DOA)　estimation　accuracy　or　cannot　be　estimated　under　the　conditions　of　few　snapshots,　low　signal-to-noise　ratio,　and　source　coherence,　the　application　of　compressed　sensing　theory　in　DOA　estimation　was　studied　in　this　paper　to　solve　the　problem　that　sparsity　adaptive　matching　pursuit　algorithm　cannot　be　effectively　estimated　in　a　noisy　environment　and　the　selection　of　a　large　initial　step　causes　overestimation.　On　the　basis　of　this　algorithm,　the　iteration　termination　conditions　of　the　algorithm　were　improved　and　optimized　by　using　the　variation　rule　of　the　iteration　residuals.　The　adaptive　adjustment　of　the　step　size　can　quickly　and　accurately　approach　the　source　sparsity.　The　simulation　results　show　that　the　proposed　algorithm　has　the　advantages　of　high　estimation　accuracy,　fast　running　speed,　and　good　robustness　to　noise.　It　promotes　the　further　fusion　of　compressed　sensing　and　DOA　estimation　under　actual　conditions.　©　2021,　Editorial　Department　of　Journal　of　Beijing　University　of　Technology.　All　right　reserved.