Array signal processing has been an active research area for the last decades. Direction of Arrival (DOA) Estimation is an important field in array signal processing where the objective is to locate the sources of the signals. It has played an important role in widespread applications such as radar, sonar, wireless communications, seismology, biomedicine, astronomy, and imaging. Numerous algorithms have been reported in the literature in the last several years, each one trying to resolve some limitations of previous ones. Need for a large number of antennas and multiple snapshots are the main limitations of the conventional DOA algorithms. Emergence of Compressed Sensing (CS) has attracted considerable research interest in the signal processing community. It makes it possible to sample sparse signals at rates far lower than the Shannon–Nyquist rate whereas signal recovering is guaranteed with high probability. CS has branched out to many new fields and has worked its way into several application areas like DOA estimation. Applying CS to DOA estimation results in the snapshot reduction and also the need for fewer number of frontend circuit chains for the arrays. CS has brought other benefits like possibility of one-bit sampling. Thus far, one-bit samplers have used constant threshold but here, time-varying threshold is proposed instead and then appropriate convex optimization problems specially for gridless CS DOA estimation is represented. The simulation results show that the proposed time-varying thresholding outperforms constant threshold samplers. Key word: Direction of arrival (DOA) estimation, compressed sensing (CS), sparse signal repre-sentation, convex optimization, one-bit sampling.