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In this paper, we introduce a low overhead scheme for the uplink channel allocation within a single cell of Cognitive Radio Wireless Mesh Network (CR-WMNs). The scheme does not rely on using a Common Control Channel (CCC). The mechanism is based on Physical layer Network Coding (PNC), in which two Secondary Users (SUs) are allowed to transmit synchronously over a randomly selected channel from a set of available channels, and without coordination for the purpose of requesting channels. The Mesh Router (MR) can detect up to 2 requests on the same channel due to the use of PNC, and replies back with a control packet which contains information about the assigned channel. We propose two PNC modulation schemes, PNC1 and PNC2, where initially SUs choose one of them to employ through the network operation. Decoding the received signals in PNC1 and PNC2 depend on their received energy and phases shifts, respectively. Simulation results show that the proposed mechanism significantly outperforms traditional schemes that rely on using one CCC, or do not use PNC in terms of channel allocation time.