Channel Estimation Based on IOTA Filter in OFDM/OQPSK and OFDM/OQAM Systems
Channel Estimation Based on IOTA Filter in OFDM/OQPSK and OFDM/OQAM Systems
Zhou, Xiao;Wang, Chengyou;Tang, Ruiguang
2019-04-07 00:00:00
applied sciences Article Channel Estimation Based on IOTA Filter in OFDM/OQPSK and OFDM/OQAM Systems Xiao Zhou , Chengyou Wang * and Ruiguang Tang School of Mechanical, Electrical and Information Engineering, Shandong University, Weihai 264209, China; zhouxiao@sdu.edu.cn (X.Z.); trg@mail.sdu.edu.cn (R.T.) * Correspondence: wangchengyou@sdu.edu.cn; Tel.: +86-631-568-8338 Received: 31 December 2018; Accepted: 1 April 2019; Published: 7 April 2019 Featured Application: This channel estimation method can be utilized to improve the underwater acoustic communication and fifth-generation (5G) wireless communication systems. Abstract: In this paper, we present a study of bit error rate (BER) for orthogonal frequency division multiplexing/offset quadrature phase shift keying (OFDM/OQPSK) and OFDM/offset quadrature amplitude modulation (OQAM) systems with an isotropic orthogonal transfer algorithm (IOTA) filter. The novel noise suppression method based on an IOTA filter is proposed to reduce the error of channel estimation caused by additive white Gaussian noise (AWGN). The OFDM/OQPSK and OFDM/OQAM systems do not insert the guard interval (GI) and pilots in the signal frames, thus they possess transmission efficiency. An analysis was carried out for convolutional coded OFDM/OQPSK and OFDM/OQAM systems in Rayleigh fading channels with generator polynomials and constraint lengths. Compared with conventional OFDM/QPSK and OFDM/QAM systems with the insertion of comb-type pilots, the proposed IOTA filter-based channel estimation method can provide significant energy per bit to time-varying noise power spectral density ratio gains over time and frequency-selective propagation Rayleigh fading channels in OFDM/OQPSK and OFDM/OQAM systems. Keywords: channel estimation; orthogonal frequency division multiplexing (OFDM); isotropic orthogonal transform algorithm (IOTA); offset quadrature phase shift keying (OQPSK); offset quadrature amplitude modulation (OQAM); additive white Gaussian noise (AWGN) 1. Introduction Wavelets have been a very hot research area in recent years. Their application ranges from function approximation, signal multiresolution representation, and image compression to signal processing and other fields. The popularity of wavelets is primarily due to their interesting structures, which can provide perfect time-frequency localization (TFL) characteristics. A few investigators have begun to exploit these time-domain and frequency-domain features of wavelets for application in wireless communication systems [1–3]. In classical orthogonal frequency division multiplexing (OFDM) systems, a guard interval (GI) is inserted in front of OFDM symbols to effectively combat the multipath effect with little loss of spectral efficiency. It is robust to inter-symbol interference (ISI), but sensitive to inter-carrier interference (ICI) due to Doppler spread in the frequency domain. Offset quadrature phase shift keying (OQPSK) and offset quadrature amplitude modulation (OQAM) are spectrally efficient modulation schemes which are alternative technologies for replacing QPSK and QAM. OQPSK and OQAM modulations possess good TFL properties by utilizing an isotropic orthogonal transfer algorithm (IOTA) filter. The polyphase IOTA filters are utilized as both transmit and receive filters to enhance robustness for channel delay Appl. Sci. 2019, 9, 1454; doi:10.3390/app9071454 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 1454 2 of 15 and Doppler spread. In OFDM/OQPSK and OFDM/OQAM systems, the orthogonal condition of the subcarriers is guaranteed from the complex domain to the real domain. Thus, the GI inserted between consecutive OFDM signal frames can be removed in OFDM/OQPSK and OFDM/OQAM systems. The ISI and ICI in OFDM/QPSK systems can be suppressed utilizing polyphase filter banks with good TFL property. Compared with OFDM systems, the TFL property of the IOTA filter can guarantee good bit error rate (BER) performance that combats ISI and ICI in OFDM/OQPSK and OFDM/OQAM systems. This paper proposes a channel estimation method based on an IOTA filter, which is applied in OFDM/OQPSK and OFDM/OQAM systems. It has high spectral and data transmission efficiency which effectively suppresses the additive white Gaussian noise (AWGN) existing at the estimated channel coefficients in the time domain. It can improve the system’s BER and normalized minimum square error (NMSE) performance, and is easy to implement in hardware. Simulation results verified that the proposed IOTA filter channel estimation method was superior to the conventional comb-type pilots insertion based least square (LS) method in terms of BER and NMSE performance under Rayleigh fading channel conditions. The remainder of this paper is organized as follows. In Sections 2 and 3, the related work and OFDM/OQPSK system model are presented. Section 4 introduces the channel coding. Section 5 illustrates the simulation results. Conclusions are presented in Section 6. 2. Related Work Recently, many experiments and theoretical analyses of OFDM-IOTA systems have been proposed. A new pilot and preamble structure for the channel estimation appropriate for the OFDM/OQAM system was proposed. A limitation of the paper was that it was implemented in an uncoded OFDM system [4]. Although a comparison of cyclic prefix (CP)-OFDM with OFDM-IOTA under a typical system was proposed, the disadvantage of the system was the existence of frequency offset error at the receiver [5]. A hardware architecture of the pulse shaping filter used in multicarrier systems was proposed in [6]. IOTA pulse shaping filters were used to reduce hardware overhead in multicarrier systems based on faster-than-Nyquist (FTN) signaling. The IOTA filter has an overhead of 28% in silicon area compared with the FTN iterative decoder. The disadvantage is that the high complexity of the hardware mapped architecture. A multiple-input multiple-output (MIMO)-IOTA system was proposed in [7], and the MIMO-IOTA system achieved better performance compared with an OFDM system at low-to-medium signal-to-noise ratios (SNRs). Raised cosine, IOTA, Hermite, and Gaussian wavelets were proposed in [8]. The BER results of the IOTA method were better than those of the square function method and slightly worse than the Hermite function method. As the SNR increased, the Hermite filter showed the best BER performance compared with IOTA and square filters. The disadvantage of the Hermite filter is that it only concentrates on ICI suppression and does not consider the effect of different types of multipath in the simulation results. The capacity of OFDM/OQAM systems with IOTA filters was evaluated through information theoretical analysis in [9]. The promising results motivate further research on the utilization of the intrinsic interference in order to explore the potential to attain maximum performance gain in future OFDM/OQAM systems. OFDM/OQAM systems showed significant spectral efficiency while compared with CP-OFDM systems. In [10], the BER performance of OFDM interleave division multiple access (IDMA) with wavelet families, such as Haar, Daubechies, and Symlets, was compared over an AWGN channel. The Daubechies wavelet has the best BER performance under 16-quadrature amplitude modulation (16-QAM). The circular 16-QAM constellation has been derived and applied in Fourier- and wavelet-based OFDM systems [11]. The circular scheme showed slightly better BER performance than the square scheme. The reason is that the power consumption of the circular constellation signals is less than that of the square scheme. To maximize the system capacity, the filter-bank-based multicarrier (FBMC) scheme provides higher capacity performance compared with the OFDM system [12]. In contrast to the OFDM system, the FBMC waveform has been demonstrated to be Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 15 Appl. Sci. 2019, 9, 1454 3 of 15 prototype filter. A new OFDM system based on a discrete cosine harmonic wavelet transform (DCHWT) for binary phase shift keying (BPSK) and QPSK signals was proposed in [13]. The less sensitive to timing error between the different cells, due to the better frequency localization of proposed DCHWT-OFDM system provided superior performance in terms of BER and the prototype filter. A new OFDM system based on a discrete cosine harmonic wavelet transform peak-to-average power ratio (PAPR) compared with the discrete cosine transform (DCT)-OFDM, (DCHWT) for binary phase shift keying (BPSK) and QPSK signals was proposed in [13]. The proposed discrete Fourier transform (DFT)-OFDM, and Haar WT-OFDM systems. However, the DCHWT-OFDM system provided superior performance in terms of BER and peak-to-average power DCHWT-OFDM and Haar WT-OFDM systems may not have significant BER improvements under ratio (PAPR) compared with the discrete cosine transform (DCT)-OFDM, discrete Fourier transform 16-QAM and 64-QAM signal constellation. (DFT)-OFDM, and Haar WT-OFDM systems. However, the DCHWT-OFDM and Haar WT-OFDM systems may not have significant BER improvements under 16-QAM and 64-QAM signal constellation. 3. OFDM/OQPSK System Model 3. OFDM/OQPSK System Model 3.1. OFDM/OQPSK Symbols 3.1. OFDM/OQPSK Symbols Figure 1 represents the real and imaginary values of OFDM/OQPSK symbols. The green triangle signature represents the OFDM/QPSK symbols in conventional CP-OFDM systems. The Figure 1 represents the real and imaginary values of OFDM/OQPSK symbols. The green triangle classical OFDM/QPSK symbols are real mapped into two parts (i.e., real and imaginary values in signature represents the OFDM/QPSK symbols in conventional CP-OFDM systems. The classical the OFDM/OQPSK-IOTA system), which are located in four quadrants. In Figure 1, the circular OFDM/QPSK symbols are real mapped into two parts (i.e., real and imaginary values in the yellow signature represents the real value of OFDM/OQPSK symbols and the blue signature OFDM/OQPSK-IOTA system), which are located in four quadrants. In Figure 1, the circular yellow represents the imaginary value of OFDM/OQPSK symbols. τ and v are the time-domain signature represents the real value of OFDM/OQPSK symbols and the blue signature represents 0 0 the imaginary value of OFDM/OQPSK symbols. t and v are the time-domain duration and duration and frequency-domain spacing for OFDM/OQPSK symbols, respectively. τ equals to 0 0 frequency-domain spacing for OFDM/OQPSK symbols, respectively. t equals to half of the half of the OFDM/QPSK symbol duration , that is, τ = T /2 . The phases and dephases of the s 0s OFDM/QPSK symbol duration T , that is, t = T /2. The phases and dephases of the real and s s mn + −+() mn real and imaginary values of OFDM/OQPSK symbols are represented as j and j , m+n (m+n) imaginary values of OFDM/OQPSK symbols are represented as j and j , respectively. mn + −+() mn mn + −+() mn m+n (m+n) m+n (m+n) respectively. If () mn+=%4 0 , then j = 1 , j = 1 ; if () mn+=%4 1 , then j = j , j =− j ; If (m + n)%4 = 0, then j = 1, j = 1; if (m + n)%4 = 1, then j = j, j = j; m+n (m+n) m+n (m+n) mn + −+() mn mn + −+() mn if (m + n)%4 = 2, then j = 1, j = 1; if (m + n)%4 = 3, then j = j, j = j; if () mn+=%4 2 , then j =−1 , j =−1 ; if () mn+=%4 3 , then j =− j , j = j ; where % where % is the modulo operation. is the modulo operation. OFDM/QPSK symbol: complex value OFDM/OQPSK symbol: real value 0 imaginary value 2×= τ T 0s Figure 1. Real and imaginary values of orthogonal frequency division multiplexing (OFDM)/offset Figure 1. Real and imaginary values of orthogonal frequency division multiplexing (OFDM)/offset quadrature phase shift keying (OQPSK) symbols. quadrature phase shift keying (OQPSK) symbols. 3.2. Design of the IOTA Filter 3.2. Design of the IOTA Filter The approximate time-domain IOTA function, which is denoted as (t), can be expressed as [14]: The approximate time-domain IOTA function, which is denoted as ξ () t , can be expressed as [14]: K 1 K 1 1 k k t x (t) = d h (t + ) + h (t ) d cos(2l ) , 4t t 4t , (1) t å k,u EGF EGF å l,t 0 0 0 0 KK − 1 2 u u t 0 0 0 1 kk t k=0 l=0 ξ ()tt =+ dh ( )+h (t− )⋅ d cos(2πl ),− 4τ≤ t≤ 4τ , (1) τ k ,υ EGF EGF l ,τ 0 0 00 0 2 υυ τ kl == 00 00 0 Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 1454 4 of 15 1 2 where t is the time and k represents the number of subcarriers. h (t) = 2 e is the extended EGF Gaussian filter (EGF) in the time domain. Normally, t and u are chosen to be 1/ 2 to maintain the 0 0 orthogonality characteristics between consecutive OFDM symbols in the time domain and adjacent p p p subcarriers in the frequency domain. When t = u = 1/ 2, t 2 [ 2 2, 2 2]. The polyphase IOTA 0 0 filter puts the IOTA values into the IOTA buffer with the length equals to half of the fast Fourier transform (FFT) size and the width equals to 8. The IOTA coefficients d can be expressed as: k,n Q 1 (2q+k) d = b e , 0 k K 1, 0 q Q 1, (2) k,n å k,q q=0 where K and Q, which are integer numbers, are two parameters of the IOTA filter. In general, K = 15 and Q = 8 are chosen in IOTA filter design [14]. Table 1 represents a list of b coefficients. k,q Table 1. b coefficients of the isotropic orthogonal transfer algorithm (IOTA) filter. k,q k q=0 q=1 q=2 q=3 q=4 q=5 q=6 q=7 0 1 0.75 1.6406 2.6367 4.6529 6.9749 11.5368 16.8193 1 1 1.875 3.4219 5.9131 9.8831 15.7769 24.8536 0 2 0.75 1.1875 3.0176 4.7681 9.0985 14.0379 23.4937 0 3 0.625 0.9609 2.2354 4.2567 7.3957 12.2028 0 0 4 0.5469 0.8320 1.9036 3.4279 6.6095 10.3934 0 0 5 0.4922 0.7451 1.6937 3.0167 5.6268 0 0 0 6 0.4512 0.6812 1.5433 2.7365 5.0687 0 0 0 7 0.4189 0.6314 1.4279 2.526 0 0 0 0 8 0.3928 0.5913 1.3356 2.3594 0 0 0 0 9 0.3709 0.558 1.2594 0 0 0 0 0 10 0.3524 0.5299 1.1951 0 0 0 0 0 11 0.3364 0.5056 0 0 0 0 0 0 12 0.3224 0.4843 0 0 0 0 0 0 13 0.31 0 0 0 0 0 0 0 14 0.2989 0 0 0 0 0 0 0 Table 2 represents a list of important parameters in the IOTA filter, where k, l, and q are set to be integers. The accuracy of IOTA filter design can reach 0.79 10 [14]. The IOTA filter which is utilized in OFDM/OQPSK and OFDM/OQAM systems increases the accuracy of channel estimation. Table 2. Important parameters in the IOTA filter. Parameters Specifications t 1/ 2 u 1/ 2 p p [ 2 2, 2 2] K 15 Q 8 k [0, 14] l [0, 14] q [0, 7] The simulation results of linear and decibel formats of the IOTA filter are represented in Figure 2a,b. When the number of OFDM symbols is t = 0, the magnitude of the IOTA filter is equal to 1. The IOTA filter is orthogonal between consecutive OFDM symbols, thus it can efficiently reduce the ISI and ICI. Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 15 The simulation results of linear and decibel formats of the IOTA filter are represented in Figure 2a,b. When the number of OFDM symbols is t = 0 , the magnitude of the IOTA filter is equal to 1. Appl. The IOTA Sci. 2019, filt 9, 1454 er is orthogonal between consecutive OFDM symbols, thus it can efficiently reduce the 5 of 15 ISI and ICI. 1.2 -20 0.8 -40 0.6 -60 0.4 -80 0.2 -100 -0.2 -120 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 (a) (b) Figure 2. IOTA filter in linear and decibel formats: (a) Linear format, (b) Decibel format. Figure 2. IOTA filter in linear and decibel formats: (a) Linear format, (b) Decibel format. 3.3. OFDM-IOTA System Model 3.3. OFDM-IOTA System Model Figure 3 represents the OFDM-IOTA system model. The incoming binary bits are first QPSK Figure 3 represents the OFDM-IOTA system model. The incoming binary bits are first QPSK modulated, modulated, t then hen every O every OFDM/QPSK FDM/QPSK s symbol ymbol is s is separated eparate into d int real o re and al and im imaginary aginar parts, y part which s, which is is called called real map. After real mapping, the OFDM symbols are symbol-phased by multiplying them real map. After real mapping, the OFDM symbols are symbol-phased by multiplying them with the mn + m+n with the phase coefficient j . At the receiver, the OFDM symbols are symbol-dephased by phase coefficient j . At the receiver, the OFDM symbols are symbol-dephased by multiplying them (m+n) −+() mn with the phase coefficient j . After inverse fast Fourier transform (IFFT) operation, the signals multiplying them with the phase coefficient j . After inverse fast Fourier transform (IFFT) are convoluted by the polyphaser IOTA filter, which can be denoted as x (m). The transmitted operation, the signals are convoluted by the polyphaser IOTA filter, which 0 can be denoted as OFDM/OQPSK signals in the time domain can be written as [15]: ξ () m . The transmitted OFDM/OQPSK signals in the time domain can be written as [15]: Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 15 M 1 N 1 j2πmn MN −− 11 j2mn i i m+n ii m +n s = a j x (m nt ) e , 0 m M 1, 0 n N 1, (3) sa=⋅ j ⋅ξ() mn− τ⋅e ,0≤mM≤ −1,0≤n≤N−1, (3) å å t 0 m,n m,n 0 mn,, mn τ 0 − j2πmn MN −− 11 0 mn == 00 m=0 n=0 ii i ˆ N Yy=⋅ξω () mn− τ⋅e + , (5) mn , m,0 n τ mn, i mn == 00 where a is the real or imaginary OQPSK symbol of the i -th signal frame on the m -th symbol mn , where a is the real or imaginary OQPSK symbol of the i-th signal frame on the m-th symbol m,n where is the receive IOTA filter. ω is the time-domain AWGN of the i -th signal frame of the nξ-th subcarrie () m r. N is the number of subcarriers within one OFDM symbol and M is the of the n-thτ subcarrier. N is the number ofmn ,subcarriers within one OFDM symbol and M is the number number of t of transmitted ransmitted OFDM/OQPSK OFDM/OQPSK symbols. symbols. In the In the OFD OFDM-IOT MA-IOTA system, sysM tem, = 300 M and = 300N and = 512. on the m -th symbol of the n -th subcarrier. As illustrated in Figure 3, the received OFDM/OQPSK N = 512 . is the transmit IOTA filter on the m -th OFDM/OQPSK symbol, and τ is the x (m) is theξtransmit () m IOTA filter on the m-th OFDM/OQPSK symbol, and t is the duration of the τ y ˆ 0 0 0symbols of the i -th frame are QPSK demodulated, de-interleaved, and finally channel mn , OFDM/OQPSK symbol. duration of the OFDM/OQPSK symbol. decoded into binary bits [16]. i i Take the i -th signal frame for example, suppose S to be the FFT of s , the received mn , mn , Input i i i frequency-domain symbols after multipath channel Ymn , can be represented as: s bit s mn , Channe l Int er- QP SK Real Symbol Polyphase P/ mn , mn , IF FT coder leaver mod map phase IO TA S ii i i YS=⋅H +W , (4) mn,, mn m,n mn, Multipath i i channel where H and W are the channel frequency response (CFR) and the frequency-domain noise mn , mn , AW GN of the i -th frame, respectively. After AWGN channel, the received time-domain symbols of the mn , i -th frame on the m -th symbol and the n -th subcarrier can be denoted as y , which is an IFFT mn , i −+() mn y Ou tput mn , of Y . The OFDM signals are dephased by multiplying them i with the coefficients j . After mn , Y bits mn , Channe l De- QP SK Real Symbol Polyphase S/ FF T deco der interleaver demo d de-map dephase IO TA P real de-mapping, the received OFDM/OQPSK signals can be represented as [15]: Channe l mn , estimation Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci Figure 3. OFDM-IOTA system model. AWGN: additive white Gaussian noise; FFT: fast Fourier Figure 3. OFDM-IOTA system model. AWGN: additive white Gaussian noise; FFT: fast Fourier transform; IFFT: inverse FFT. transform; IFFT: inverse FFT. i i Suppose the FFT transform of y is Y , after the polyphaser IOTA filter, the estimated mn , mn , CFR H of the i -th frame can be expressed as: mn , ii −+()mn i i ˆˆ HY =⋅ 1.4 ⋅ j /X +W , (6) mn,, mn p m,n where X are the preamble symbols of the i -th OFDM signal frame. W is the p mn , frequency-domain AWGN in H . mn , h H Supposing is the IFFT transform of , since the noise suppression process will not be mn , mn , carried out in the LS criterion, it degrades the estimation accuracy of channel impulse responses (CIRs). In practice, the OFDM/OQPSK system utilizes an improved minimum mean square error (IMMSE) method to suppress the noise impact on the initial CIR estimation, and the estimated CIR h is expressed as [16]: mn , ˆ ˆ hh ⋅|| mn,, m n h = , (7) mn , αα ⋅+ || h (1− )⋅ A mn , i where A = max (|h |) denotes the maximum amplitude, and α denotes the suppression im ,n 01 ≤≤ nN− factor. In practice, α can be chosen in the range of (0.99,1) according to different modulation modes which are accommodated for environments. EN / b0 i i ˆ ˆ H h Supposing is the FFT transform of , R is the real value of the Y , the received mn , mn , mn , mn , OFDM/OQPSK symbols of the i -th frame X can be obtained based on LS method: mn , ii −+()mn ˆˆ X =⋅ 1.4YH ⋅ j / . (8) mn,, mn mn, Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci ξ (dB) 0 Appl. Sci. 2019, 9, 1454 6 of 15 Take the i-th signal frame for example, suppose S to be the FFT of s , the received m,n m,n frequency-domain symbols after multipath channel Y can be represented as: m,n i i i i Y = S H + W , (4) m,n m,n m,n m,n i i where H and W are the channel frequency response (CFR) and the frequency-domain noise of the m,n m,n i-th frame, respectively. After AWGN channel, the received time-domain symbols of the i-th frame on the m-th symbol and the n-th subcarrier can be denoted as y , which is an IFFT of Y . The OFDM m,n m,n (m+n) signals are dephased by multiplying them with the coefficients j . After real de-mapping, the received OFDM/OQPSK signals can be represented as [15]: M 1 N 1 j2mn i i Y = y x (m nt ) e + w , (5) å å t 0 m,n m,n 0 m,n m=0 n=0 where x (m) is the receive IOTA filter. w is the time-domain AWGN of the i-th signal frame on the 0 m,n m-th symbol of the n-th subcarrier. As illustrated in Figure 3, the received OFDM/OQPSK symbols of the i-th frame y ˆ are QPSK demodulated, de-interleaved, and finally channel decoded into binary m,n bits [16]. Suppose the FFT transform of y ˆ is Y , after the polyphaser IOTA filter, the estimated CFR m,n m,n H of the i-th frame can be expressed as: m,n i i i (m+n) i ˆ ˆ ˆ H = 1.4 Y j /X + W , (6) m,n m,n P m,n where X are the preamble symbols of the i-th OFDM signal frame. W is the frequency-domain P m,n AWGN in H . m,n Supposing h is the IFFT transform of H , since the noise suppression process will not be m,n m,n carried out in the LS criterion, it degrades the estimation accuracy of channel impulse responses (CIRs). In practice, the OFDM/OQPSK system utilizes an improved minimum mean square error (IMMSE) method to suppress the noise impact on the initial CIR estimation, and the estimated CIR h is m,n expressed as [16]: ˆ ˆ h jh j m,n m,n h = , (7) m,n 2 2 ajh j + (1 a) A m,n where A = max (jh j) denotes the maximum amplitude, and a denotes the suppression factor. m,n 0nN 1 In practice, a can be chosen in the range of (0.99, 1) according to different modulation modes which are accommodated for E /N environments. b 0 i i e ˆ e ˆ Supposing H is the FFT transform of h , R is the real value of the Y , the received m,n m,n m,n m,n OFDM/OQPSK symbols of the i-th frame X can be obtained based on LS method: m,n i i (m+n) ˆ ˆ e X = 1.4 Y j /H . (8) m,n m,n m,n 4. Channel Coding 4.1. Time Diversity in Jakes Model For time diversity, channel coding plus inter-leaver can be used in the time domain. However, to make the technique effective, the time frame has to be greater than the channel coherence time. In this work, we consider a frequency-selective environment and adopt a Rayleigh fading channel model to simulate the time diversity. Subcarriers in different OFDM symbols are considered to fade independently, and subcarriers in the same OFDM symbol experience identical fades. In the time domain, we use the Jakes model to simulate different fading rates, generating a different time diversity Appl. Sci. 2019, 9, 1454 7 of 15 environment. Table 3 represents the main simulation parameters for OFDM/OQPSK, OFDM/QPSK, OFDM/OQAM, and OFDM/QAM systems. The signal modulation patterns are OQAM, QAM, OQPSK, and QPSK, respectively. The symbol rate is 12 kbit/s, the length of FFT is 512, and the carrier frequency is 2 GHz. The fast fading model is the Jakes spectrum and the channel coding is a convolutional encoder with a code rate of 1/2. The inter-leaver is a block inter-leaver with 300 OFDM symbols. The channel decoding algorithm in the systems is Viterbi decoding. Table 3. Main simulation parameters in this paper. Parameters Specifications Symbol duration T QPSK: 1/6000 s, 16-QAM: 1/3000 s Symbol rate 12 kbit/s Guard interval (GI) length OFDM-IOTA: 0, CP-OFDM: 128 symbols System model OFDM-IOTA / CP-OFDM The length of FFT 512 Carrier frequency 2 GHz Fast fading model Jakes spectrum Number of multi-paths 6 Code rate 1/2 a 0.995 Inter-leaver Block inter-leaver (300 OFDM symbols) Doppler spread 20, 40, 60, 80 Hz 4.2. Convolutional Encoder and Viterbi Decoder In OFDM systems, the most widely used channel coding types are block codes and convolutional codes. Convolutional codes have memory, unlike block codes, which provides output using past information bits. If the number of registers is 6, then the constraint length equals to 7 [17,18]. The convolutional encoder consists of a code rate of 1/2, memory of 6, with code generator polynomials 133 and 171 in octal format [17,18]. The convolutional encoder can improve the accuracy of channel estimation for the receivers in both OFDM-IOTA and CP-OFDM systems. The Viterbi algorithm operates by computing a metric for every possible path in the trellis [13]. The path with the lower metric is retained and the other path is discarded. This process is repeated until the algorithm completes its forward search through the trellis and reaches the termination node, and finally makes a decision on maximum likelihood path. The sequence symbols associate with the path are then released to the destination as the Viterbi decoder output. The Viterbi decoder algorithm can find the lowest Hamming distance to demodulate the input binary bits correctly. 5. Simulation Results 5.1. The Performance of the OFDM/OQPSK System Figure 4 represents BER performance over Rayleigh fading channels with different Doppler spread [18]. At the target BER of 10 , the IOTA filter channel estimation method under Doppler spread 20 Hz outperforms the IOTA channel estimation method under Doppler spread of 40, 60, and 80 Hz by about 0.4, 5.5, and 9.7 dB E /N gains. At the target BER of 2 10 , under the b 0 Doppler spread of 20 Hz, the ideal channel estimation (ICE) method outperforms the IOTA channel estimation method under Doppler spread of 40, 60, and 80 Hz by about 0.4, 6.0, and 9.8 dB E /N b 0 gains. The reason is that when the channel is under fast mobile velocity, the Rayleigh channel is under the condition of severe frequency selectivity, and thereby it causes large amounts of bit errors. Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 15 spread 20 Hz outperforms the IOTA channel estimation method under Doppler spread of 40, 60, and −4 80 Hz by about 0.4, 5.5, and 9.7 dB EN / gains. At the target BER of 21 × 0 , under the Doppler b 0 spread of 20 Hz, the ideal channel estimation (ICE) method outperforms the IOTA channel estimation method under Doppler spread of 40, 60, and 80 Hz by about 0.4, 6.0, and 9.8 dB EN / b 0 gains. The reason is that when the channel is under fast mobile velocity, the Rayleigh channel is Appl. Sci. 2019, 9, 1454 8 of 15 under the condition of severe frequency selectivity, and thereby it causes large amounts of bit errors. -1 -2 -3 IOTA, f = 20 Hz ICE, f = 20 Hz -4 IOTA, f = 40 Hz ICE, = 40 Hz IOTA, = 60 Hz -5 ICE, f = 60 Hz IOTA, f = 80 Hz ICE, f = 80 Hz -6 0 2 4 6 8 10 12 14 16 18 20 E /N (dB) b 0 Figure 4. Bit error rate (BER) performance of the OFDM/OQPSK system over Rayleigh fading Figure 4. Bit error rate (BER) performance of the OFDM/OQPSK system over Rayleigh fading channels channels with Doppler spread of 20, 40, 60, and 80 Hz. ICE: ideal channel estimation. with Doppler spread of 20, 40, 60, and 80 Hz. ICE: ideal channel estimation. The acc The accuracy uracy of of ch channel annel est estimation imation can can be ev be evaluated aluated b by y the NMSE, the NMSE, which which is expressed as: is expressed as: NN −− 11 ICE 2 ICE 2 N 1 N 1 NMSE=− |hh |2 |h | 2, (9) mn,, mn mn, ICE ICE NMSE = h h / h , (9) nn == 00 å m,n å m,n m,n n=0 n=0 ICE where h is the ICE result on the m -th subcarrier of the n -th OFDM/OQPSK symbol which can mn , ICE where h is the ICE result on the m-th subcarrier of the n-th OFDM/OQPSK symbol which can be m,n ˆ be obtained under the condition of no AWGN. is the estimated CIR for the IOTA filter method mn , obtained under the condition of no AWGN. h is the estimated CIR for the IOTA filter method on the m,n on the m -th subcarrier of the n -th OFDM/OQPSK symbol. m-th subcarrier of the n-th OFDM/OQPSK symbol. Figure 5 illustrates the NMSE versus EN / for the proposed OFDM/OQPSK system over b 0 Figure 5 illustrates the NMSE versus E /N for the proposed OFDM/OQPSK system over b 0 Rayleigh fading Rayleigh fading channels channels with with differen differentt Doppler spread Doppler spread.. The The figure shows th figure shows that at the accuracy of the accuracy of channel estimation can be greatly improved when the value of Doppler spread decreased. As shown channel estimation can be greatly improved when the value of Doppler spread decreased. As shown in Figur in Figure e 5, 5, when the N when the NMSE MSE v value alue is is0.1, the 0.1, the EN E / / N gaps gapsbetween between the NMSE perfo the NMSE performance rmance c curves urves b 0 b 0 of proposed IOTA filter method with Doppler spread of 20, 40, 60, and 80 Hz are about 0.8, 3.2, of proposed IOTA filter method with Doppler spread of 20, 40, 60, and 80 Hz are about 0.8, 3.2, and and 4.5 dB, respectively. The NMSE simulation results verify that IOTA filter has good orthogonality 4.5 dB, respectively. The NMSE simulation results verify that IOTA filter has good orthogonality properties in time and frequency domains, which can be utilized as a wavelet platform in the proposed properties in time and frequency domains, which can be utilized as a wavelet platform in the OFDM/OQPSK system. proposed OFDM/OQPSK system. 5.2. The Performance of the OFDM/QPSK System 5.2. The Performance of the OFDM/QPSK System The BER performance of the OFDM/QPSK system over Rayleigh fading channels with different The BER performance of the OFDM/QPSK system over Rayleigh fading channels with different Doppler spread is presented in Figure 6. The OFDM/QPSK system adopts comb-type pilots insertion Doppler spread is presented in Figure 6. The OFDM/QPSK system adopts comb-type pilots insertion for perfect channel estimation. At the target BER of 10 , the E /N gaps of the LS method under b 0 Doppler spread of 20, 40, 60, and 80 Hz are about 8.5, 2.0, and 0.5 dB. Moreover, the E /N gaps Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci 0 between the BER performance curves of ICE method with Doppler spread of 20, 40, 60, and 80 Hz are about 7.0, 2.2, and 0.8 dB at the target BER of 10 . BER Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 15 −3 for perfect channel estimation. At the target BER of 10 , the EN / gaps of the LS method under b 0 Doppler spread of 20, 40, 60, and 80 Hz are about 8.5, 2.0, and 0.5 dB. Moreover, the EN / gaps b 0 Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 15 between the BER performance curves of ICE method with Doppler spread of 20, 40, 60, and 80 Hz Appl. Sci. 2019, 9, 1454 9 of 15 −4 −3 for perfect channel estimation. At the target BER of 10 , the EN / gaps of the LS method under are about 7.0, 2.2, and 0.8 dB at the target BER of 10 . b 0 Doppler spread of 20, 40, 60, and 80 Hz are about 8.5, 2.0, and 0.5 dB. Moreover, the EN / gaps b 0 0.7 between the BER performance curves of ICE method with Doppler spread of 20, 40, 60, and 80 Hz IOTA, f = 20 Hz −4 are about 7.0, 2.2, and 0.8 dB at the target BER of 10 . IOTA, f = 40 Hz 0.6 IOTA, = 60 Hz 0.7 IOTA, f = 20 Hz IOTA, f = 80 Hz IOTA, f = 40 Hz 0.5 0.6 IOTA, f = 60 Hz IOTA, f = 80 Hz 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 / (dB) E /N (dB) E N b 0 b 0 Figure 5. Normalized minimum square error (NMSE) performance of the OFDM/OQPSK system Figure 5. Normalized minimum square error (NMSE) performance of the OFDM/OQPSK system over Figure 5. Normalized minimum square error (NMSE) performance of the OFDM/OQPSK system over Rayleigh fading channels with Doppler spread of 20, 40, 60, and 80 Hz. Rayleigh fading channels with Doppler spread of 20, 40, 60, and 80 Hz. over Rayleigh fading channels with Doppler spread of 20, 40, 60, and 80 Hz. LS, f = 20 Hz ICE, f = 20 H LS, z f = 20 Hz LS, f = 40 Hz d ICE, f = 20 Hz -1 d ICE, f = 40 Hz LS, f = 40 Hz -1 LS, f = 60 Hz ICE, f = 40 Hz ICE, f = 60 Hz -2 LS, f = 60 Hz LS, f = 80 Hz d ICE, f = 60 Hz ICE, f = 80 Hz d d -2 LS, f = 80 Hz -3 ICE, f = 80 Hz -3 -4 -5 -4 -6 -5 0 2 4 6 8 10 12 14 16 18 20 E /N (dB) b 0 Figure 6. BER performance of the OFDM/QPSK system over Rayleigh fading channels with Doppler Figure 6. BER performance of the OFDM/QPSK system over Rayleigh fading channels with Doppler spread of 20, 40, 60, and 80 Hz. LS: least square. spread of 20, 40, 60, and 80 Hz. LS: least square. -6 Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci 0 2 4 6 8 10 12 14 16 18 20 E /N (dB) b 0 Figure 6. BER performance of the OFDM/QPSK system over Rayleigh fading channels with Doppler spread of 20, 40, 60, and 80 Hz. LS: least square. Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci BER BER NMSE NMSE Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 15 Appl. Sci. 2019, 9, 1454 10 of 15 Figure 7 presents the NMSE performance of the OFDM/QPSK system over Rayleigh fading channels with different Doppler spread, which can be seen is that the LS method with f = 20 Hz Figure 7 presents the NMSE performance of the OFDM/QPSK system over Rayleigh fading outperforms the LS method with f = 40 Hz , f = 60 Hz , and f = 80 Hz by about 4.0, 6.0, and channels with different Doppler spread, which can be seen is that the LS method with f = 20Hz d d d d outperforms the LS method with f = 40Hz, f = 60Hz, and f = 80Hz by about 4.0, 6.0, and 6.1 dB 6.1 dB EN / gains at the NMSE d of 0.1. As s dhown in Figure 7 d , the LS method has very low NMSE b 0 E /N gains at the NMSE of 0.1. As shown in Figure 7, the LS method has very low NMSE value with b 0 value with the increase of EN / . It can suppress the AWGN impact and improve the accuracy of b 0 the increase of E /N . It can suppress the AWGN impact and improve the accuracy of the estimated the estimated CIR, thereby it can increase the accuracy of channel estimation. CIR, thereby it can increase the accuracy of channel estimation. LS, f = 20 Hz LS, = 40 Hz 0.9 d LS, f = 60 Hz 0.8 LS, f = 80 Hz 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2 4 6 8 10 12 14 16 18 20 E /N (dB) b 0 Figure 7. NMSE performance of the OFDM/QPSK system over Rayleigh fading channels with Doppler Figure 7. NMSE performance of the OFDM/QPSK system over Rayleigh fading channels with spread of 20, 40, 60, and 80 Hz. Doppler spread of 20, 40, 60, and 80 Hz. 5.3. The Performance of the OFDM/OQAM System 5.3. The Performance of the OFDM/OQAM System Figure 8 illustrates the BER performance of the proposed OFDM/OQAM system over Rayleigh Figure 8 illustrates the BER performance of the proposed OFDM/OQAM system over Rayleigh fading channels with different Doppler spread. As shown in Figure 8, when the maximum Doppler fading channels with different Doppler spread. As shown in Figure 8, when the maximum Doppler spread increased from 20 Hz to 60 Hz, the proposed IOTA filter method demonstrates its advantage in spread increased from 20 Hz to 60 Hz, the proposed IOTA filter method demonstrates its advantage tracking the channel variation. The BER curve gaps between the IOTA filter method with Doppler in tracking the channel variation. The BER curve gaps between the IOTA filter method with spread of 20, 40, and 80 Hz are about 1.8 and 3.5 dB at the target BER of 10 . In addition, the BER −4 Doppler spread of 20, 40, and 80 Hz are about 1.8 and 3.5 dB at the target BER of 10 . In addition, curve gaps between the ICE method with Doppler spread of 20, 40, and 80 Hz are about 2.0 and 3.1 dB the BER curve gaps between the ICE method with Doppler spread of 20, 40, and 80 Hz are about 2.0 at the target BER of 10 . The BER curves under Doppler spread of 40 and 60 Hz are very similar and −4 and 3.1 dB at the target BER of 10 . The BER curves under Doppler spread of 40 and 60 Hz are the BER curves declined rapidly as the E /N increased. It can be seen that AWGN is the main factor b 0 very similar and the BER curves declined rapidly as the EN / increased. It can be seen that affecting the accuracy of channel estimation in the lower E /N zone, but the IOTA filter can maintain b b 0 orthogonality between subcarriers to counteract Rayleigh fading. AWGN is the main factor affecting the accuracy of channel estimation in the lower EN / zone, b 0 Figure 9 presents the NMSE performance of the OFDM/OQAM system over Rayleigh fading but the IOTA filter can maintain orthogonality between subcarriers to counteract Rayleigh fading. channels with different Doppler spread. As shown in Figure 9, the channel estimation results can be Figure 9 presents the NMSE performance of the OFDM/OQAM system over Rayleigh fading accurately measured by the NMSE values. When the NMSE value is 0.02, the E /N gaps between the channels with different Doppler spread. As shown in Figure 9, the channel estimation results can be NMSE performance curves of the proposed IOTA filter method with the Doppler spread of 20, 40, and accurately measured by the NMSE values. When the NMSE value is 0.02, the EN / gaps between b 0 80 Hz are about 1.5 and 4.0 dB, respectively. The IOTA filter is a good choice that can be well adopted the NMSE performance curves of the proposed IOTA filter method with the Doppler spread of 20, in the proposed OFDM/OQAM system. Under the maximum Doppler spread of 40 and 60 Hz, the 40, and 80 Hz are about 1.5 and 4.0 dB, respectively. The IOTA filter is a good choice that can be well NMSE curves almost overlap, but the IOTA method with a Doppler spread of 40 Hz still outperforms adopted in the proposed OFDM/OQAM system. Under the maximum Doppler spread of 40 and 60 the Doppler spread of 60 Hz by about 0.03 dB. Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci NMSE Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 15 Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 15 Hz, the NMSE curves almost overlap, but the IOTA method with a Doppler spread of 40 Hz still Hz, the NMSE curves almost overlap, but the IOTA method with a Doppler spread of 40 Hz still Appl. Sci. 2019, 9, 1454 11 of 15 outperforms the Doppler spread of 60 Hz by about 0.03 dB. outperforms the Doppler spread of 60 Hz by about 0.03 dB. IOTA, f = 20 Hz IOTA, f = 20 Hz ICE, f = 20 Hz ICE, = 20 Hz -1 -1 10 IOTA, f = 40 Hz IOTA, f = 40 Hz ICE, f = 40 Hz ICE, f = 40 Hz IOTA, f = 60 Hz IOTA, f = 60 Hz -2 -2 d ICE, f = 60 Hz ICE, f = 60 Hz IOTA, f = 80 Hz IOTA, = 80 Hz -3 -3 10 ICE, f = 80 Hz 10 ICE, f = 80 Hz -4 -4 -5 -5 -6 -6 0 5 10 15 20 25 0 5 10 15 20 25 E /N (dB) E /N (dB) b 0 b 0 Figure 8. BER performance of the OFDM/OQAM system over Rayleigh fading channels with Figure Figure 8. 8. BER BER performance performance of the of the OFDM/ OFDM/OQAM OQAM system syste over m over Rayleigh fading channels with Rayleigh fading channels with Doppler Doppler spread of 20, 40, 60, and 80 Hz. spr Doppler sprea ead of 20, 40, d of 60, 20, 40, 60, and 80 Hz. and 80 Hz. 0.06 0.06 IOTA, f = 20 Hz IOTA, f = 20 Hz IOTA, f = 40 Hz IOTA, f = 40 Hz IOTA, f = 60 Hz 0.05 IOTA, f = 60 Hz 0.05 IOTA, f = 80 Hz IOTA, f = 80 Hz 0.04 0.04 0.03 0.03 0.02 0.02 0.01 0.01 0 5 10 15 20 25 0 5 10 15 20 25 / (dB) E N E /N (dB) b 0 b 0 Figure 9. NMSE performance of the OFDM/OQAM system over Rayleigh fading channels with Figure Figure 9. 9. NM NMSE SE performance of the OFD performance of the OFDM/OQAM M/OQAM syst system em over Rayleigh fading channels with over Rayleigh fading channels with Doppler Doppler sprea spread d of of 20, 40, 60, 20, 40, 60, and and 80 Hz 80 Hz.. Doppler spread of 20, 40, 60, and 80 Hz. Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci BER BER NM NMSE SE Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 15 Appl. Sci. 2019, 9, 1454 12 of 15 5.4. The Performance of the OFDM/16-QAM System Figure 10 illustrates the BER performance of OFDM/16-QAM system over Rayleigh fading 5.4. The Performance of the OFDM/16-QAM System channels with different Doppler spread. The OFDM/16-QAM system uses comb-type pilots insertion Figure 10 illustrates the BER performance of OFDM/16-QAM system over Rayleigh fading to estimate the CFR. Compared with the ICE method under f = 20 Hz , the ICE method with channels with different Doppler spread. The OFDM/16-QAM system uses comb-type pilots insertion Doppler spread of 40, 60, and 80 Hz has EN / degradation about 2.0, 8.0, and 10.5 dB at the target b 0 to estimate the CFR. Compared with the ICE method under f = 20Hz, the ICE method with Doppler −3 −3 spr BER o eadf of 1040,. At the ta 60, and 80 rget HzBER of has E /21 N × 0 degradation , the LS mabout ethod u 2.0, nde 8.0, r Dand oppl10.5 er spdB reaat d o the f 20 tar Hget z pr BER ovidof es 3 3 10 1.6, 7. . At 6, and 9 the tar .7 get dBBER EN /of 2 gai 10 ns compa , the LS red w method ith the LS method under D under Doppler spread of oppl 20er spread 40 Hz provides , 60 1.6, , a 7.6, nd b 0 and 9.7 dB E /N gains compared with the LS method under Doppler spread 40, 60, and 80 Hz. 80 Hz. LS, f = 20 Hz ICE, f = 20 Hz LS, f = 40 Hz -1 ICE, f = 40 Hz LS, f = 60 Hz ICE, f = 60 Hz LS, f = 80 Hz -2 ICE, f = 80 Hz 10 d -3 -4 0 5 10 15 20 25 E /N (dB) b 0 Figure 10. BER performance of OFDM/16-QAM system over Rayleigh fading channels with Doppler Figure 10. BER performance of OFDM/16-QAM system over Rayleigh fading channels with Doppler spread of 20, 40, 60, and 80 Hz. spread of 20, 40, 60, and 80 Hz. Figure 11 illustrates the NMSE performance of the OFDM/16-QAM system over Rayleigh fading Figure 11 illustrates the NMSE performance of the OFDM/16-QAM system over Rayleigh channels with different Doppler spread. When the NMSE value is 0.05, the LS method with Doppler fading channels with different Doppler spread. When the NMSE value is 0.05, the LS method with spread of 20 Hz outperforms the LS method with Doppler spread of 40, 60, and 80 Hz by about 1.0, Doppler spread of 20 Hz outperforms the LS method with Doppler spread of 40, 60, and 80 Hz by 3.0, and 5.0 dB E /N gains. Based on the simulation results of the OFDM/OQAM system and the about 1.0, 3.0, and 5.0 dB EN / gains. Based on the simulation results of the OFDM/OQAM b 0 OFDM/16-QAM system with comb-type pilot insertion, the OFDM/OQAM system enhances the system and the OFDM/16-QAM system with comb-type pilot insertion, the OFDM/OQAM system accuracy of channel estimation significantly when it utilizes the NMSE value as the measurement. enhances the accuracy of channel estimation significantly when it utilizes the NMSE value as the measurement. 6. Conclusions This paper proposes a novel channel estimation method based on IOTA filter in OFDM/OQPSK and OFDM/OQAM systems. The channel estimation method provides a high data transmission rate and spectral efficiency while the IOTA wavelet can suppress the AWGN existing at the estimated CIRs of the OFDM receiver. Simulation results verify that the channel estimation method provides good BER and NMSE performance under both static and dynamic frequency-selective channels. The IOTA filter can guarantee orthogonality between different subcarriers and suppress the ICI Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci BER Appl. Sci. 2019, 9, x FOR PEER REVIEW 13 of 15 efficiently in the frequency domain. Meanwhile, the IOTA filter reduces the ISI among consecutive OFDM frames in the time domain and reduces the BER significantly. The channel encoder and channel decoder are adopted to provide robust channel estimation against AWGN in both Appl. Sci. 2019, 9, 1454 13 of 15 OFDM-IOTA and CP-OFDM systems. 0.45 LS, f = 20 Hz LS, f = 40 Hz 0.4 d LS, f = 60 Hz 0.35 LS, f = 80 Hz 0.3 0.25 0.2 0.15 0.1 0.05 0 5 10 15 20 25 E /N (dB) b 0 Figure 11. NMSE performance of the OFDM/16-QAM system over Rayleigh fading channels with Figure 11. NMSE performance of the OFDM/16-QAM system over Rayleigh fading channels with Doppler spread of 20, 40, 60, and 80 Hz. Doppler spread of 20, 40, 60, and 80 Hz. 6. Conclusions Compared with ICE and LS channel estimation methods, the proposed channel estimation method has better performance. The IOTA filter not only provides better performance but also has This paper proposes a novel channel estimation method based on IOTA filter in OFDM/OQPSK high data transmission rate and spectral efficiency since it does not require GI in front of each OFDM and OFDM/OQAM systems. The channel estimation method provides a high data transmission rate frame. With the improvement of the fifth-generation (5G) technology, there are more demands for and spectral efficiency while the IOTA wavelet can suppress the AWGN existing at the estimated CIRs high transmission data rate and spectral efficiency in wireless communication systems. Therefore, of the OFDM receiver. Simulation results verify that the channel estimation method provides good the proposed IOTA filter channel estimation method has broad software and hardware application BER and NMSE performance under both static and dynamic frequency-selective channels. The IOTA prospects and can be utilized in ultra-wideband (UWB) OFDM communication systems [18–20], filter can guarantee orthogonality between different subcarriers and suppress the ICI efficiently in the optical communication systems, and OFDM time division dual (TDD) communication systems frequency domain. Meanwhile, the IOTA filter reduces the ISI among consecutive OFDM frames in the [21–23]. time domain and reduces the BER significantly. The channel encoder and channel decoder are adopted In the future, we will compare IOTA wavelet with other wavelets for channel estimation in to provide robust channel estimation against AWGN in both OFDM-IOTA and CP-OFDM systems. OFDM systems. We will make a better adoption of radio frequency filtering technology in Compared with ICE and LS channel estimation methods, the proposed channel estimation frequency-selective and dynamic channels. method has better performance. The IOTA filter not only provides better performance but also has high data transmission rate and spectral efficiency since it does not require GI in front of each OFDM Author Contributions: X.Z. and C.W. conceived the algorithm and designed the experiments; X.Z. and R.T. frame. With the improvement of the fifth-generation (5G) technology, there are more demands for performed the experiments; X.Z. and C.W. analyzed the results; X.Z. drafted the manuscript; X.Z., C.W., and high transmission data rate and spectral efficiency in wireless communication systems. Therefore, R.T. revised the manuscript. All authors read and approved the final manuscript. the proposed IOTA filter channel estimation method has broad software and hardware application Funding: This work was supported by the National Natural Science Foundation of China (No. 61702303) and prospects and can be utilized in ultra-wideband (UWB) OFDM communication systems [18–20], optical the Shandong Provincial Natural Science Foundation, China (No. ZR2017MF020). communication systems, and OFDM time division dual (TDD) communication systems [21–23]. In the future, we will compare IOTA wavelet with other wavelets for channel estimation in OFDM Conflicts of Interest: The authors declare no conflict of interest. systems. We will make a better adoption of radio frequency filtering technology in frequency-selective References and dynamic channels. Author Contributions: X.Z. and C.W. conceived the algorithm and designed the experiments; X.Z. and R.T. performed the experiments; X.Z. and C.W. analyzed the results; X.Z. drafted the manuscript; X.Z., C.W., and R.T. Appl. Sci. 2019, 9, x; doi: FOR PEER REVIEW www.mdpi.com/journal/applsci revised the manuscript. All authors read and approved the final manuscript. NMSE Appl. Sci. 2019, 9, 1454 14 of 15 Funding: This work was supported by the National Natural Science Foundation of China (No. 61702303) and the Shandong Provincial Natural Science Foundation, China (No. ZR2017MF020). Conflicts of Interest: The authors declare no conflict of interest. References 1. Galande, N.A.; Shah, A.M. Implementation of OFDM by using wavelet for optimization of wireless communication system. In Proceedings of the IEEE International Conference on Recent Trends in Electronics, Information and Communication Technology, Bangalore, India, 20–21 May 2016; pp. 451–455. [CrossRef] 2. Du, J.F.; Signell, S. 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