- Email: [email protected]
BER performance improvement in CE-OFDM-CPM system using Equalization Techniques over Frequency-Selective Channel
Available online at www.sciencedirect.com Available online at www.sciencedirect.com Available online at www.sciencedirect.com Available online at www.sciencedirect.com
Procedia Computer Science 00 (2018) 000–000 Available online at www.sciencedirect.com Procedia Computer Science 00 (2018) 000–000 Procedia Computer Science 00 (2018) 000–000 Procedia Computer Science 00 (2018) 000–000
ScienceDirect
Procedia Computer Science 151 (2019) 1016–1021
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
International Workshop on Microwave Engineering, Communications Systems and Technologies (MECST’2019) International Workshop on Microwave Engineering, Communications Systems and Technologies International Workshop on Microwave Engineering, Communications Systems and Technologies (MECST’2019) International Workshop on Microwave Engineering, April 29 – May 2, 2019, Communications Leuven, Belgium Systems and Technologies (MECST’2019) (MECST’2019) April 29 – May 2, 2019, Leuven, Belgium Aprilimprovement 29 – May 2, 2019, Leuven, Belgium BER performance CE-OFDM-CPM system April 29 – May 2, 2019,in Leuven, Belgium
BER performance improvement CE-OFDM-CPM system using Equalization Techniques overin Frequency-Selective Channel BER performance improvement in CE-OFDM-CPM system BER performance improvement in CE-OFDM-CPM system using Equalization Techniques over Channel a a Frequency-Selective b b using Equalization Techniques over Frequency-Selective Channel J. Mestoui *, M. El ghzaoui , A. Hmamou , J. Foshi using Equalization Techniques over Frequency-Selective Channel a a b b J. Mestoui El ghzaoui IA, ETTI, FPE-UMI BP 512 Boutalamine, Meknès, MOROCCO a*, M.Errachidia a, A. Hmamou b, J. Foshib EEIMP, FST Errachidia, ETTI, BP 512,a,Boutalamine, Meknes,bMorocco J. Mestoui M. El ghzaoui A. Hmamou ,, J. a*, J. Mestoui *, M.Errachidia El ghzaoui , A. Hmamou J. Foshi Foshib IA, ETTI, FPE-UMI BP 512 Boutalamine, Meknès, MOROCCO a
b
a
Abstract
ab EEIMP, IA, ETTI, a b IA, ETTI, EEIMP, b
FST Errachidia, ETTI,BP BP512 512,Boutalamine, Boutalamine,Meknès, Meknes,MOROCCO Morocco FPE-UMI Errachidia FPE-UMI Errachidia FST Errachidia, ETTI,BP BP512 512,Boutalamine, Boutalamine,Meknès, Meknes,MOROCCO Morocco EEIMP, FST Errachidia, ETTI, BP 512, Boutalamine, Meknes, Morocco
Abstract One key weakness of multicarrier signals such as OFDM (Orthogonal frequency division multiplexing) is the high peak-to-average Abstract Abstract power ratio (PAPR). Nonlinear distortions caused by the power amplifier are aggravated by high PAPR, which in turn affects the One key weakness of multicarrier signals such as OFDM (Orthogonal frequency division multiplexing) is the high peak-to-average OFDM signal. These nonlinearitiessignals in amplifiers cause both inter-Symbol interference and inter-carrier interference (ICI) in One key weakness of Nonlinear multicarrier as OFDM frequency division(ISI) multiplexing) is the high power ratio (PAPR). distortionssuch caused by the (Orthogonal power amplifier are aggravated by high PAPR, which inpeak-to-average turn affects the Onesystem. key weakness of multicarrier signals suchtoasprevent OFDM spectral (Orthogonal frequency division multiplexing) is thefrom highinter-modulation peak-to-average the A “power back-off” is required broadening and performance degradation power ratio (PAPR). distortions causedcause by theboth power amplifier are aggravated by high PAPR, which in turn affects OFDM signal. These Nonlinear nonlinearities in amplifiers inter-Symbol interference (ISI) and inter-carrier interference (ICI)the in power ratio (PAPR). Nonlinear distortions caused by the power aggravated by high PAPR, which inOFDM turn affects the distortion. Constant OFDM (CE-OFDM) provides aamplifier solution are to the high (ISI) PAPR issue in OFDM. signal is OFDM signal. TheseEnvelope nonlinearities in amplifiers cause both inter-Symbol interference and inter-carrier interference (ICI) in the system. A “power back-off” is required to prevent spectral broadening and performance degradation from inter-modulation OFDM signal.byThese nonlinearities in amplifiers cause both inter-Symbol interference (ISI) and inter-carrier interference (ICI) in transformed, way of phase modulation (PM), to a constant envelope signal, thereby alleviating the need for a power back-off the system.Constant A “powerEnvelope back-off”OFDM is required to prevent spectrala broadening degradation from OFDM inter-modulation distortion. (CE-OFDM) provides solution to and the performance high PAPR issue in OFDM. signal is the system. A “powerfor back-off” is required to prevent spectraloperation broadening and performance degradation from inter-modulation (IBO) and Constant allowing the most efficient power amplifier possible. In this paper ofsignal MLSE distortion. Envelope OFDM (CE-OFDM) provides a solutionsignal, to thethereby high PAPR issuethe in implementation OFDM. OFDM is transformed, by way of phase modulation (PM), to a constant envelope alleviating the need for a power back-off distortion. Constant Envelope OFDM (CE-OFDM) provides a solution to the high isPAPR issuea performance in OFDM. OFDM signal is (Maximum-Likelihood Sequence Estimation) channel equalization in CE-OFDM-CPM proposed, gain comparison transformed, by way of phase modulation (PM), to a constant envelope signal, thereby alleviating the need for a power back-off (IBO) and allowing for the most efficient power amplifier operation possible. In this paper the implementation of MLSE transformed, byover wayfast of fading phase modulation (PM), to a constant envelope signal, thereby alleviating the need for a power back-off and evaluation channels well be presented and discussed. (IBO) and allowing for the most efficient channel power amplifier operation possible. In isthis paper athe implementation of MLSE (Maximum-Likelihood Sequence Estimation) equalization in CE-OFDM-CPM proposed, performance gain comparison (IBO) and allowing for the most efficient power amplifier operation possible. In this paper the implementation of MLSE (Maximum-Likelihood Sequence Estimation) channel equalization in CE-OFDM-CPM is proposed, a performance gain comparison and evaluation over fast fading channels well be presented and discussed. (Maximum-Likelihood SequencebyEstimation) channel equalization in CE-OFDM-CPM is proposed, a performance gain comparison © The Authors. Published Elsevier and2019 evaluation over fast fading channels wellB.V. be presented and discussed. and over fast fadingarticle channels well be and discussed. Thisevaluation is an open access under thepresented CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) © 2019 The Authors. Published by Elsevier B.V. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Conference Program Chairs. © 2019isThe Published by Elsevier This anAuthors. open access article under B.V. the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) © 2019 The Authors. by Elsevier This is an open accessPublished article under the CC B.V. BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) This is anunder openresponsibility access article under the CC BY-NC-ND (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review of the Conference Program Chairs. license Peer-review ofVA, theunder Conference Chairs. This is OFDM, anunder openresponsibility access CMP, article the Program CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Keywords: PAPR, ISI, ICI, ; Peer-review underCE-OFDM, responsibility of theMLSE, Conference ProgramBER Chairs. Peer-review under responsibility of the Conference Program Chairs. Keywords: OFDM, CE-OFDM, CMP, VA, MLSE, PAPR, ISI, ICI, BER ; Keywords: OFDM, CE-OFDM, CMP, VA, MLSE, PAPR, ISI, ICI, BER ; Keywords: OFDM, CE-OFDM, CMP, VA, MLSE, PAPR, ISI, ICI, BER ; 1. Introduction
1. Introduction OFDM is widely accepted as an attractive transmission technique for different types of broadband transmission 1. Introduction 1. Introduction systems [1,is2].widely It is also a veryas promising technique for delivering highfor datadifferent rate multimedia overtransmission the mobile OFDM accepted an attractive transmission technique types of services broadband radio channel. The performance of such systems is limited by the severe effects of multiple delay spread. In to OFDM widely accepted an attractive transmission technique types of services broadband systems [1,is It is also a veryas promising technique for delivering highfor datadifferent rate multimedia overtransmission theorder mobile OFDM is2].widely accepted as an attractive transmission technique for different types of to broadband transmission overcome this problem a guard interval (cyclic prefix/suffix) is added to each OFDM symbol, efficiently combat the systems [1, 2]. The It is performance also a very promising technique for delivering high data rate of multimedia services over In theorder mobile radio channel. of such systems is limited by the severe effects multiple delay spread. to systems [1,effect, 2]. It is also a veryofpromising technique for delivering high data ratethe multimedia services over the mobile multi-path theaprice some loss in spectral efficiency, depending on of un-extended and radio channel. Theatperformance of such systems is limited by the severe effects of ratio multiple delay spread. Inextended orderthe to overcome this problem guard interval (cyclic prefix/suffix) is added to each OFDM symbol, to efficiently combat radio channel. The performance of such systems is limited by the severe effects of multiple delay spread. In order to symbol periods. overcome this problem aprice guardofinterval (cyclic prefix/suffix) is added to eachon OFDM symbol, to efficiently combat the multi-path effect, at the some loss in spectral efficiency, depending the ratio of un-extended and extended overcome thisenvelope problem a guard interval (cyclic prefix/suffix) is added(CE-OFDM) to each OFDM asymbol, to efficiently combat the Constant frequency multiplexing modification to OFDM which multi-path effect, at theorthogonal price of some loss in division spectral efficiency, depending on theisratio of un-extended and extended symbol periods. multi-path effect, at the price of some loss in spectral efficiency, depending on the ratio of un-extended and extended eliminates the large peak power tofrequency average power ratio (PAPR) inherent in OFDM 4]. The high PAPR OFDM symbol periods. Constant envelope orthogonal division multiplexing (CE-OFDM) is a [3, modification to OFDM which symbol periods. signal is transformed, by way of phase modulation, to a constant envelope signal, thereby alleviating the need for a Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a modification to OFDM which eliminates the large peak power to average power ratio (PAPR) inherent in OFDM [3, 4]. The high PAPR OFDM Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a modification to OFDM which eliminates the large peak power to average power ratio (PAPR) inherent in OFDM [3, 4]. The high PAPR OFDM signal is transformed, by way of to phase modulation, to a (PAPR) constant inherent envelopeinsignal, thereby need for a eliminates the large peak power average power ratio OFDM [3, 4].alleviating The high the PAPR OFDM signal is transformed, by way of phase modulation, to a constant envelope signal, thereby alleviating the need for a signal is transformed, by way of phase modulation, to a constant envelope signal, thereby alleviating the need for a * Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . E-mail address: [email protected] * Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . * E-mail Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . address: [email protected] 1877-0509 2019 TheAuthors. Authors. Published by; Elsevier * E-mail Corresponding author. Tel.: +0-000-000-0000 fax: +0-000-000-0000 . 1877-0509 ©©2019 The Published by Elsevier B.V.B.V. address: [email protected] This is open article under under the This is an anaddress: open access access article the CC CC BY-NC-ND BY-NC-NDlicense license(http://creativecommons.org/licenses/by-nc-nd/4.0/) (http://creativecommons.org/licenses/by-nc-nd/4.0/) E-mail [email protected] 1877-0509 © 2019 The Authors. Published by Elsevier B.V. Peer-review under of of thethe Conference Program Chairs. underresponsibility responsibility Conference Program Chairs. 1877-0509 © 2019 The article Authors. Published Elsevier B.V. This is an open access under the CCby BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) 10.1016/j.procs.2019.04.143 1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under theConference CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the Program Chairs. This is an open access article under theConference CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the Program Chairs. Peer-review under responsibility of the Conference Program Chairs.
J.Mestoui, M.El ghzaoui,etA.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000 J. Mestoui al. / Procedia Computer Science 151 (2019) 1016–1021
1017
power back off and allowing for the most efficient power amplifier operation possible[5]. The performance and bandwidth of the CE-OFDM system has been studied in [5, 6]. CE–OFDM has been found to compare favorably to conventional OFDM, over a two-path fading channel in the presence of clipping [7]. For uncoded waveforms, CEOFDM has been shown to offer some significant performance advantages over OFDM on high frequency (HF) multipath fading channels. In this paper, a CE-OFDM-CPM modulation is proposed which makes use of constant envelope scheme instead of non-constant envelope scheme. The optimal way of receiving CPM signals in frequency selective fading channel is to use the maximum likelihood sequence-estimator (MLSE). This receiver is referred to as the MLSE CE-OFDM-CPM equalizer and it is implemented using the Viterbi Algorithm (VA). The MLSE is implemented using the VA because the CPM signal can be described as a finite state machine. To facilitate the description of the VA, a MLSE CPM receiver for an AWGN channel is introduced first. In addition to improved BER performance both in AWGN and frequency selective fading channel a MLSE equalizer is implemented in a frequency selective fading channel. A performance evaluation of CEOFDM in fast fading channels, using various developed and adapted practical channel equalizer techniques with low complexity and high accuracy, will be presented in this paper. 2. Conventional OFDM system 2.1. OFDM signal model Consider an OFDM system that transmits N symbols sn(i) in the ith OFDM symbol period through N subchannels of subcarrier spacing 1 / (NTf). The transmitted baseband OFDM signal is expressed as x(t )
Ts NT f
N 1
s n (i)v(t iNT )e
j
N 1 2 n ( t iNT ) 2 NT f
(1)
i n 0
where T is the data symbol period, NT is the OFDM symbol period, B=1 / Tf is approximately the total bandwidth of the OFDM signal, and v(t) is the OFDM symbol pulse shaping filter. The received signal is r[i] =
Nc -1
h[l]x[i - l] + n[i], l=0
i = 0,.......,NB - 1
(2)
Transmitting a cyclic prefix during the guard interval makes the linear convolution with the channel equivalent to circular convolution. Thus
1
r i NDFT
j
2 ik NDFT
i k e H k X
0,...........NB 1
(3)
Where {H[k]} is the DFT of {h[i]} and {S[k]} is the DFT of {s[i]}. 2.2. PAPR analysis in OFDM system OFDM signal has an approximately Gaussian amplitude distribution when the number of subcarriers is large. Therefore, very high peaks in the transmitted signal can occur. This property is often measured via the signal's peakto-average power ratio. To be able to transmit and receive these peaks without clipping the signal, there is two possibility. The first possibility that the A/D and D/A need to be designed with high demands on range and precision. But, if the dynamic ranges of the A/D and D/A are increased, the resolution also needs to be increased in order to maintain the same quantization noise level. Therefore, an OFDM signal may require expensive A/Ds and D/As compared to many other modulation formats, and for some applications suitable A/Ds and D/As may not be available at all. Also, a large power back-off of the amplifiers is necessary. Intentional or accidental clipping of the OFDM signal often occurs in practice. The clipping of a received sample affects all subcarriers in the system. The sensitivity to clipping effects is investigated in [8]. The second possibility is that the RF power amplifiers (PA) have to be operated in a very large linear region. Otherwise, the signal peaks get distorted, leading to intermodulation distortion (IMD) among the subcarriers and out-of-band radiation. A simple way to avoid is to use PA of large dynamic range but this makes the transmitter costly. Thus, it is highly desirable to reduce the PAPR. To alleviate this problem, constant envelope OFDM (CE-OFDM) signal has been introduced in [5, 6], which combines orthogonal frequency division multiplexing and phase modulation or frequency modulation.
J.Mestoui, M.El ghzaoui,etA.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000 J. Mestoui al. / Procedia Computer Science 151 (2019) 1016–1021
1018
3. CE-OFDM system model The baseband CE-OFDM signal is, j t s t Ae
(4)
Where A is the signal amplitude. The phase signal during the ith block is written as: N
(t) i 2 hcN Ii,k qk t iTB , k 1
Where
(t) (iT ) (iT ),
iTB t (i 1)TB
(5)
0
The phase memory may be used in conjunction with a phase unwrapper at the receiver to ensure a continuous phase at the symbol boundaries and hence better spectral containment. Here h refers to modulation index; N is the represents M-PAM data symbols; TB is the ith block interval, and represents the set number of sub-carriers where is the variance of the data of subcarrier waveforms. The normalizing constant, , is set to √ . Assuming that the data is symbols, and consequently the variance of the phase signal will be independent and identically distributed, it follows that M2 1 (6) I2 3 are The signal energy and the bite energy (7)
Es A2TB Eb
Es N log2 (M)
(8)
4. Optimal equalization: Maximum-Likelihood sequence estimation The optimal equalizer performs maximum-likelihood sequence estimation (MLSE) and it outputs the sequence that maximizes the probability of the received signal {rn}, or equivalently, it minimizes the Euclidean distance [9-12]. The MLSE-equalizer can be efficiently implemented by the Viterbi algorithm and it has a computational complexity of |s|K per decoded symbol, A being the modulation constellation e.g. QPSK, QAM, etc. Unfortunately there is currently implementation of the MLSE-equalizer in Matlab (mlseeq.m) which can be used. 4.1. CE-OFDM-CPM receiver for the AWGN channel In this section, we introduce the optimum CE-OFDM-CPM receiver for the AWGN channel. The optimum CEOFDM-CPM receiver consists of an MLSE block preceded by a metric computation block connected to a template signal generator. Figure 1 shows the structure of the optimum CPM receiver. The received signal is given by
r(t) s(t, In ) n(t)
(9)
Where is the M-ary (M is the size of the alphabet) CE-OFDM-CPM signal associated with the is AWGN. transmitted symbol sequence and MLSE CE-OFDM-CPM Receiver CE-OFDMDATA CPM signal {Ik}
𝑠𝑠 𝑡𝑡 𝐼𝐼𝑛𝑛
AWGN
𝑟𝑟 𝑡𝑡
Metric computation
𝑉𝑉𝑛𝑛
MLSE (VA)
𝑇𝑇 𝑡𝑡 − 𝑛𝑛𝑛𝑛
Signal Generator
Fig. 1. Optimum CE-OFDM-CPM receiver.
Déodulation CE-OFDM
DATA {Îk}
J.Mestoui, M.El ghzaoui, A.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000
J. Mestoui et al. / Procedia Computer Science 151 (2019) 1016–1021
1019
is the matrix of template signals using the channel estimation , and is the matrix of branch metrics and are speciefied as , where is the size of that correspond to the n-th symbol. The dimensions for is the total number of states in the equalizer trellis. the CE-OFDM-CPM alphabet and The MLSE (VA) block in Figure 1 performs MLSE using the Viterbi algorithm. The use of the Viterbi algorithm is a plausible solution to detect the symbols in the CE-OFDM-CPM signal because the behavior of CE-OFDM-CPM signals can be described with a finite-state trellis. 4.2. MLSE CE-OFDM-CPM Equalizer for frequency selective channel This section builds on the optimum MLSE CE-OFDM-CPM receiver for AWGN channels presented in Section (IV.A). Using knowledge of the channel, the MLSE CE-OFDM-CPM receiver is modified to receive and equalize the received signal. The structure for the MLSE CPM Equalizer is shown in Figure 2. The single addition to the MLSE CE-OFDM-CPM receiver structure consists of a channel estimator block, the output of which is used to reduce the effects of ISI introduced by a frequency selective channel. Although transparent to the structure, the optimum MLSE CE-OFDM-CPM receiver for AWGN channels presented in Section (IV.A) and the MLSE equalizer presented here differ in the method by which the template signals are generated and in the complexity of the MLSE trellis. The received signal is now given by and is defined as:
r(t)
s(t, In )h(t)d n(t)
(10)
is the Where is the M-ary CE-OFDM-CPM signal associated with the transmitted symbol sequence , impulse response for baseband frequency selective channels and is AWGN. is the matrix of template signals using the channel estimation , and is the matrix of branch metrics that , where is the size of the correspond to the n-th symbol. The dimensions for and are speciefied as is the total number of states in the equalizer trellis. The Channel Estimator block CE-OFDM-CPM alphabet and refers to the process of estimating the channel impulse response. A condition for true maximum likelihood is that the channel estimate ̂ be an accurate model of the actual channel otherwise the performance is sub-optimal. The two key differences between the equalizer that is presented here and the MLSE CE-OFDM-CPM receiver presented in section (4.1) are the configuration of the MLSE trellis and the template signal generator. The MLSE equalizer trellis is more complex because each state contains memory of previously transmitted symbols. The template signal generator for the MLSE equalizer differs from the MLSE CE-OFDM-CPM receiver in that it now accounts for the channel effects (ISI). The template signals use the channel estimate to account for the effect of ISI. The template signal generation for the MLSE equalizer is different from that for the MLSE CE-OFDM-CPM receiver in section (IV.A). While the template signals for the MLSE receiver (section 4.1) are only associated with a phase transition, the template signals for the MLSE equalizer presented here are associated with a phase transition, a symbol history, and a channel estimate. MLSE CE-OFDM-CPM Receiver 𝑠𝑠 𝑡𝑡 𝐼𝐼𝑛𝑛
Metric computation
𝑡𝑡 + 𝑛𝑛 𝑡𝑡 𝑟𝑟 𝑡𝑡
Channel Estimator
𝑡𝑡
𝑉𝑉𝑛𝑛
MLSE (VA)
𝑇𝑇 𝑡𝑡 − 𝑛𝑛𝑛𝑛
Signal Generator
Fig. 2. MLSE equalizer structure. 5. Simulation results In this section, the BER performance of the MLSE equalizer over Saleh-Valenzuela is presented. The multipath channel h(t) is simulated using the Saleh-Valenzuela channel model [11] which assumes that the received rays arrive
J.Mestoui, M.El ghzaoui,etA.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000 J. Mestoui al. / Procedia Computer Science 151 (2019) 1016–1021
1020
in clusters. Moreover, the BER performance of the proposed receiver is compared to the case without ISI as well (case AWGN channel). The simulations parameters are DFT size NDFT = 1024, a cyclic prefix Ng = 48, 2πh=1, M=4 and L = 15 length Hamming window FIR, having a normalized cutoff frequency fc = 0.4. In Figure 3 (a) the performance of MLSE equalizer in terms of BER performance is given. As expected, MLSE (case Saleh-Valenzuela channel, which is a severe channel,) estimation performs better in terms of BER, and is only approximately 3.5dB worse than AWGN performance at a BER of 10-4. 0
0
10
10
AWGN Saleh-Valenzuela
-1
10
-1
10
-2
-2
10
BER
BER
10
-3
10
OFDM-IBO=10dB OFDM-IBO=6dB OFDM-IBO=4dB OFDM-IBO=0dB CE-OFDM
-4
-4
10
10
-5
-5
10
10
-6
10
-3
10
-6
0
5
10
15 SNR (dB)
20
25
10
30
0
5
10 15 SNR (dB)
20
25
Fig. 3. (a). Performance of MLSE equalizer for CE-OFDM. (b). OFDM versus CE-OFDM-CPM under AWGN channel
In Figure 3(b), the OFDM systems perform better than the CE-OFDM-CPM systems at law SNR event we use a nonlinear amplifier because CE-OFDM-CPM suffer from a threshold effect. But at law SNR CE-OFDM-CPM systems perform better much than OFDM systems. Amplifier nonlinearities can significantly degrade the OFDM performance. Note that the power efficiency includes not only the SNR needed to achieve a target BER but also the energy consumed in the amplifier. In OFDM, it is critical to maintain the linear relation between the applied message and the amplitude of the transmitted signal, thus linear Class A or AB amplifiers, which are not power efficient, are usually used. CE-OFDM-CPM will be perhaps the most popular modulation technique used in the second generation cellular system. The envelope of the CE-OFDM-CPM modulated signals stays the same while its phase is varied by message signals. In OFDM, message signals are transported by varying the amplitudes of two carriers. CE-OFDM-CPM offers many advantages over OFDM, which makes it a better choice of the current mobile applications. 0
0
10
10
-1
-1
10
10
ZF LMSE MMSE
-3
10
-2
10
BER
BER
-2
10
ZF LMSE MMSE
-3
10
-4
-4
10
10
0
5
10
15 20 SNR (dB)
25
30
0
5
10
15 20 SNR (dB)
25
30
Fig. 4. BER Performance versus SNR for different Equalizers with and without channel estimation
The issue of amplifier efficiency is very important in the design of mobile terminals. The constant envelope of CEOFDM-CPM signals allows efficient nonlinear amplifiers to be used for amplification. In contrast, the performance of OFDM schemes is seriously compromised by amplifier nonlinearities. CE-OFDM-CPM signals require the transmit
J.Mestoui, M.El ghzaoui,etA.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000 J. Mestoui al. / Procedia Computer Science 151 (2019) 1016–1021
1021
power amplifiers to operate in a strictly linear region to preserve the transmitted signal properties at the expense of reduced power efficiency due to a large power back-off (IBO) requirement. This is perhaps the most important reason that CE-OFDM-CPM is usually preferred to OFDM in many wireless systems. As mentioned previously, OFDM schemes occupy less bandwidth than the CE-OFDM-CPM schemes. Thus, the OFDM systems can achieve a spectral efficiency up to 2.5 bps/Hz, which cannot be obtained even with a high spectral efficiency CE-OFDM-CPM system. While CE-OFDM-CPM systems have many advantages over OFDM systems, they also have certain disadvantages, especially in the high spectral efficiency CE-OFDM-CPM systems. In Figure 4, the Bit error rate (BER) versus the average SNR is plotted for the proposed equalizer with and without channel estimation schemes over a 2-path channel, QPSK modulation, DFT size NDFT = 1024, and a cyclic prefix Ng = 48. Signal-to-Noise Ratio (SNR) of the channel noise is changed between 0 and 30dB, and the BER is calculated by two approaches: a) No Channel Estimation and b) Pilot Channel Estimation with 8 pilots. Simulation results show that the performance of ZF is worse than the other two, and the performance of MMSE is slightly better than LMSE at high SNRs. The equalizers with channel estimation (a) yield the best performance, and they yield the worst performance without channel estimation (b). Therefore, the performance of an equalizer is dependent on the channel estimate. 6. Conclusion In this paper, two modulation techniques, OFDM and CE-OFDM-CPM, are studied. Particularly, the performance of OFDM and CE-OFDM-CPM is evaluated when taking amplifier nonlinearities into account. In addition, we introduced the optimum MLSE equalizer for CE-OFDM-PM for Saleh-Valenzuela channel which is a severe channel, the performance over it is only approximately 1.4 dB worse than AWGN performance at a bit error rate of 10-4. This paper fully reviews channel equalizers strategies in CE-OFDM systems. It describes channel Equalizers, which may be based on MLSE-Equalizer, ZF-Equalizer MMSE) or MMSE-Equalizer, with or without channel estimation. In CE-OFDM systems, efficient channel estimation schemes are essential for coherent detection of a received signal. Further research will provide insight into next generation digital communication systems that require power efficiency, high data rates and robustness in harsh channel conditions. References [1] R. D. van Nee, OFDM for Wireless Multimedia Communications. Artech House Publishers, Boston-London, January 2000. [2] Z. Wang and G. B. Giannakis, “Wireless multicarrier communications: Where Fourier meets Shannon,” IEEE Signal Process. Mag., vol. 17, No. 3, pp. 29–48, May 2000. [3] S. H. Han and J. H. Lee, An overview of peak-to-average power ratio reduction techniques for multicarrier transmission, IEEE Wireless Communications Magazine, vol. 12, pp. 56_65, April 2005. [4] J. Tellado-Mourelo, Peak to Average Power Reduction for Multicarrier Modulation. PhD thesis, Stanford University, Sept1999. [5] S. Thompson, A. Ahmed, J. Proakis, J. Zeidler, and M. Geile, “Constant Envelope OFDM,” EEE Trans. Commun., vol. 56, no. 8, pp.1300– 1312, August2008. [6] S. C. Thompson, “Constant Envelope OFDM Phase Modulation,” Ph.D. dissertation, Department Electrical Engineering (Communications Theory and Systems), University of California, SanDiego,2005. [7] Y. Tsai, G. Zhang, and J. Pan, “Orthogonal frequency division multi plexing with phase modulation and constant envelope design, ”in Proc. IEEE Milcom, vol. 4, October 2005, pp. 2658–2664. [8] R. Gross, and D. Veeneman [1993], “Clipping Distortion in DMT ADSL Systems,” Electronics Letters, 29, 24, pp. 2080-2081. [9] M. Chiu and C. Chao, “Analysis of LMS-Adaptive MLSE equalization on multipath fading channels,” IEEE Trans. Commun., vol. 44, no. 12, pp. 1684–1692, Dec. 1996. [10]. J. Wu and A. H. Aghvami, “A new adaptive equalizer with channel estimator for mobile radio communications,” IEEE Trans. Veh. Technol., vol. 45, no. 3, pp. 1178–1190, Aug. 1996. [11] J. T. Chenand, Y. C. Wang, “Adaptive MLSE equalizers with parametric tracking for multipath fast-fading channels,” IEEE Trans. Commun., vol.49, no.4, pp. 655-663, April2001. [12] H. Meyr, M. Moeneclaey and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation and Signal Processing, John Wiley& Sons, 1998.
Procedia Computer Science 00 (2018) 000–000 Available online at www.sciencedirect.com Procedia Computer Science 00 (2018) 000–000 Procedia Computer Science 00 (2018) 000–000 Procedia Computer Science 00 (2018) 000–000
ScienceDirect
Procedia Computer Science 151 (2019) 1016–1021
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
International Workshop on Microwave Engineering, Communications Systems and Technologies (MECST’2019) International Workshop on Microwave Engineering, Communications Systems and Technologies International Workshop on Microwave Engineering, Communications Systems and Technologies (MECST’2019) International Workshop on Microwave Engineering, April 29 – May 2, 2019, Communications Leuven, Belgium Systems and Technologies (MECST’2019) (MECST’2019) April 29 – May 2, 2019, Leuven, Belgium Aprilimprovement 29 – May 2, 2019, Leuven, Belgium BER performance CE-OFDM-CPM system April 29 – May 2, 2019,in Leuven, Belgium
BER performance improvement CE-OFDM-CPM system using Equalization Techniques overin Frequency-Selective Channel BER performance improvement in CE-OFDM-CPM system BER performance improvement in CE-OFDM-CPM system using Equalization Techniques over Channel a a Frequency-Selective b b using Equalization Techniques over Frequency-Selective Channel J. Mestoui *, M. El ghzaoui , A. Hmamou , J. Foshi using Equalization Techniques over Frequency-Selective Channel a a b b J. Mestoui El ghzaoui IA, ETTI, FPE-UMI BP 512 Boutalamine, Meknès, MOROCCO a*, M.Errachidia a, A. Hmamou b, J. Foshib EEIMP, FST Errachidia, ETTI, BP 512,a,Boutalamine, Meknes,bMorocco J. Mestoui M. El ghzaoui A. Hmamou ,, J. a*, J. Mestoui *, M.Errachidia El ghzaoui , A. Hmamou J. Foshi Foshib IA, ETTI, FPE-UMI BP 512 Boutalamine, Meknès, MOROCCO a
b
a
Abstract
ab EEIMP, IA, ETTI, a b IA, ETTI, EEIMP, b
FST Errachidia, ETTI,BP BP512 512,Boutalamine, Boutalamine,Meknès, Meknes,MOROCCO Morocco FPE-UMI Errachidia FPE-UMI Errachidia FST Errachidia, ETTI,BP BP512 512,Boutalamine, Boutalamine,Meknès, Meknes,MOROCCO Morocco EEIMP, FST Errachidia, ETTI, BP 512, Boutalamine, Meknes, Morocco
Abstract One key weakness of multicarrier signals such as OFDM (Orthogonal frequency division multiplexing) is the high peak-to-average Abstract Abstract power ratio (PAPR). Nonlinear distortions caused by the power amplifier are aggravated by high PAPR, which in turn affects the One key weakness of multicarrier signals such as OFDM (Orthogonal frequency division multiplexing) is the high peak-to-average OFDM signal. These nonlinearitiessignals in amplifiers cause both inter-Symbol interference and inter-carrier interference (ICI) in One key weakness of Nonlinear multicarrier as OFDM frequency division(ISI) multiplexing) is the high power ratio (PAPR). distortionssuch caused by the (Orthogonal power amplifier are aggravated by high PAPR, which inpeak-to-average turn affects the Onesystem. key weakness of multicarrier signals suchtoasprevent OFDM spectral (Orthogonal frequency division multiplexing) is thefrom highinter-modulation peak-to-average the A “power back-off” is required broadening and performance degradation power ratio (PAPR). distortions causedcause by theboth power amplifier are aggravated by high PAPR, which in turn affects OFDM signal. These Nonlinear nonlinearities in amplifiers inter-Symbol interference (ISI) and inter-carrier interference (ICI)the in power ratio (PAPR). Nonlinear distortions caused by the power aggravated by high PAPR, which inOFDM turn affects the distortion. Constant OFDM (CE-OFDM) provides aamplifier solution are to the high (ISI) PAPR issue in OFDM. signal is OFDM signal. TheseEnvelope nonlinearities in amplifiers cause both inter-Symbol interference and inter-carrier interference (ICI) in the system. A “power back-off” is required to prevent spectral broadening and performance degradation from inter-modulation OFDM signal.byThese nonlinearities in amplifiers cause both inter-Symbol interference (ISI) and inter-carrier interference (ICI) in transformed, way of phase modulation (PM), to a constant envelope signal, thereby alleviating the need for a power back-off the system.Constant A “powerEnvelope back-off”OFDM is required to prevent spectrala broadening degradation from OFDM inter-modulation distortion. (CE-OFDM) provides solution to and the performance high PAPR issue in OFDM. signal is the system. A “powerfor back-off” is required to prevent spectraloperation broadening and performance degradation from inter-modulation (IBO) and Constant allowing the most efficient power amplifier possible. In this paper ofsignal MLSE distortion. Envelope OFDM (CE-OFDM) provides a solutionsignal, to thethereby high PAPR issuethe in implementation OFDM. OFDM is transformed, by way of phase modulation (PM), to a constant envelope alleviating the need for a power back-off distortion. Constant Envelope OFDM (CE-OFDM) provides a solution to the high isPAPR issuea performance in OFDM. OFDM signal is (Maximum-Likelihood Sequence Estimation) channel equalization in CE-OFDM-CPM proposed, gain comparison transformed, by way of phase modulation (PM), to a constant envelope signal, thereby alleviating the need for a power back-off (IBO) and allowing for the most efficient power amplifier operation possible. In this paper the implementation of MLSE transformed, byover wayfast of fading phase modulation (PM), to a constant envelope signal, thereby alleviating the need for a power back-off and evaluation channels well be presented and discussed. (IBO) and allowing for the most efficient channel power amplifier operation possible. In isthis paper athe implementation of MLSE (Maximum-Likelihood Sequence Estimation) equalization in CE-OFDM-CPM proposed, performance gain comparison (IBO) and allowing for the most efficient power amplifier operation possible. In this paper the implementation of MLSE (Maximum-Likelihood Sequence Estimation) channel equalization in CE-OFDM-CPM is proposed, a performance gain comparison and evaluation over fast fading channels well be presented and discussed. (Maximum-Likelihood SequencebyEstimation) channel equalization in CE-OFDM-CPM is proposed, a performance gain comparison © The Authors. Published Elsevier and2019 evaluation over fast fading channels wellB.V. be presented and discussed. and over fast fadingarticle channels well be and discussed. Thisevaluation is an open access under thepresented CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) © 2019 The Authors. Published by Elsevier B.V. © 2019 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the Conference Program Chairs. © 2019isThe Published by Elsevier This anAuthors. open access article under B.V. the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) © 2019 The Authors. by Elsevier This is an open accessPublished article under the CC B.V. BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) This is anunder openresponsibility access article under the CC BY-NC-ND (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review of the Conference Program Chairs. license Peer-review ofVA, theunder Conference Chairs. This is OFDM, anunder openresponsibility access CMP, article the Program CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Keywords: PAPR, ISI, ICI, ; Peer-review underCE-OFDM, responsibility of theMLSE, Conference ProgramBER Chairs. Peer-review under responsibility of the Conference Program Chairs. Keywords: OFDM, CE-OFDM, CMP, VA, MLSE, PAPR, ISI, ICI, BER ; Keywords: OFDM, CE-OFDM, CMP, VA, MLSE, PAPR, ISI, ICI, BER ; Keywords: OFDM, CE-OFDM, CMP, VA, MLSE, PAPR, ISI, ICI, BER ; 1. Introduction
1. Introduction OFDM is widely accepted as an attractive transmission technique for different types of broadband transmission 1. Introduction 1. Introduction systems [1,is2].widely It is also a veryas promising technique for delivering highfor datadifferent rate multimedia overtransmission the mobile OFDM accepted an attractive transmission technique types of services broadband radio channel. The performance of such systems is limited by the severe effects of multiple delay spread. In to OFDM widely accepted an attractive transmission technique types of services broadband systems [1,is It is also a veryas promising technique for delivering highfor datadifferent rate multimedia overtransmission theorder mobile OFDM is2].widely accepted as an attractive transmission technique for different types of to broadband transmission overcome this problem a guard interval (cyclic prefix/suffix) is added to each OFDM symbol, efficiently combat the systems [1, 2]. The It is performance also a very promising technique for delivering high data rate of multimedia services over In theorder mobile radio channel. of such systems is limited by the severe effects multiple delay spread. to systems [1,effect, 2]. It is also a veryofpromising technique for delivering high data ratethe multimedia services over the mobile multi-path theaprice some loss in spectral efficiency, depending on of un-extended and radio channel. Theatperformance of such systems is limited by the severe effects of ratio multiple delay spread. Inextended orderthe to overcome this problem guard interval (cyclic prefix/suffix) is added to each OFDM symbol, to efficiently combat radio channel. The performance of such systems is limited by the severe effects of multiple delay spread. In order to symbol periods. overcome this problem aprice guardofinterval (cyclic prefix/suffix) is added to eachon OFDM symbol, to efficiently combat the multi-path effect, at the some loss in spectral efficiency, depending the ratio of un-extended and extended overcome thisenvelope problem a guard interval (cyclic prefix/suffix) is added(CE-OFDM) to each OFDM asymbol, to efficiently combat the Constant frequency multiplexing modification to OFDM which multi-path effect, at theorthogonal price of some loss in division spectral efficiency, depending on theisratio of un-extended and extended symbol periods. multi-path effect, at the price of some loss in spectral efficiency, depending on the ratio of un-extended and extended eliminates the large peak power tofrequency average power ratio (PAPR) inherent in OFDM 4]. The high PAPR OFDM symbol periods. Constant envelope orthogonal division multiplexing (CE-OFDM) is a [3, modification to OFDM which symbol periods. signal is transformed, by way of phase modulation, to a constant envelope signal, thereby alleviating the need for a Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a modification to OFDM which eliminates the large peak power to average power ratio (PAPR) inherent in OFDM [3, 4]. The high PAPR OFDM Constant envelope orthogonal frequency division multiplexing (CE-OFDM) is a modification to OFDM which eliminates the large peak power to average power ratio (PAPR) inherent in OFDM [3, 4]. The high PAPR OFDM signal is transformed, by way of to phase modulation, to a (PAPR) constant inherent envelopeinsignal, thereby need for a eliminates the large peak power average power ratio OFDM [3, 4].alleviating The high the PAPR OFDM signal is transformed, by way of phase modulation, to a constant envelope signal, thereby alleviating the need for a signal is transformed, by way of phase modulation, to a constant envelope signal, thereby alleviating the need for a * Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . E-mail address: [email protected] * Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . * E-mail Corresponding author. Tel.: +0-000-000-0000 ; fax: +0-000-000-0000 . address: [email protected] 1877-0509 2019 TheAuthors. Authors. Published by; Elsevier * E-mail Corresponding author. Tel.: +0-000-000-0000 fax: +0-000-000-0000 . 1877-0509 ©©2019 The Published by Elsevier B.V.B.V. address: [email protected] This is open article under under the This is an anaddress: open access access article the CC CC BY-NC-ND BY-NC-NDlicense license(http://creativecommons.org/licenses/by-nc-nd/4.0/) (http://creativecommons.org/licenses/by-nc-nd/4.0/) E-mail [email protected] 1877-0509 © 2019 The Authors. Published by Elsevier B.V. Peer-review under of of thethe Conference Program Chairs. underresponsibility responsibility Conference Program Chairs. 1877-0509 © 2019 The article Authors. Published Elsevier B.V. This is an open access under the CCby BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) 10.1016/j.procs.2019.04.143 1877-0509 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under theConference CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the Program Chairs. This is an open access article under theConference CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the Program Chairs. Peer-review under responsibility of the Conference Program Chairs.
J.Mestoui, M.El ghzaoui,etA.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000 J. Mestoui al. / Procedia Computer Science 151 (2019) 1016–1021
1017
power back off and allowing for the most efficient power amplifier operation possible[5]. The performance and bandwidth of the CE-OFDM system has been studied in [5, 6]. CE–OFDM has been found to compare favorably to conventional OFDM, over a two-path fading channel in the presence of clipping [7]. For uncoded waveforms, CEOFDM has been shown to offer some significant performance advantages over OFDM on high frequency (HF) multipath fading channels. In this paper, a CE-OFDM-CPM modulation is proposed which makes use of constant envelope scheme instead of non-constant envelope scheme. The optimal way of receiving CPM signals in frequency selective fading channel is to use the maximum likelihood sequence-estimator (MLSE). This receiver is referred to as the MLSE CE-OFDM-CPM equalizer and it is implemented using the Viterbi Algorithm (VA). The MLSE is implemented using the VA because the CPM signal can be described as a finite state machine. To facilitate the description of the VA, a MLSE CPM receiver for an AWGN channel is introduced first. In addition to improved BER performance both in AWGN and frequency selective fading channel a MLSE equalizer is implemented in a frequency selective fading channel. A performance evaluation of CEOFDM in fast fading channels, using various developed and adapted practical channel equalizer techniques with low complexity and high accuracy, will be presented in this paper. 2. Conventional OFDM system 2.1. OFDM signal model Consider an OFDM system that transmits N symbols sn(i) in the ith OFDM symbol period through N subchannels of subcarrier spacing 1 / (NTf). The transmitted baseband OFDM signal is expressed as x(t )
Ts NT f
N 1
s n (i)v(t iNT )e
j
N 1 2 n ( t iNT ) 2 NT f
(1)
i n 0
where T is the data symbol period, NT is the OFDM symbol period, B=1 / Tf is approximately the total bandwidth of the OFDM signal, and v(t) is the OFDM symbol pulse shaping filter. The received signal is r[i] =
Nc -1
h[l]x[i - l] + n[i], l=0
i = 0,.......,NB - 1
(2)
Transmitting a cyclic prefix during the guard interval makes the linear convolution with the channel equivalent to circular convolution. Thus
1
r i NDFT
j
2 ik NDFT
i k e H k X
0,...........NB 1
(3)
Where {H[k]} is the DFT of {h[i]} and {S[k]} is the DFT of {s[i]}. 2.2. PAPR analysis in OFDM system OFDM signal has an approximately Gaussian amplitude distribution when the number of subcarriers is large. Therefore, very high peaks in the transmitted signal can occur. This property is often measured via the signal's peakto-average power ratio. To be able to transmit and receive these peaks without clipping the signal, there is two possibility. The first possibility that the A/D and D/A need to be designed with high demands on range and precision. But, if the dynamic ranges of the A/D and D/A are increased, the resolution also needs to be increased in order to maintain the same quantization noise level. Therefore, an OFDM signal may require expensive A/Ds and D/As compared to many other modulation formats, and for some applications suitable A/Ds and D/As may not be available at all. Also, a large power back-off of the amplifiers is necessary. Intentional or accidental clipping of the OFDM signal often occurs in practice. The clipping of a received sample affects all subcarriers in the system. The sensitivity to clipping effects is investigated in [8]. The second possibility is that the RF power amplifiers (PA) have to be operated in a very large linear region. Otherwise, the signal peaks get distorted, leading to intermodulation distortion (IMD) among the subcarriers and out-of-band radiation. A simple way to avoid is to use PA of large dynamic range but this makes the transmitter costly. Thus, it is highly desirable to reduce the PAPR. To alleviate this problem, constant envelope OFDM (CE-OFDM) signal has been introduced in [5, 6], which combines orthogonal frequency division multiplexing and phase modulation or frequency modulation.
J.Mestoui, M.El ghzaoui,etA.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000 J. Mestoui al. / Procedia Computer Science 151 (2019) 1016–1021
1018
3. CE-OFDM system model The baseband CE-OFDM signal is, j t s t Ae
(4)
Where A is the signal amplitude. The phase signal during the ith block is written as: N
(t) i 2 hcN Ii,k qk t iTB , k 1
Where
(t) (iT ) (iT ),
iTB t (i 1)TB
(5)
0
The phase memory may be used in conjunction with a phase unwrapper at the receiver to ensure a continuous phase at the symbol boundaries and hence better spectral containment. Here h refers to modulation index; N is the represents M-PAM data symbols; TB is the ith block interval, and represents the set number of sub-carriers where is the variance of the data of subcarrier waveforms. The normalizing constant, , is set to √ . Assuming that the data is symbols, and consequently the variance of the phase signal will be independent and identically distributed, it follows that M2 1 (6) I2 3 are The signal energy and the bite energy (7)
Es A2TB Eb
Es N log2 (M)
(8)
4. Optimal equalization: Maximum-Likelihood sequence estimation The optimal equalizer performs maximum-likelihood sequence estimation (MLSE) and it outputs the sequence that maximizes the probability of the received signal {rn}, or equivalently, it minimizes the Euclidean distance [9-12]. The MLSE-equalizer can be efficiently implemented by the Viterbi algorithm and it has a computational complexity of |s|K per decoded symbol, A being the modulation constellation e.g. QPSK, QAM, etc. Unfortunately there is currently implementation of the MLSE-equalizer in Matlab (mlseeq.m) which can be used. 4.1. CE-OFDM-CPM receiver for the AWGN channel In this section, we introduce the optimum CE-OFDM-CPM receiver for the AWGN channel. The optimum CEOFDM-CPM receiver consists of an MLSE block preceded by a metric computation block connected to a template signal generator. Figure 1 shows the structure of the optimum CPM receiver. The received signal is given by
r(t) s(t, In ) n(t)
(9)
Where is the M-ary (M is the size of the alphabet) CE-OFDM-CPM signal associated with the is AWGN. transmitted symbol sequence and MLSE CE-OFDM-CPM Receiver CE-OFDMDATA CPM signal {Ik}
𝑠𝑠 𝑡𝑡 𝐼𝐼𝑛𝑛
AWGN
𝑟𝑟 𝑡𝑡
Metric computation
𝑉𝑉𝑛𝑛
MLSE (VA)
𝑇𝑇 𝑡𝑡 − 𝑛𝑛𝑛𝑛
Signal Generator
Fig. 1. Optimum CE-OFDM-CPM receiver.
Déodulation CE-OFDM
DATA {Îk}
J.Mestoui, M.El ghzaoui, A.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000
J. Mestoui et al. / Procedia Computer Science 151 (2019) 1016–1021
1019
is the matrix of template signals using the channel estimation , and is the matrix of branch metrics and are speciefied as , where is the size of that correspond to the n-th symbol. The dimensions for is the total number of states in the equalizer trellis. the CE-OFDM-CPM alphabet and The MLSE (VA) block in Figure 1 performs MLSE using the Viterbi algorithm. The use of the Viterbi algorithm is a plausible solution to detect the symbols in the CE-OFDM-CPM signal because the behavior of CE-OFDM-CPM signals can be described with a finite-state trellis. 4.2. MLSE CE-OFDM-CPM Equalizer for frequency selective channel This section builds on the optimum MLSE CE-OFDM-CPM receiver for AWGN channels presented in Section (IV.A). Using knowledge of the channel, the MLSE CE-OFDM-CPM receiver is modified to receive and equalize the received signal. The structure for the MLSE CPM Equalizer is shown in Figure 2. The single addition to the MLSE CE-OFDM-CPM receiver structure consists of a channel estimator block, the output of which is used to reduce the effects of ISI introduced by a frequency selective channel. Although transparent to the structure, the optimum MLSE CE-OFDM-CPM receiver for AWGN channels presented in Section (IV.A) and the MLSE equalizer presented here differ in the method by which the template signals are generated and in the complexity of the MLSE trellis. The received signal is now given by and is defined as:
r(t)
s(t, In )h(t)d n(t)
(10)
is the Where is the M-ary CE-OFDM-CPM signal associated with the transmitted symbol sequence , impulse response for baseband frequency selective channels and is AWGN. is the matrix of template signals using the channel estimation , and is the matrix of branch metrics that , where is the size of the correspond to the n-th symbol. The dimensions for and are speciefied as is the total number of states in the equalizer trellis. The Channel Estimator block CE-OFDM-CPM alphabet and refers to the process of estimating the channel impulse response. A condition for true maximum likelihood is that the channel estimate ̂ be an accurate model of the actual channel otherwise the performance is sub-optimal. The two key differences between the equalizer that is presented here and the MLSE CE-OFDM-CPM receiver presented in section (4.1) are the configuration of the MLSE trellis and the template signal generator. The MLSE equalizer trellis is more complex because each state contains memory of previously transmitted symbols. The template signal generator for the MLSE equalizer differs from the MLSE CE-OFDM-CPM receiver in that it now accounts for the channel effects (ISI). The template signals use the channel estimate to account for the effect of ISI. The template signal generation for the MLSE equalizer is different from that for the MLSE CE-OFDM-CPM receiver in section (IV.A). While the template signals for the MLSE receiver (section 4.1) are only associated with a phase transition, the template signals for the MLSE equalizer presented here are associated with a phase transition, a symbol history, and a channel estimate. MLSE CE-OFDM-CPM Receiver 𝑠𝑠 𝑡𝑡 𝐼𝐼𝑛𝑛
Metric computation
𝑡𝑡 + 𝑛𝑛 𝑡𝑡 𝑟𝑟 𝑡𝑡
Channel Estimator
𝑡𝑡
𝑉𝑉𝑛𝑛
MLSE (VA)
𝑇𝑇 𝑡𝑡 − 𝑛𝑛𝑛𝑛
Signal Generator
Fig. 2. MLSE equalizer structure. 5. Simulation results In this section, the BER performance of the MLSE equalizer over Saleh-Valenzuela is presented. The multipath channel h(t) is simulated using the Saleh-Valenzuela channel model [11] which assumes that the received rays arrive
J.Mestoui, M.El ghzaoui,etA.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000 J. Mestoui al. / Procedia Computer Science 151 (2019) 1016–1021
1020
in clusters. Moreover, the BER performance of the proposed receiver is compared to the case without ISI as well (case AWGN channel). The simulations parameters are DFT size NDFT = 1024, a cyclic prefix Ng = 48, 2πh=1, M=4 and L = 15 length Hamming window FIR, having a normalized cutoff frequency fc = 0.4. In Figure 3 (a) the performance of MLSE equalizer in terms of BER performance is given. As expected, MLSE (case Saleh-Valenzuela channel, which is a severe channel,) estimation performs better in terms of BER, and is only approximately 3.5dB worse than AWGN performance at a BER of 10-4. 0
0
10
10
AWGN Saleh-Valenzuela
-1
10
-1
10
-2
-2
10
BER
BER
10
-3
10
OFDM-IBO=10dB OFDM-IBO=6dB OFDM-IBO=4dB OFDM-IBO=0dB CE-OFDM
-4
-4
10
10
-5
-5
10
10
-6
10
-3
10
-6
0
5
10
15 SNR (dB)
20
25
10
30
0
5
10 15 SNR (dB)
20
25
Fig. 3. (a). Performance of MLSE equalizer for CE-OFDM. (b). OFDM versus CE-OFDM-CPM under AWGN channel
In Figure 3(b), the OFDM systems perform better than the CE-OFDM-CPM systems at law SNR event we use a nonlinear amplifier because CE-OFDM-CPM suffer from a threshold effect. But at law SNR CE-OFDM-CPM systems perform better much than OFDM systems. Amplifier nonlinearities can significantly degrade the OFDM performance. Note that the power efficiency includes not only the SNR needed to achieve a target BER but also the energy consumed in the amplifier. In OFDM, it is critical to maintain the linear relation between the applied message and the amplitude of the transmitted signal, thus linear Class A or AB amplifiers, which are not power efficient, are usually used. CE-OFDM-CPM will be perhaps the most popular modulation technique used in the second generation cellular system. The envelope of the CE-OFDM-CPM modulated signals stays the same while its phase is varied by message signals. In OFDM, message signals are transported by varying the amplitudes of two carriers. CE-OFDM-CPM offers many advantages over OFDM, which makes it a better choice of the current mobile applications. 0
0
10
10
-1
-1
10
10
ZF LMSE MMSE
-3
10
-2
10
BER
BER
-2
10
ZF LMSE MMSE
-3
10
-4
-4
10
10
0
5
10
15 20 SNR (dB)
25
30
0
5
10
15 20 SNR (dB)
25
30
Fig. 4. BER Performance versus SNR for different Equalizers with and without channel estimation
The issue of amplifier efficiency is very important in the design of mobile terminals. The constant envelope of CEOFDM-CPM signals allows efficient nonlinear amplifiers to be used for amplification. In contrast, the performance of OFDM schemes is seriously compromised by amplifier nonlinearities. CE-OFDM-CPM signals require the transmit
J.Mestoui, M.El ghzaoui,etA.Hmamou, J.Foshi/ Procedia Computer Science 00 (2018) 000–000 J. Mestoui al. / Procedia Computer Science 151 (2019) 1016–1021
1021
power amplifiers to operate in a strictly linear region to preserve the transmitted signal properties at the expense of reduced power efficiency due to a large power back-off (IBO) requirement. This is perhaps the most important reason that CE-OFDM-CPM is usually preferred to OFDM in many wireless systems. As mentioned previously, OFDM schemes occupy less bandwidth than the CE-OFDM-CPM schemes. Thus, the OFDM systems can achieve a spectral efficiency up to 2.5 bps/Hz, which cannot be obtained even with a high spectral efficiency CE-OFDM-CPM system. While CE-OFDM-CPM systems have many advantages over OFDM systems, they also have certain disadvantages, especially in the high spectral efficiency CE-OFDM-CPM systems. In Figure 4, the Bit error rate (BER) versus the average SNR is plotted for the proposed equalizer with and without channel estimation schemes over a 2-path channel, QPSK modulation, DFT size NDFT = 1024, and a cyclic prefix Ng = 48. Signal-to-Noise Ratio (SNR) of the channel noise is changed between 0 and 30dB, and the BER is calculated by two approaches: a) No Channel Estimation and b) Pilot Channel Estimation with 8 pilots. Simulation results show that the performance of ZF is worse than the other two, and the performance of MMSE is slightly better than LMSE at high SNRs. The equalizers with channel estimation (a) yield the best performance, and they yield the worst performance without channel estimation (b). Therefore, the performance of an equalizer is dependent on the channel estimate. 6. Conclusion In this paper, two modulation techniques, OFDM and CE-OFDM-CPM, are studied. Particularly, the performance of OFDM and CE-OFDM-CPM is evaluated when taking amplifier nonlinearities into account. In addition, we introduced the optimum MLSE equalizer for CE-OFDM-PM for Saleh-Valenzuela channel which is a severe channel, the performance over it is only approximately 1.4 dB worse than AWGN performance at a bit error rate of 10-4. This paper fully reviews channel equalizers strategies in CE-OFDM systems. It describes channel Equalizers, which may be based on MLSE-Equalizer, ZF-Equalizer MMSE) or MMSE-Equalizer, with or without channel estimation. In CE-OFDM systems, efficient channel estimation schemes are essential for coherent detection of a received signal. Further research will provide insight into next generation digital communication systems that require power efficiency, high data rates and robustness in harsh channel conditions. References [1] R. D. van Nee, OFDM for Wireless Multimedia Communications. Artech House Publishers, Boston-London, January 2000. [2] Z. Wang and G. B. Giannakis, “Wireless multicarrier communications: Where Fourier meets Shannon,” IEEE Signal Process. Mag., vol. 17, No. 3, pp. 29–48, May 2000. [3] S. H. Han and J. H. Lee, An overview of peak-to-average power ratio reduction techniques for multicarrier transmission, IEEE Wireless Communications Magazine, vol. 12, pp. 56_65, April 2005. [4] J. Tellado-Mourelo, Peak to Average Power Reduction for Multicarrier Modulation. PhD thesis, Stanford University, Sept1999. [5] S. Thompson, A. Ahmed, J. Proakis, J. Zeidler, and M. Geile, “Constant Envelope OFDM,” EEE Trans. Commun., vol. 56, no. 8, pp.1300– 1312, August2008. [6] S. C. Thompson, “Constant Envelope OFDM Phase Modulation,” Ph.D. dissertation, Department Electrical Engineering (Communications Theory and Systems), University of California, SanDiego,2005. [7] Y. Tsai, G. Zhang, and J. Pan, “Orthogonal frequency division multi plexing with phase modulation and constant envelope design, ”in Proc. IEEE Milcom, vol. 4, October 2005, pp. 2658–2664. [8] R. Gross, and D. Veeneman [1993], “Clipping Distortion in DMT ADSL Systems,” Electronics Letters, 29, 24, pp. 2080-2081. [9] M. Chiu and C. Chao, “Analysis of LMS-Adaptive MLSE equalization on multipath fading channels,” IEEE Trans. Commun., vol. 44, no. 12, pp. 1684–1692, Dec. 1996. [10]. J. Wu and A. H. Aghvami, “A new adaptive equalizer with channel estimator for mobile radio communications,” IEEE Trans. Veh. Technol., vol. 45, no. 3, pp. 1178–1190, Aug. 1996. [11] J. T. Chenand, Y. C. Wang, “Adaptive MLSE equalizers with parametric tracking for multipath fast-fading channels,” IEEE Trans. Commun., vol.49, no.4, pp. 655-663, April2001. [12] H. Meyr, M. Moeneclaey and S. A. Fechtel, Digital Communication Receivers: Synchronization, Channel Estimation and Signal Processing, John Wiley& Sons, 1998.