Chapter 1 Introduction Abstract As the introductory content of this thesis, this chapter ?rstly introduces the development process and key technologies of broadband digital communications systems and the main noise and interference in it, and describes the characteristics and detrimental effects of NBI and IN, raising the main research topic, i.e., NBI and IN in broadband communications systems; Secondly, a comprehensive survey on the current research on the technologies of NBI and IN mitigation is given, with the major problems and challenges that the current related researches are faced with; Later the key problems to be solved and the research aims are given, based on which the research routine, the main research contents, the technological roadmap, the research outcomes and contributions of this thesis are described; Finally, a brief introduction to the structure of the thesis contents is presented. 1.1 Research Background and Aims Since the originator of information theory, Sir Claude E. Shannon, proposed informa- tion theory to lay the foundation of communications technologies in 1948 [1], modern communications theory, techniques and systems have gone through plenty of devel- opment and evolution. Through technological evolution and application practice, the communications system developed from the earliest analog communications system, to the digital communications system gradually. Since the 1990s, digital communi- cations have been developing through a long-term process of over 30 years, with the bandwidth growing, the rate increasing, and tremendous changes have taken place till now. Broadband digital communications have a solid basis of technologies, covering most of the populations all over the world. The research and industrial applications on broadband digital communications technologies are developing very fast, push- ing the modern communications technologies towards the prospects and aims of high-speed, low-latency, ultra-reliability, wide-coverage, ubiquitous-connection. ﹛With the development of modern society, many strict requirements of the sta- bility, robustness and reliability for broadband digital communications systems are challenging the people*s ever-increasing communications needs and the demands 2 1 Introduction of big data as well as ※everything interconnection§ for Internet of Things (IoT). However, the noise and interference in communications systems are always a severe bottleneck that limits the communications system performance. Especially for the special noise and interference widely existing in broadband communications sys- tems, such as narrowband interference (NBI) and impulsive noise (IN), due to the characteristics different from those of Gaussian white noise, such as complication, randomness, sparsity, and intensiveness, the state-of-the-art methods can only ※pas- sively§ combat against them, resulting in lots of drawbacks. The unfavorable impacts cannot be effectively mitigated, and it is even harder to completely eliminate them accurately, leading to inevitable performance loss to broadband digital communica- tions systems. In order to ensure the effective and correct transmission of broadband communications systems, to improve the network throughput and quality of ser- vice (QoS), and to meet the requirements of the next generation communications technologies including ultra-reliability and high-speed, this dif?culty limiting the communications system performance should be overcome. Hence, it is in desperate need to study key technologies on NBI and IN mitigation and cancellation. ﹛In this background, this thesis cuts in the research from the scienti?c problems of how to mitigate the impacts of NBI on synchronization, how to improve the time- frequency interleaving performance of communications systems in the presence of NBI and IN, and how to accurately recover and eliminate NBI and IN. The thesis fol- lows the investigation routine of ※scrambling for mitigation, diversity for avoidance, recovery for cancellation§, and a series of speci?c researches on the key technologies are carried out. The thesis proposes the frame design method to effectively mitigate NBI, the optimal time-frequency joint interleaving scheme for maximizing time- frequency diversities, and accurate recovery and elimination algorithms based on the theory of sparse recovery. From multiple aspects, the capability of mitigating and eliminating NBI and IN for the next generation broadband communications systems is fully improved. Through the research in this thesis, it is expected to provide the- oretical basis and technological support for the further research of the researchers in this area, and meanwhile, to endeavor to boost the standardization and industrial applications of the research technologies in this thesis. ﹛As the introductory content of this thesis, this chapter ?rstly introduces the devel- opment process and key technologies of broadband digital communications systems and the main noise and interference in it, and describes the characteristics and detri- mental effects of NBI and IN, raising the main research topic, i.e., NBI and IN in broadband communications systems; Secondly, a comprehensive survey on the cur- rent research on the technologies of NBI and IN mitigation is given, with the major problems and challenges that the current related researches are faced with; Later the key problems to be solved and the research aims are given, based on which the research routine, the main research contents, the technological roadmap, the research outcomes and contributions of this thesis are described; Finally, a brief introduction to the structure of the thesis contents is presented. 1.1 Research Background and Aims 3 1.1.1 An Overview of Digital Communication Systems There are various types of standards, formation and corresponding techniques of modern broadband communication systems. Among them, the basic components mainly include the signal source, the transmitter, the channel (with noise and inter- ference), the receiver, and the signal sink [2]. The signal source is the component that generates the information of interest, which is commonly denoted by a binary bit stream. The bit stream is coded in the digital domain at the transmitter using channel coding, and then it is modulated using some kind of constellation mapping. Afterwards, the modulated symbols are converted from digital to analog signal by a digital-to-analog converter (DAC), and then pass the shaping ?lter. After frequency upshifting, the transmit signal is formulated by the analog front end, and sent to the channel. The signal passes through the fading channel and reaches the receiver, during which the signal suffers from the noise and interference in the channel. After receiving the signal coupled from the analog front end in the receiver, the received signal is down-converted in frequency and converted from analog to digital signal using an analog-to-digital converter (ADC), which generates the received digital baseband signal. After that, the processes of synchronization, noise and interference mitigation, channel estimation and equalization, demapping and decoding are car- ried out, and the binary bit stream conveying the information of interest is recovered. Finally, the recovered information is passed to the signal sink [3, 4]. Among these processes, the estimation, mitigation and elimination of noise and interference are an important part of broadband digital communication systems. Whether the noise and interference can be effectively mitigated, estimated and eliminated, has a signi?cant impact on the performance of many other parts such as synchronization, channel estimation, demapping and decoding, etc. Thus, the mitigation and elimination of noise and interference is the core problem of this research. ﹛In digital communication systems, all the components except the source and the sink, can be regarded as a kind of ※digital interface§, or ※binary interface§ [5]. The function of the binary interface is to provide a physical-layer digital interface of the exchange of binary information bit streams for the source and the sink. Meanwhile, it will provide a binary data transmission link for upper-layers and try to guarantee the reliability and accuracy of the transmission of the binary bit streams to improve the transmission rate, which is also the aims and functionality of digital communication systems. There are many advantages of applying binary interface (i.e. digitalization). For example, it is easy to design digital logic and circuits. Digital transmission algorithms have a better performance and a higher stability. According to Shannon*s Theorem of source/channel separation [6], the source coding and channel coding can be independent of each other. ﹛Recent years are witnessing a rapid growth of digital communication systems, and an enormous amount of technical and industrial applications and completed standards are brought into reality. In the evolution of digital communication technologies and standard architecture, the most representative one is the evolution of wireless com- munication technologies and standards. The ?rst-generation wireless communication 4 1 Introduction (1G) is operating in an analog mode, supporting only voice telephone and a low speed. For example, the AMPS (Advanced Mobile Phone System) [7] is a representative 1G system. In the 1990s, the second-generation wireless communication system (2G) has developed digital communication mode, such as the IS-95 system [8] and the GSM (Global System for Mobile Communications) system [9, 10], which signi?- cantly improved the quality of voice telephone and even supported a low-rate data service, so it was rapidly applied in a wide range. With the ever-increasing demand of communication data rate, 2G standards were further evolved. The international standardization organization 3GPP (3rd Generation Partnership Project) proposed the WCDMA (Wideband CDMA) system [11], United States proposed cdma2000 [12], and China proposed TD-SCDMA standards [13]. These are the three domi- nant standards that formed the third-generation wireless communication (3G). In the beginning of the 21st century, 3GPP proposed the long term evolution (LTE) project, and put forward the LTE release-8 standards series, which opened up the fourth generation wireless communications (4G). The standards series of LTE release-10 put forward right after made the technological architecture of 4G more thorough, which is called LTE-Advanced (LTE-A) standards. The evolutionary key technolog- ical proposal in the 4G standards series is orthogonal frequency division multiplex- ing (OFDM) [14每17] and multiple-input multiple-output (MIMO) [2, 18每20]. The OFDM technique is capable of mitigating frequency-selective fading effectively, and improving the spectral ef?ciency signi?cantly. The MIMO technique is able to fully exploit the spatial diversity to improve the system capacity, which further improves the data rate of the 4G system by a giant leap. Recently, in order to satisfy the desper- ate demands of many different and new scenarios including low power consumption, wide coverage, high rate, low latency, and ultra reliability, the 4G standards are evolving rapidly towards 5G in the project of the international telecommunications union (ITU) International Mobile Telecommunications-2020 (IMT-2020) [21每23]. The development of the new generation of wireless communication technologies calls for more advanced and pioneering communication techniques to guarantee the service quality in various different complicated scenarios. To this end, this thesis is dedicated to the study of the mitigation and elimination of the new and special noise and interference, which is aimed at providing a better and more advanced technology for the next generation wireless communications as well. ﹛The development of broadband digital communication technologies also pushed forward the development of wireless digital terrestrial multimedia broadcasting tech- niques. After an evolution process of around 20 years, there are mainly four inter- nationally adopted common standards for digital television terrestrial broadcasting (DTTB) systems. The ?rst one is the ATSC standard based on single carrier modula- tion proposed by the Advanced Television Systems Committee (ATSC) of the United States [24]. The second one is the Digital Video Broadcasting-Terrestrial (DVB-T) standard based on coded OFDM technique proposed by the European Telecommuni- cations Standards Institute (ETSI) [25]. The third one is the Integrated Service Digital Broadcasting-Terrestrial (ISDB-T) standard based on distinct sub-channel OFDM technique proposed by Japan [26]. The fourth one is the Digital Terrestrial Multi- media Broadcasting (DTMB) standard based on Time Domain Synchronous OFDM 1.1 Research Background and Aims 5 (TDS-OFDM) technique proposed by China [27]. In recent years, with the develop- ment of coded modulation techniques, the DTTB system standards are also evolving continuously. Various more advanced systems, including the ATSC3.0 standards [28], the DVB-T2 standards [29], and the DTMB-A (DTMB-Advanced) systems [30], are developed based on the standards mentioned above. The high performance Low Density Parity Check (LDPC) code [31, 32] is introduced to the advanced standards. The advanced techniques such as the quadrature amplitude modulation (QAM) [33, 34] with high modulation order or amplitude phase shift keying (APSK) [35, 36], and bit-interleaved coded modulation (BICM) [36每38], are introduced as well, which facilitates a higher rate and better performance, approaching the channel capacity. There also exist many complicated noise and interference in terrestrial wireless multi- media broadcasting channels, such as narrowband interference and impulsive noise, which is still the major factor that constraints the performance of the DTTB sys- tems [39每41]. ﹛Apart from these, the rapid development in many areas such as wireless local area networks, wireline communication networks, and the newly emerging internet of things, is also pushing forward wider industrial applications of digital commu- nication technologies. The representative of wireless metropolitan access networks (WMAN) is IEEE 802.16 standards series, namely the WiMAX [42] standards series, covering outdoor cell areas, which is similar to the application scenarios of wireless cellular communications. The standards of wireless local area networks mainly refer to the broadband wireless local access networks (WLAN) systems speci?ed by the IEEE 802.11 standards series, which is commonly called WiFi (Wireless Fidelity). WiFi adopted the 4G key technologies, such as OFDM and MIMO, so a high-quality indoor short range wireless access service is provided, and great commercial suc- cess has been achieved [43]. The wireless access in vehicular environments (WAVE) system speci?ed by the IEEE 802.11p standards [44] is an extended application of wireless local area networks in the scenarios of vehicular communications. As far as wireline communication networks are concerned, the representative standards include the wireline broadband digital television system speci?ed by DVB-C or DVB-C2 standards [45], the broadband power line communications (PLC) systems speci?ed by the ITU-T G.9960 standards [46] and the IEEE P1901 [47], and the con- ventional ?ber optics communications systems, etc. Among these wireline systems, broadband power line communication systems do not rely on dedicated communica- tion cables, so it is very easy to deploy the PLC system in practice. The transmission rate can reach 500 Mbps [48], and even 1 Gbps based on the reported research in lit- erature [49]. The coverage area is in the order of 100 m [50]. Thus, PLC systems have been widely applied in many areasd, such as smart home, smart city, etc. The repre- sentative of newly emerging internet of things is the narrowband internet of things system (NB-IoT) based on cellular networks proposed in 2016 [51每53], which is able to support the networking of an enormous amount of nodes with very low energy consumption and a very wide coverage. One thing that should be noted is that, no matter in the wireless local area networks or in the wireline systems, narrowband interference and impulsive noise widely and prevailingly exist, and they have a great 6 1 Introduction impact on the communication performance of the networks. Thus, it is necessary to study effective techniques to deal with this issue. ﹛With the ever-increasing development of the theory and technologies of broad- band digital communications and its wide applications in different scenarios, related advanced technologies are continuously being studied and proposed by both the academia and industry, which also facilitates the maturity of the new broadband digital communication technologies. Speci?cally, many researches on the key tech- nologies of point-to-point transmission have set a solid theoretical and technological basis for the continuous increase of the performance of digital communications. Among them, some of the key techniques include: block transmission multi-carrier OFDM modulation, cyclic pre?xed OFDM (CP-OFDM), zero padding OFDM (ZP- OFDM), and time-domain synchronous OFDM (TDS-OFDM) [14, 16, 54], which is able to improve the spectral ef?ciency of digital communication transmissions, and avoid inter-symbol interference and inter block interference. The accuracy of equal- ization can be improved, and a lower complexity of implementation can be achieved. Thus, it has been widely adopted by many different cutting-edge broadband digi- tal communication systems. On the other hand as a contrary technique, the single carrier techniques such as the single carrier frequency division multiple access (SC- FDMA) [55] is proposed, but the performance of single carrier techniques is worse than that of OFDM techniques in the presence of multipath fading. Since OFDM systems have a strict requirement on accurate synchronization, the synchronization techniques such as frame synchronization, carrier recovery and synchronization, tim- ing synchronization and sampling frequency recovery, are the key parts that guarantee the reliability of block transmission [56每59]. As far as the coded modulation tech- niques are concerned, the highly ef?cient channel coding and decoding techniques such as the Turbo code [60] adopted by LTE or LTE-A, the LDPC code adopted by the data link in the enhanced mobile broadband (eMBB) scenario of 5G [21], can approach the channel capacity. The high order constellation mapping and demap- ping techniques (such as QAM and APSK constellation mapping modulation) can signi?cantly improve the spectral ef?ciency and data rate. Bit-interleaved coded modulation (BICM) and iterative decoding BICM (BICM-ID) techniques [61] are able to make full use of the signal space diversity (SSD) to improve the equivalent channel capacity between mapping and demapping [62]. The interleaving techniques can provide time, frequency, and coordinate diversity gains [63每65]. Multiple anten- nas techniques (such as MIMO-OFDM techniques, massive MIMO techniques) can provide space diversity gain and increase the degrees of freedom, which signi?cantly increases the spectral ef?ciency [2]. ﹛Although the development of the technological standards evolution and industrial applications of broadband digital communication techniques is rapid and furious, the various kinds of noise and interference in modern broadband communication sys- tems cannot be avoided. Furthermore, the complicated and time variant narrowband interference and impulsive noise in the communication systems will have a great and direct impact on the performance and functionality of the point to point trans- mission techniques mentioned above, which is a serious bottleneck that constraints the performance of communication systems. Therefore, in order to further improve 1.1 Research Background and Aims 7 and overcome the performance limit of broadband digital communication systems, the issues of narrowband interference and impulsive noise cannot be neglected, and should be paid high attention to. 1.1.2 Noises and Interferences There exist many kinds of noises and interferences in broadband digital communica- tions systems. As is generally acknowledged, noise is a detrimental factor generated by some random noise source inside or outside the communications system, lead- ing to impacts on the correct reception of the signal of interest, which is commonly represented by its random probability distribution; interference is a detrimental sig- nal caused by some outside interfering source or inner derivative signal, leading to interference to the correct reception of the valuable signal, which can be represented by the deterministic frequency spectrum, the random power spectrum density, or the random probability distribution of the interference signal [66每68]. Viewed from the de?nition, interference is somewhat different from noise, but there are also some rela- tions between them. The difference is that, the reason of generation and the source of noise and interference are different; the relation is that, both noise and interference have some random property and they are mixed up with the signal of interest, lead- ing to unfavorable impacts on the correct transmission and reception of the signal of interest. ﹛There are many different ways to classify noise and interference. According to their logical relation with the signal of interest, they can be classi?ed into additive noise and multiplicative noise; According to their linearity, they can be classi?ed into linear noise and nonlinear noise; According to the generation and source, they can be classi?ed into system inner intrinsic noise (such as thermal noise inside ampli?ers and electronic components, the shot noise of semiconductors, the intermodulation or harmonic interference caused by the device nonlinearity) and outside noise (such as cosmic background noise, atmospheric noise, electromagnetic radiation noise, impul- sive noise generated by switching of electrical devices, interference from co-channel narrowband service); According to the cause and source, they can be classi?ed into hostile interference (such as military electronic countermeasure interference, bar- rage jamming and frequency hopping interference) and unintentional interference (such as co-channel interference between different services on unlicensed public frequency bands); According to the probability distribution characteristics, they can be classi?ed into white Gaussian noise (such as thermal noise and shot noise) and non-Gaussian noise (such as colored background noise, impulsive noise and narrow- band interference), etc. [69每72]. ﹛No matter in the wireless channel or wired transmission environment, there always exist different kinds of noise and interference in communications systems. Some typ- ical noises and interferences commonly seen in broadband digital communications systems are described as follows. 8 1 Introduction Noise: The noise from inside the system is called ※system intrinsic noise§, and the noise from outside is called ※outside noise§ or ※external noise§. The distribution of the system intrinsic noise is commonly random, which should be expressed in probability distribution functions. It is dif?cult to mitigate or suppress the system intrinsic noise due to its randomness. However, the intensity of system intrinsic noise is normally not strong, which is particularly harmful to analog circuits but is not so severe for digital circuits and digital communications systems whose electric levels have large variation [69]. On the other hand, external noise might be distributed randomly, but also likely to be from deterministic signals, whose intensity is usually far larger than that of system intrinsic noise, sometimes signi?cantly higher than the amplitude of the signal of interest. Hence, external noise has severe impacts on digital communications systems [68]. Nevertheless, it is easier to ?nd the rules of the distribution of external noise than intrinsic noise, so more effective methods of mitigation might be found. Some typical noises are listed as follows: Additive white Gaussian noise (AWGN): The most typical, commonly seen and used model of background noise, which belongs to the category of system intrinsic noise. The cause of AWGN is the molecule thermal motion or the electric charge motion inside the electronic components that constitute the communications sys- tem. Because of the physical inherent characteristics of its cause of formation, AWGN cannot be eliminated. It is widely applied in the channel and noise model- ing, analysis and practical simulation for communications systems. Typical AWGN includes the thermal noise caused by the intrinsic thermal motion of molecules or electrons, and the hot noise caused by the motion of discrete electric charges, etc [67]. Band-limited white noise is a special case of AWGN, which can be regarded as a kind of AWGN with a ?at noise power spectrum density in the limited working bandwidth [70]. Colored background noise: Colored background noise should be classi?ed into system intrinsic noise whose power spectrum density function is different from that of AWGN, since it is not ※?at§ in the frequency band of interest and thus not satis?ed with the de?nition and condition of ※white noise§. Contrarily, its power spectrum density ?uctuates with frequency, re?ecting a characteristic of ※color§. The commonly seen colored background noise include the 1/f noise concentrated mainly in low frequency band caused by the direct current passing through dis- continuous medium in electronic components (i.e., ※?icker noise§), division noise mainly signi?cant in high frequency in transistors, most audio noise whose spec- trum is in mainly non-white low frequency band (such as pink noise, brown noise), and auto-regression noise [70]. Impulsive noise: Impulsive noise (IN), is de?ned as a bursting and impulsive out- side noise in literature, whose pulse duration is suf?ciently small with respect to the signal duration [68, 72]. As generally acknowledged in literature, quantita- tively speaking, for block transmission systems, such as the orthogonal frequency division multiplexing (OFDM) system, IN can be regarded as a pulse noise signal whose nonzero pulse duration is no more than 5% of the OFDM symbol dura- tion [73, 74]. Due to its time-domain bursting and impulsive characters, IN is 1.1 Research Background and Aims 9 usually called ※pulse noise§. The cause of IN is various, commonly including the atmospheric noise produced in the atmosphere space, the spark noise produced by vehicles and electric devices, the runtime noise of industrial facilities, and the switching noise of household appliances, etc [50, 69]. Other types of noises: Apart from the typical noises mentioned above, there are some other noises in communications systems, such as the multiplicative noise having a multiplicative relation with the signal, the phase noise having an impact on the modulation phase of the signal, the nonlinear noise caused by nonlinear com- ponents or nonlinear signal processing operations like the clipping noise caused by the clipping operation to mitigate high peak-to-average-power-ratio (PAPR) in OFDM systems, and the quantization noise due to insuf?cient bit accuracy in the process of analog-to-digital conversion and other ?oat-point or ?xed-point quantization [70, 71]. Interference: Interference mainly comes from a certain interfering source outside the system, which is coupled into the communications system through a certain medium and mixed up with the signal of interest in time or frequency domain, resulting in detrimental effects on the correct reception, demodulation and decoding of the information signal. The interference signal can normally be represented by its deterministic spectrum or random power spectrum density [68]. Some kinds of interference signals might also come from inside the system itself. Some typical interferences in broadband digital communications systems are listed as follows: Narrowband interference: In literature, narrowband interference (NBI) is com- monly de?ned as a narrowband and spectrally-sparse interfering signal outside the system, whose effective bandwidth is suf?ciently narrow with respect to the signal working bandwidth [68, 75]. As a duality of IN, it is generally acknowl- edged in literature that, the NBI in OFDM systems can be quantitatively de?ned as an interfering signal, where the ratio of the bandwidth occupied by its nonzero frequency components to the OFDM working bandwidth is no more than 5% [76, 77]. In some references, NBI is equivalently called ※narrowband noise§ [66], but in this thesis it is called NBI for consistency. NBI is prevailing existing in broadband digital communications systems with various causes, such as the NBI caused by the radio frequency leakage or wired coupling from the radiation of neighboring wireless devices or the interfering source in the same wired network topology [50, 67], and the interference to the broadband communication service from the co-channel narrowband licensed service or narrowband amateur radio service, etc [68, 69]. Electronic countermeasures interference: It belongs to intended malicious inter- ferences, whose purpose is to disturb the normal transmission of the target com- munications system. The electronic countermeasures interference commonly seen include frequency-hopping interference (the frequency location of interference hops in a certain law or randomly), barrage jamming (jamming the whole work- ing band), step disturbance (random or mixed frequency-sweeping interference to target signal); likewise, the NBI (such as single or multi-tone interference), and 10 1 Introduction impulsive interference (can be regarded as a kind of IN generated by intermittently transmitting high-power interfering signals), etc [68]. Other outside interferences: The other interferences coming from outside inter- fering sources still include the adjacent channel interference generated by other services in adjacent bands (such as the interference caused by the spectrum leak- age of adjacent-band services), co-channel interference in the same band with the signal of interest (such as the interfering signal received by the UEs in the cell edge from the same frequency of the BS in the adjacent cell, as well as pilot contamination)[2], wireless coupling noise or crosstalk noise in wired communi- cations, and electromagnetic interference (EMI) generated by the working circuits of electric and electronic devices, etc. [72]. System inherent interference: The interference signals produced inside the commu- nications system, such as the cross-modulation interference (caused by high-order harmonics due to outside interfering signals or the nonlinear effects on the informa- tion signal at the receiver), intermodulation interference (the interference caused by the harmonics falling into the band of information signal because of the non- linear operations on the different frequencies of the signal of interest), and image frequency interference (the image frequency components falling within the range of the intermediate frequency ?lter caused by frequency mixing and conversion), etc. [78]. 1.1.3 Characteristics and Detrimental Effects of NBI and IN NBI and IN exists widely in broadband digital communications systems and have signi?cant detrimental effects on the system performance, which should be paid great attention to and the mitigation schemes need to be studied. In the following contents, the special distribution, the widely existing causes, and the detrimental effects on communications systems of NBI and IN are described. (1) Special Distribution of NBI and IN According to the Shannon information theory, noise and interference are the most essential and fundamental constraints to the communications system performance. If there is no noise or interference, theoretically, the channel capacity can be in?nity [79, 80]. In the AWGN channel, the channel capacity has a closed-form solution [1], which has been studied comprehensively. AWGN is an additive stationary random process whose power spectrum density is ?at (i.e. ※white§) and follows a multivari- ate Gaussian distribution [66]. However, NBI and IN are different from AWGN. No matter in characteristics and statistical distributions, or in the causes and detrimental effects, they are different in essence, so we cannot deal with them using conven- tional AWGN model, theory and method. Firstly, NBI does not belong to white noises, because its spectrum or power spectrum density is limited in a narrow band thus not re?ecting a ※white§ character as in AWGN [75]. Secondly, the statistical distribution of IN is non-Gaussian [81], whose amplitude distribution usually follows 1.1 Research Background and Aims 11 the Middleton Class A distribution [73, 74, 82, 83]; Meanwhile, the joint multivari- ate distribution of the signal samples of NBI or IN does not follow a multivariate Gaussian distribution, and the amplitude of each sample does not have the charac- ter of the covariance of multivariate Gaussian distribution [84, 85]. Besides, due to the impulsive, bursting and instantaneous characters of IN, its distribution can be regarded as a non-stationary (neither stationary nor wide-sense stationary) random process [86每88]. Although in some literature part of the characters of the statisti- cal NBI or IN model is expressed by single-variable Gaussian distribution function, these references still insist that it is only a special extension of Gaussian variable within part of the features of NBI or IN: for example, for the band-limited Gaussian noise (BLGN) model of NBI, although the amplitude of each tone interferer is a sin- gle Gaussian variable, multiple tone interferers do not follow multivariate Gaussian distribution [84, 85, 89]; In the Gaussian mixture model of IN, the occurrence time of each nonzero pulse sample follows Poisson or Bernoulli distribution, so the model does not belong to conventional AWGN model despite the fact that the amplitude of its nonzero entries is a single Gaussian variable [90]. ﹛The time and frequency domain locations of NBI and IN have obvious irregular and random distributing characters [86, 91]. Usually, the intensity of the power spectrum density of NBI and IN is very high (typically 15每20 dB, sometimes 50 dB, over the background noise ?oor [88]), and they are mixed up with the signal of interest in both time and frequency domains completely, making it very dif?cult to distinguish between them [92]. Hence, it is hard to correctly analyze the theoretical performance bound of the channel in the presence of NBI and IN. It is dif?cult to mitigate and estimate NBI and IN, which will signi?cantly impact the communications system performance. (2) NBI and IN Widely Exist in Broadband Communications NBI and IN widely exist in different channel environments and application scenar- ios of current broadband communications systems and standards, and have become an inevitably important aspect constraining the system performance of broadband communications systems. ﹛Channels and systems with IN: ?rstly, in outdoor wireless communication chan- nels, such as digital terrestrial television broadcasting channel and cellular wireless communication channel, there exists IN from ignition of transportation vehicles and weeding machines [93], and the IN generated by the switching of central air- conditioner, heater, lighting and household appliances [94]. Secondly, various wired communication channels, such as power line communication (PLC) networks, asym- metric digital subscriber line (ADSL), cabled TV lines, etc, suffer from the IN from the switching, plugging or topology changing of electric devices in the same power grid [88, 95, 96], and the coupling IN from the vehicle ignition, sparks, lightning and atmospheric noise [97], electric device leakage [50] and pulse radiation leakage [98]. In indoor wireless communications scenarios, there are also widely existing IN. For instance, it is shown by experimental tests that, there are IN in both the public Industrial Scienti?c and Medical (ISM) band and the 4 GHz high-frequency band, whose bandwidth can reach 40 MHz [99]. Besides, in the scenarios like internet of 12 1 Introduction vehicles (IoV), IN also prevails, such as the radio frequency coupling IN in wire- less IoV IEEE 802.11p Wireless Access in Vehicular Environments (WAVE) system [44, 100]; In smart grid and wired Vehicle-to-Grid (V2G) networks, such as the smart IoV speci?ed by HomePlug Green PHY standards, there also exists IN that impacts wired devices [101]. The operation of vehicle engines also introduces severe IN to IoV devices [102]. ﹛Channels and systems with NBI: on one hand, for wireless communications sys- tems, the broadband wireless service networks working in the ISM unlicensed pub- lic band, such as the communication equipment in Wireless Local Area Networks (WLAN) [92], Wireless Metropolitan Area Networks (WMAN), wireless IoV [103], will suffer from interference from other unlicensed narrowband services (like blue- tooth [104], cordless telephone, gate control, microwave oven, baby monitor, etc) [75, 105]; The narrowband signal produced by unlicensed amateur radio also has an impact on public unlicensed services, or spectrum leakage and abnormal usage of spectrum will also produce NBI to broadband communications in some licensed band [106]; Broadband multimedia wireless transmission systems and wireless digi- tal terrestrial television broadcasting systems suffer from the co-channel NBI caused by analog broadcasting signals [39], and the NBI produced by the secondary users of cognitive radio who exploit the ※white band§ of digital television [40, 41]; Also, analog narrowband broadcasting signals will generate NBI to broadband communi- cations systems like spread-spectrum and multi-carrier based systems [107]. On the other hand, wired communications systems like OFDM-based broadband PLC sys- tems [108, 109] ADSL [106], ADSL [106] and cabled digital television broadcasting (such as digital video broadcasting-cable, DVB-C) suffer from NBI produced by the narrowband working harmonics from household appliances [50] (microwave oven [110], water heater, personal computers [111]). In addition, NBI exists in plenty of other scenarios, such as in the scenario of internet of things (IoT), the Narrowband Internet-of-Thing (NB-IoT) signal generates NBI to LTE (Long Term Evolution) or LTE-A (LTE-Advanced) cellular wireless communications systems working in the same in-band mode [51每53]; Ultra-Wideband (UWB) systems tend to suffer from NBI caused by many licensed or unlicensed wireless services with overlapping spectrum because of its very wide spectrum range [112, 113], and the malicious NBI aimed at UWB systems is also widely encountered in electronic countermeasure [114, 115]; The radio frequency nonlinearity due to the carrier ingress or carrier leakage at the transmitter will also introduce single-tone carrier remaining interference to the communications system itself, etc. [75]. (3) Detrimental Effects of NBI and IN on Communications Systems NBI or IN has severe detrimental effects on the normal running of each module in the communications system, thus resulting in signi?cant impacts on the performance of various broadband communications systems. ﹛The major harmful effects of NBI: in the presence of NBI, it is easy for the dynamic range of the digital correlator or the front-end high-speed analog-to-digital-converter (ADC) at the receiver to be saturated. Likewise, analog receivers like rake do not have the inherent mechanism of eliminating the interference energy from decision 1.1 Research Background and Aims 13 statistics, leading to signi?cant performance degradation with NBI [113]; Also, NBI has signi?cant detrimental effects on the synchronization performance (including frame synchronization, timing recovery and carrier estimation) of the receivers of broadband communications systems, especially multicarrier OFDM systems [116]; Furthermore, it is shown by theoretical analysis that, the bit error rate (BER) of the Fourier transform and wavelet transform based OFDM systems signi?cantly increase in the presence of NBI [117]; It is proved by experiments that, when NBI is present, the BER performance of OFDM-based systems suffers from severe degra- dation [118]; It is validated that NBI might lead to complete loss of the data carried in sub-carriers, and signi?cant increase of BER, symbol error rate (SER) as well as block error rate (BLER)[108]. For instance, UWB systems are very sensitive to NBI from many licensed or unlicensed services because of its mechanism of collecting the energy all over the frequency domain [113]. ﹛The major harmful effects of IN: it is shown in literature that, IN has severe impacts on the performance of digital communications receivers like decoding and demapping [119每122]; Due to the wide spectrum affected by IN, for multicarrier systems, almost all the OFDM sub-carriers are contaminated, especially when the intensity of IN is large enough to reach a certain threshold, leading to error recep- tion of the whole OFDM block and performance degradation that channel coding cannot compensate [123]; The pulses of IN might occur in bursts in multiple con- tinuous symbols, resulting in the failure of Viterbi decoding [124]; According to the analysis in literature, the currently widely applied broadband multicarrier systems like OFDM-based systems tend to be affected by IN more easily than single-carrier systems [125]; It is further shown by theoretical analysis and experimental tests that, IN brings signi?cant performance degradation to the accuracy of demapping and decoding of multicarrier system receivers [96]; When the energy of IN exceeds some certain threshold, it is dif?cult to eliminate the impacts on all the sub-carriers using conventional signal processing methods [126], and inevitable bursting errors will appear in block transmission data [127]; It is shown by practical tests in wire- less broadband multimedia transmission systems that, IN has severe impacts on the performance of the OFDM system receiver modulated in 64QAM [128]. ﹛Consequently, because of the special distribution, wide existence and severe detri- mental effects of NBI and IN, it is in desperate need to research on the key tech- nologies to effectively suppress, estimate and eliminate NBI and IN, which is utmost urgent for ensuring the performance of broadband communications systems. 1.2 Related Works and Challenges 1.2.1 Related Works and Problems on NBI Mitigation As far as the problem of NBI mitigation, current existing researches in literature mainly include three basic categories, i.e., receiver-side frequency-domain estimation 14 1 Introduction and mitigation, transmitter-side time-domain ?ltering and receiver-side time-domain equalization, and transmitter-side orthogonal coding based mitigation. (1) Receiver-side frequency-domain estimation and mitigation Nilsson proposed an NBI estimation method based on the rule of frequency-domain linear minimum mean square error (LMMSE) exploiting the values in null sub- carriers close to the real locations of NBI as measurement data [129]; Drawbacks: This method requires a large amount of reserved virtual sub-carriers, which is a great waste of spectrum resource, and it also requires the power spectrum density and central frequency location of the NBI to be known a priori, which is dif?cult to satisfy in practice, so the practical value of this method is relatively low. ﹛Darsena proposed a successive interference cancelation method by sequentially doing symbol decision and error estimation for each sub-carrier in a recursive and iterative manner [76, 130]; Drawbacks: This method requires accurate channel esti- mation in the stage of sub-carrier symbol decision, and requires to know the accurate power spectrum density of NBI in the stage of error estimation, which is unpractical in realistic systems; Besides, the estimation error at some certain sub-carrier will accumulate and propagate to all the subsequent sub-carriers, leading to performance deterioration. ﹛In addition, the receiver-side frequency-domain mitigation methods include the frequency threshold excision (FTE) method based on the decision according to the prede?ned threshold, which excludes the sub-carrier data with an amplitude larger than the given threshold [114, 131每133]; Drawbacks: The operation of directly excluding the sub-carrier will cause spectrum leakage and data loss, and it is easy to cause false alarm because of spectrum leakage or the peak power of OFDM signals in frequency-selective channels, leading to more loss of information data. (2) Transmitter-side time-domain ?ltering and receiver-side time-domain equalization Stamoulis designed an MMSE based NBI mitigation method using a nonlinear deci- sion feedback equalizer [134]; Drawbacks: This method requires the accurate second- order statistics of the received signal to be known, otherwise the performance will be greatly degraded. ﹛An optimized receiver with wide linear-zero forcing (WL-ZF) equalizer was designed based on the rule of constrained minimum mean output energy (CMMOE), and thus a related method to mitigate the impacts of NBI on receivers was proposed [135, 136]; Drawbacks: This method requires the prior statistical information of NBI to be known, and the receiver has to know the ideally accurate channel impulse response (CIR), which is, however, very dif?cult to accurately estimate in the pres- ence of NBI in practice. ﹛Coulson and Kelleci proposed an NBI suppression method by designing a time- domain suppression ?lter based on the linear prediction rule ahead of the discrete Fourier transform (DFT) at the transmitter, which is able to reduce spectrum leakage compared with the FTE method [132, 137]; Drawbacks: This method is effective only if the OFDM signal is under ?at fading and the suppression ?lter has to be 1.2 Related Works and Challenges 15 designed in the frequency location of the NBI, which requires the precise location of NBI to be known in advance; Besides, this method is complicated to design and hard to implement ef?ciently. (3) Transmitter-side orthogonal coding based mitigation Gerakoulis and Wu proposed an interference suppressing OFDM (IS-OFDM) method for NBI mitigation, which spreads the transmitted signal power over all the sub- carriers using orthogonal spreading codes like orthogonal Walsh code at the transmit- ter [77, 138]; Drawbacks: The performance signi?cantly degrades in high interference-to-signal ratio (ISR), making the method not working; And the required operation of orthogonal coding brings in additional high complexity. ﹛On the basis of IS-OFDM systems, Popescu and Yaddanapudi proposed an NBI- avoidance method to mitigate the impacts of NBI and its spectrum leakage on related sub-carriers using the spectral shaping technique or the FTE method [139, 140]; Drawbacks: The spectral shaping operation and the FTE processing will introduce non-orthogonal property between sub-carriers; In addition, the performance of this method degrades when the number of nonzero entries of NBI is so large that many sub-carriers are forced to be set as zeros, so its applicability is relatively low. ﹛It can be concluded from the above-mentioned existing conventional methods of NBI mitigation that, there are many drawbacks in the current research, such as the unstable performance of NBI mitigation, data loss, unrealistic assumptions, impractical for realistic systems, high implementation complexity, and dif?culties in deployment, etc. The aims and strategies of most of the existing methods are ※passively§ mitigate the effects of NBI whereas they cannot effectively and accurately estimate the NBI signal, leading to the fact that they cannot completely eliminate the impacts of NBI in essence. Therefore, it is in great need to study a series of practice- oriented, realistic-system-applicable, stable and ef?cient methods of NBI mitigation and elimination. Designing the algorithms that are able to ※actively§ reconstruct the NBI accurately and eliminate NBI completely, is the key to solving this problem. 1.2.2 Related Works and Problems on IN Mitigation Aimed at the problem of IN mitigation, the existing research literature works have addressed three basis categories, mainly including the receiver-side nonlinear oper- ation method, the transmitter-side preprocessing method, and the receiver-side post- processing method. (1) Receiver-side nonlinear operation method The detrimental effects of too large amplitude of IN were constrained by clipping the time-domain samples that exceed a threshold [123]; Drawbacks: The clipping operation will introduce nonlinear distortion, leading to system performance loss; Because the clipping operation did not accurately estimate and eliminate the IN components, the impacts of IN cannot be completely excluded; In addition, it is 16 1 Introduction dif?cult to obtain the accurate locations of time-domain samples where IN occurs, so part of the samples affected by IN would be left out without processing when the intensity of IN did not exceed the prede?ned threshold. ﹛The time-domain components of IN in the samples whose power exceeds the threshold can be eliminated by blanking these samples [141]; Drawbacks: When the PAPR of the OFDM signal is high, it is dif?cult to correctly estimate the precise locations of IN, so it is much probable to cause false alarm and mistakenly set the data not affected by IN to zeros, leading to additional performance loss; Besides, part of the samples affected by IN whose amplitude did not exceed the threshold would be left out. ﹛Zhidkov tried to con?gure two thresholds for the clipping and blanking operations as a compromise of the two processing techniques [126]; Drawbacks: This combined scheme still has the drawback of either the clipping method or the blanking one; Because the locations of IN cannot be accurately obtained, part of the time-domain samples affected by IN is left out; When the PAPR of the OFDM signal is relatively high, it is much likely to cause false alarm and make the data set to zeros; When doing the clipping operation, the impacts of IN were not effectively mitigated and the detrimental effects remained; Nonlinear distortion might be introduced, etc. (2) Transmitter-side preprocessing method Matsuo and Haring studied the coding and decoding method using complex number for information data at the transmitter and receiver. Since IN was not encoded but only decoded by the complex number, it was equivalent to spreading its energy over all the sub-carriers by dispersive ?ltering processing, so the impacts of IN were suppressed; At the receiver, based on the Turbo recursive decoding mechanism and maximum a posterior (MAP) estimation, the signi?cance of information signal with respect to IN was improved by multiple iterative decoding [142每144]; Drawbacks: The design of effective complex number codes is dif?cult and costs large complexity; Additional coding and decoding complexity should be included in the transmitter and receiver; large extra delay was introduced by iterative decoding with high implementation complexity; The performance of the iterative method of IN mitigation degraded signi?cantly when the intensity of IN is large. ﹛Another major transmitter-side preprocessing method is precoding frequency algebraic interpolation method: the frequency-domain OFDM symbols were pre- coded in the equivalent complex-valued Reed-Solomn (RS) codes [124, 145, 146], or precoded in the equivalent complex-valued or real-valued Bose-Chaudhuri- Hocquenghem (BCH) codes [147, 148], and the receiver exploited the received information at the known pilots with some certain distribution patterns, or contin- uous zero symbols [148, 149] for frequency-domain algebraic interpolation and decoding [150], thus mitigating the impacts of IN; Drawbacks: Extra complexity of precoding and decoding should be included to both the transmitter and receiver, and additional delay was produced; enough number of known pilots [124] or continu- ous zero symbols [147, 148] should be con?gured in the frequency domain. It was derived by theoretical analysis that, the distribution of the known pilots should satisfy a certain pattern in order to be the necessary and suf?cient condition of successful 1.2 Related Works and Challenges 17 decoding [124], and the distribution of the successive zero symbols should appear in sequence [148, 149], but it is dif?cult for these two conditions to be satis?ed in practical systems. (3) Receiver-side post-processing method Tulino made an assumption in research that, IN was independently identically dis- tributed (i.i.d) and occurred with a certain probability. It was also assumed that, the accurate location of IN in the time-domain sample of the OFDM symbol was known to the receiver, and thus the sample contaminated by IN could be directly excluded [151]; Drawbacks: In practical systems, it is not possible for the receiver to directly obtain the accurate location of IN; the operation of excluding the sample will cause time-domain data loss and introduce non-orthogonality between OFDM sub-carriers and inter-carrier interference (ICI), which will lead to demodulation and decoding errors of OFDM symbols when the IN appears intensively (with a relatively large probability). ﹛Rinne proposed a dynamic detection method using the prede?ned power or energy threshold, which online judges whether the OFDM data block was contaminated by IN. If so, this OFDM data block was deleted as a whole [152]; Drawbacks: This method causes too much loss of information, and signi?cantly reduces the system throughput; ﹛Apart from these, an important receiver-side post-processing method is the diver- sity combining method [153每155], which utilized the channel physical state diversity of different channels, and combined them in a certain manner, expecting to achieve diversity gain and improve the reliability of wireless communications systems in the presence of IN; Dubey provided a theoretical closed-form analysis of the BER of the system performance using selection combining method in the presence of IN [154]; Drawbacks: In practical communications systems, usually it is not easy to simul- taneously get multiple physical channels with multiple different characteristics, so the physical channel diversity cannot be achieved in essence [155]; The combining of multiple sub-channels based on the same category of physical channel is lack of applicability, and the combining performance is also affected by the correlation between different channels; Besides, the method of diversity combining is still in the mode of ※passively§ combatting against IN, which is not capable of eliminating the impacts of IN completely. ﹛It can be observed from these categories of conventional IN mitigation methods mentioned above that, there are plenty of drawbacks for the existing researches, such as the nonlinear distortion introduced by the operation of IN mitigation, the information data loss, the reduction of spectrum ef?ciency due to excessive time- frequency resources consumption, the false alarm and errors caused by inaccurate estimation, the high complexity of paradigm design, the unrealistic assumptions of the system and the available conditions of estimation, etc. The mechanism of most of the existing methods of IN mitigation is ※passive§ mitigation, which cannot accurately reconstruct and eliminate the IN signal. In all, it is necessary to study 18 1 Introduction highly ef?cient, robust and applicable algorithms of NBI and IN mitigation and elimination, in order to ※actively§ reconstruct and eliminate NBI and IN, which is also the main research aim of this thesis. 1.3 Key Research Problems and Research Aims As far as the drawbacks of the above-mentioned conventional methods of NBI and IN mitigation are concerned, in order to overcome the many dif?culties and challenges the current research is faced with, this thesis is concentrated on the center of ※the key technologies of NBI and IN mitigation and cancelation§, and is intended to focus on solving the following three key scienti?c problems: ﹛Scienti?c Problem 1: How to overcome the severe impacts of NBI on the receiver synchronization performance. The existence of NBI severely impacts the perfor- mance of frame synchronization and carrier synchronization of the receiver, leading to great challenge to the synchronization-sensitive OFDM systems. Conventional design of synchronization frame structure and synchronization algorithms cannot mitigate NBI, thus causing the performance degradation in the presence of NBI, which is not capable of supporting the requirements of the improvement of the next- generation communications system performance and the accurate synchronization of OFDM systems. Hence, new synchronization frame structures and synchronization methods that can effectively mitigate NBI should be investigated. ﹛Scienti?c Problem 2: How to improve the performance of the time-frequency interleaving scheme in the simultaneous presence of both IN and NBI. In the seri- ous transmission environment where NBI and IN are simultaneously present, great impacts are imposed on the accuracy of demapping and decoding of the current broadband communications systems. However, conventional interleaving schemes were not jointly designed for aiming at the requirements of avoiding NBI and IN, and thus the optimal time and frequency diversities cannot be provided, resulting in limited interleaving performance gain. Hence, It is very urgent for guaranteeing the communications system performance in complicated serious channels to study novel time-frequency combined interleaving schemes. ﹛Scienti?c Problem 3: How to break the bottleneck of conventional passive methods of mitigating NBI and IN to achieve accurate recovery and elimination. As is previ- ously described, conventional methods of NBI and IN mitigation or estimation fall mostly in the category of ※passively§ combatting against the noise and interference, which is constrained by the limitation of conventional signal processing methods. The existing methods cannot accurately recover the precise time or frequency domain locations of NBI or IN, and cannot estimate their amplitude accurately, either. Thus, the unfavorable in?uences left by the noise and interference cannot be effectively eliminated, which has become a major bottleneck limiting the system performance improvement of existing communications systems. It is in desperate need to change the passive scheme to an active one, and introduce new signal processing theories and methods to establish the framework of highly ef?cient recovery. New algorithms 1.3 Key Research Problems and Research Aims 19 that can effectively reconstruct NBI and IN accurately should be devised, in order to break the bottleneck of conventional methods and the fundamental limitation of the system performance. ﹛Through the study of these three scienti?c problems, this thesis is expecting to achieve the following related research aims: ﹛Research Aim 1: Designing an optimized synchronization frame structure effec- tively improving the NBI mitigation performance and the highly ef?cient synchroniza- tion algorithm. The proposed frame structure outperforms the conventional frame design schemes in spectrum ef?ciency, and has signi?cant gain in the same condition of frame synchronization accuracy and carrier recovery accuracy. ﹛Research Aim 2: Investigating the optimal time-frequency combined interleav- ing scheme that can maximize time-frequency diversity gains in the presence of NBI and IN. Theoretically, the time-frequency interleaving scheme investigated can simultaneously achieve the target of the maximum time diversity gain and frequency diversity gain. Thus the capability of avoiding NBI and IN through interleaving for coded block transmission systems is improved to the most extent, and the system BER is signi?cantly reduced. ﹛Research Aim 3: Proposing the ef?cient and accurate sparse recovery framework and algorithms based on the new sparse recovery theory, realizing the accurate recovery and cancelation of NBI and IN. The estimation accuracy of recovering NBI and IN of the propose method is approaching the estimation theoretical bound; In the circumstance of the simultaneous existence of NBI and IN, the proposed method helps the performance of the system BER and the estimation accuracy of noise and interference outperform conventional mitigation methods signi?cantly, which is able to approach the system performance where there is no NBI or IN present. 1.4 Main Works and Contributions The research on key technologies of NBI and IN mitigation and cancelation is regarded as the kernel of this thesis. The relation framework of the scienti?c prob- lems the works of this thesis are faced with, the main research idea adopted, and the major research contents and technical routine is illustrated in Fig. 1.1. The research framework of this thesis is elaborated mainly surrounding the following three major research routines. ﹛Major Research Routine 1: Aimed at Scienti?c Problem 1, i.e., how to overcome the severe impacts of NBI on the receiver synchronization performance, this thesis cuts in from the perspective of smart mitigation of NBI and follows the research idea of designing the optimized ※scrambling§ synchronization frame structure that effec- tively mitigates NBI. Proposed in the research routine are the optimized design of synchronization frame structure mitigating NBI and the ef?cient and robust receiver synchronization algorithm, as well as designing novel high spectrum-ef?cient and robust synchronization frame structure to signii?cantly improve the accuracy of frame synchronization and carrier recovery in the presence of NBI. The research 20 1 Introduction Fig. 1.1 The illustration of the research framework, scienti?c problems and the main research contents outcomes have been published in one EI-indexed paper in the international confer- ence IEEE International Symposium on Power Line Communications, and the core technique has achieved one national invention patent. The core technology of frame structure design has been adopted by the Chinese national standards for broadband power line communications〞physical layer, and one standardization proposal has been submitted to the international telecommunications union. The technology stud- ied is promisingly to be widely applied in various communications systems like power line communications and wireless communications severely contaminated by NBI, to achieve ef?cient and accurate synchronization. ﹛Major Research Routine 2: Aimed at Scienti?c Problem 2, i.e., how to improve the performance of the time-frequency interleaving scheme in the simultaneous pres- ence of both IN and NBI, this thesis follows the research idea of trying to provide the maximized time-frequency diversity gains and avoid NBI and IN. The optimal time-frequency combined interleaving scheme in the presence of NBI and IN is pro- posed. Proposed in the research routine are the optimized scheme for interleaving parameters to maximize the time-frequency diversity gains, and the block cyclic shift- ing technique for symbol interleaving to maximize the frequency diversity gain. The research aims of theoretically maximizing time-frequency diversity gains, effectively avoiding the impacts of NBI and IN on the demapping and decoding performance of coded block transmission systems, and signi?cantly reducing the system BER in the condition of reducing the delay of conventional interleavers, are accomplished. The research outcomes have been published in one SCI-indexed journal paper in IEEE Transactions on Power Delivery, and in one EI-indexed paper in IEEE Interna- tional Conference on Communications (ICC). The proposed technology of the opti- mal time-frequency combined interleaving has been adopted by the next-generation