Radar systems need a high target detection probability and therefore a high signal-to-noise ratio (SNR). For limited transmit power, this performance feature is improved, if a long pulse of high energy is chosen. However, this degrades the target resolution in the range direction. Therefore, pulse compression technique is used where phase coded signals instead of simple rectangular pulses are transmitted. A pulse compression filter is applied in the receiver to compress the long transmit signal to a narrow peak.The matched filter (MF) is a typical pulse compression filter. It is used to maximize the target detection probability. However, an MF output contains not only the mainlobe, but also range sidelobes, which deteriorate the range resolution in multi-target situations due to the masking effect. To achieve a high target detection probability and a high range resolution even in multi-target situations, phase coded signals, which have an impulse-like signal at the MF output, are required.In this thesis an alternative receive filter, the mismatched filter (MMF), is designed, which shows perfect behaviour in range resolution with only a small degradation in the detection probability. Different MMF design procedures are presented for both aperiodic and periodic transmit signals. The optimal MMF performance, combined with a systematic code search, is investigated. It is shown that the MMF approach has clear advantages against the MF approach. There exist a lot of phase coded signals which have very low or even zero range sidelobes in the MMF output signals and high SNR gains.A new MMF design procedure is developed using a complementary structure. Here, two phase coded signals are sent and two individual MMFs process the echo signals. By summation of these two responses all range sidelobes can be avoided. The developed MMFs for complementary codes fully eliminate range sidelobes and maximize the SNR simultaneously. The SNR loss is in many cases only 0.2dB compared to the MF approach. In addition, full multiplicities of good code pairs based on the MMF procedure exist for arbitrary code lengths.The MMF design procedure is further extended for the applications in multi-signal situations, where the influence of mutual interference between radar signals can be dominant and disturbs the signal of interest. A new design approach is developed in this thesis by using the product theorem. Sets of periodic phase coded signals and the corresponding MMFs are designed so that the MMFs not only extract their corresponding transmit signals with high SNR gains but also suppress the mutual interference signals. The resulting signal sets are available for almost unlimited code lengths.