Direction of Arrival (DoA) estimation is an important topic in radar application and has significant importance for advanced driver assistant systems in the automotive industry. While there is an increasing need for higher resolution and increased target detection and DoA estimation performance, such improvements often require increased hardware cost, complexity and size. With the increase in computational power of modern systems, Compressive Sensing methods have become more attractive as alternative methods for DoA estimation to the established ones, which often rely on uniform linear arrays (ULA) and the acquisition of multiple snapshots to provide good performance. Compressive Sensing methods have been shown to fit very well into the DoA estimation framework and have the ability to use far fewer snapshots, provide super resolution capabilities and by nature, utilise sparse spatial sampling, i.e. sparse antenna arrays. The latter point is the key incentive of this thesis. Specifically, Bayesian Compressive Sensing (BCS) which in addition to point estimates also provides measures of uncertainty is used in this thesis, to generate and use sparse linear array structures for DoA estimation. In particular, the entropy of the recovered coefficient vector is reduced in each step. Two array generation algorithms are proposed building on the same concept to generate sensor arrays for the consideration of a uniformly spaced, linear grid of possible sensor locations and for a Multiple In Multiple Out (MIMO) array setup. Utilising sparse arrays with BCS has the potential to reduce the hardware complexity of the circuit board, reduce energy consumption and heat generation, as well as ultimately saving costs in production and operation. The proposed array generation algorithms are first tested and assessed with simulated Frequency-Modulated Continuous-Waveform (FMCW) radar data, where it is shown that the generated algorithms achieve good estimation and detection performance with a heavily reduced number of sensors compared to their fully filled template arrays. Moreover, they are shown to outperform randomly generated arrays in most cases that have been studied. To add practical insight, the generated antenna arrays are tested with measured data that has been captured in two measurement campaigns with a Texas Instruments Cascade Evaluation board, featuring an 86 element virtual ULA, which has been used as the grid of possible sensor positions for the array generations. The simulated results are affirmed by the measured data, although more sensors tend to be required depending on the clutter present in the scene. It is shown, that BCS can work very well with the proposed, heavily sparse arrays tested on both simulated and measured data, which translates directly to a possible reduction in required hardware antennas. Although in this thesis the possible sensor positions have been confined to a grid of positions spaced by half the wavelength, it is easily possible to extend the procedure to a more finely divided search space.