On cooperative spectrum sensing with improved energy detector over erroneous control channel

Abstract

In this paper, we present expressions for optimal number of secondary users (SUs) by minimizing the global error rate for a given fusion rule at the fusion center (FC). Expressions for optimal number of SUs are presented for AND, OR and MAJORITY fusion rules. We show that optimal number of SUs depends on effective probability of false alarm (P f e) and effective probability of miss detection (Pme) of a SU over erroneous control channel. Using improved energy detector as an example feasibility regions are derived for OR, AND and MAJORITY rules.

Optimal Number of Cognitive Users in $K$ -Out-of- $M$ Rule

“…• GOP-III: Substituting β 10 = β 01 = 2, β 00 = β 11 = 0, P 0 = P 1 = 0.5 and K = 1 in (6), we get the optimization problem for finding the optimal M that minimizes the total error rate for the OR rule [19], [20]. • GOP-IV: Substituting β 10 = β 01 = 2, β 00 = β 11 = 0, P 0 = P 1 = 0.5 and K = M in (6), we get the optimization problem for finding the optimal M that minimizes the total error rate for the AND rule [21]. • GOP-V: Substituting β 10 = β 01 = 2, β 00 = β 11 = 0, P 0 = P 1 = 0.5 and K = ⌈M/2⌉ in (6), we get the optimization problem for finding the optimal M that minimizes the total error rate of the MAJORITY rule [21].…”

“…• GOP-IV: Substituting β 10 = β 01 = 2, β 00 = β 11 = 0, P 0 = P 1 = 0.5 and K = M in (6), we get the optimization problem for finding the optimal M that minimizes the total error rate for the AND rule [21]. • GOP-V: Substituting β 10 = β 01 = 2, β 00 = β 11 = 0, P 0 = P 1 = 0.5 and K = ⌈M/2⌉ in (6), we get the optimization problem for finding the optimal M that minimizes the total error rate of the MAJORITY rule [21]. Note that GOP-II to GOP-V have been addressed in literature while GOP-I is a new optimization problem.…”

“…In [18], the optimal K and the optimal detection threshold of the multi-hop CR network are derived. Some studies on optimizing the M are as follows; the optimum value of M that minimizes the total error rate for (i) OR rule is obtained in [19], [20] (ii) for AND and (iii) MAJORITY rule in [21]. In [15], the optimal M to maximize the energy efficiency is obtained through an exhaustive search algorithm.…”