Blind signal detection is very important in various applications such as cognitive radio, spectrum surveillance, and eavesdropping. This gets trickier when one needs to deal with burst signals (as opposed to continuously transmitted signals) in non-cooperative environments. Here, existing methods for signal detection are studied and developed to use for burst detection. For the special case of downlink time division multiple access (TDMA) burst transmission, performances of these detection methods are improved by proposing a blind synchronisation algorithm which is applied to the output result of detection algorithms. The results of Monte–Carlo simulations demonstrate the performance of the proposed detection and synchronisation algorithms.