Most　of　the　direction　of　arrival　(DOA)　coherent　signal　estimation　methods　based　on　coprime　array　do　not　consider　the　influence　of　noise.　Therefore,　in　this　paper,　we　propose　a　signal　subspace　based　atomic　norm　minimization　(ANM)　method　to　estimate　the　DOA　of　coherent　coprime　array.　Firstly,　we　use　the　relationship　between　the　linear　array　and　the　coprime　array　to　directly　map　and　interpolate　the　matrix　containing　only　the　signal　subspace　in　the　coprime　array　to　obtain　the　signal　subspace　of　the　linear　array,　and　then　solve　the　ANM　problem　to　recover　the　rank.　Finally,　the　DOA　of　coherent　sources　was　obtained　through　the　application　of　the　matrix　enhancement　and　matrix　pencil　(MEMP)　method　to　construct　the　enhancement　matrix.　The　proposed　method　can　estimate　the　coherent　signal　more　accurately　and　is　more　robust　to　noise.　The　results　of　numerical　simulations　substantiate　the　superiority　of　the　proposed　algorithm.　©　2024　Copyright　held　by　the　owner/author(s).