# A Review of Research on Spectrum Sensing Based on Deep Learning
## 2 Spectrum-Sensing Methods  
### Spectrum-Sensing Modeling and Performance Metrics  
Depending on the idle or busy state of the primary user, signal detection at the secondary user can be modeled as the following binary hypothesis testing problem shown in Equation (1) below.  
\[\begin{cases}H_{0}:y(n)=w(n)\\ H_{1}:y(n)=hs(n)+w(n)\end{cases} \tag{1}\]  
where \(y(n)\) denotes the nth received sample, \(w(n)\) is an additive noise following a zero-mean cyclically symmetric complex Gaussian distribution, \(s(n)\) denotes the cognitive primary signal, and h denotes the channel gain, that is kept constant over the sensing period. In addition, \(H_{0}\) and \(H_{1}\) denote the two hypotheses of non-existence and presence, respectively, for the cognitive primary signal in a certain frequency band.  
There are several main performance metrics for evaluating a spectrum-sensing algorithm: probability of detection, probability of false alarm, and probability of missed detection, etc.  
1. Detection probability (\(P_{d}\)): This is the probability that a secondary user detects the presence of the primary user when the primary user is present, denoted by \(P_{d}=P_{r}\{H_{1}\mid H_{1}\}\).
2. False alarm probability (\(P_{f}\)): This is the probability that a secondary user incorrectly believes that the primary user exists when the primary user does not exist, denoted by \(f=P_{r}\{H_{1}\mid H_{0}\}\).
3. Missed detection probability (\(P_{m}\)): This is the probability that a secondary user mistakenly believes that the primary user does not exist when the primary user exists,  
Figure 2: Structural layout of the paper.  
which can be expressed as \(P_{m}=P_{r}\{H_{0}\mid H_{1}\}\). The sum of the probability of having a detection and the probability of missing a detection is 1, which can be expressed as \(P_{m}+P_{d}=1\).  
In cognitive radio spectrum-sensing experiments, the probability of detection (\(P_{d}\)) and the probability of false alarm (\(P_{f}\)) are widely adopted as fundamental performance metrics to assess the cognitive user's ability to detect the presence or absence of the primary signal. In general, trends in detection probability and false alarm probability are positively correlated. As the probability of false alarm increases, the probability of detection also increases. Additionally, when discussing leakage detection probability in conjunction, it is evident from \(P_{m}+P_{d}=1\) that higher false alarm probabilities correspond to higher detection probabilities while leading to lower leakage detection probabilities.  
To determine the effectiveness of a spectrum-sensing algorithm, the ideal scenario is to achieve both a very low false alarm probability and a high detection probability, indicating optimal performance. However, in practical terms, it is necessary to assess whether the detection probability is sufficiently high under the assumption of a constant false alarm probability.  
Spectrum sensing can be categorized into two types: single-node spectrum sensing and cooperative spectrum sensing. These correspond to independent sensing by a single user and sensing by multiple sub-users, respectively [24]. In the subsequent sections, we will focus on highlighting the single-node spectrum-sensing approaches and provide an overview of various cooperative spectrum-sensing techniques.