The performance of our signal strength estimation procedure is displayed by the pie charts and the histograms. The horizontal approach is showed in Figure 6.4 and 6.5 and the vertical approach is showed in Figure 6.6 and 6.7.
In this experiment, consider the channels are under the sub-band oriented case in which each occupied sub-band has an individual and fixed SNR randomly chosen from 0 ∼ 30 (dB). We separate the whole 0 ∼ 30 (dB) into several small non-overlapping SNR regions with each one of them 5 (dB) in width. After applying the rules (5.9) to the final decision patterns, the fusion center will then identify a SNR region for each sub-band. If the true SNR lies in the estimation region, the sub-band is called perfect estimation. The notation +1 Gap means that the true SNR is underestimated by one gap of the SNR region. Both horizontal and vertical approaches are tested for DFE and EFE respectively. The statistics are collected by testing 5 ∗ 105 sub-bands.
−1 Gap
Histogram of the estimation error (Decision Feedback)
Error Decisions
(a) (b)
Figure 6.4: The pie chart and the histogram of the Decision Feedback Estimation (DFE) under 5 × 105 sub-bands using horizontal approach.
−1 Gap
Histogram of the estimation error (Energy Feedback)
Error Decisions
(a) (b)
Figure 6.5: The pie chart and the histogram of the Energy Feedback Estimation (EFE) under 5 × 105 sub-bands using horizontal approach.
−1 Gap
3.5x 105Histogram of the estimation error (Decision Feedback)
Gap
Error Decisions
(a) (b)
Figure 6.6: The pie chart and the histogram of the Decision Feedback Estimation (DFE) under 5 × 105 sub-bands using vertical approach.
−1 Gap
Histogram of the estimation error (Energy Feedback)
Error Decisions
(a) (b)
Figure 6.7: The pie chart and the histogram of the Energy Feedback Estimation (EFE) under 5 × 105 sub-bands using vertical approach.
First, the EFE shows a higher accuracy in the signal strength estimation for both horizontal and vertical approaches. This is the advantage of using the non-quantized energy information but it takes large transmission overhead for reporting. Although the DFE approaches have lower estimation accuracy, they can save the reporting bits while still achieving the accuracy around 85% combined the perfect with +1 Gap. The best estimation performance is the EFE of vertical approach with 72% being perfect estimates and 23% one scale higher. Besides, it also achieves a lowest 3% error rate.
Noted that here the notation error in the pie charts means the proportion of the error decision sub-bands, i.e. the total number of false alarm and missing sub-bands. As you can see in Figure 6.4 ∼ 6.7, all of the four estimation procedures can achieve a low enough error rate with 6% and 3% respectively. Compare the horizontal approach with the vertical approach, it can be found that the vertical approach has better accuracy.
Since the vertical approach applies the BH procedure to test the different levels of hypotheses inside a single sub-band, it can decide the signal strength independently without affecting by other sub-bands. However, the horizontal approach is used by applying the BH procedure to the different sub-bands for the same level of hypotheses.
The conditions of other sub-bands may affect the decision results.
The histograms in Figure 6.4 ∼ 6.7 show the distributions of the estimation error.
It can be found that the true signal strength is almost underestimate with a big part of +1 Gap. This characteristic can become the superiority for applying the SNR switching rule in the twice BH procedure because we have great confidence once the estimation strength exceeds the predefined threshold SNR. The characteristic may result from the conservative nature of controlling FSR. In Figure 4.2(a), it shows that controlling the FSR can leads to a low false alarm ratio at the same time ,and the events of false alarm in signal strength estimation here means that the estimation regions are higher than the true signal strength regions, i.e. the left side of the histograms. Since the four histograms all achieve the overestimation rate less than 1%, the proposed horizontal and vertical
approaches can still control the FSR.
Chapter 7 Conclusions
The decision fusion method was presented for cooperative spectrum sensing of wide-band cognitive radio systems using multiple hypotheses testing. Both FSR and FIR were defined based on the false discovery rate criterion and were shown to be controlled under a desired level by the BH procedure. Simulations showed that the decision fusion method can achieve a performance comparable to the energy fusion method while saving the overhead of reporting information. Moreover, the nominal SNR mode for a realistic operation was discussed. The results showed that the system seems to operate under a better balance between the missing and false alarm ratios by trading off some perfor-mance in the low SNR region. After introducing the SNR switching rule, the combined FSR and FIR approach performed the best and had both satisfactory false alarm and missing ratios. For estimating the signal strength, both EFE and DFE can achieve a low enough error rate of the availability of the sub-bands while the EFE showed a high accu-racy to the strength estimation. Although the DFE had worse accuaccu-racy, the true signal strength was almost underestimated. Compared to other spectrum sensing algorithms, our proposed methods have the advantages of wideband sensing, controllable error rates, lower complexities, and the ability for signal strength estimation. The overall sensing time and the average reporting bits can be further studied for future works.
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