In cognitive radio networks, in order to avoid interference form secondary users to the primary license holders of the spectrum, reliable spectrum sensing is necessary. In scenarios where the noise samples are correlated, the spectrum sensing methods optimized considering impairment by independent noise samples will not provide optimum performances. To address this issue, a locally optimum detection method for random signals under a weakly correlated noise model over fading channels is proposed. The probabilities of false alarm and detection of the proposed detector in the low signal to noise ratio regime are analyzed. The average probabilities are calculated over different channel gains. Numerical and simulation results demonstrate the superiority of the proposed method over the known energy detection method with comparable complexities. Furthermore, we consider the scenario where the estimated correlation is different from the real correlation and investigate the effect of this correlation mismatch on the probabilities of false alarm and detection of the proposed method.

A novel soft-decision decoding method motivated by the idea of sphere decoding is proposed for Reed–Solomon (RS) codes. Sphere decoding reduces the complexity of finding the closest lattice point to a given point by confining the search to points that fall inside a sphere around the given point. In the authors’ proposed scheme, in order to reduce the search even further, the search effort is concentrated on the most probable lattice points. To do so, they first find the most reliable positions of the codeword. Then a sphere decoder is used to select symbol values for these positions. The proposed sphere decoder chooses the acceptable symbol values for each position from a pre-determined ordered set of most probable transmitted symbols. Each time the most reliable code symbols are selected, they are used to find the rest of RS symbols. If the resulting codeword is within the search radius, it is saved as a candidate transmitted codeword. The ordering used in the algorithm helps finding the candidate codewords quickly resulting in an efficient decoding method. Simulation results indicate considerable coding gains over hard decision decoding with a feasible complexity. The performance is also superior to the soft decision Koetter–Vardy method.

Two new iterative soft decision decoding methods for Reed-Solomon (RS) codes are proposed. These methods are based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. In the first proposed method, we take advantage of the cyclic structure of RS codes. Based on this property, we can apply the belief propagation algorithm on any cyclically shifted version of the received symbols with the same binary parity check matrix. For each shifted version of received symbols, the distribution of reliability values will change and deterministic errors can be avoided. This method results in considerable performance improvement of RS codes compared to hard decision decoding. The performance is also superior to some popular soft decision decoding methods. The second method is based on information correction in BP decoding. It means that we determine least reliable bits and by changing their channel information, the convergence of the decoder is improved. Compared to the first method, this method needs less BP iterations (less complexity) but its performance is not as good.

A new iterative soft decision decoding method for Reed-Solomon (RS) codes is proposed. This method is based on bit level belief propagation (BP) decoding. In order to make BP decoding effective for RS codes, we use an extended binary parity check matrix with a lower density and reduced number of 4-cycles compared to the original binary parity check matrix of the code. In our proposed method, we take advantage of the cyclic structure of RS codes. Based on this property, we can apply the belief propagation algorithm on any cyclically shifted version of the received symbols with the same binary parity check matrix. For each shifted version of received symbols, the geometry of the factor graph will change and deterministic errors can be avoided. Our method results in considerable performance improvement of RS codes compared to hard decision decoding. The performance is also superior to some popular soft decision decoding methods.

A new soft decision decoding method for Reed-Solomon (RS) codes is proposed. This method uses sphere decoding in an effort to reduce the decoding complexity. With sphere decoding, instead of considering all of the possible transmitted codewords to determine the most probable one, we only consider the codewords whose distances from the received signal are smaller than a specific search radius. This results in a considerable reduction in the complexity. For an (N,K) RS code, we consider a set of K most reliable and independent positions of a codeword and for each of these positions, an ordered list of most probable transmitted symbols in decreasing order of probability is determined. We start from the hard-decision decoded codeword and we try to find more probable codewords. The search is started by selecting a tentative solution consisting of the K most reliable code symbols whose distance from the corresponding symbols in the received vector is less than the search radius. The acceptable values for each of these K code symbols are determined based of the ordered set of most probable transmitted symbols which means that for each code symbol, we start from the most probable one. We re-encode these K code symbols. If the resulting codeword is within the search radius, we add it to the list of the candidate transmitted codewords. The ordering that was discussed earlier will help finding the candidate codewords quickly. Our method results in considerable improvement of the performance of RS codes compared to hard decision decoding with a moderate increase in complexity.