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Symbol-Based Multi-Layer Iterative Successive Interference 1 Symbol-Based Multi-Layer Iterative Successive Interference Cancellation for Faster-Than-Nyquist Signaling Qiang Li12, Feng-Kui Gong12, Pei-Yang Song1 and Sheng-Hua Zhai34 1 State Key Laboratory of Integrated Service Networks (ISN), Xidian University, Shaanxi, Xi’an 710071, China 2 Collaborative innovation center of information sensing and understanding, Shaanxi, Xi’an 710071, China 3 School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China 4 CAST-Xi’an Institute of Space Radio Technology, Xi’an 710071, China Abstract—A symbol-based multi-layer iterative successive in- interference (ISI). Nevertheless, the orthogonality of Nyquist terference cancellation (MLISIC) algorithm is proposed to elim- signaling is at the cost of sacrificing the spectrum efficiency. inate the inter-symbol interference (ISI) for faster-than-Nyquist By deliberately introducing ISI, higher transmission rate and (FTN) signaling. The computational complexity of the proposed MLISIC algorithm is much lower than most existing block-based spectrum efficiency can be supported in the FTN system. estimation algorithms. By comparison with existing symbol-based Besides, FTN transmission can moderate the need for high- algorithms, the proposed MLISIC algorithm has higher estima- order modulations and low rolling factors. Thus, the adverse tion accuracy. Furthermore, by means of utilizing more accurate effect of the phase noise distortion and the timing error can symbols and elaborate length of successive interference cancella- be mitigated. tion, an improved MLISIC (IMLISIC) algorithm is presented to further promote the estimation accuracy. Simulation results show FTN signaling was first proposed by Mazo in 1970s. It in mild ISI cases, the proposed MLISIC and IMLISIC algorithms is demonstrated in [2] that as long as the time acceleration can approximate the theoretical performance even using 256- parameter τ is no less than 0.802, i.e., 0:802 ≤ τ ≤ 1, the amplitude phase shift keying (APSK) which is adopted in digital minimum distance of uncoded binary sinc pulse transmission video broadcasting-satellite-second generation extension (DVB- is not reduced in FTN signaling. Compared with the traditional S2X), i.e., bit error rate (BER) performance degradation is about 0.03 dB when the signal-to-noise ratio is high. In other words, Nyquist system, the FTN system can transmit about 25% more using the proposed MLISIC and IMLISIC algorithms in mild ISI symbols in the same bandwidth without bit error rate (BER) cases, the spectrum efficiency can be improved with negligible performance degradation. The calculation of the minimum BER performance degradation. In moderate ISI cases, BER distance for FTN signaling was then given in [3]. Due to performance degradation of our proposed IMLISIC algorithm the fact that the pulse response of sinc pulse is infinite in is no more than 0.13 dB when adopting 64/128/256-APSK, which is still satisfying. Besides, compared with existing symbol-based time domain, raised-cosine (RC) pulses are introduced for algorithms, the greater BER performance improvement can be FTN signaling in [4]. Since then, FTN signaling has been achieved under severer ISI circumstances. widely investigated in different aspects [5], such as FTN Index Terms—Successive interference cancellation, inter- signaling using non-binary or high-order modulations [6], [7]. symbol interference (ISI), faster-than-Nyquist (FTN) signaling, The constrained capacity for FTN signaling is also clarified in amplitude phase shift keying (APSK), digital video broadcasting- [8], which shows that the FTN system can achieve a higher satellite-second generation extension (DVB-S2X). capacity than the Nyquist system unless sinc pulse is adopted. The advantages of frequency-domain FTN systems can be I. INTRODUCTION found in [9], [10]. In addition, FTN signaling has been applied arXiv:1903.01878v1 [eess.SP] 25 Feb 2019 ITH the rapid development of the wireless commu- to more scenarios, such as multi-carrier [11]–[13] and multi- W nication technology in recent years, wireless devices input-multi-output (MIMO) [14], [15] systems. Especially grow exponentially, which results in more and more demand for satellite communications, FTN signaling is investigated for communication services. In addition, the high-throughput as an innovative method to improve spectrum efficiency in satellite becomes a trend due to the scarcity of spectrum [16], [17]. A receiver architecture for FTN signaling in the resources in satellite communications. High-order modula- digital video broadcasting-satellite-second generation (DVB- tions such as 256-amplitude phase shift keying (APSK) and S2) standard [18] is also presented [19]. low rolling factors such as 0.05 are recommended in dig- On account of the violation of the Nyquist criterion in FTN ital video broadcasting-satellite-second generation extension system, it is inevitable to introduce undesired ISI. Hence, lots (DVB-S2X) [1], however, they are sensitive to the phase noise of research literature focused on the ISI cancellation algo- distortion and timing error respectively. As a non-orthogonal rithms. As known, the optimal ISI cancellation algorithm is the transmission scheme, faster-than-Nyquist (FTN) signaling has maximum likelihood sequence estimation (MLSE), which is attracted much more attention. not practical due to its non-deterministic polynomial (NP)-hard When designing the traditional communication system, the computational complexity. Based on the M-algorithm and the Nyquist criterion must be followed to avoid the inter-symbol Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, J. B. Anderson 2 proposed the M-BCJR algorithm for FTN signaling in [20]. cancellation. The IMLISIC algorithm has higher estima- Since the M-BCJR algorithm only keeps several maximum tion accuracy than the MLISIC algorithm. Hence, the states as possible states at each time, it can maintain the good proposed IMLISIC algorithm can achieve better BER performance when reducing the computational complexity of performance than the proposed MLISIC algorithm even the BCJR algorithm. But the computational complexity of when their computational complexities are equal. the M-BCJR algorithm is still prohibitive for the practical 4) Fourthly but not the last, simulation results show that implementation. In [9], [21], the truncated Viterbi algorithm our proposed algorithms are characteristic by higher and M-algorithm are also investigated for the uncoded single- estimation accuracy than the FDE algorithm in [22] and carrier FTN system. In 2013, a low complexity and effective the SSSgbKSE algorithm in [27] in mild and moderate frequency-domain equalizer (FDE) for the FTN system is ISI cases. For all the modulation types adopted in proposed [22]. To a certain extent, however, its spectrum effi- DVB-S2 and DVB-S2X, our proposed algorithms can ciency is decreased because of the insertion of guard interval, approximate the theoretical performance in mild ISI e.g., cyclic prefix. As a commendable method to eliminate cases. Even under moderate ISI circumstances, for which ISI, the performance of precoding in the FTN system can be the SSSgbKSE algorithm is not suitable, the proposed found in [23]–[25]. An iterative FTN detector in the presence algorithms perform quite well. of phase noise and carrier frequency offset is also developed The rest of this paper is organized as follows: Section in a factor graph framework [26]. Two successive symbol-by- II introduces the system model of FTN signaling. The con- symbol sequence estimators are proposed to estimate binary strained capacity for FTN signaling is also covered in Section and 4-quadrature amplitude modulation (QAM) FTN signaling II. Section III discusses the proposed MLISIC and IMLISIC in [27]. It is proved that one of these two sequence estimators, algorithms in detail. Simulation results are demonstrated in which is named after successive symbol-by-symbol with go- Section IV. Section V makes a brief conclusion. back-K sequence estimator (SSSgbKSE), performs well in mild ISI cases and can significantly increase the transmission rate and spectrum efficiency. The semi-definite relaxation- II. FTN SYSTEM MODEL AND THE CONSTRAINED based sequence estimation presented in [28] shows pretty good CAPACITY performance, but its computational complexity is disappoint- ing when the block length is not that small. In order to better illustrate our proposed algorithms, the FTN system model is first introduced in this section. After Inspired by the successive symbol-by-symbol sequence es- that, the relation among Shannon capacity, the capacity of FTN timators in [27], we present a multi-layer iterative successive system and the capacity of Nyquist system is briefly explained. interference cancellation (MLISIC) algorithm in this paper. And then, the improved MLISIC (IMLISIC) algorithm is proposed to further promote the estimation accuracy. The main A. FTN System Model contributions of this paper are summarized as follows: 1) Firstly, in consideration of the promising prospect of P- Q-SRRC Tx Bits Mapping AWGN FTN signaling in satellite communications, FTN signal- upsampler filter ing is extended to high-order APSK modulations, which Sequence P- Q-SRRC Rx Bits Demapping are adopted in DVB-S2X, in this paper. As far as we estimator downsampler filter know, this is the first effort in the literature reported. In Fig. 1. The FTN system model addition, all the modulation types adopted in DVB-S2X are evaluated in FTN systems. The FTN system model used in
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