Transmission Performance of an OFDM-Based Higher-Order Modulation Scheme in Multipath Fading Channels

Journal of Sensor and Actuator Networks

Article Transmission Performance of an OFDM-Based Higher-Order Modulation Scheme in Multipath Fading Channels

Hiroyuki Otsuka 1,*, Ruxiao Tian 2 and Koki Senda 2

1 Department of Information and Communications Engineering, Kogakuin University, Tokyo 163-8677, Japan 2 Graduate School of Engineering, Kogakuin University, Tokyo 163-8677, Japan; [email protected] (R.T.); [email protected] (K.S.) * Correspondence: [email protected]; Tel.: +81-3-3340-2865

Received: 26 February 2019; Accepted: 24 March 2019; Published: 27 March 2019

Abstract: Fifth-generation (5G) mobile systems are a necessary step toward successfully achieving further increases in data rates. As the use of higher-order quadrature amplitude modulation (QAM) is expected to increase data rates within a limited bandwidth, we propose a method for orthogonal frequency division multiplexing (OFDM)-based 1024- and 4096-QAM transmission with soft-decision Viterbi decoding for use in 5G mobile systems. Through evaluation of the transmission performance of the proposed method over multipath fading channels using link-level simulations, we determine the bit error rate (BER) performance of OFDM-based 1024- and 4096-QAM as a function of coding rate under two multipath fading channel models: extended pedestrian A (EPA) and extended vehicular A (EVA). We also demonstrate the inﬂuence of phase error on OFDM-based 1024- and 4096-QAM and clarify the relationship between phase error and the signal-to-noise ratio (SNR) penalty required to achieve a BER of 1 10 2. This work provides an eﬀective solution for introducing higher-order × − modulation schemes in 5G and beyond.

Keywords: mobile communication; higher-order modulation; 1024- and 4096-QAM; OFDM; multipath fading channels; SNR penalty; link-level simulations

1. Introduction Fifth-generation (5G) mobile systems are being developed worldwide with the objectives of increasing system capacity and data rates, achieving low latency, improving user throughput, and supporting “Internet of Things” services. These systems are expected to deliver peak data rates of up to 20 Gbps and 100 times higher typical data rates per user (user throughput) [1–4]. Fourth-generation (4G) mobile systems such as long term evolution (LTE) and LTE-Advanced mobile systems apply quadrature phase shift keying (QPSK), 16-quadrature amplitude modulation (QAM), and 64-QAM for the symbol modulation of orthogonal frequency division multiplexing (OFDM), as deﬁned by Release 8 of the Third Generation Partnership Project (3GPP) standards body. Although the highest modulation scheme under Release 8 was 64-QAM for LTE, 3GPP Release 12 discussed the implementation of 256-QAM, and more recently, 3GPP Release 15 introduced 1024-QAM support. Nevertheless, the application areas and/or conditions for these post-64-QAM schemes are currently very limited [5–7]. One of the most noteworthy technological pathways toward implementing 5G is increasing infrastructure density, which can reduce the distance between the user equipment (UE) and evolved node B (eNB), thereby improving the link budget between UE and eNB. The small-cell strategy is one of a number of denser infrastructure approaches in which a macro-cell is divided into several

J. Sens. Actuator Netw. 2019, 8, 19; doi:10.3390/jsan8020019 www.mdpi.com/journal/jsan J. Sens. Actuator Netw. 2019, 8, 19 2 of 15 small-cells [8,9], which can improve both system capacity and link budget because each eNB in a small-cell is directly connected to a core network. As another small-cell strategy, the concept of a phantom cell, has been proposed to provide efficient management of radio resources and mobility operation, where small-cells are overlaid on a macro-cell [10,11]. This approach splits the control and user-data planes; that is, the macro-eNB manages all UE within the overlaid cells, although UE can connect to a neighboring low-power eNB in the small-cell. Heterogeneous networks (HetNets) are another solution of denser infrastructures in which small- or pico-cells with low-power eNBs are installed within the coverage area of a macro-cell [12–16]. The objective of HetNet is to allow the UE to access pico-cells that overlap within a geographical coverage area even when the UE is within the coverage of a donor macro-cell. In other words, when the traffic in the donor macro-cell increases, its UE can access the pico-cells automatically. Through this mechanism, HetNet can increase system capacity, particularly when there is the heavy traffic in the macro-cell. Relay systems are an alternative approach to denser infrastructures that are primarily useful in improving cell edge performance in macro-cells [17–19]. In this scheme, a relay node (RN) installed at a macro-cell edge where the received signal power from the serving eNB is low can transmit a strengthened signal to the UE. Thus, the RN can physically reduce the distance between eNB and UE. Three-dimensional (3D) beamforming is another key technology for achieving 5G in which antenna beams can be individually tailored to each UE in the elevation domain through the use of a massive multiple-input and multiple-output (MIMO) antenna architectures. The use of 3D beamforming by MIMO antennas enables directs signal transmission toward a target UE, potentially increasing the received signal-to-noise ratio (SNR) or signal-to-interference plus noise ratio (SINR) while reducing the interference directed to adjacent cells and other UEs [20–22]. New technologies such as the small-cell strategy, HetNets, relay systems, and 3D beamforming that improve the received SINR will enhance the introduction of higher-order QAM schemes. Previously, we proposed OFDM-based 256-, 1024-, and 4096-QAM for use in mobile systems and determined the fundamental transmission performance needed for the use of hard-decision Viterbi decoding in a typical additive white Gaussian noise (AWGN) channel [23–26]. However, the transmission performance of higher-order QAM with soft-decision Viterbi decoding in multipath fading channels has not been sufficiently investigated. On the basis of this background, in this study we investigate the transmission performance of OFDM-based 1024- and 4096-QAM with soft-decision Viterbi decoding in multipath fading channels using link-level simulations. Specifically, we clarify the bit error rate (BER) performance of OFDM-based 1024- and 4096-QAM as a function of coding rate under two multipath fading channel models: extended pedestrian A (EPA) and extended vehicular A (EVA). We also demonstrate the influence of phase error on OFDM-based 1024- and 4096-QAM and clarify the relationship between phase error and the SNR penalty required to achieve a BER of 1 10 2. × − This paper is organized as follows. In Section2, we introduce an OFDM-based 1024- and 4096-QAM transmission model and its associated computer simulation conditions. In Section3, we discuss the BER performance of OFDM-based 1024- and 4096-QAM in multipath fading channels and the SNR penalty in the presence of phase error. Finally, we conclude our work in Section4.

2. Transmission Model and Simulation Conditions

2.1. Application Example Higher-order modulation schemes require higher levels of received SINR to correctly demodulate transmission signals, because the higher-order modulation scheme is very sensitive to noise, nonlinear distortion, interference, and multipath fading. To keep higher received SINR, higher-order modulation schemes such as 1024- and 4096-QAM can be implemented in point-to-point systems, e.g., in backhaul links with line-of-sight propagation conditions. Figure1 shows an application example of higher-order modulation schemes used in HetNet, where a large macro-cell operated by macro-eNB is combined J. Sens. Actuator Netw. 2019, 8, 19 3 of 15

J. Sens. Actuator Netw. 2019, 8, 19 3 of 15 with pico-cells operated by pico-eNB. In this case, the downlink SINR received at pico-eNB will be higherpico-eNB because is fixed the and transmission the antennas link of between pico-eNB the ar macro-eNBe located higher and pico-eNB than UE. isConsequently, ﬁxed and the antennasa higher- oforder pico-eNB modulation are located scheme higher can be thanimplemented UE. Consequently, to the backhaul a higher-order link between modulation the macro-eNB scheme and can pico- be implementedeNB, as shown to in theFigure backhaul 1. Figure link 1 also between includes the a macro-eNB relay system and operated pico-eNB, by a as relay shown node, in where Figure the1. Figurerelay node1 also is includesinstalled aaround relay systema macro-cell operated edge byto recover, a relay node, amplify where and retransmit the relay node to the is UE, installed a now aroundstrengthened a macro-cell but previously edge to recover,poor signal amplify received and from retransmit the macro-eNB. to the UE, Similarly, a now strengthened a higher-order but previouslymodulation poor scheme signal can received be implemented from the to macro-eNB. the backhaul Similarly, link between a higher-order the macro-eNB modulation and relay scheme node can[26,27]. be implementedIt is also expected to the that backhaul higher-order link between modulation the macro-eNBschemes will and be used relay to node directly [26, 27link]. Itbetween is also expectedeNBs and that UE higher-orderover limited modulationareas, e.g., in schemes small-cell will systems be used with to directly very little link betweeninterference, eNBs inand indoor UE overenvironments, limited areas, and so e.g., on. in However, small-cell in systems the near with future, very higher-order little interference, modulation in indoor schemes environments, will diffuse andthrough so on. the However, use of inenhanced the near future,technologies higher-order such modulationas powerful schemes coding will and diﬀ usehighly through precise the use3D ofbeamforming. enhanced technologies such as powerful coding and highly precise 3D beamforming.

Figure 1.1.Application Application example example of higher-orderof higher-order modulation modulation schemes schemes such as such 1024- andas 1024- 4096-quadrature and 4096- amplitudequadrature modulation amplitude (QAM)modulation in backhaul (QAM) links in backhaul for pico-evolved links for node pico-evolved B (eNB) and node a relay B (eNB) node. and UE =a userrelay equipment. node. UE = user equipment.

2.2. Transmission Model Figure2 2 shows shows aa transmissiontransmission modelmodel ofof anan OFDM-based OFDM-based higher-orderhigher-order modulationmodulation schemesschemes inin downlink with a single antenna branch. The transmitter includes an encoder, a QAM mapper, a pilot insertion, an inverse fast Fourier transform (IFFT),(IFFT), andand aa cycliccyclic preﬁxprefix (CP)(CP) insertion.insertion. Input baseband signals are encoded via turbo coding whichwhich isis typicallytypically usedused inin 4G4G systems.systems. The encoded signals are converted to QAM mapper to produceproduce aa 1024-1024- oror 4096-QAM4096-QAM signal.signal. Then, the IFFT forms OFDMOFDM signals. Finally, aa CPCP inin thethe formform of of a a copy copy of of the the tail tail of of a a symbol symbol placed placed at at its its beginning beginning is insertedis inserted to reduceto reduce inter inter symbol symbol interference. interference. Pilot Pilot insertion insertion is used is toused estimate to estimate the channel the channel response response at the receiver at the sidereceiver under side multipath under multipath fading conditions. fading conditions. At the receiver At the side,receiver ﬁrst side, the CP first is the removed CP is removed and the FFT and then the separatesFFT then theseparates individual the individual subcarrier subcarrier components comp andonents converts and them converts to QAM them format. to QAM Each format. component Each signalcomponent is then signal demodulated is then demodulated by the QAM de-mapper. by the QAM Finally, de-mapper. the soft-decision Finally, the Viterbi soft-decision decoding isViterbi used todecoding output theis used original to basebandoutput the signals. original Channel baseband estimation signals. and Channel channel estimation equalization and are channel used to compensateequalization receivedare used signalsto compensate distorted receiv by multipathed signals fading. distorted by multipath fading.

J. Sens. Actuator Netw. 2019, 8, 19 4 of 15 J. Sens. Actuator Netw. 2019, 8, 19 44 of of 15 J. Sens. Actuator Netw. 2019, 8, 19 4 of 15

Figure 2. Transmission model of orthogonal frequency division multiplexing (OFDM)-based 1024-

andFigure 4096-QAM. 2. Transmission IFFT = inverse model fastof orthogonal Fourier transform; frequenc FFTy division = fast Fourier multiplexing transform; (OFDM)-based AWGN = additive 1024- Figure 2. Transmission model of orthogonal frequency division multiplexing (OFDM)-based 1024- and Figurewhiteand 4096-QAM. Gaussian 2. Transmission noise.IFFT = inverse model fastof orthogonal Fourier transform; frequenc FFTy division = fast Fourier multiplexing transform; (OFDM)-based AWGN = additive 1024- 4096-QAM. IFFT = inverse fast Fourier transform; FFT = fast Fourier transform; AWGN = additive andwhite 4096-QAM. Gaussian IFFTnoise. = inverse fast Fourier transform; FFT = fast Fourier transform; AWGN = additive whiteFigure Gaussian 3 shows noise. a block diagram of the turbo encoder (coding rate = 1/3), which uses two identical convolutional encoders (1st and 2nd encoders) with a constraint length of four and one internal Figure3 3 shows shows aa blockblock diagramdiagram of of thethe turboturbo encoderencoder (coding (coding rate rate = 1/3),1/3), which uses two identical interleaver.Figure 3Figure shows 4 a showsblock diagram a block ofdiagram the turbo of encoderthe soft-decision (coding rate Viterbi = 1/3), decoder, which uses which two comprises identical convolutional encoders (1st and 2nd encoders) with a constraint length of four and one internal convolutionaltwo single soft-in encoders soft-out (1st (SISO) and decoders2nd encoders) that work with iteratively, a constraint with length the output of four of and the firstone decoderinternal interleaver. Figure Figure 44 showsshows aa blockblock diagramdiagram ofof thethe soft-decisionsoft-decision ViterbiViterbi decoder,decoder, which which comprises comprises interleaver.(SISO decoder Figure 1) feeding 4 shows into a the block second diagram decoder of the (SISO soft-decision decoder 2) Viterbito form decoder,a turbo decoding which comprises iteration. two single soft-in soft-out (SISO) decoders that work iteratively, with the output of the ﬁrstfirst decoder twoDuring single this soft-in process, soft-out interleaver (SISO) and decoders de-inte thatrleaver work blocks iteratively, re-order with the the data output [28,29]. of the first decoder (SISO decoder 1) feeding into the second decoder (SISO decoder 2) to to form form a a turbo turbo decoding decoding iteration. iteration. (SISO decoder 1) feeding into the second decoder (SISO decoder 2) to form a turbo decoding iteration. During this process, interleaver andand de-interleaverde-interleaver blocksblocks re-orderre-order thethe datadata [[28,29].28,29]. During this process, interleaver and de-interleaver blocks re-order the data [28,29].

Figure 3. Block diagram of turbo encoder. xk is the first systematic bit (original input bit). zk and zk’ Figure 3. Block diagram of turbo encoder. xk is the ﬁrst systematic bit (original input bit). zk and zk’ areFigure the outputs3. Block ofdiagram 1st and of 2nd turbo encoders, encoder. respectively. xk is the first systematic bit (original input bit). zk and zk’ are the outputs of 1st and 2nd encoders, respectively. Figureare the 3.outputs Block diagramof 1st and of 2nd turbo encoders, encoder. respectively. xk is the first systematic bit (original input bit). zk and zk’ are the outputs of 1st and 2nd encoders, respectively.

Figure 4. Block diagram of soft-decision Viterbi decoder. SISO = soft-in soft-out. Figure 4. Block diagram of soft-decision Viterbi decoder. SISO = soft-in soft-out. The computerFigure simulation4. Block diagram parameters of soft-decision are listed Viterbi in Tabledecoder.1. TheSISO IFFT= soft-in/FFT soft-out. size is 2048 which The computerFigure simulation4. Block diagram parameters of soft-decision are listed Viterbi in Tabledecoder. 1. SISOThe =IFFT/FFT soft-in soft-out. size is 2048 which corresponds to a transmission bandwidth of 20 MHz, and the subcarrier spacing of OFDM is 15 kHz. corresponds to a transmission bandwidth of 20 MHz, and the subcarrier spacing of OFDM is 15 kHz. The codingThe computer rates of the simulation turbo encoder parameters are assumed are listed to be 1in/3, Table 1/2, 2 /3,1. 3The/4, and IFFT/FFT 1, andthe size constraint is 2048 lengthwhich The codingThe computer rates of simulationthe turbo encoder parameters are assumed are listed to inbe Table 1/3, 1/2, 1. The2/3, 3/4,IFFT/FFT and 1, sizeand isthe 2048 constraint which iscorresponds ﬁxed at four. to a QAM transmission signals arebandwidth mapped of by 20 the MHz, rule and of Gray-code. the subcarrier The spacing CP is produced of OFDM using is 15 kHz. 1024 correspondslengthThe coding is fixed rates to at a transmission four.of the QAM turbo signals bandwidthencoder are are mapped of assumed 20 MHz, by theto and berule the1/3, of subcarrier 1/2,Gray-code. 2/3, 3/4, spacing The and CP 1, of andis OFDM produced the constraintis 15 using kHz. Thelength coding is fixed rates at four.of the QAM turbo signals encoder are are mapped assumed by theto be rule 1/3, of 1/2, Gray-code. 2/3, 3/4, Theand CP1, and is produced the constraint using length is fixed at four. QAM signals are mapped by the rule of Gray-code. The CP is produced using

J. Sens. Actuator Netw. 2019, 8, 19 5 of 15 samples for seven OFDM symbols, the ﬁrst of which uses 160 samples as the CP, with the remaining six using 144 samples. This is referred to as normal CP in LTE mobile systems.

Table 1. Simulation parameters. QPSK = quadrature phase shift keying.

Parameter Value Symbol modulation QPSK to 4096-QAM Turbo encoding Encoder Coding rate R = 1/3, 1/2, 2/3, 3/4, 1 Constraint length = 4 Signal mapping Gray code Transmission bandwidth 20 MHz IFFT/FFT size 2048 Cyclic preﬁx length 144 The number of transmitter/receiver antennas 1/1 Decoder Soft-decision Viterbi decoding

The multipath fading channels specify the following two profiles, extended pedestrian A (EPA) and extended vehicular A (EVA), whose delay profiles represent low and medium delay spreads, respectively, as listed in Table2[ 30]. Doppler frequency shift is an apparent change in the carrier frequency due to the relative motion of two objects (here, the eNB and UE). The maximum Doppler frequency shift is fixed at 5 Hz, assuming a UE velocity of 3 km/h for the carrier frequency band of 2 GHz.

Table 2. Multipath fading channels used in the simulation. EPA = extended pedestrian A; EVA = extended vehicular A.

Type Parameter Value Path delay (ns) 0, 30, 70, 90, 110, 190, 410 EPA Path gain (dB) 0, 1, 2, 3, 8, 17.2, 20.8 − − − − − − Path delay (ns) 0, 30, 150, 310, 370, 710, 1090, 1730, 2510 EVA Path gain (dB) 0, 1.5, 1.4, 3.6, 0.6, 9.1, 7.0, 12.0, 16.9 − − − − − − − −

3. Simulation Results

3.1. Fundamental Bit Error Rate (BER) Performance under Additive White Gaussian Noise (AWGN) Figure5a,b shows the signal constellation for 1024- and 4096-QAM, respectively, at the transmitter side. As the multilevel (order) of QAM increases, the Euclidean distance among signal constellations naturally shortens, as shown in Figure5. Figure6 shows the observed instantaneous OFDM spectrum for 1200 subcarriers containing 1024- or 4096-QAM symbol modulation signals. Figure7 plots the fundamental BER against received SNR of 1024-QAM at various coding rates, R, under an AWGN channel condition. The BER is measured by comparing the demodulated serial bits with the original binary serial bits. In this work, we assume a benchmark BER of 1 10 2. When turbo × − coding and soft-decision Viterbi decoding are used, the SNRs needed to achieve a BER of 1 10 2 × − at coding rates R of 1/3, 1/2, 2/3, and 3/4, which are approximately 14 dB, 19 dB, 23 dB, and 25 dB, respectively. The BER at a coding rate of one, i.e., without coding (w/o), is also plotted as a reference. Figure8 plots the fundamental BER against received SNR of 4096-QAM at various coding rates under the condition of AWGN channels. The SNRs needed to achieve a BER of 1 10 2 at coding rates × − of 1/3, 1/2, 2/3, and 3/4 are approximately 16 dB, 22 dB, 28 dB, and 30 dB, respectively. Relative to 1024-QAM, the SNRs needed to achieve the benchmark BER of 1 10 2 for 4096-QAM are increased by × − J. Sens. Actuator Netw. 2019, 8, 19 6 of 15 approximately 2 dB, 3 dB, 5 dB, and 5 dB at coding rates of 1/3, 1/2, 2/3, and 3/4, respectively. Figure9 shows an overall comparison of BERs for QPSK, 16-, 64-, 256-, 1024-, and 4096-QAM at coding rates of 1/3 (blue lines) and 3/4 (red lines). The SNRs required for 4096-QAM at these coding rates are, J.J. Sens. Sens. Actuator Actuator Netw. Netw. 2019 2019, ,8 8, ,19 19 66 ofof 1515 respectively,J. Sens. Actuator 17 dB Netw. and 2019 26, 8 dB, 19 higher than those required for QPSK. Current LTE mobile systems6 of 15 use a a link adaptation technology that can choose a modulation scheme and coding rates depending on link adaptationaa link link adaptation adaptation technology technology technology that that canthat can choosecan choose choose a modulation a a mo modulationdulation scheme scheme scheme andand and codingcoding coding rates rates depending dependingdepending on on on the the channel quality, i.e., received SNR or SINR. The results in Figure 9 suggest that if 4096-QAM is channelthethe channel quality,channel quality, i.e.,quality, received i.e., i.e., received received SNR orSNR SNR SINR. or or SINR. SINR. The The results The results results inFigure in in Figure Figure9 suggest 9 9 suggest suggest that that that if if 4096-QAM if 4096-QAM 4096-QAM isis is used used for the “modulation and coding sets (MCS)”, 4096-QAM at coding rates of 1/3 or 3/4 can be for theusedused “modulation for for the the “modulation “modulation and coding and and sets coding coding (MCS)”, sets sets (MCS)”, 4096-QAM(MCS)”, 4096-QAM 4096-QAM at coding at at coding ratescoding of rates rates 1/3 orof of 31/3 /1/34 canor or 3/4 3/4 be can assignedcan be be to assigned to a UE at received SINRs of more than 16 dB or 30 dB, respectively. Similarly, 1024-QAM a UEassigned atassigned received to to a a SINRsUE UE at at received ofreceived more SINRs thanSINRs 16 of of dBmore more or than 30than dB, 16 16 respectively.dB dB or or 30 30 dB, dB, respectively. Similarly,respectively. 1024-QAM Similarly, Similarly, 1024-QAM at1024-QAM a coding rate atat aa codingcoding raterate ofof 1/31/3 cancan bebe assignedassigned toto aa UEUE atat receivedreceived SINRSINR ofof moremore thanthan 1414 dB.dB. of 1/3at can a coding be assigned rate of 1/3 to acan UE be at assigned received to SINRa UE at of received more than SINR 14 of dB. more than 14 dB.

(a) (b) (a(a) ) (b(b) ) FigureFigure 5.5. SignalSignal constellationconstellation atat transmittertransmitter sideside forfor ((aa)) 1024-QAM1024-QAM andand ((bb)) 4096-QAM4096-QAM [26].[26]. FigureFigure 5. Signal 5. Signal constellation constellation at at transmitter transmitter sideside for ( (aa)) 1024-QAM 1024-QAM and and (b) ( b4096-QAM) 4096-QAM [26]. [ 26].

Figure 6. OFDM spectrum at transmitter side. FigureFigure 6.6. OFDMOFDM spectrumspectrum atat transmittertransmitter side.side. Figure 6. OFDM spectrum at transmitter side.

FigureFigure 7.7. FundamentalFundamental bitbit errorerror raterate (BER)(BER) performanceperformance ofof 1024-QAM1024-QAM asas aa functionfunction ofof codingcoding rate.rate. FigureFigure 7. Fundamental 7. Fundamental bit bit error error rate rate (BER) (BER) performanceperformance of of 1024-QAM 1024-QAM as asa function a function of coding of coding rate. rate. SNRSNR == signal-to-noisesignal-to-noise ratio.ratio. SNR =SNRsignal-to-noise = signal-to-noise ratio. ratio.

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Figure 8. Fundamental BER performance of 4096-QAM as a function of coding rate [26]. FigureFigure 8.8. Fundamental BER performance of 4096-QAM asas aa functionfunction ofof codingcoding raterate [[26].26].

Figure 9. BER performance for QPSK to 4096-QAM atat codingcoding ratesrates ofof 11/3/3 andand 33/4./4. QPSKQPSK == quadrature Figure 9. BER performance for QPSK to 4096-QAM at coding rates of 1/3 and 3/4. QPSK = quadrature phase shift keying.keying. phase shift keying. 3.2. SNR Penalty in the Presence of Phase Error 3.2. SNR Penalty in the Presence of Phase Error We thenthen evaluateevaluate thethe inﬂuenceinfluence ofof phasephase errorerror whichwhich isis measuredmeasured inin unitsunits ofof radians. Figure 1010a,ba,b We then evaluate the influence of phase error which is measured in units of radians. Figure 10a,b shows photos of signal constellationsconstellations for 1024- and 4096-QAM, 4096-QAM, respectively, respectively, at a phase error of 0.08. shows photos of signal constellations for 1024- and 4096-QAM, respectively, at a phase error of 0.08. In general, the BER worsens as the phase error increases,increases, because higher-order QAM has a weakness In general, the BER worsens as the phase error increases, because higher-order QAM has a weakness for errors in in amplitude amplitude and and phase phase as as a aresult result of of the the shortening shortening Euclidean Euclidean distance. distance. In some In some cases, cases, the for errors in amplitude and phase as a result of2 the shortening Euclidean distance. In some cases, the theQAM QAM can canno longer no longer meet meet a BER a BER of 1 of × 10 1 −2 10even− even if SNR if SNRis increased. is increased. QAM can no longer meet a BER of 1 × 10×−2 even if SNR is increased. Figure 1111 shows shows the the BER BER of of 1024-QAM 1024-QAM as aas function a function of phase of phase error error at a codingat a coding rate of rate 1/3. of At 1/3. phase At Figure 11 shows the BER of 1024-QAM as a function of phase2 error at a coding rate of 1/3. At errorsphase oferrors 0.10 andof 0.10 0.15, and the SNRs0.15, the needed SNRs to achieveneeded ato BER achieve of 1 a10 BER− are of increased 1 × 10−2 byare approximately increased by phase errors of 0.10 and 0.15, the SNRs needed to achieve× a BER of 1 × 10−2 are increased by 1.5approximately dB and 5 dB, 1.5 respectively, dB and 5 dB, relative respectively, to the no-phase-error relative to the no-phase-error case. When the case. phase When error the is increased phase error to approximately 1.5 dB and 5 dB, respectively, relative to the2 no-phase-error case. When the phase error 0.20,is increased 1024-QAM to 0.20, can 1024-QAM no longer achieve can no longer a BER ofachieve 1 10 a− BEReven of if 1 the × 10 SNR−2 even is increased. if the SNR is increased. is increased to 0.20, 1024-QAM can no longer achieve× a BER of 1 × 10−2 even2 if the SNR is increased. Figure 12 showsshows thethe SNRSNR penaltypenalty neededneeded toto achieveachieve aa BERBER ofof 11 × 1010−−2 against phase error for Figure 12 shows the SNR penalty needed to achieve a BER of 1× × 10−2 against phase error for 1024-QAM1024-QAM atat variousvarious codingcoding rates.rates. It is clearly observed that the SNR penalty increases as the phase 1024-QAM at various coding rates. It is clearly observed that the SNR penalty increases as the phase error increases.increases. TheThe SNRSNR penalty penalty is is approximately approximately 6 dB6 dB at at a phasea phase error error of 0.05of 0.05 and and a coding a coding rate rate of 3 /of4. error increases. The SNR penalty is approximately 6 dB at a phase error of 0.05 and a coding rate of

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3/4.3/4. ToTo reducereduce thethe SNRSNR penaltypenalty toto belowbelow 33 dB,dB, thethe phasephase errorerror cannotcannot exceedexceed 0.040.04 atat codingcoding ratesrates ofof 3/43/4 oror below.below. FigureFigure 1313 showsshows thethe BERBER ofof 4096-QAM4096-QAM asas aa functionfunction ofof phasephase errorerror atat aa codingcoding raterate ofof 1/3.1/3. AtAt −2 phasephase errorserrors ofof 0.080.08 andand 0.12,0.12, thethe SNSNRsRs neededneeded toto achieveachieve aa BERBER ofof 11 ×× 1010−2 areare increasedincreased byby approximatelyapproximately 22 dBdB andand 44 dB,dB, respectively,respectively, relativerelative toto thethe no-phase-errorno-phase-error case.case. WhenWhen thethe phasephase errorerror −2 isis increasedincreased 0.16,0.16, 4096-QAM4096-QAM cancan nono longerlonger achieveachieve aa BERBER ofof 11 ×× 1010−2,, eveneven ifif thethe SNRSNR isis increased.increased. FigureFigure 1414 showsshows thethe BERBER ofof 4096-QAM4096-QAM asas aa functionfunction ofof phasephase errorerror atat aa codingcoding raterate ofof 3/4.3/4. RelativeRelative toto thethe casecase forfor whichwhich thethe codingcoding raterate ofof 1/3,1/3, thethe BERBER isis worse,worse, andand whenwhen thethe phasephase errorerror isis increasedincreased toto −2 0.04,0.04, 4096-QAM4096-QAM cancan nono longerlonger achieveachieve aa BERBER ofof 11 ×× 1010−2 eveneven ifif thethe SNRSNR isis increased.increased. −2 FigureFigure 1515 plotsplots thethe SNRSNR penaltypenalty neededneeded toto achieveachieve aa BERBER ofof 11 ×× 1010−2 againstagainst phasephase errorerror forfor 4096-4096- QAMQAM atat variousvarious codingcoding rates.rates. AtAt aa phasephase errorerror ofof 0.030.03 andand aa codingcoding raterate ofof 2/3,2/3, thethe SNRSNR penaltypenalty ofof 4096-QAM4096-QAM isis approximatelyapproximately 66 dB.dB. ToTo reducereduce thethe SNRSNR penaltypenalty toto lessless thanthan 33 dB,dB, thethe phasephase errorerror mustmust bebe nono greatergreater thanthan 0.0240.024 atat aa codingcoding raterate ofof 3/43/4 oror below.below. −2 FigureFigure 1616 plotsplots thethe SNRSNR penaltypenalty requiredrequired toto achieveachieve aa BERBER ofof 11 ×× 1010−2 againstagainst phasephase errorerror forfor QPSK,J.QPSK, Sens. Actuator 16-,16-, 64-,64-, Netw. 256-,256-,2019 1024-,1024-,, 8, 19 andand 4096-QAM4096-QAM atat aa codingcoding raterate ofof 1/3.1/3. PhasePhase errorerror severelyseverely impactsimpacts 1024-81024- of 15 andand 4096-QAM4096-QAM comparedcompared withwith existingexisting QAMQAM andand QPSKQPSK schemes.schemes. ToTo limitlimit ththee SNRSNR penaltypenalty toto belowbelow 3 dB, the phase errors for 16-, 64-, 256-, 1024-, and 4096-QAM must be no greater than 0.39, 0.31, 0.18, To3 dB, reduce the phase the SNR errors penalty for 16-, to 64-, below 256-, 3 dB,1024-, the and phase 4096-QAM error cannot must exceedbe no greater 0.04 at than coding 0.39, rates 0.31, of 0.18, 3/4 0.12, and 0.11, respectively. or0.12, below. and 0.11, respectively.

((aa)) ((bb))

FigureFigure 10. 10. SignalSignal constellation constellation at at a a phase phase error error of of 0.08 0.08 radian radian for for ( (aa)) 1024-QAM 1024-QAM and and ( (bb)) 4096-QAM.4096-QAM.

J. Sens. ActuatorFigure Netw. 11. BER 2019 performance, 8, 19 of 1024-QAM as a function of phase error at a coding rate of 1/3 [26]. 9 of 15 FigureFigure 11.11. BERBER performanceperformance ofof 1024-QAM1024-QAM asas aa functionfunction ofof phasephase errorerror atat aa codingcoding raterate ofof 1/31/3 [26].[26].

Figure 12. SNR penalty against phase error for 1024-QAM [26]. Figure 12. SNR penalty against phase error for 1024-QAM [26].

Figure 13. BER performance of 4096-QAM as a function of phase error at a coding rate of 1/3 [26].

Figure 14. BER performance of 4096-QAM as a function of phase error at a coding rate of 3/4.

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Figure 13 shows the BER of 4096-QAM as a function of phase error at a coding rate of 1/3. At phase errors of 0.08 and 0.12, the SNRs needed to achieve a BER of 1 10 2 are increased by approximately × − 2 dB and 4 dB, respectively, relative to the no-phase-error case. When the phase error is increased 0.16, 4096-QAM can no longer achieve a BER of 1 10 2, even if the SNR is increased. Figure 14 shows the × − BER of 4096-QAM as a function of phase error at a coding rate of 3/4. Relative to the case for which the coding rate of 1/3, theFigure BER is 12. worse, SNR penalty and when against the phase phase error error for is 1024-QAM increased [26]. to 0.04, 4096-QAM can no longer achieve a BER ofFigure 1 1012. SNR2 even penalty if the against SNR is phase increased. error for 1024-QAM [26]. × −

Figure 13. BER performance of 4096-QAM as a function of phase error at a coding rate of 1/3 [26]. Figure 13. BERBER performance performance of of 4096-QAM 4096-QAM as as a a function function of phase error at a coding rate of 1/3 1/3 [[26].26].

FigureFigure 14. 14. BERBER performance performance of of 4096-QAM 4096-QAM as as a a function function of of phase phase error error at at a a coding coding rate rate of of 3/4. 3/4. Figure 14. BER performance of 4096-QAM as a function of phase error at a coding rate of 3/4. Figure 15 plots the SNR penalty needed to achieve a BER of 1 10 2 against phase error for × − 4096-QAM at various coding rates. At a phase error of 0.03 and a coding rate of 2/3, the SNR penalty of

4096-QAM is approximately 6 dB. To reduce the SNR penalty to less than 3 dB, the phase error must be no greater than 0.024 at a coding rate of 3/4 or below. Figure 16 plots the SNR penalty required to achieve a BER of 1 10 2 against phase error for × − QPSK, 16-, 64-, 256-, 1024-, and 4096-QAM at a coding rate of 1/3. Phase error severely impacts 1024- and 4096-QAM compared with existing QAM and QPSK schemes. To limit the SNR penalty to below 3 dB, the phase errors for 16-, 64-, 256-, 1024-, and 4096-QAM must be no greater than 0.39, 0.31, 0.18, 0.12, and 0.11, respectively. J. Sens. Actuator Netw. 2019, 8, 19 10 of 15 J.J. Sens.Sens. ActuatorActuator Netw.Netw. 20192019,, 88,, 1919 1010 ofof 1515

Figure 15. SNR penalty against phase error for 4096-QAM [26]. FigureFigure 15.15. SNRSNR penaltypenalty againstagainst phasephase errorerror forfor 4096-QAM4096-QAM [26].[26].

Figure 16. SNR penalty against phase error for QPSK to 4096-QAM at a coding rate of 1/3. FigureFigure 16.16. SNRSNR penaltypenalty againstagainst phasephase errorerror forfor QPSKQPSK toto 4096-QAM4096-QAM atat aa codingcoding raterate ofof 1/3.1/3. 3.3. BER Performance in Multipath Fading Channels 3.3.3.3. BERBER PerformancePerformance inin MultipathMultipath FadingFading ChannelsChannels Next, we evaluate the BER performance of 1024- and 4096-QAM in the multipath fading channels Next, we evaluate the BER performance of 1024- and 4096-QAM in the multipath fading listedNext, in Table we2 evaluate. Figure 17thea,b BER show performance the signal constellations of 1024- and for 4096-QAM 1024- and 4096-QAM,in the multipath respectively, fading channels listed in Table 2. Figure 17a,b show the signal constellations for 1024- and 4096-QAM, channelsobserved atlisted a receiver in Table side 2. a ffFigureectedby 17a,b EPA show fading. the Figure signal 18 constellationsshows the instantaneous for 1024- and OFDM 4096-QAM, spectrum respectively, observed at a receiver side affected by EPA fading. Figure 18 shows the instantaneous respectively,observed at the observed receiver at side. a receiver Channel side estimation affected andby EPA channel fading. equalization, Figure 18 asshows shown the in instantaneous Figure2, play OFDM spectrum observed at the receiver side. Channel estimation and channel equalization, as OFDMan important spectrum role toobserved compensate at the these receiver distorted side. signals Channel at theestimation receiver side.and channel If the channel equalization, estimation as shown in Figure 2, play an important role to compensate these distorted signals at the receiver side. shownand channel in Figure equalization 2, play an do important not work role suffi tociently, compensate the BER these performance distorted worsens.signals at the receiver side. If the channel estimation and channel equalization do not work sufficiently, the BER performance If theFigure channel 19 estimationplots the BER and of channel 1024-QAM equalization against received do not SNRwork under sufficiently, EPA fading the BER at coding performance rates of worsens. worsens.1/3, 1/2, 2 /3, and 3/4. The broken line indicates the BER obtained without fading (w/o fading), i.e., under FigureFigure 1919 plotsplots thethe BERBER ofof 1024-QAM1024-QAM againstagainst recereceivedived SNRSNR underunder EPAEPA fadingfading2 atat codingcoding ratesrates ofof static conditions. At a coding rate of 1/3, the SNR needed to achieve a BER of 1 10− is approximately 1/3, 1/2, 2/3, and 3/4. The broken line indicates the BER obtained without fading× (w/o fading), i.e., 1/3,20 dB, 1/2, which 2/3, and is approximately3/4. The broken 6 dBline higher indicates than the what BER is obtained required without under thefading static (w/o condition. fading), Thisi.e., under static conditions. At a coding rate of 1/3, the SNR needed to achieve a BER of 1 × 10−−22 is underbehavior static is similar conditions. to that At observed a coding at therate other of 1/3, coding the rates.SNR Theneeded performance to achieve degradation a BER of is1 assumed× 10 is approximately 20 dB, which is approximately 6 dB higher than what is required under the static approximatelyto be affected by 20 Doppler dB, which frequency is approximately shift and by 6 imperfectionsdB higher than in thewhat channel is required estimation under process. the static condition.condition. ThisThis behaviorbehavior isis similarsimilar toto thatthat observedobserved atat thethe otherother codingcoding rates.rates. TheThe performanceperformance degradationdegradation isis assumedassumed toto bebe affeaffectedcted byby DopplerDoppler frequencyfrequency shiftshift andand byby imperfectionsimperfections inin thethe channelchannel estimationestimation process.process. FigureFigure 2020 plotsplots thethe BERBER ofof 1024-QAM1024-QAM againsagainstt receivedreceived SNRSNR underunder thethe EVAEVA fadingfading model.model. ComparedCompared toto thethe EPAEPA fadingfading case,case, thethe BERBER performancperformancee isis significantlysignificantly degraded.degraded. AtAt aa codingcoding raterate ofof 1/3,1/3, thethe SNRSNR requiredrequired toto achieveachieve aa BERBER ofof 11 ×× 1010−−22 isis approximatelyapproximately 2222 dB,dB, whichwhich isis approximatelyapproximately

J. Sens. Actuator Netw. 2019, 8, 19 11 of 15

8J. dBSens. higher Actuator than Netw. that 2019 is, 8 required, 19 under the static condition. At coding rates above 2/3, 1024-QAM11 ofcan 15 no longer achieve a BER of 1 × 10−2. 8 dB Figurehigher 21than plots that the is requiredBER of 4096-QAM under the againststatic condition. received SNRAt coding under rates EPA above fading 2/3, at coding1024-QAM rates can of 1/3,no longer 1/2, 2/3, achieve and 3/4.a BER At of a 1coding × 10−2. rate of 1/3, the SNR required to achieve a BER of 1 × 10−2 is approximatelyFigure 21 plots22 dB, the which BER of is 4096-QAM approximately against 7 dBrece higherived SNR than under that EPAis required fading atunder coding the rates static of condition.1/3, 1/2, 2/3, This and behavior 3/4. At is a similar coding to rate that ofobserved 1/3, the at SNR the otherrequired coding to achieverates. Relative a BER to of 1024-QAM, 1 × 10−2 is theapproximately SNRs required 22 dB,to achieve which isa BERapproximately of 1 × 10−2 7at dBcoding higher rates than of that1/3, 1/2,is required 2/3, and under 3/4 under the staticEPA fadingcondition. are increasedThis behavior by approximately is similar to that 2–5 observed dB. at the other coding rates. Relative to 1024-QAM, the SNRsFigure required 22 plots tothe achieve BER of a4096-QAM BER of 1 against× 10−2 at rece codingived ratesSNR underof 1/3, EVA 1/2, 2/3,fading. and At 3/4 a codingunder EPArate offading 1/3, the are SNR increased required by approximately to achieve a BER 2–5 of dB. 1 × 10−2 is approximately 24 dB, which is approximately 9 dB Figurehigher 22than plots that the is BERrequired of 4096-QAM under the against static condition.received SNR At codingunder EVArates fading. greater At than a coding 1/2, 4096- rate QAMof 1/3, can the noSNR longer required achieve to achieve a BER of a BER1 × 10 of−2 .1 × 10−2 is approximately 24 dB, which is approximately 9 dB higher than that is required under the static condition. At coding rates greater than 1/2, 4096- J. Sens. Actuator Netw. 2019, 8, 19 11 of 15 QAM can no longer achieve a BER of 1 × 10−2.

(a) (b)

Figure 17. Signal constellation(a) at receiver side under EPA fading for ((ba)) 1024-QAM and (b) 4096- QAM. Figure 17.17. SignalSignal constellationconstellation at at receiver receiver side side under under EPA EPA fading fading for (fora) 1024-QAM (a) 1024-QAM and ( band) 4096-QAM. (b) 4096- QAM.

Figure 18. OFDM spectrum observed at receiver side under EPA fading. J. Sens. Actuator Netw.Figure 2019, 8 ,18. 19 OFDM spectrum observed at receiver side under EPA fading. 12 of 15

Figure 18. OFDM spectrum observed at receiver side under EPA fading.

Figure 19. BER performance of 1024-QAM at various coding rates under EPAEPA fading.fading.

Figure 20 plots the BER of 1024-QAM against received SNR under the EVA fading model. Compared to the EPA fading case, the BER performance is signiﬁcantly degraded. At a coding rate of 1/3, the SNR required to achieve a BER of 1 10 2 is approximately 22 dB, which is approximately × −

Figure 20. BER performance of 1024-QAM at various coding rates under EVA fading.

Figure 21. BER performance of 4096-QAM at various coding rates under EPA fading.

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8 dB higher than that is required under the static condition. At coding rates above 2/3, 1024-QAM can 2 no longer achieveFigure a19. BER BER of performance 1 10− . of 1024-QAM at various coding rates under EPA fading. ×

Figure 19. BER performance of 1024-QAM at various coding rates under EPA fading.

Figure 20. BER performance of 1024-QAM at various coding rates under EVA fading.fading.

Figure 21 plots the BER of 4096-QAM against received SNR under EPA fading at coding rates of 1/3, 1/2, 2/3, and 3/4. At a coding rate of 1/3, the SNR required to achieve a BER of 1 10 2 is approximately × − 22 dB, which is approximately 7 dB higher than that is required under the static condition. This behavior is similar to that observed at the other coding rates. Relative to 1024-QAM, the SNRs required to achieve a BER of 1 10 2 at coding rates of 1/3, 1/2, 2/3, and 3/4 under EPA fading are increased by × − approximatelyFigure 2–5 20. dB. BER performance of 1024-QAM at various coding rates under EVA fading.

Figure 21. BER performance of 4096-QAM at various coding rates under EPA fading.

FigureFigure 21. 21. BERBER performance performance of of 4096-QAM 4096-QAM at at various various coding coding rates rates under under EPA EPA fading. fading.

Figure 22 plots the BER of 4096-QAM against received SNR under EVA fading. At a coding rate of 1/3, the SNR required to achieve a BER of 1 10 2 is approximately 24 dB, which is approximately 9 dB × − higher than that is required under the static condition. At coding rates greater than 1/2, 4096-QAM can no longer achieve a BER of 1 10 2. × − J. Sens. Actuator Netw. 2019, 8, 19 13 of 15 J. Sens. Actuator Netw. 2019, 8, 19 13 of 15

Figure 22. BER performance of 4096-QAM at various coding rates under EVA fading. Figure 22. BER performance of 4096-QAM at various coding rates under EVA fading. 4. Conclusions 4. Conclusions In this paper, we proposed OFDM-based 1024-and 4096-QAM schemes that apply soft-decision ViterbiIn decodingthis paper, for we use proposed in the 5G OFDM-based environment and1024-a beyond.nd 4096-QAM Using link-level schemes simulations, that apply wesoft-decision presented Viterbithe transmission decoding performancefor use in the of the5G proposedenvironment scheme and under beyond. two Using multipath link-level fading simulations, channel models, we presentedextended pedestrianthe transmission A (EPA) performance and extended of the vehicular proposed A (EVA), scheme as under functions two ofmultipath coding rate. fading Under channel EPA models,fading, the extended SNRs required pedestrian to achieve A (EPA) a BERand ofextended 1 10 2 vewerehicular determined A (EVA), to as be functions approximately of coding 20 dB rate. and × − Under22 dB at EPA a coding fading, rate ofthe 1 /3SNRs for 1024- required and 4096-QAM, to achieve respectively, a BER of which1 × 10 are−2 approximatelywere determined 6 dB to and be 7 approximatelydB higher than 20 what dB and is required 22 dB at under a coding the staticrate of condition. 1/3 for 1024- Similarly, and 4096-QAM, under EVA respectively, fading, the which SNRs arerequired approximately to achieve 6 a dB BER and of 17 dB10 higher2 is approximately than what is 22required dB and under 24 dB the at a static coding condition. rate of 1/ 3Similarly, for 1024- × − underand 4096-QAM, EVA fading, respectively, the SNRs required which are to approximatelyachieve a BER of 8 dB1 × and10−2 9is dB approximately higher than what22 dBis and required 24 dB atunder a coding the static rate of condition. 1/3 for 1024- We alsoand found4096-QAM, that, under respectively, EVA fading, which 1024- are approximately and 4096-QAM 8 can dB noand longer 9 dB higherachieve than a BER what of is 1 required10 2 at under coding the rates static greater condition. than 2We/3 andalso 1found/2, respectively. that, under We EVA determined fading, 1024- the × − andrelationship 4096-QAM between can no phase longer error achieve and the a BER SNR of penalty 1 × 10 required−2 at coding to achieve rates greater a BER ofthan 1 2/310 and2 for 1/2, the × − respectively.proposed scheme We determined as well as for the the relationship existing QAM betw andeen QPSKphase scheme.error and We the found SNR thatpenalty 1024-QAM required can to achieveno longer a BER achieve of 1 × a 10 BER−2 for of the 1 proposed10 2, at phase scheme errors as well of 0.20as for or the above existing even QAM if the and SNR QPSK is increased. scheme. × − WeSimilarly, found 4096-QAMthat 1024-QAM can no can longer no longer achieve achieve a BER ofa BER 1 10 of 21 at× 10 phase−2, at errors phase of errors 0.16 or of above. 0.20 or To above limit × − eventhe SNR if the penalty SNR is to increased. below 3 dB,Similarly, the phase 4096-QAM errors for can 16-, no 64-, longer 256-, achieve 1024-, anda BER 4096-QAM of 1 × 10−2 cannot at phase be errorshigher of than 0.16 0.39, or above. 0.31, 0.18, To limit 0.12, andthe SNR 0.11, penalty respectively. to below In our 3 dB, future the work,phase weerrors will for use 16-, system-level 64-, 256-, 1024-,computer and simulation4096-QAM to cannot clarify be the higher user throughputthan 0.39, 0.31 performance, 0.18, 0.12, of and mobile 0.11,systems respectively. in which In our 1024- future and work,4096-QAM we will are use incorporated system-level into computer the modulation simulation and codingto clarify sets the (MCS). user throughput performance of mobile systems in which 1024- and 4096-QAM are incorporated into the modulation and coding sets (MCS).Author Contributions: Conceptualization, H.O. and R.T.; Investigation, H.O. and R.T. and K.S.; Data curation, R.T. and K.S.; Writing—original draft preparation, H.O.; Writing—review and editing, H.O.; Visualization, R.T. Authorand K.S.; Contributions: Supervision, H.O.; Conceptualization, Project administration, H.O. and H.O.; R.T.; FundingInvestigatio acquisition,n, H.O. and H.O. R.T. and K.S.; Data curation, R.T.Funding: and K.S.;This Writing—original research was funded draft by preparation, JSPS KAKENHI H.O.; GrantWriting—review Number JP18K11277, and editing, Grant-in-Aid H.O.; Visualization, for Scientific R.T. andResearch K.S.; Supervision, (C). H.O.; Project administration, H.O.; Funding acquisition, H.O. Funding:Acknowledgments: This researchThe was authors funded would by JSPS like KAKENHI to thank T. OtaGran andt Number M. Nakamura JP18K11277, who areGrant-in-Aid graduates for of KogakuinScientific ResearchUniversity (C). for their contributions to construct link-level simulations. Conflicts of Interest: The authors declare no conflict of interest. Acknowledgments: The authors would like to thank T. Ota and M. Nakamura who are graduates of Kogakuin University for their contributions to construct link-level simulations. References Conflicts of Interest: The authors declare no conflict of interest. 1. 3GPP News. 3GPP system standards heading into the 5G era. 3GPP, 2014. Available online: Referenceshttp://www.3gpp.org /news-events/3gpp-news/1614-sa_5g (accessed on 18 March 2019).

1. 3GPP News. 3GPP system standards heading into the 5G era. 3GPP, 2014. Available online: http://www.3gpp.org/news-events/3gpp-news/1614-sa_5g (accessed on 18 March 2019).

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2. Draft new recommendation ITU-R M. IMT for 2020 and beyond. ITU-R, September 2015. Available online: https://www.itu.int/dms_pubrec/itu-r/rec/m/R-REC-M.2083-0-201509-I!!PDF-E.pdf (accessed on 18 March 2019). 3. Soldani, D.; Manzalini, A. Horizon 2020 and beyond: On the 5G operating system for a truly digital society. IEEE Veh. Tech. Mag. 2015, 10, 32–42. [CrossRef] 4. Nakamura, T.; Benjebbour, A.; Kishiyama, Y.; Suyama, S.; Imai, T. 5G radio access: Requirements, concept and experimental trials. IEICE Trans. Commun. 2015, E98B, 1397–1406. [CrossRef] 5. Mu, Q.; Liu, L.; Chen, L.; Jiang, Y. CQI table design to support 256 QAM in small cell environment. In Proceedings of the 2013 International Conference on Wireless Communications and Signal Processing, Hangzhou, China, 24–26 October 2013; pp. 1–5. [CrossRef] 6. Mao, J.; Abdullahi, M.A.; Xiao, P.; Cao, A. A low complexity 256QAM soft demapper for 5G mobile system. In Proceedings of the 2016 European Conference on Networks and Communications (EuCNC), Athens, Greece, 27–30 June 2016; pp. 1–6. [CrossRef] 7. 3GPP TR 36.783. Evolved Universal Terrestrial Radio Access (E-UTRA); Introduction of 1024 Quadrature Amplitude Modulation (QAM) in LTE downlink (Release 15). 3GPP, April 2017. Available online: https://portal.3gpp.org/desktopmodules/Specifications/SpecificationDetails.aspx?specificationId=3207 (accessed on 18 March 2019). 8. Dahlman, E.; Dimou, K.; Parkvall, S.; Tullberg, H. Future wireless access small cells and heterogeneous deployments. In Proceedings of the ICT 2013, Casablanca, Morocco, 6–8 May 2013. [CrossRef] 9. Elsherif, A.R.; Chen, W.P.; Ito, A.; Ding, Z. Resource allocation and inter-cell interference management for dual-access small cells. IEEE J. Sel. Areas Commun. 2015, 33, 1082–1096. [CrossRef] 10. Ishii, H.; Kishiyama, Y.; Takahashi, H. A novel architecture for LTE-B: C-plane/U-plane split and phantom cell concept. In Proceedings of the 2012 IEEE Globecom Workshops, Anaheim, CA, USA, 3–7 December 2012; pp. 624–630. [CrossRef] 11. Maria, A.D.; Panno, D. A radio resource management scheme in future ultra-dense phantom networks. In Proceedings of the 2017 IEEE 13th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), Rome, Italy, 9–11 October 2017; Volume 1, pp. 1–6. [CrossRef] 12. Ghosh, A.; Ratasuk, R.; Mondai, B.; Mangalvedhe, N.; Thomas, T. LTE-advanced: next-generation wireless broadband technology. IEEE Wireless Commun. 2010, 17, 10–22. [CrossRef] 13. Khandekar, A.; Bhushan, N.; Tingfang, J.; Vanghi, V. LTE Advanced: Heterogeneous Networks. In Proceedings of the 2010 European Wireless Conference (EW), Lucca, Italy, 12–15 April 2010; pp. 978–982. [CrossRef] 14. Deb, S.; Monogioudis, P.; Miernik, J.; Seymour, J.P. Algorithms for Enhanced Inter-Cell Interference Coordination (eICIC) in LTE HetNets. IEEE/ACM Trans. Netw. 2014, 22, 137–150. [CrossRef] 15. Kikuchi, K.; Otsuka, H. Proposal of Adaptive Control CRE in Heterogeneous Networks. In Proceedings of the 2012 IEEE 23rd International Symposium on Personal, Indoor and Mobile Radio Communications–(PIMRC), Sydney, Australia, 9–12 September 2012. [CrossRef] 16. Nakazawa, S.; Naganuma, N.; Otsuka, H. Enhanced adaptive control CRE in heterogeneous networks. In Proceedings of the 2017 14th IEEE Annual Consumer Communications & Networking Conference (CCNC), Las Vegas, NV, USA, 8–11 January 2017; pp. 645–646. [CrossRef] 17. 3GPP TR 36.806. Relay architectures for E-UTRA (LTE-Advanced). 3GPP, March 2010. Available online: http://www.qtc.jp/3GPP/Specs/36806-900.pdf (accessed on 18 March 2019). 18. Saleh, A.B.; Redana, S.; Raaf, B.; Riihonen, T.; Hamalainen, J.; Wiehman, R. Performance of amplify-and-forward and decode-and-forward relays in LTE-Advanced. In Proceedings of the 2009 IEEE 70th Vehicular Technology Conference Fall, Anchorage, AK, USA, 20–23 September 2009. [CrossRef] 19. Bulakci, O.; Redana, S.; Raaf, B.; Hamalainen, J. Performance enhancement in LTE-Advanced relay networks via relay site planning. In Proceedings of the 2010 IEEE 71st Vehicular Technology Conference, Taipei, Taiwan, 16–19 May 2010. [CrossRef] 20. Song, Y.; Yun, X.; Nagata, S.; Chen, L. Investigation on elevation beamforming for future LTE-Advanced. In Proceedings of the 2013 IEEE International Conference on Communications Workshops (ICC), Budapest, Hungary, 9–13 June 2013. [CrossRef] J. Sens. Actuator Netw. 2019, 8, 19 15 of 15

21. Hu, Z.; Liu, R.; Kang, S.; Su, X.; Xu, J. 3D beamforming methods with user-specific elevation beamforming. In Proceedings of the 9th International Conference on Communications and Networking in China, Maoming, China, 14–16 August 2014; pp. 383–386. [CrossRef] 22. Koppenborg, J.; Halbauer, H.; Saur, S.; Hoek, C. 3D beamforming trials with an active antenna. In Proceedings of the 2012 International ITG Workshop on Smart Antennas (WSA), Dresden, Germany, 7–8 March 2012; pp. 110–114. [CrossRef] 23. Iwamoto, M.; Matsuoka, S.; Iwasaki, H.; Otsuka, H. Transmission Performance of OFDM with 1024-QAM in the Presence of EVM Degradation. In Proceedings of the IEEE Asia Pacific Conference on Wireless and Mobile, Bali, Indonesia, 28–30 August 2014; pp. 12–16. [CrossRef] 24. Ota, T.; Nakamura, M.; Otsuka, H. Performance Evaluation of OFDM-based 256- and 1024-QAM in Multipath Fading Propagation Conditions. In Proceedings of the 2017 Ninth International Conference on Ubiquitous and Future Networks (ICUFN), Milan, Italy, 4–7 July 2017; pp. 554–556. [CrossRef] 25. Tian, R.; Senda, K.; Ota, T.; Otsuka, H. Transmission performance of OFDM-based 1024-QAM in multipath fading conditions. IEICE Commun. Express 2018, 7, 272–277. [CrossRef] 26. Tian, R.; Ota, T.; Otsuka, H. Influence of phase error on OFDM-based 4096-QAM with turbo coding. In Proceedings of the 2018 International Conference on Information Networking (ICOIN), Chiang Mai, Thailand, 10–12 January 2018; pp. 352–355. [CrossRef] 27. Otsuka, H.; Tanoi, N.; Ogura, N.; Kubo, T.; Asai, T.; Okumura, Y. Performance analysis of fiber-optic inband relaying in the presence of self-interferences. In Proceedings of the 2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall), Vancouver, BC, Canada, 14–17 September 2014. [CrossRef] 28. Mathworks Documentations. Turbo Encoder. Available online: https://jp.mathworks.com/help/comm/ref/ turboencoder.html?lang=en (accessed on 18 March 2019). 29. 3GPP TS 36.212. Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and channel coding (Release 13). 3GPP, June 2016. Available online: https://www.arib.or.jp/english/html/overview/doc/STD-T104v4_10/5_Appendix/Rel13/36/36212-d20.pdf (accessed on 18 March 2019). 30. 3GPP TS 36.104. Evolved Universal Terrestrial Radio Access (E-UTRA); Base Station (BS) radio transmission and reception (Release 8). 3GPP, May 2008. Available online: http://www.qtc.jp/3GPP/Specs/36104-820.pdf (accessed on 18 March 2019).

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