# Superimposed Training Combined Approach for a Reduced Phase of Spectrum Sensing in Cognitive Radio
## 1 Introduction  
Cognitive radio (CR) is envisioned as one of the technologies that will alleviate the demand for more radio frequency (RF) spectrum required by future wireless communications systems and networks. In CR networks, the shift is towards the implementation of opportunistic spectrum access mechanisms, in which a frequency band can be accessed not only by its spectrum license holder, i.e., the primary user (PU) but also by secondary users (SUs) in a non-intrusive way [1, 2]. In other words, SUs are allowed to access a licensed frequency band only when the PUs' signals are idle either in time or geographic location [3]. Hence, the RF spectrum availability can be improved given that the underutilized frequencies can be exploited by SUs, creating the need for different approaches [4]. One of these is spectrum sensing, which must be performed by SUs to know the available frequency bands by detecting the PUs' transmissions. The most popular spectrum sensing algorithm is the energy detector, which does not need to know any information about the PUs' signals (i.e., blind spectrum sensing) and stands out for its computational simplicity and promptness. However, its detection performance rapidly deteriorates under noise power uncertainty [5] and in the low signal-to-noise ratio (SNR), where a high number of samples are required to attain a certain detection performance [6]. Alternatively, other blind spectrum sensing algorithms have been proposed to overcome the shortcoming of the energy detector, such as Maximum-to-Minimum Eigenvalue, Maximum Eigenvalue Detection, Covariance Absolute Value, and Covariance Frobenius Norm [7]. These algorithms are based on the statistical covariance or auto-correlation of the received signals, which increases the computational complexity since they require a high number of samples. Therefore, their performance drastically deteriorates if the number of received samples is small. In contrast, pilot (or training) symbols, commonly included in the PUs' transmitted signals for synchronization and channel estimation purposes, can be used to improve the detection of PUs if such patterns are known by the SUs. Indeed, previous investigations have demonstrated the significant improvement in terms of detection performance achieved by algorithms that combine training and data sequences to perform spectrum sensing, especially in the low SNR region [8; 9; 10; 11; 12]. For example, in [8], an enhanced detector for real-valued PUs' signals with embedded pilots (e.g., digital TV signals) is proposed for spectrum sensing over a lossless channel. This detector takes advantage of both the known pilot symbols and the energy of the received signal to improve the detection performance of SUs. In [9] a semi-blind spectrum sensing algorithm is designed by exploiting the knowledge of a training sequence that is time-multiplexed with binary phase shift keying (BPSK) modulated PU's signals. Interestingly, the detector consists of the linear combination of the matched filter output, the energy, and pseudo-energy of the received signal, thus enhancing the detection performance of SUs while keeping a relatively low computational complexity. Alternatively to time-multiplexed training sequences, in [12] it is considered that low-power training information is superimposed (i.e., added) to the PU's data prior transmission for its own convenience. Hence, a detector for superimposed training (ST)-based PUs' signals buried in noise is designed. The results show that the detection performance improves significantly even with very low-power training sequences. However, a lossless channel is considered in the design of the detector, which is not the case in a practical wireless scenario. Furthermore, in order to take advantage of the training sequence, a realistic model for spectrum sensing implies to consider other important aspects.