This thesis presents mainly simulation and measurement results of metamaterial based transmitter and receiver antennas for a Doppler radar system operating at 5.8 GHz and indoor, outdoor and through-wall performances of the Doppler radar system after the integration of field and the realized transmitter and receiver antennas. Firstly, the antennas are modeled via 3D electromagnetic simulation program CST:Microwave Studio and related parameters are calculated. Afterwards, in order to observe antenna performances, radiation pattern and gain characteristics of realized antennas are measured in laboratory environment including anechoic chamber. Another essential objective of this thesis is to examine and analyze applicability and effectiveness of the metamaterial based antennas for a 5.8 GHz Doppler radar system. For this reason, a double negative index metamaterial structure is integrated to a patch antenna for the transmitter. For the receiver antenna, a near-zero index medium is designed to locate over patch antenna. Accordingly, significant improvements in size and bandwidth for the transmitter and in gain and directivity for the receiver in addition to improvement of its psychical size are obtained. It is shown that return loss, radiation pattern and gain measurement results of the designed antennas agree well with the simulations for a desired frequency band. According to the experimental data, the realized transmitter antenna has a higher directivity value as compared to the simulated one, therefore it radiates most of the power into narrower area. Additionally, the measured one has a wider bandwidth. The measurement results of receiver antenna are consistent with simulation in terms of bandwidth, return-loss, radiation pattern of horizontal direction and gain value. The last part of the thesis is devoted to expressing the application of the designed antennas to the low-power, short-range Doppler radar system, which is designed to detect the speed of the human or moving target in the indoor/outdoor environment or behind the wall. Improvements on the performance of the radar system integrated with metamaterial antennas are discussed and performances results are commented.