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Cognitive radio based smart grid communications Chapter 6 223

application of CR based SGs, the SMs behave as SUs and look for the available
frequency bands to convey measurement data to the data collector units. The CR
systems authorize the SG components to perceive the unoccupied frequency
bands and utilize these frequency bands without causing interference to PUs
[46]. The SS transaction can be explained depending on the signal detection the-
ory that can be simply expressed as follows [61].

η kðÞ : H 0
ykðÞ ¼ (6.1)
skðÞ + η kðÞ : H 1
where y(k) shows the sample to be investigated at each instant k, η(k) stands for
additive noise and s(k) denotes the transmitted signal. There are two possible
hypothesis which are noise-only (H 0 ) and signal-plus-noise (H 1 ). The
Eq. (6.1) can be generalized by taking into account fading and shadowing
effects of wireless channels as follows.

η kðÞ : H 0
ykðÞ ¼ (6.2)
h skðÞ + η kðÞ : H 1
where h denotes a complex random variable. In addition, all possible results of
the signal detection process can be listed below and can be illustrated as in
Fig. 6.9.

ð
Decide in favor of H 0 when H 0 is true H 0 j H 0 Þ
Decide in favor of H 1 when H 1 is true H 1 j H 1 Þ
ð
(6.3)
ð
Decide in favor of H 1 when H 0 is true H 1 j H 0 Þ
ð
Decide in favor of H 0 when H 1 is true H 0 j H 1 Þ
While the (H 1 jH 0 ) case is referred as false alarm, the (H 0 jH 1 ) case is called
as missed detection and the other cases are correct detection. The goal of a sig-
nal detector is to keep missed detection and false alarm detection rates as min-
imal as possible while trying to maximize correct detections rates.

FIG. 6.9 Hypothesis tests and possible results for spectrum sensing process.