Abstract The focus of this thesis is on the binary signal detection problem, i.e., if a signal or signals are present or not. Depending on the application, the signal to be detected can be either unknown or known. The detection is based on some function of the received samples which is compared to a threshold. If the threshold is exceeded, it is decided that signal(s) is (are) present. Energy detectors (radiometers) are often used due to their simplicity and good performance. The main goal here is to develop and analyze energy based detectors as well as power-law based detectors. Different possibilities for setting the detection threshold for a quantized total power radiometer are analyzed. The main emphasis is on methods that use reference samples. In particular, the cell-averaging (CA) constant false alarm rate (CFAR) threshold setting method is analyzed. Numerical examples show that the CA strategy offers the desired false alarm probability, whereas a more conventional strategy gives too high values, especially with a small number of reference samples. New performance analysis of a frequency sweeping channelized radiometer is presented. The total power radiometer outputs from different frequencies are combined using logical-OR, sum and maximum operations. An efficient method is presented for accurately calculating the likelihood ratio used in the optimal detection. Also the effects of fading are analyzed. Numerical results show that although sweeping increases probability of intercept (POI), the final probability of detection is not increased if the number of observed hops is large. The performance of a channelized radiometer is studied when different CFAR strategies are used to set the detection threshold. The proposed iterative methods for setting the detection threshold are the forward consecutive mean excision (FCME) method with the CA scaling factors in final detection decision (FCME+CA), the backward consecutive mean excision (BCME) method with the CA scaling factors in detection (BCME+CA) and a method that uses the CA scaling factors for both censoring and detection (CA+CA). Numerical results show that iterative CFAR methods may improve detection performance compared to baseline methods. Finally, a method to set the threshold of a power-law detector that uses a nonorthogonal transform is presented. The mean, variance and skewness of the decision variable in the noise-only case are derived and these are used to find a shifted log-normal approximation for the distribution of the decision variable. The accuracy of this method is verified through simulations.