Joint Subchannel Pairing and Power Control for Cognitive Radio Networks with Amplify-and-Forward Relaying

Algorithm 1

Hungarian method [27] for subchannel pairing.

(1) Let matrix 𝐔=[−𝑈_𝑛,𝑚]_𝑁×𝑁, and the following operations are for 𝐔.

(2) Subtract the smallest entry in each row from all the entries of its row.

(3) Subtract the smallest entry in each column from all the entries of its column.

(4) Draw lines through appropriate rows and columns so that all the zero entries of matrix are

   covered and the minimum number of such lines is used.

(5) Test for optimality: (i) If the minimum number of covering lines is 𝑁, an optimal assignment

   of zeros is possible and this algorithm finishes. (ii) If the minimum number of covering lines

   is less than 𝑁, an optimal assignment of zeros is not yet possible, and then go to Step  6.

(6) Determine the smallest entry not covered by any line. Subtract this entry from each uncovered

   row, and then add it to each covered column. Return to Step  3.