Compressive　sensing　(CS)　provides　a　new　paradigm　for　efficient　data　gathering　in　wireless　sensor　networks　(WSNs).　The　theory　of　CS　allows　to　reconstruct　all　sensor　data　of　the　network,　while　only　collecting　a　small　number　of　measurements　at　a　sink.　In　this　paper,　we　consider　a　scenario　where　a　sink　collects　spatially　correlated　sensor　data　from　n　sensor　nodes　randomly　deployed　in　a　region.　We　investigate　the　fundamental　limitation　of　data　gathering　with　CS　in　such　a　scenario,　in　terms　of　capacity　and　delay.　We　construct　a　scheduling　and　routing　scheme　based　on　CS　for　data　gathering　in　WSNs.　We　show　that　the　proposed　scheme　can　achieve　a　per-node　transport　capacity　of　Θ(1/log　n)　under　physical　interference　model.　Furthermore,　we　also　study　the　delay　performance　of　the　proposed　scheme　and　show　that　the　delay　for　collecting　a　snapshot　with　CS　is　Θ(√n　log　n).　In　particular,　our　results　demonstrate　that　the　proposed　scheme　can　achieve　a　capacity　gain　of　Θ(n/log　n)　over　the　case　without　CS　and　the　delay　can　also　be　reduced　by　a　factor　of　Θ(√n/log　n).　©　2011　IEEE.