Detection of jointly active primary systems

Recent studies in cognitive radios consider the detection of multiple bands for a better utilization of the spectrum. If the cognitive radio (CR) is an ultra wideband (UWB) or a wideband system, then the CR should ensure all the coexisting primary systems in these bands are detected before the CR can start data transmission. In this work, we study the primary system detection performance of a wideband CR assuming that there are multiple coexisting primary systems and that these primary systems may be jointly active. Accordingly, we consider the implementation of (i) a maximum a posteriori (MAP) based detection (i.e., joint detection) that takes into account the statistics of simultaneously operating systems in independent bands, and (ii) a Neyman-Pearson (NP) test based detection that optimizes the threshold values independently in each band (i.e., independent detection). In addition to obtaining the probabilities of false alarm and detection expressions for these two methods, we use the threshold values obtained from joint detection so as to achieve the optimum NP test based independent detection results with a simpler implementation. We also provide the performance comparison of joint and independent detection for various practical scenarios when there are multiple active primary systems.