In Chapter 9, we discussed how wideband spectrum scanning can be achieved in a cognitive radio: The spectrum range of interest to the radio is first segmented into a set of Nb subbands, each of which may still be wide enough to contain several different channels. At a given time instant n, a cognitive radio can sense only one of these subbands. Hence, if the subband i, for 1 ≤ i ≤ Nb, is sensed at time n, the radio’s spectrum observation is a signal Y[n] that is a noise-corrupted version of the superposition of signals within subband i. The radio needs to detect signals contained in this sensing observation Y[n].

If the radio scans a single channel, then detecting whether there is any signal activity in the channel based on a sensed signal is straightforward: The particular channel is isolated by means of a bandpass filter (BPF), so the sensed signal Y[n] only contains frequencies within the span of this channel. Depending on the type of a priori knowledge available regarding the signal in this particular channel, one of the detection procedures discussed in Chapter 4 can, for instance, be used to make a detection decision. In particular, if the signal was assumed to be simply a Gaussian-distributed random signal with a certain average power and the only contamination is an additive Gaussian noise, then the optimal detection will simply be to compute the received signal power and compare it to a threshold. ...

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