In ambient backscatter communication (AmBC) systems, passive tags connect to a reader by reflecting an ambient radio frequency (RF) signal. However, the reader may not know the channel states and RF source parameters and can experience interference. The traditional energy detector (TED) appears to be an ideal solution. However, it performs poorly under these conditions. To address this, we propose two new detectors: (1) A joint correlation-energy detector (JCED) based on the first-order correlation of the received samples and (2) An improved energy detector (IED) based on the p-th norm of the received signal vector. We compare the performance of the IED and TED under generalized noise modeled using the McLeish distribution and derive a general analytical formula for the area under the receiver operating characteristic (ROC) curves. Based on our results, both detectors outperform TED. For example, the probability of detection with a false alarm rate of 1% for JCED and IED is 14% and 5% higher, respectively, compared to TED. These gains are even higher using the direct interference cancellation (DIC) technique, with increases of 16% and 7%, respectively. Overall, our proposed detectors offer better performance than the TED, making them useful tools for improving AmBC system performance.