Expectation Maximization Aided Modified Weighted Sequential Energy Detector for Distributed Cooperative Spectrum Sensing

TL;DR

A modified WSED (mWSED) is proposed that uses the primary user states information over the window to aggregate only the highly correlated ED samples in its test statistic and its performance improves by increasing the average number of neighbors per SU in the network, and by increasing the SNR or the number of samples per energy statistic.

Abstract

Energy detector (ED) is a popular choice for distributed cooperative spectrum sensing because it does not need to be cognizant of the primary user (PU) signal characteristics. However, the conventional ED-based sensing usually requires large number of observed samples per energy statistic, particularly at low signal-to-noise ratios (SNRs), for improved detection capability. This is due to the fact that it uses the energy only from the present sensing interval for the PU detection. Previous studies have shown that even with fewer observed samples per energy statistics, improved detection capabilities can be achieved by aggregating both present and past ED samples in a test statistic. Thus, a weighted sequential energy detector (WSED) has been proposed, but it is based on aggregating all the collected ED samples over an observation window. For a highly dynamic PU over the consecutive sensing intervals, that involves also combining the outdated samples in the test statistic that do not correspond to the present state of the PU. In this paper, we propose a modified WSED (mWSED) that uses the primary user states information over the window to aggregate only the highly correlated ED samples in its test statistic. In practice, since the PU states are a priori unknown, we also develop a joint expectation-maximization and Viterbi (EM-Viterbi) algorithm based scheme to iteratively estimate the states by using the ED samples collected over the window. The estimated states are then used in mWSED to compute its test statistics, and the algorithm is referred to here as the EM-mWSED algorithm. Simulation results show that EM-mWSED outperforms other schemes and its performance improves by increasing the average number of neighbors per SU in the network, and by increasing the SNR or the number of samples per energy statistic.

Figures (10)

• Figure 1: A graphical representation of the two-state Markov chain model describing the change in primary user activity over the sensing intervals. The parameters $\alpha$ and $\beta$ represent the transition probabilities of switching between the two states in the Markov model.
• Figure 2: Energy statistics of SUs from a single trial vs. DCSS iterations for $(a)$$N=10$, $c=0.2$, $(b)$$N=10$, $c=0.5$, and $(c)$$N=60$, $c=0.2$, when SNR $=-3$ dB, number of samples per energy statistic $L=12$, and the PU follows the two-state Markov model with $\alpha=\beta=0.1$.
• Figure 3: Probability density functions (pdfs) of mWSED test statistics $T_i$ for SU $i$ under $H_0$ and $H_1$ with uniformly distributed non-zero weights when the number of averaged ED samples are $(a)$$C=4$, $(b)$$C=20$, and $(c)$$C=90$, with SNR $=-3$ dB and $L=12$.
• Figure 4: A notional view of the correspondence between the primary user states $\left(\{s_{i,d}\in\{0,1\}, \forall d=1,2,\ldots,D\}\right)$ and the ED samples $\left(\{x_{i,d}, \forall d=1,2,\ldots,D\}\right)$ collected by the SU $i$ in an observation window of length $D$.
• Figure 5: Receiver operating characteristic curves for mWSED, WSED, and conventional ED when $N=10$, $c=0.2$, $L=12$, SNR$=-3$ dB, and PU follows a two-state Markov chain with varying $\alpha$ and $\beta$.