1 Introduction
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We provide a highly accurate recursive algorithm to compute the probability of detection for odd degrees of freedom. It should be noted that the mathematical derivation shows the steps of the algorithm when evaluating the detection probability in case of odd degrees of freedom, i.e., it is an algorithm rather than a mathematical derivation. An example of the algorithm importance is the Marcum function in Matlab which accepts only integer values in its third argument. Therefore, when the number of degrees of freedom is odd, the third argument is no longer accepted and the Marcum function cannot be used to evaluate the detection probability in this case. However, our algorithm solves this problem.
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We derive a closed-form expression over a Nakagami-m fading channel. Here, we use closed form in the sense that no summation and no integration are required. The accuracy of the closed form is very close to the previously reported expressions in which summation and integration are used to get highly accurate results. Our new expressions show how the ratio of the Nakagami parameter m and the average signal-to-noise ratio which affects the receiver operation characteristics (ROC) curves.
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We compare the derived expressions to the reported expressions in [14, 15] in which summation and integration are used. We also compare our derived expressions to other recently reported expressions, e.g., [16, 17], and we show that our new derived expressions can be used with no limitations. Moreover, the derived expressions are more accurate than the recently reported ones with less or almost the same computational complexity.