The maximum a posterior (MAP) decoding scheme is presented here for cooperative communication networks that adopt the parity forwarding as a cooperation protocol. The MAP decoder is optimal in the sense that it minimises the error probability. The authors consider a wireless network that is composed of two sources: two relays and a single destination. A closed-form expression is derived for upper bound on the bit error probability. The complexity of derivation comes from the fact that although the source generates data with equal probability, the data received at the destination does not have the same a priori probability. That is because of the error that occurs in the source-to-relay link. Therefore, the MAP decoding rule cannot be simplified to the maximum likelihood decoding rule. The results show that the analytical upper bound is very tight and almost coincides with the exact error probability obtained from simulations at higher values of the signal-to-noise ratio. Accordingly, the closed-form expression of the upper bound can be used to fully study and understand the diversity performance of the system.

Spectrum sensing is the most important component in the cognitive radio (CR) technology. Spectrum sensing has considerable technical challenges, especially in wideband systems where higher sampling rates are required which increases the complexity and the power consumption of the hardware circuits. Compressive sensing (CS) is successfully deployed to solve this problem. Although CS solves the higher sampling rate problem, it does not reduce complexity to a large extent. Spectrum sensing via CS technique is performed in three steps: sensing compressed measurements, reconstructing the Nyquist rate signal, and performing spectrum sensing on the reconstructed signal. Compressed detectors perform spectrum sensing from the compressed measurements skipping the reconstruction step which is the most complex step in CS. In this paper, we propose a novel compressed detector using energy detection technique on compressed measurements sensed by the discrete cosine transform (DCT) matrix. The proposed algorithm not only reduces the computational complexity but also provides a better performance than the traditional energy detector and the traditional compressed detector in terms of the receiver operating characteristics. We also derive closed form expressions for the false alarm and detection probabilities. Numerical results show that the analytical expressions coincide with the exact probabilities obtained from simulations.

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