Sensor networks have been shown to be useful in diverse applications. One of the important applications is the collaborative detection based on multiple sensors to increase the detection performance. To exploit the spectrum vacancies in cognitive radios, we consider the collaborative spectrum sensing by sensor networks in the likelihood ratio test (LRT) frameworks. In the LRT, the sensors make individual decisions. These individual decisions are then transmitted to the fusion center to make the final decision, which provides better detection accuracy than the individual sensor decisions. We provide the lowered-bounded probability of detection (LBPD) criterion as an alternative criterion to the conventional Neyman-Pearson (NP) criterion. In the LBPD criterion, the detector pursues the minimization of the probability of false alarm while maintaining the probability of detection above the pre-defined value. In cognitive radios, the LBPD criterion limits the probabilities of channel conflicts to the primary users. Under the NP and LBPD criteria, we
provide explicit algorithms to solve the LRT fusion rules, the probability of false alarm, and the probability of detection
for the fusion center. The fusion rules generated by the algorithms are optimal under the specified criteria. In the spectrum sensing, the fading channels influence the detection accuracies. We investigate the single-sensor detection and collaborative detections of multiple sensors under various fading channels, and derive testing statistics of the LRT with known fading statistics.