# On Transform Domain Communication Systems under Spectrum Sensing Mismatch: A Deterministic Analysis
## 1 Introduction  
The fifth generation (5G) of wireless systems is designed to fuel new communication paradigms, such as the Internet of Things (IoT) and mobile Internet services, where numerous sensors and devices are interconnected and demanded for improvements of several issues. The rapid development of IoT has triggereda 1000-fold data traffic increase by 2020 for 5G and related network scenarios [1]. However, it introduces a large amount of unexpected electromagnetic interference that may cause the failure of the transmission. Therefore, investigating higher spectral efficiency technology becomes one of the key breakthroughs. Meanwhile, due to the fast growth of IoT, 5G also needs to support massive access among users and/or devices [2; 3]. To achieve higher transmission speed and more reliable QoS (quality of services), future wireless communication systems require more smart waveforms to tackle frequency band scarcity and various interferences. By introducing the concept of cognitive radio (CR) [4; 5; 6; 7], wireless networks could obtain better frequency utilization and transmission, leading to more robust transmission. To accommodate the rapidly increasing demand for wireless broadband communications in smart grid networks, research efforts are currently ongoing to enable the networks to utilize the TV spectrum according tothe cognitive radio paradigm [8; 9]. In recent years, regulatory bodies, such as the FCC, have approved the dynamic access of unlicensed sensor networks, referred to in the following as secondary sensor networks to the TV white space (TVWS) spectrum [10; 11; 12]. The existing regulations circumvent the need for sensing algorithms for establishing the availability of free TVWS spectrum [13; 14; 15]. In [16], the authors presented a systematic approach to exploit TVWS for device-to-device communications with the aid of the existing cellular infrastructure. In TVWS, the unlicensed users are required to periodically access a database so as to acquire information on the spectrum usage of the licensed users. The authors in [17] developed a stochastic analytical framework that allows us to account for the PU activity dynamics, the quality dynamics among the different channels, and the overhead induced by the database access. In [18], the TVWS authors studied the throughput achievable by an unlicensed sensor network over the TV white space spectrum in the presence of coexisting interference. Detecting the signals of primary users in the wideband spectrum is a key issue for cognitive radio networks [19]. In [20], the authors proposed a novel signal detection algorithm based on the Riemannian distance and Riemannian mean, which is different from the traditional eigenvalue-based detector derived with the generalized likelihood ratio criterion. Following a general analytic framework, named spectrally-modulated and spectrally-encoded [21; 22; 23], various multicarrier waveforms can be generated based on the need of CR user, e.g., orthogonal frequency division multiplex (OFDM) and multicarrier code division multiple access (MC-CDMA) [24]. As another type of overlay CR application, the transform domain communication system (TDCS) was proposed for supporting reliable communications with low spectral density through spectrum bin nulling and frequency domain spreading [25]. Hence, TDCS can be viewed as a proactive anti-jammer transmission scheme when some spectrum bands are disturbed by intentional jammers [26]. The foundations of TDCS are established by the Air Force Institute of Technology [27; 28], which is able to dynamically update systematic parameters using spectrum sensing and spectrum nulling. To simplify the implementation complexity of TDCS, the authors in [29] proposed an efficient OFDM-based TDCS transceiver. Recently, by analyzing the advantages of sequence investigation and a two-dimension spreading method, a series of advances have been presented to improve TDCS for practical utilizations [7; 8], i.e., peak to average power ratio problems, ideal multi-user networks without interference, etc.