Multiple-input-multiple-output (MIMO) radar and frequency diverse array (FDA) radar have gained significant attention from researchers community due to their numerous advantages over the phased-array radars. The distinguishing features of MIMO radar and FDA radar are waveform diversity and frequency diversity, respectively, while their phased-array counterpart lacks any such diversity. The hybridization form of MIMO and phased-array radars, called phased-MIMO radar, has also attracted the researchers attention due to its capability of combining the benefits of both. In this dissertation, phased-MIMO radar with closely spaced antennas and FDA radar with small inter-antenna frequency offset have been studied. To analyse the performance of radar, ambiguity function has proved to be a useful foundation. We have formulated ambiguity functions of phased- MIMO and FDA radars and derived their important mathematical properties. We have shown that FDA radar can promise better range resolution as compared to that of phased-array radar. For FDA we have proposed two novel schemes of inter-antenna frequency offset. Firstly, it is the time-dependent frequency offset as compared to the constant offset in the existing FDA. With the proposed idea a range-dependent beampattern can be synthesized with the maximum constantly illuminating the given target location. This is in contrast to the time-modulated beampattern with constant frequency offset. Secondly, we have proposed non-uniform (logarithmically increasing) frequency offset as compared to the uniform offset in the existing FDA. The proposed frequency offset promises a beampattern with a maximum only at the given target location. On the contrary, beampattern of FDA with uniform frequency offset exhibits multiple maxima in the visible range. The proposed schemes can provide a strong foundation for the development of modern radars capable of scanning the space more intelligently. We have investigated the proposed schemes only for linear array but they can be extended to planar arrays to scan the space in three dimensions.