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Similarly, from Figure 7, we can see that the proposed CSS scheme provides higher reporting time savings than the conventional cluster scheme.

The proposed CSS scheme outperforms the cluster and global CV rule-based conventional cluster CSS scheme when the cluster size is small, i.e., n0 < 8.

Compared with simulations on a conventional cluster of Central Processing Units (CPUs), GPU-based computations allow us to use a significant (16 times) larger number of mesh points within similar computation times.

As illustrated in Equation 26 and in the simulation result of Figure 6, it can be concluded that the energy efficiency of the proposed scheme is the upper bound of the conventional cluster scheme for all cases of k.

When the cluster size is large, i.e., n0 > 8, the sensing error probability of the proposed method is slightly higher than that of the conventional cluster scheme, which utilizes a CV rule at both cluster headers and FC.

The error probabilities of the global CV rule-based conventional direct reporting scheme, the cluster and global CV rule-based conventional cluster reporting scheme, and the proposed CSS scheme are then observed according to different values of cluster size.

Figure 7 Reporting time saving of the proposed and the conventional cluster-based CSS schemes.

Figure 6 Energy consumption efficiency of the proposed and conventional cluster-based CSS schemes.

On the one hand, in the conventional cluster-tree topology, we know that | V ℓ V ℓ, p | = | V ℓ | - | V ℓ, p | < | V ℓ | since a cluster-child can only do ranging with its parent node.

We also assume that each cluster utilizes a separate reporting channel to transmit the sensing result from local nodes to the cluster header in the case of a conventional cluster-based CSS scheme, and the guard interval between time slots is ignored.

Note that the proposed clustering algorithm with t max=70 still notably outperforms the conventional clustering algorithm.