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

Abstract

In this letter, we obtain a generalized expression for the optimal number of cognitive users (CUs) for the K-out-of-M rule that minimizes the Bayes risk at the fusion center (FC) over noisy control channels. We show many existing and new are special cases of the proposed solution. Numerical results are presented using energy detector. However, the expressions for optimal M obtained in this letter are applicable to any detector used in cooperative spectrum sensing.

Performance evaluation of hard‐decision and soft‐data aided cooperative spectrum sensing over Nakagami‐m fading channel

“…\forall k, \end{align}$$where $$\bar{P}_{m,k} = 1-\bar{P}_{d,k}$$ denotes miss‐detection probability of a CR and $$d_k$$ represents the k th CR hard(binary)‐decision. For a non‐cooperative CR user by considering error ( q ) in S‐channels, the modified expressions of $$P_f$$ and $$P_m$$ can be stated as [57], $$$$\begin{align} P_{fe} &= {P_{f}}(1 - q) + (1 - {P_{f}})q, \end{align}$$$$ $$$$\begin{align} P_{me} &= {P_{m}}(1 - q) + (1 - {P_{m}})q, \end{align}$$$$where $$P_{f}$$ and $$P_{m}$$ are taken from () and (), respectively. Inaccurate sensing channels lower the CR users performing specification reliability.…”

“…The expressions for total false alarm, detection, and miss‐detection probabilities with an error can be defined using the generalised k ‐out‐of‐ N rule [57]: $$$$\begin{align} Q_{fe} &= \sum _{k=n}^N \binom{N}{k} (P_{fe})^k (1-{P_{fe}})^{N-k}, \end{align}$$$$ $$$$\begin{align} Q_{de} &= \sum _{k=n}^N \binom{N}{k} (P_{de})^k (1-{P_{de}})^{N-k}, \end{align}$$$$ $$$$\begin{align} Q_{me} &= 1-\sum _{k=n}^N \binom{N}{k} (1-P_{me})^k(P_{me})^{N-k}. \end{align}$$$$Moreover, based on k values, the aforementioned generalized fusion rule yields different alternative fusion methods.…”

Comprehensive performance analysis of data‐fusion aided cooperative cognitive radio network over η − μ fading channel

“…In [16,17], the performance of different censoring schemes for HDCS-aided CSS is evaluated over individual fading environments. An optimisation of CSS via AER is discussed under the influence of noise and Rayleigh fading in [10,18,19]. The η − μ model is a generalised fading model developed recently to characterise the multipath fading if the PU signal received with small-scale variations and non-line-of-sight component [20].…”

“…P m, j = Pr {d j = 0 ℋ 1 }, P m, j = P m , ∀ j (18) where d j is the jth user binary decision. At FC, all the decisions are gathered and a generalised n-out-of-N rule (also called as a voting rule) is performed for obtaining a final decision about PU.…”

Spectrum monitoring in heterogeneous cognitive radio network: How to cooperate?

“…The hard‐combining rule comprises OR, AND, and M ‐out‐of‐ N ‐rules (MOON rule). In the MOON rule, the final decision (yes/no) is confirmed if M ‐out‐of‐ N CUs supports the same [22, 23]. The mathematical modelling of the distribution function of the M number of CUs’ confirmation (yes/no) is achieved by the binomial distribution if all the CUs decide the decision with same probability [24].…”