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Adaptive Sub-Nyquist Spectrum Sensing for Ultra-Wideband Communication Systems †

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Adaptive Sub-Nyquist Spectrum Sensing for Ultra-Wideband Communication Systems † S S symmetry Article Adaptive Sub-Nyquist Spectrum Sensing for Ultra-Wideband Communication Systems † Yong Lu , Shaohe Lv and Xiaodong Wang * Science and Technology on Parallel and Distributed Processing Laboratory, National University of Defense Technology, Changsha 410073, China; [email protected] (Y.L.); [email protected] (S.L.) * Correspondence: [email protected] † This paper is an extended version of our paper published in 2014 IEEE 17th International Conference on Computational Science and Engineering (CSE), Chengdu, China, 19–21 December 2014. Received: 14 January 2019; Accepted: 3 March 2019; Published: 7 March 2019 Abstract: With the ever-increasing demand for high-speed wireless data transmission, ultra-wideband spectrum sensing is critical to support the cognitive communication over an ultra-wide frequency band for ultra-wideband communication systems. However, it is challenging for the analog-to-digital converter design to fulfill the Nyquist rate for an ultra-wideband frequency band. Therefore, we explore the spectrum sensing mechanism based on the sub-Nyquist sampling and conduct extensive experiments to investigate the influence of sampling rate, bandwidth resolution and the signal-to-noise ratio on the accuracy of sub-Nyquist spectrum sensing. Afterward, an adaptive policy is proposed to determine the optimal sampling rate, and bandwidth resolution when the spectrum occupation or the strength of the existing signals is changed. The performance of the policy is verified by simulations. Keywords: ultra-wideband spectrum sensing; energy detection; cognitive radio; sub-Nyquist sensing; Chinese remainder theorem 1. Introduction After decades of rapid development, wireless technologies have been intensively applied to almost every field from daily communications to mobile medical and battlefield communications. Whether you admit it or not, wireless communication technologies have become an essential part of our daily life. According to the global mobile data traffic forecast report [1] by Cisco, the expected overall mobile data traffic will be 77 exabytes per month by 2022, almost a 4-fold increase over that in 2018. As a result of the ever-increasing demand for higher speed wireless communication, more and more spectrum will be consumed in the near future. S In terms of the Shannon theorem: C = Wlog(1 + N ) (where C refers to communication capacity, S stands for signal, N refers to noise.), the communication capacity depends on the bandwidth and the signal-to-noise ratio (SNR). The required bandwidth increases in pace with the growth of wireless transmission rate. For example, from 802.11ac to 802.11ad, though the transmission rate increases from 1.35 Gbps to 7 Gbps, the corresponding bandwidth consumed also increases from 160 MHz to 2160 MHz. In 2013, Koenig achieved 100 Gbps wireless transmission rate with a 35 GHz band at the sub-THz frequency [2] using their customized communication system. The fact that advances in wireless technologies rely on the spectrum resource makes spectrum very scarce and precious. Despite the fact that we can use a wide range of wireless spectrum from 3 Hz to 3000 GHz, most of the spectrum has been already allocated to specific organization. However, in terms of current licensed users, the spectrum utilization remains low and a large mount of spectrum is still underutilized [3]. Symmetry 2019, 11, 342; doi:10.3390/sym11030342 www.mdpi.com/journal/symmetry Symmetry 2019, 11, 342 2 of 18 To handle this man-made spectrum scarcity [4], cognitive radio (CR) technology is proposed. In a cognitive network, when the licensed spectrum is underutilized by the licensed users (primary users, PUs), unlicensed users (secondary users, SUs) can utilize the licensed spectrum. With cognitive radio technologies, we can expand current transmission to unoccupied frequency bands to get a broader transmission bandwidth. In fact, Qualcomm and many other companies have already proposed such a solution to 4G LTE, which is called LTE-U (LTE in unlicensed spectrum) [5]. LTE-U can use the 4G LTE radio communication technology in unlicensed spectrum, for example, the 5 GHz band used by dual-band Wi-Fi equipment. LTE-U can not only greatly increase the LTE transmission rate but also highly improve the spectrum efficiency. With the purpose of finding more available spectrum resource, SUs take advantages of the spectrum sensing process to detect the occupation condition of a spectrum segment. As with cognitive networks, spectrum sensing is fundamental and crucial. Many algorithms, including matched filtering [6], energy detection [7], and cyclostationary feature detection [8], are proposed to deal with spectrum sensing. However, most of the researchers pay attention to the sensing of a narrowband frequency range. To satisfy the ever-increasing transmission demand, only when we search across an ultra-wideband spectrum range can we find out enough available spectrum for communication. As a result, traditional narrow band spectrum sensing technologies are incapable of sensing in an ultra-wideband communication system. The ability to perform ultra-wideband spectrum sensing is essential to future communication systems. However, there are many challenges to conduct the ultra-wideband spectrum sensing with the Nyquist sampling rate, i.e., the sampling rates are at least twice the bandwidth of the signal. In ultra-wideband communication systems, several GHz or an even larger spectrum is utilized to handle high transmission rate. For example, in Koenig’s [2] system, the related sampling rate should be 70 GHz or higher, which is arduous to carry out. On one hand, it is almost impossible to implement such a high speed analog-to-digital converter (ADC). On the other hand, even if we can produce such a high speed ADC, the fact that it is expensive and energy-consuming makes it unable to deploy on mobile devices. Can we just deal with the ultra-wideband spectrum sensing using undersampled data whose sampling rate is less than the Nyquist rate? In fact, as early as 20 years ago, Xia [9] proposed an algorithm to recover a high frequency from its undersampled data. During the past several years, many researchers devoted themselves to it. In 2014, Hassanieh et al. [10] propose a wideband spectrum sensing method using a sparse FFT algorithm with sub-Nyquist sampling rates. Though sub-Nyquist sensing technologies are promising, there are more challenges. Main Challenges. The main challenge to handle ultra-wideband spectrum sensing with sub-Nyquist sampling rates is the information loss resulting from the sub-Nyquist sampling, which makes us unable to recover the frequency information from the sampled data. That is, we cannot infer the frequency occupancy status from the undersampled data. There are two main reasons that cause information loss. Spectrum Leakage. We usually use a finite set of samples to compute the energy of the signal. However, to the discrete Fourier transformation (DFT) process, the sampled signals are treated as periodic in time. Consequently, the signals we use for DFT are actually: xN(n) = x(n)w(n), (1) where xN(n) is truncated from x(n). w(n) is a windowing function. Since only the finite N points are used, w(n) can be regarded as a rectangular window. We can evaluate the consequence of truncating by transforming xN(n) into the frequency domain: XN(w) = X(w) ∗ W(w). (2) Symmetry 2019, 11, 342 3 of 18 W(w) is a sinc function. Its sidelobes result in non-zero values in the vicinity frequencies of XN(w), thus making spectrum leakage happen. Aliasing Effect. When the sampling rate is lower than the Nyquist rate, i.e.: fs < 2W ( fs is the sampling rate and W is the bandwidth of the signal), aliasing happens. Just as Figure1 shows, high frequencies and lower frequencies overlap when aliasing occurs. Figure 1. Illustration of aliasing. Previous study on sub-Nyquist sensing, including compressed sensing and several other works, mainly focuses on designing different sampling modes, which allow frequencies to be recovered from the undersampled data. However, most of the systems are very complex and are strict with time synchronization. They try to reconstruct the whole signal and then detect the spectrum occupancy, thus leading to huge computation and energy-consuming. Actually, in terms of spectrum sensing, there is little need to recover the whole signal. We only need to reconstruct the frequencies we are interested in. Based on these considerations, this paper introduces SNSS (Sub-Nyquist Spectrum Sensing) to address this problem. SNSS makes full use of the Chinese Remainder Theorem (CRT) to recover all the frequency information that we are interested in from the undersampled data, thus making it possible to sense the ultra-wideband spectrum with relatively low sampling rates and computing resources. Unlike the previous algorithm, SNSS conducts energy detection directly on the aliased data and then reconstruct the frequency occupancy status. SNSS can simplify the system architecture and reduce the computation amount. Additionally, the spectrum usage in a modern wireless communication system is time-varying in practice, i.e., an idle spectrum segment becomes unavailable immediately when the PU is active. To provide efficient cognitive communication, spectrum sensing should be sensitive to the change of spectrum occupancy. Besides, the signal strength at a given frequency band is time-varying. For example, when the PU is mobile, the signal observed at a static position varies persistently. It is critical to keep tracking the PU’s behavior even when the signal from the PU is weak. However, the implementation of most sub-Nyquist spectrum sensing methods do not take into account the effects of network dynamics. In fact, when the behaviors of PUs change, they cannot adjust the runtime parameters to adapt to the varying conditions. Based on these observations, this paper proposes ASNSS (Adaptive Sub-Nyquist Spectrum Sensing) to deal with the dynamics. The contributions of this paper are as below.
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