Fast and Accurate Approximations for the Analysis of Energy Detection in Nakagami-m Channels

Abstract

Original citationHorgan, D.; Murphy C. C. (2013) Abstract-Previous research has identified several exact methods for the evaluation of the probability of detection for energy detectors operating on Nakagami-m faded channels. However, these methods rely on discrete summations of complicated functions, and so can take a prohibitively long time to evaluate. In this paper, three approximations for the probability of detection in Nakagami-m faded channels, having distinct regions of applicability, are derived. All have closed forms, and enable the fast and accurate computation of key performance metrics.

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“…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.…”

“…13) is not consistent with increasing m. For example, the result at the value of m = 3 is worse than the result at the value of m = 1, 2 as can be seen in Figure 5. We note also that the probability of misdetection approaches zero at the point of (1 − P fa ) for the expressions reported by [16,17]. Figure 6 shows the simulation results for all expressions when evaluated at a high value ofγ .…”

“…The derived expressions are evaluated and compared with the numerical integration of (18) and with the expressions reported by [14][15][16][17] In the odd case, the simulation is compared to the recursive formula (13,16) in AWGC, and in the even case, the simulation is compared to (10) in AWGC and to ( [14], Eq. 14).…”

“…13) has some discrepancies when the false alarm probability or the value of m increases. Moreover, the result of ( [17], Eq. 13) is not consistent with increasing m. For example, the result at the value of m = 3 is worse than the result at the value of m = 1, 2 as can be seen in Figure 5.…”

“…As the probability of false alarm increases, however, a discrepancy arises between ([16], Eq. 13) and ( [17], Eq. 13) when compared to the new expressions and/or the work of [14,15].…”