This process can take minutes to hours depending on

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sweeps of a single bandwidth. This process can take minutes to hours depending on the frequency resolution of the sweep. Figure 1 shows the PSD of a pulse shaped QPSK signal collected by the spectrum analyzer. 1.3 Primary Signal Detection In this laboratory, we discuss the detection of wireless signals, which constitutes the basic step in spectrum opportunity detection. 2
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Figure 1: Power Spectral Density of a Pulse Shaped QPSK Signal. The spectrum sensor essentially performs a binary hypothesis test on whether or not there are primary signals in a particular channel 1 . The channel is idle under the null hypothesis and busy under the alternate: H 0 (idle) vs . H 1 (busy) . (3) Under the idle scenario, the received signal is essentially the ambient noise in the RF environment, and under the busy scenario, the received signal would consist of the PU signal and the ambient noise; thus: H 0 : y ( k ) = w ( k ) H 1 : y ( k ) = s ( k ) + w ( k ) for k = 1 , .., n , where n is the number of received samples, w ( k ) represents ambient noise, and s ( k ) represents the PU signal. Intuitively, the received signal will have more energy when the channel is busy than when it is idle, thus forming the underlying concept in the energy detector which we discuss in detail in Section 1.3.1. When aspects of the signal structure are known one can exploit the structure; a special case leads to the cyclostationary detector discussed in Section 1.3.2. Regardless of the precise signal model or detector used, sensing errors are inevitable due to additive noise, limited observations, and the inherent randomness of the observed data. False alarms (Type I errors) occur if an idle channel is detected as busy. On the other hand, missed detections (Type II errors) occur when a busy channel is detected as idle. Consequently, a false alarm may lead to a potentially wasted opportunity for the SU to transmit while a missed detection could potentially lead to a collision with the PU, leading to wasted transmissions for both PU and SU. 1 Here we use channel in a general sense: it represents a signal dimension (time, frequency, and code, etc.) that can be allocated to a particular user. 3
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The performance of a detector is characterized by two parameters, the probability of missed detection ( P MD ) and the probability of false alarm ( P F A ) which are defined as: ǫ = P F A = Prob { Decide H 1 |H 0 } ; δ = P MD = Prob { Decide H 0 |H 1 } . A typical receiver operating characteristic (ROC), which is a plot of 1 - δ , the probability of detection ( P D ), versus P F A , is shown in Figure 2. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Probability of False Alarm ε Probability of Detection 1 - δ δ ε Figure 2: Typical receiver operating characteristic. To motivate the practical aspects of spectrum sensing in the latest wireless communication stan- dards, the proposed sensing requirements of the IEEE 802.22 Wireless Regional Area Network (WRAN) standard are summarized in Table 1 [11, 5].
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