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This work addresses the problem of direction-of-arrival (DOA) estimation using spatial compressive sensing (SCS) with bias mitigation via an expected likelihood (EL) approach. Compressive sensing (CS)-based estimation approaches such as SCS suffer from two main bias sources: a) a grid-bias resulting from the discretization of the azimuth bearing space and b) an inherent-bias which is the result of regularized L1 optimization underpinning sparse signal recovery. This work investigates the SCS bias sources and proposes a novel application of the EL approach to mitigate both SCS bias sources to produce two competitive maximum likelihood (ML) surrogate algorithms for DOA estimation. The DOA estimation performance and practical suitability of the proposed approaches are demonstrated via simulation. Simulations demonstrate that SCS with the EL-based bias mitigation is able to provide improved DOA estimation accuracy without the need for intensive regularization parameter tuning.