In this paper, we consider a data collection network (DCN) system where sensors take samples and transmit them to a Fusion Center (FC). Signal correlation is modeled with signal sparseness. The number of compressed measurements which allows correct signal recovery at FC is investigated. This is done by studying the probability of signal recovery failure. The joint typical decoder (JT decoder) similar to the one proposed by Akcakaya and Tarokh is used to avoid dependence on particular choice of recovery routines. The following interesting results have been obtained: 1) The detection failure probability linearly converges to zero as the number of sensors increases. 2) The number of compressed measurements per sensor (PSM) needed for successful recovery converges to sparsity as the number of sensors increases.