Wireless Communications and Mobile Computing

Volume 2018, Article ID 4181626, 10 pages

https://doi.org/10.1155/2018/4181626

## Superposition Coded Modulation Based Faster-Than-Nyquist Signaling

^{1}State Key Laboratory of ISN, Xidian University, Xi’an, China^{2}Science and Technology on Communication Networks Laboratory, Shijiazhuang, China^{3}Department of EEIS, University of Science and Technology of China, Hefei, China

Correspondence should be addressed to Baoming Bai; nc.ude.naidix.liam@iabmb

Received 24 November 2017; Accepted 31 March 2018; Published 16 May 2018

Academic Editor: Luca Reggiani

Copyright © 2018 Shuangyang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A structure of faster-than-Nyquist (FTN) signaling combined with superposition coded modulation (SCM) is considered. The so-called FTN-SCM structure is able to achieve the constrained capacity of FTN signaling and only requires a low detection complexity. By deriving a new observation model suitable for FTN-SCM, we offer the power allocation based on a proper detection method. Simulation results show that, at any given spectral efficiency, the bit error rate (BER) curve of FTN-SCM lies clearly outside the minimum signal-to-noise ratio (SNR) boundary of orthogonal signaling with a larger alphabet. The achieved data rates are also close to the maximum data rates of the certain shaping pulse.

#### 1. Introduction

With the demand and the growth of advanced signal processing capabilities at base stations, the need of efficient backhauling solutions to transmit a large amount of data increases significantly. Thus, as one of the most important parts of deploying the fifth-generation (5G) cellular network, more efficient backhauling techniques need to be applied [2]. Conventionally, the capacity of networks is enlarged by consuming more time/bandwidth/spatial resources. However, this solution may not always be possible, due to the practical reasons. Hence, as an alternative method to gain more capacity, FTN signaling has recently received a lot of attention. An overview of FTN signaling for 5G communication systems was provided in [3].

FTN signaling is an extension of traditional linear modulation and a classical way of nonorthogonal signal transmission, which was first proposed by Mazo in 1975 [4]. Mazo discovered that, with* sinc* pulse as the shaping pulse, the minimum squared Euclidean distance of binary phase shift keying (BPSK) modulated pulses remains the same even when the symbol rate is, to some extent, higher than the Nyquist criterion. His work indicates that there are roughly 25% more bits that could be transmitted in the same bandwidth compared to that of Nyquist signaling, with almost the same error performance over additive white Gaussian noise (AWGN) channels. Recently, Rusek et al. proved that FTN signaling is able to bring more degrees of freedom (DoF) over the AWGN channel [5, 6] compared to orthogonal signaling. As a result, a higher spectral efficiency is expected for FTN signaling and, indeed, fascinating simulation results have already been reported. In [7], a precoded FTN system with quadrature phase shift keying (QPSK) modulation was presented, which, as simulation results imply, requires lower SNR to reach the BER < compared to that of the constrained capacity of 8-PSK for orthogonal signaling with the same spectral efficiency. However, there is still no such signaling method existing in the literature that is able to outperform orthogonal signaling constrained by a larger alphabet at any preferred spectral efficiency. The reason for this problem lies in the complexity of maximum-likelihood (ML) detection for FTN signals growing exponentially with the size of the alphabet and with the number of taps of intersymbol interference (ISI), respectively. When the system requires high spectral efficiency, conventional FTN signaling systems need either an alphabet with a larger size or a compression factor of a smaller value to meet the requirements. Consequently, the required ML detection complexity becomes prohibitively high and a suboptimal detection method has to be utilized, which in return somehow damages the performance. Hence, in this paper, we attempt to solve such an issue by considering SCM [8–13].

SCM is a special case of multilevel coding (MLC) [8], which offers an excellent solution to transmissions with severe interference. With the use of the fast Fourier transform- (FFT-) based technique proposed in [9], the detection complexity of SCM system is , where is denoted as the frame length [10]. Moreover, with proper Gaussian assumption, the optimization for SCM systems is easier than that of conventional bit interleaved coded modulation (BICM) systems [10]. SCM has also been proven to have promising performance over a variety of channels [11, 12]. More advantages of SCM can be found in [10] and the references therein.

The idea of combining SCM with FTN signaling first appeared in [14], where FTN signals are treated as the sum of several orthogonal signals with different time delays; thus it allows the successive interference cancellation (SIC) detection at the receiver. However, in [1], it has been proven that the aforementioned structure cannot bring any gain in terms of DoF. Hence, a so-called “full-FTN" structure has been proposed in [1] along with its proof of achieving the constrained capacity of FTN signaling. In this structure, the signals are viewed as the sum of several FTN signals of the same compression factor and the SIC is also utilized to reduce the detection complexity. Different from the traditional FTN signaling, to gain a higher spectral efficiency, this structure utilizes more layers rather than a small compression factor. Since, with SIC detection, the detection complexity grows linearly with the number of layers and exponentially with the number of ISI taps, the overall detection complexity of this structure is normally very low. On the other hand, since at each layer, the symbol rate still exceeds the signal bandwidth, the DoF gain of FTN signaling is maintained. However, this structure still lacks a well-designed equalizer to perform SIC, because the common equalizers for FTN signaling, such as the one in [15], require the utilization of the whitening filter in the receiver. This is rather difficult and even impossible when the FTN signal, at each layer, is corrupted by both the colored noise and the signals from other layers. Hence, it is needed to derive a new observation model, which allows the SIC and the detection for each individual layer at the same time. It should also be noted that the combination of FTN signaling and SCM bypasses the obstacle of designing the channel code in terms of different compression factors. Similar to the traditional SCM, an identical code can be utilized for all layers of FTN-SCM, which makes the design and implementation of FTN-SCM system very easy. By simply adjusting the number of superposition layers and the power allocation, FTN-SCM is able to provide a wide range of spectral efficiencies with excellent performance.

The main contributions of this paper are summarized in the following:(1)We adapt the idea from [1] and provide a more generalized FTN-SCM scheme.(2)A new channel observation model suitable for FTN-SCM is introduced.(3)The detection method and the corresponding power allocation for FTN-SCM are also discussed.(4)Simulation results show that, for BER , FTN-SCM requires lower SNR than that of the orthogonal signaling with a larger alphabet at any given spectral efficiency.

The rest of this paper is organized as follows. The diagram of FTN-SCM is provided in Section 2. Then, the new channel observation is derived in Section 3. In Section 4, the detection method is described, along with the power allocation derivation. Our numerical results are presented in Section 5, and finally a brief conclusion is provided in Section 6.

#### 2. System Model

The transmitter structure of FTN-SCM is illustrated in Figure 1. Assume that the sequence carrying information bits is separated into substreams, namely, . Each subsequence of , say , is then encoded by its corresponding encoder generating the codeword of length . is the permuted version of , which is afterward modulated in the form of BPSK with an average symbol energy , where is a pregiven power, is the compression factor, and is the symbol time. represents the modulated symbols at the th layer, which are then superposed directly with the modulated symbols from other layers. The transmitted symbol sequence is obtained as the superposition is finished, where the th symbol of is given as . The FTN modulator is able to shape the transmitted signal for the given input based on a certain -orthogonal pulse . Without loss of generality, an FTN-SCM signal can be expressed as