Channel Estimation Based on Statistical Frames and ... - MDPI

applied sciences Article

Channel Estimation Based on Statistical Frames and Confidence Level in OFDM Systems Xiao Zhou , Chengyou Wang * , Ruiguang Tang

and Mingtong Zhang

School of Mechanical, Electrical and Information Engineering, Shandong University, Weihai 264209, China; [email protected] (X.Z.); [email protected] (R.T.); [email protected] (M.Z.) * Correspondence: [email protected]; Tel.: +86-631-568-8338 Received: 13 August 2018; Accepted: 7 September 2018; Published: 10 September 2018







Featured Application: This channel estimation method can be utilized to improve the communication quality of OFDM receiver. Abstract: Channel estimation is an important module for improving the performance of the orthogonal frequency division multiplexing (OFDM) system. The pilot-based least square (LS) algorithm can improve the channel estimation accuracy and the symbol error rate (SER) performance of the communication system. In pilot-based channel estimation, a certain number of pilots are inserted at fixed intervals between OFDM symbols to estimate the initial channel information, and channel estimation results can be obtained by one-dimensional linear interpolation. The minimum mean square error (MMSE) and linear minimum mean square error (LMMSE) algorithms involve the inverse operation of the channel matrix. If the number of subcarriers increases, the dimension of the matrix becomes large. Therefore, the inverse operation is more complex. To overcome the disadvantages of the conventional channel estimation methods, this paper proposes a novel OFDM channel estimation method based on statistical frames and the confidence level. The noise variance in the estimated channel impulse response (CIR) can be largely reduced under statistical frames and the confidence level; therefore, it reduces the computational complexity and improves the accuracy of channel estimation. Simulation results verify the effectiveness of the proposed channel estimation method based on the confidence level in time-varying dynamic wireless channels. Keywords: channel estimation; orthogonal frequency division multiplexing (OFDM); statistical frame; confidence level; symbol error rate (SER)

1. Introduction The orthogonal frequency division multiplexing (OFDM) system has been widely used in modern wireless communication systems due to its high spectrum efficiency and strong multipath fading resistance ability [1]. In the time-domain synchronous (TDS)-OFDM system, a pseudo-random (PN) sequence can be used as the guard interval (GI) for symbol synchronization and channel estimation. The TDS-OFDM system channel estimation is always implemented in an iterative way for cyclic reconstruction and reduces the inter-symbol interference (ISI). ISI and inter-carrier interference (ICI) may affect the accuracy of channel estimation [2]. Cyclic prefix (CP)-OFDM technology is often used in modern wireless communications [3,4]. In order to obtain diversity gain, multiple transmit and receive antennas can be used in the CP-OFDM system. The advantage of the technology is to improve the performance of wireless communication systems [5,6]. The offset quadrature amplitude modulation (OQAM) technology can improve the accuracy of channel estimation and improve the performance

Appl. Sci. 2018, 8, 1607; doi:10.3390/app8091607

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of the wireless communication system, and the modulation technology can be used as a candidate technology for 4G and 5G communication [7]. The pilot-based channel estimation method requires transmitting a large number of pilots repeatedly, which reduces the data transmission rate and spectrum efficiency. The basis of linear interpolation is to assume that the transmission function of each sub-channel between adjacent pilots varies linearly according to a certain slope. In the use of linear interpolation filtering, the interpolation is completed within the duration of each OFDM symbol, and the interpolation among OFDM symbols is independent of each other. Therefore, the channel can be allowed to change rapidly along the time dimension. The remainder of this paper is organized as follows. In Sections 2 and 3, the related work and system model are presented. Section 4 introduces the block-type pilot-based least square (LS), improved minimum mean square error (IMMSE), threshold value and Chi-square distribution channel estimation methods. Section 5 illustrates the channel estimation method based on statistical frames and the confidence level. The experimental results and comparison analysis are presented in Section 6. Conclusions are presented in Section 7. 2. Related Work To estimate the channel impulse response (CIR) at the CP-OFDM receiver, some conventional channel estimation methods are used in order to reduce the variance of noise and the channel estimation errors. The first method is the pilot-based LS algorithm [8,9]. It directly divides the received signals from the pilot symbols in the frequency domain, and the amount of computation is very small. However, the LS estimation ignores the effect of additive white Gaussian noise (AWGN). In the actual OFDM communication system, the channel estimation is sensitive to the effect of AWGN [10]. When the variance of noise is large, the accuracy of channel estimation is reduced to a large extent. The second method is the minimum mean square error (MMSE) method [11]. The MMSE algorithm has a good effect on suppressing ICI and AWGN. The MMSE algorithm uses the statistical characteristics of noise and the channel matrix; therefore, its computational complexity is high. The MMSE algorithm involves the inverse operation of the matrix. The inverse operation is more complex as the number of subcarriers increases. The third method is linear MMSE (LMMSE) estimation [12,13]. The LMMSE method can exhibit good performance under multipath channels; however, the LMMSE estimator suffers a performance floor at a high signal-to-noise ratio (SNR). The LMMSE method [14] can suppress the AWGN in the time domain, but it also has disadvantages. The construction of the autocorrelation matrix of the CIR requires a priori knowledge of the power and the delay of each channel. If the prior knowledge of the wireless channel is unknown, the channel statistical characteristics will not be matched with the actual transmission channel. The inverse of the channel matrix in the LMMSE algorithm increases the calculation complexity. The fourth method is the IMMSE method [15]. It simplifies the matrix calculation of the MMSE and LMMSE methods; therefore, it can be utilized in the hardware of the OFDM system. The fifth method is the threshold value channel estimation method [16]. It can be adopted to the slow multipath fading channel, but the disadvantage is that it is difficult to determine the suitable value under the multipath transmission channels with a larger Doppler spread. The sixth method is the Chi-square distribution-based channel estimation method [17]. The false alarms are removed in the channel estimation results; therefore, more accurate channel estimation results are obtained. The seventh method is the Haar wavelet channel estimation method [18]. In the literature [18], the Haar wavelet method can suppress the noise effectively based on a time-domain threshold, which is a standard deviation of noise obtained by wavelet decomposition. At the same time, the proposed Haar wavelet method improves the data transmission rate and spectrum efficiency while suppressing the AWGN effectively.

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3. System Model 3. System Model Figure 1 represents the system model of the CP-OFDM system utilizing the proposed confidence 1 represents system[17]. model CP-OFDM system the utilizing the proposed confidence levelFigure channel estimationthe method At of thethe OFDM transmitter, incoming binary bits are first level channel estimation method [17]. At the OFDM transmitter, the incoming binary bits are grouped and mapped according to a pre-specified modulation scheme: 16 QAM. After insertingfirst the grouped and mapped to a pre-specified modulation scheme: QAM. After inserting the block-type pilots, the 16according QAM symbols are converted into parallel streams16by a serial to parallel block. block-type the 16 QAM symbols areblock converted into streams by asequence serial to parallel block. The inversepilots, fast Fourier transform (IFFT) is used to parallel transform the data Xˆ i (n) with N ˆ i (n) with The inverse fast Fourier transform (IFFT) block is used to transform the data sequence X rows into time-domain signal xˆ (n) , where N is the number of sampling points within one OFDM N rows into time-domain signal xiˆ i (n), where N is the number of sampling points within one OFDM symbol. Then, symbols in in order order to to reduce reduce the the ICI ICI and and symbol. Then, the the CP CP is is inserted inserted into into the the time-domain time-domain OFDM OFDM symbols ˆ ISI. The Thetransmitted transmittedsignals signals passed through the multipath channels hi (nAWGN ) with ISI. areare thenthen passed through the multipath fading fading channels hˆ i (n) with ˆ ) after wi (nthe the parallel serial block. AWGN w ˆ i (n) after parallel to serialto block. Xˆ i (n) Binary bits

16 QAM symbol modulation

Block pilots insertion

Serial /parallel



xˆ i (n)

IFFT



Cyclic prefix addition

Parallel /serial

Multipath channel

Yˆi (n) Binary 16 QAM bits symbol demodu -lation

Statistical buffer

Channel estimation

Parallel /serial



hˆ i (n)

yˆ i (n)

FFT



AWGN Cyclic prefix removal

Serial /parallel

⊕

ˆ i (n) w

Figure 1. 1. System division System model model of of cyclic cyclic prefix prefix (CP)-OFDM. (CP)-OFDM. OFDM: orthogonal frequency division multiplexing; QAM: quadrature amplitude amplitude modulation; modulation; IFFT: IFFT: inverse inverse fast Fourier transform; FFT: fast multiplexing; Fourier transform.

At the receiver, the CP is removed after the serial to parallel conversion. After After removing removing the the CP, CP, the time-domain received OFDM OFDM symbols symbols yˆyˆii(nn)) are alternated in the fast Fourier transform transform (FFT). (FFT). After OFDM symbols symbols YˆYˆi ((nn)) are After that, that, the the frequency-domain frequency-domain OFDM are transformed transformed from from the the parallel parallel to to serial serial i block. The estimated CIR is obtained in the channel estimation block. There are two blocks in the red block. The estimated CIR is obtained in the channel estimation block. There are two blocks in the red dashed box: the first one is the channel estimation block, which represents the channel estimation dashed box: the first one is the channel estimation block, which represents the channel estimation method based on the confidence level; the second one is statistical buffer block, which represents method based on the confidence level; the second one is statistical buffer block, which represents the the number of statistical frames T. The noise in the multipath channel is further suppressed in the number of statistical frames T . The noise in the multipath channel is further suppressed in the statistical buffer block. At last, the binary information bits are obtained after the 16 QAM symbol statistical buffer block. At last, the binary information bits are obtained after the 16 QAM symbol demodulation scheme. demodulation scheme. 4. Block-Type Pilot-Based LS, IMMSE, Threshold Value and Chi-square Distribution Channel 4. Block-Type Pilot-Based LS, IMMSE, Threshold Value and Chi-square Distribution Channel Estimation Methods Estimation Methods 4.1. Block-Type Pilot-Based LS Channel Estimation Method 4.1. Block-Type Pilot-Based LS Channel Estimation Method After multipath fading and AWGN, the time-domain received OFDM symbols yˆ i (n) can be represented as: After multipath fading and AWGN, the time-domain received OFDM symbols yˆ i (n) can be yˆ i (n) = xˆ i (n) ⊗ hˆ i (n) + w ˆ i (n), 0 ≤ n < N, (1) represented as: where ⊗ represents the cyclic convolution operation and i is the frame number. The frequency-domain ˆ (n), 0 ≤ n < N , yˆ (n) = xˆ i (n) ⊗ hˆi (n) + w (1) received OFDM symbols Yˆ i (n) cani be represented as: i

where ⊗ represents the cyclic convolution operation and i is the frame number. The frequencyˆ i (n) · H ˆ i (n) + W ˆ i (n), 0 ≤ n < N. Yˆ i (n) = X (2) domain received OFDM symbols Yˆi (n) can be represented as:

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In the LS channel estimation method, block-type pilots are used to estimate the channel state information. It can be shown that the estimated channel frequency response (CFR) at pilots by the LS method is represented as: Yˆ (n ) ˆ i (n p ) = i p + W ˆ i ( n p ), H (3) ˆ i (n p ) X ˆ i (n p ) and Yˆ i (n p ) are the transmitted and received pilot signals on the n p -th pilot symbol, where X ˆ i (n p ) is the frequency-domain AWGN on the n p -th pilot symbol. W After one-dimensional linear interpolation, the estimated CFR is obtained in the entire frequency domain, which can be represented by: ˆ (n p ) + 1 H ˆ i ( n + l ) = (1 − l )H ˆ (n p + Q), 0 ≤ n < N, H Q i Q i

(4)

ˆ i (n p ) denotes the channel estimation results for the n p -th pilot symbol. H ˆ i (n p + Q) represents where H the channel estimation value of the (n p + Q)-th pilot symbol. Q represents the interval between two pilot symbols. The time-domain estimated CIR hˆ i (n) could be obtained by the IFFT calculation of ˆ i (n). Usually, hˆ LS,i (n) contains time-domain noise w H ˆ i (n), which can be denoted by: hˆ LS,i (n) = hˆ i (n) + w ˆ i (n), 0 ≤ n < N.

(5)

The advantage of block-type pilot-based LS channel estimation is that the channel correlation time is very small, and it is not sensitive to the Doppler effect. The block-type pilot-based LS channel estimation method can be used for mobile reception, and it is simple to design the pattern, easy to implement and saves hardware resources. The disadvantage of the method is that because the interval between pilot points occupies a long time, interpolation filtering cannot accurately reflect the variation of the CIR. 4.2. IMMSE Channel Estimation Method Through the LS channel estimation in the OFDM receiver, it may not suppress the effect of noise efficiently in the time and frequency domains. The channel response values beyond the length of GI are set to zero to remove the impact of AWGN in this method. ˆ LS,i (n) obtained by the LS channel estimation method is converted As shown in Figure 1, the CFR H into time-domain CIR hˆ LS,i (n) with n = 0, 1, 2, · · · , N − 1 by the IFFT operation. Assuming that L is the number of points of GI, the length of CIR should be no longer than that of the GI. To suppress the AWGN effectively, hˆ LS,i (n) should be considered to be AWGN when n ≥ L. It can be given by: ( hˆ LS,i (n) =

hˆ LS,i (n), 0,

0 ≤ n < L, L ≤ n < N.

(6)

The cross covariance of hˆ i (n) and yˆ i (n) is given by [11]: Rhˆ (n)yˆ (n) = Lσˆ h2 xˆ i∗ (n), 0 ≤ n < N, i

i

(7)

where (·)∗ is the operation of complex conjugate transpose. The autocorrelation of yˆ i (n) is given by [11]: Ryˆ i (n)yˆ i (n) = I σˆ h2 |xˆ i (n)|2 + N σˆ n2 , 0 ≤ n < N, (8)

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where I is the number of multipaths and N is the number of subcarriers. σˆ h2 and σˆ n2 are the estimated channel and noise variance, respectively. The estimated MMSE CIR hˆ MMSE,i (n) could be represented as: hˆ MMSE,i (n) =

I σˆ h2 xˆ i∗ (n)xˆ i (n)hˆ LS,i (n) , 0 ≤ n < N. I σˆ h2 |xˆ i (n)|2 + N σˆ n2

(9)

In the dynamic multipath condition, it is difficult to differentiate hˆ i (n) and w ˆ i (n). Suppose 2 2 ˆ |xˆ i (n)| = 1. In the worst multipath condition, suppose σn = max(|hi (n)|), 0 ≤ n < L. Equation (9) can be represented as: hˆ MMSE,i (n) =

I σˆ h2 hˆ LS,i (n) , 0 ≤ n < N. I σˆ h2 + N σˆ n2

(10)

Suppose σˆ h2 = |hˆ LS,i (n)|2 . After suppressing the AWGN in time domain, the estimated CIR hˆ IMMSE,i (n) can be expressed as [15]: hˆ IMMSE,i (n) =

2 hˆ LS,i (n) · |hˆ LS,i (n)| , 0 ≤ n < N. 2 α · |hˆ LS,i (n)| + (1 − α) · A2

(11)

i

In Equation (11), α is the suppression factor, which is usually chosen in the value region of [0.99, 1]. Ai = max (|hˆ LS,i (n)|). 0≤ n < N

The disadvantage of the IMMSE method in time domain is that it suppresses some paths with small energy as the noise. The IMMSE algorithm involves the multiplication and division operations of N points, with large amount of computation and high complexity. Therefore, it is hard to implement in the hardware of the OFDM receiver. 4.3. Threshold Value Channel Estimation Method The OFDM symbols will be affected by the noise in the wireless channel during the transmission process inevitably. The noise will cause the estimation error of the estimated CIRs and thereby increase the bit error rate (BER) or symbol error rate (SER) performance of the system. Therefore, AWGN is an important factor leading to the decrease of channel estimation accuracy. To suppress the noise and improve the accuracy of channel estimation effectively, many literature works have studied the noise suppression channel estimation methods. The threshold noise suppression method is a commonly-used method in OFDM receivers. The channel estimation method that remains the most significant taps (MST) can suppress noise in the channel estimation results. However, when the number of channels is unknown, the threshold value needs to be set according to the known SNR, so this method is not easy to apply. In the literature [16], the wavelet transform is utilized to estimate the standard deviation of noise; it is used as the threshold value of noise suppression, and the threshold value varies with the change of SNR. The paper proposes the best threshold for computing the noise suppression by optimizing the minimum square error (MSE) of subcarriers, and the threshold value channel estimation results hˆ thre,i (n) after noise suppression are expressed as [18]: ( hˆ thre,i (n) =

hˆ LS,i (n), 0,

|hˆ LS,i (n)| ≥ λ , 0 ≤ n < N. |hˆ LS,i (n)| < λ

(12)

In Equation (12), λ is a threshold value that can be defined according to the noise variance σˆ n2 . Normally, λ is set in the threshold region of [0.001, 0.2]. The advantage of the threshold suppression method is that the calculation is simple, but the selection of the threshold will vary with the difference of SNR and channel characteristics. Therefore, the effect of noise suppression is very sensitive to the selection of the threshold. Its disadvantage is that it cannot separate the smaller energy paths from the AWGN in the channel estimation results. That is,

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it may restore the noise with the larger energy as paths or suppress the paths with small energy as noise. The method of averaging the mean value of the continuous multiple channel estimation results can effectively suppress the noise in the channel estimation results, and the channel estimation method based on the filter matching can also suppress the noise effectively. 4.4. Chi-Square Distribution Channel Estimation Method The Chi-square distribution channel estimation method can reduce the false alarms caused by AWGN in the estimated CIRs. Reducing the false alarm probability by utilizing the properties of the Chi-square distribution is an efficient way to further improve the accuracy of channel estimation. The power summation of the n-th tap during T consecutive frames, i.e., from the M-th to the ( M + T − 1)-th frame of the estimated CIR, could be represented as: M + T −1

∑

σ2FL (n) =

|w ˆ i (n)|2 , M > 0, 0 ≤ n < N.

(13)

i= M

The power distribution function (PDF) of σ2FL,l satisfies the Chi-square distribution and is given by: pχ2 (σ2FL (n)) =

2 1 T −1 − σFL (n) 2 2 e ( σ ) , 0 ≤ n < N. FL,l 2 N Γ( N )

(14)

In the literature [15], most of the false alarms in the estimated CIRs can be effectively reduced according to the Chi-square distribution, which can be represented by: ( hˆ Chi,i (n) =

hˆ LS,i (n), 0,

2 ˆ ˆ v2 , M ≥ T ∑iM = M− T +1 |hLS,i ( n )| ≥ 3T σ , 0 ≤ n < N. otherwise

(15)

The disadvantage of Equation (15) is that the variance of noise σˆ v2 has not been determined in the literature [15]. In order to define the variance of noise accurately, σˆ v2 can be represented as: σˆ v2

N −1

=

∑

n =0

2 (hˆ LS,i (n) − hˆ thre,i (n)) , 0 ≤ n < N. N

(16)

In the Chi-square distribution channel estimation method, T can be chosen from the regions of [1, 20]. The larger the value of T is, the higher the accuracy of channel estimation is. In this article, the value of T is chosen by odd values to suppress the noise. 5. Channel Estimation Based on Statistical Frames and the Confidence Level The confidence level shows that the true value of the estimated CIR has a certain probability to fall around the measurement interval. The confidence level gives the credibility of the measured values of the measured CIRs. This probability is called the confidence level. The paper presents an OFDM channel estimation method based on statistical frames and the confidence level, it has good performances in both static and dynamic multipath channels. The method is based on the statistical frames T and confidence level Ki (n). For every T consecutive frames, the channel estimation results are counted once. The number of real and imaginary parts hˆ re,i (n), hˆ im,i (n) is counted in the intervals of (−∞, 0) and (0, +∞). Assume the number of times that hˆ re,i (n), which occurs in the intervals of (−∞, 0) and (0, +∞), is si1 , si2 . The number of times that hˆ im,i (n), which occurs in the intervals of (−∞, 0) and (0, +∞), is si3 and si4 . The maximum number of hˆ re,i (n), which occurs in the intervals of

re ,i

im,i

intervals of ( −∞ ,0) and (0, +∞) . Assume the number of times that hˆre ,i (n) , which occurs in the intervals of ( −∞ ,0) and (0, +∞) , is si 1 , si 2 . The number of times that hˆim,i (n) , which occurs in the intervals of ( −∞ ,0) and (0, +∞) , is si 3 and si 4 . The maximum number of hˆre ,i (n) , which occurs in Appl. Sci. 2018, 8, 1607 7 of 16 the intervals of ( −∞ ,0) and (0, +∞) , is denoted as sre . The maximum number of hˆim,i (n) , which

sim occurs occurs the (intervals as ofsim . s(ren)and can beinrepresented ( −∞ ,0)asand (0, +∞ ) , is denoted hˆ im,i (−∞, 0in ) and 0, +∞), isof denoted sre . The maximum number , which the intervals of (−∞, 0) and (0, +∞), is denoted as sim . sre and sim can be represented as: as: (

sre = max[si 1 ,si 2 ] , sre  = max[si1 , si2 ], sim == max max[[ssi3i 3,,ssi4i 4 ]].. sim

(17) (17)

The ThePDF PDFof ofnoise noiseobeys obeysaaGaussian Gaussiandistribution. distribution.The ThePDF PDFof ofthe theGaussian Gaussiandistribution distributionof ofnoise noise under different statistical frames is represented in Figure 2. The literature [15] represents the figure under different statistical frames is represented in Figure 2. The literature [15] represents the figure of of the PDF real parts path and noise. The disadvantage is that it does consider the PDF ofof thethe real parts of of thethe path and thethe noise. The disadvantage is that it does notnot consider the the size of the statistical frames, which could affect the probability of the noise distribution. When size of the statistical frames, which could affect the probability of the noise distribution. When the

ˆ LS,i (np())hˆLS, (n)) in T increase fromtofive to thirteen, the probability that occurs in the the statistical frames statistical frames T increase from five thirteen, the probability that p(h occurs the positive i and negative intervals may increase. positive and negative intervals may increase.

p(hˆLS,i (n))

T5 = 13

T4 = 11

T3 = 9

T2 = 7

T1 = 5

0

hˆ LS,i (n)

Figure Figure2.2.The Theprobability probabilitydistribution distributionfunction functionofofthe theGaussian Gaussiandistribution distributionofofnoise noiseunder underdifferent different statistical statisticalframes. frames.

According to the PDF of the Gaussian distribution, if hˆ LS,i (n) is noise, the number of its real (n) is noise, the number of its real According to the PDF of the Gaussian distribution, if hˆLS, i part or imaginary part appears in the positive and negative intervals nearly equal, that is sre ≈ T/2. ≈T /2. part or imaginary part appears in the positive and negative intervals nearly equal, thatinisthesrestatistical ˆ If hLS,i (n) is the multipath, the number of the real part or the imaginary part appearing equal the statistical number, thatimaginary is sre ≈ T.part Therefore, the more sre hˆLS,i (n)is isapproximately Ifinterval the multipath, the tonumber of the frame real part or the appearing in the is closer to T, the higher the confidence level of hˆ LS,i (n) is; the more sre is closer to T/2, the lower the sre ≈ T Therefore, statistical interval approximately equal to the statistical that is by confidence level ofisthe confidence level Ki (nframe ) can number, also be obtained the .soft decision hˆ LS,i (n) is. The sre is can T , the higher method, be to represented by: the confidence level of hˆ LS,i (n) is; the more sre is closer to the more which closer  of the hˆ (n) is. The confidence level K (n) can also be T / 2 , the lower the confidence level i 1, siM =LS,iT     obtained by the soft decision method, which can be represented by:    β 1 , siM = T − 1 β 2 , siM = T − 2 , 0 ≤ n < N − 1, Ki ( n ) = (18)  ..    .,    0,

.. . siM = 0

where β 1 , β 2 ∈ (0, 1) are the ranges of confidence level Ki (n). Take the maximum of the four values of sre and sim is siM . siM can be represented as: siM = max[sre , sim ].

(19)

Compare siM with statistical frames T. To simplify the calculation of the confidence level, Ki (n) is obtained by using the hard decision method. If siM is equal to the statistical frames T, Ki (n) is one;

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else, Ki (n) is zero. For example, when the statistical frame T1 is chosen to be five, the confidence level Ki1 (n) is represented by: ( 1, 0,

Ki 1 ( n ) =

siM1 = 5 , 0 ≤ n < N. siM1 < 5

(20)

When the statistical frame T2 is chosen to be seven, the confidence level Ki2 (n) is represented by: ( Ki 2 ( n ) =

1, 0,

siM2 = 7 , 0 ≤ n < N. siM2 < 7

(21)

When the statistical frame T3 is chosen to be nine, the confidence level Ki3 (n) is represented by: ( Ki 3 ( n ) =

1, 0,

siM3 = 9 , 0 ≤ n < N. siM3 < 9

(22)

When the statistical frame T4 is chosen to be eleven, the confidence level Ki4 (n) is represented by: ( Ki 4 ( n ) =

1, siM4 = 11 , 0 ≤ n < N. 0, siM4 < 11

(23)

When the statistical frame T5 is chosen to be thirteen, the confidence level Ki5 (n) is represented by: ( Ki 5 ( n ) =

1, siM5 = 13 , 0 ≤ n < N. 0, siM5 < 13

(24)

In the confidence level channel estimation method, channel estimation results after noise reduction ˆhCL,i (n) can be represented as:  hˆ LS,i (n) · Ki1 (n),       hˆ LS,i (n) · Ki2 (n), ˆhCL,i (n) = hˆ LS,i (n) · Ki3 (n),    hˆ LS,i (n) · Ki4 (n),    ˆ hLS,i (n) · Ki5 (n),

siM1 = 5 siM2 = 7 siM3 = 9 , 0 ≤ n < N. siM4 = 11 siM5 = 13

(25)

The IMMSE channel estimation method needs a large number of multiplication and division arithmetic; therefore, its calculation complexity is higher. The threshold value method may suppress the paths as noise, which induces the reduction of channel estimation precision in the dynamic channels since it is not easy to choose the suitable threshold value. The statistical frames and confidence level based channel estimation method only increases the logic judgment and storage resources, and the computational complexity is low, so it is convenient for hardware implementation. 6. Simulation Results 6.1. The Performance in Static Multipath Channels The profiles for the China digital television (DTV) Test 1st (CDT1) [18], Brazil A, Brazil B and Brazil D channel models are shown in Tables 1 and 2, respectively. The Brazil A, Brazil B and Brazil D channels were developed from the Brazilian field test on digital terrestrial television broadcasting (DTTB). The main simulation parameters based on the CP-OFDM system are represented in Table 3. Table 4 proposes a computational complexity comparison of the five channel estimation methods. A simplified radix-two IFFT/FFT approach whose implementation cost is much lower is adopted to process the cyclic convolution operation, and the IFFT/FFT is taken based on 2N points. The five channel estimation methods are based on 2N points division, and N = 300 is utilized in the proposed CP-OFDM

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system. The confidence level method only needs T-point addition/subtraction; therefore, it reduces the complexity of hardware implementation largely. This section presents the SER performance comparison between the LS method, the threshold value method, the IMMSE method, the Chi-square distribution method and the confidence level method. Table 1. Profiles for the China digital television (DTV) Test 1st (CDT1) and Brazil A multipath fading channels. CDT1

Tap 1 2 3 4 5 6

Brazil A

Delay (µs)

Power (dB)

Delay (µs)

Power (dB)

0 −1.8 0.15 1.8 5.7 18

0 −20 −20 −10 −14 −18

0 0.15 2.22 3.05 5.86 5.93

0 −13.8 −16.2 −14.9 −13.6 −16.4

Table 2. Profiles for the Brazil B and Brazil D multipath fading channels. Brazil B

Tap

Brazil D

Delay (µs)

Power (dB)

Delay (µs)

Power (dB)

0 0.3 3.5 4.4 9.5 12.7

0 −12 −4 −7 −15 −22

0 0.48 2.07 2.90 5.71 5.78

−0.1 −3.9 −2.6 −1.3 0.0 −2.8

1 2 3 4 5 6

Table 3. Simulation parameters of CP-OFDM systems. SPS: symbols per second; CP: cyclic prefix; OFDM: orthogonal frequency division multiplexing; QAM: quadrature amplitude modulation; IMMSE: improved minimum mean square error. Parameters

Specifications

Baseband signal rate

7.56 × 106 SPS

System model Modulation mode Guard interval length Subcarrier number Doppler spread

CP-OFDM 16 QAM 180 300 20/60/80 Hz

Pilots insertion types

Block-type pilots

α in IMMSE method

0.995

λ in threshold value method

0.05

Table 4. Computational complexity comparison of channel estimation methods. LS: least square; IFFT: inverse fast Fourier transform; FFT: fast Fourier transform. Operation Mode

LS [8,9]

IMMSE [15]

Threshold Value [16]

Chi-square Distribution [17]

Confidence Level

IFFT/FFT (2N points) Addition/Subtraction Multiplication Division

1 0 0 2N

1 N N+4 2N

1 N 0 2N

1 2N 2N 2N

1 T 0 2N

The conventional LS, IMMSE, threshold value, Chi-square distribution and confidence level methods are presented in the CP-OFDM system. In this paper, statistical OFDM signal frame T is chosen

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to be 5, 7, 9, 11 and 13 in the CP-OFDM receivers to calculate the confidence level. The modulation mode 16 QAM is chosen to equalize the constellation signals in the receiver of the CP-OFDM system. The length of CP is 180 OFDM subcarriers, and the OFDM symbol consists of 300 subcarriers. In the five channel estimation methods, block-type pilots are inserted in all the subcarriers of the OFDM symbols in the frequency domain. In the simulation, the Doppler spread is chosen to be 20 Hz, 60 Hz and 80 Hz in Brazil A, Brazil B and Brazil D, respectively. Figures 3 and 4 present the SER performance in the 16 QAM-modulated CP-OFDM system over static CDT1 and Brazil A, respectively. As shown in Figure 3, the gap of the SNR gain among T1 = 5, Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 17 8, x FOR PEER 11 of 17 T2 Appl. = 7, Sci. T3 2018, = 9 and T4 = 11 REVIEW is about 1.5 dB, 0.5 dB and 0.3 dB at the SER of 10−2 , respectively. 1

10 1 10

0

10 0 10

-1

SER SER

10 -1 10

-2

10 -2 10

-3

10 -3 10

-4

10 -4 10 0 0

T1 = 5 T =5 T21 = 7 T =7 T32 = 9 T =9 T43 = 11 T4 = 11 5 5

10 10

SNR (dB) SNR (dB)

15 15

20 20

25 25

Figure 3. Symbol error rate (SER) performance of the 16 QAM-modulated CP-OFDM system over Figure 3. Symbol error raterate (SER) performance of the 16 QAM-modulated CP-OFDM system over Figure 3. Symbol error (SER) performance of the 16 QAM-modulated CP-OFDM system over static China digital television (DTV) Test 1st (CDT1). SNR: signal-to-noise ratio. static China digital television (DTV) TestTest 1st 1st (CDT1). SNR: signal-to-noise ratio. static China digital television (DTV) (CDT1). SNR: signal-to-noise ratio. 1

10 1 10

0

10 0 10

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10 -1 10

-2

10 -2 10

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-4

10 -4 10 0 0

T1 = 5 T =5 T21 = 7 T =7 T32 = 9 T =9 T43 = 11 T4 = 11 5 5

10 10

SNR (dB) SNR (dB)

15 15

20 20

25 25

Figure 4. SER performance of the 16 16 QAM-modulated CP-OFDM system over static Brazil A. A. Figure 4. SER performance of the QAM-modulated CP-OFDM system over static Brazil Figure 4. SER performance of the 16 QAM-modulated CP-OFDM system over static Brazil A.

In Figure 4, the gap of the SNR gain among T1 = 5, T2 = 7 , T3 = 9 and T4 =11 is about 1.4 dB, 0.8 In Figure 4, the gap of the SNR gain among T1 = 5, T2 = 7 , T3 = 9 and T4 =11 is about 1.4 dB, 0.8 , respectively. Therefore, the SER curves of T = 5 have the best SER dB and 0.7 dB at the SER of 10−2 dB and 0.7 dB at the SER of 10−2, respectively. Therefore, the SER curves of T11 = 5 have the best SER gain under the CDT1 and Brazil A multipath fading channels. gain under the CDT1 and Brazil A multipath fading channels. Figure 5 presents the SER performance of the proposed confidence level channel estimation Figure 5 presents the SER performance of the proposed confidence level channel estimation method over static CDT1. Compared with the threshold value method, the ideal channel estimation method over static CDT1. Compared with the threshold value method, the ideal channel estimation

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In Figure 4, the gap of the SNR gain among T1 = 5, T2 = 7, T3 = 9 and T4 = 11 is about 1.4 dB, 0.8 dB and 0.7 dB at the SER of 10−2 , respectively. Therefore, the SER curves of T1 = 5 have the best SER gain under the CDT1 and Brazil A multipath fading channels. Figure 5 presents the SER performance of the proposed confidence level channel estimation method over static CDT1. Compared with the threshold value method, the ideal channel estimation method outperforms the threshold value estimation method with the SNR gains by only about 0.1 dB SNR gains at the target SER of 10–2 . The proposed confidence level method outperforms the conventional LS method by about a 1.6 dB SNR gap at the target SER of 10−3 . It could be seen that Appl. Sci. 2018,main 8, x FOR PEERthat REVIEW 12 of 17 AWGN is the factor impacts the accuracy of channel estimation [16]. 0

10

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SER

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LS, T1=5 Threshold value, T1=5 Confidence level, T1=5

-4

10

Ideal estimation, T1=5 IMMSE, T1=5 Chi-square distribution, T1=5

-5

10

0

5

10

15

20

25

SNR (dB)

Figure 5. SER performance of the 16 QAM-modulated CP-OFDM system over static CDT1. LS:LS: least Figure 5. SER performance of the 16 QAM-modulated CP-OFDM system over static CDT1. least square; IMMSE: improved minimum mean square error. square; IMMSE: improved minimum mean square error.

Under thethe static CDT1 multipath channel, thethe threshold value method hashas thethe best channel Under static CDT1 multipath channel, threshold value method best channel estimation performance since CDT1 belongs to to thethe light frequency selective fading channel. In In thethe estimation performance since CDT1 belongs light frequency selective fading channel. static multipath fading condition, the interference caused by noise is relatively small. Therefore, static multipath fading condition, the interference caused by noise is relatively small. Therefore, selecting a suitable the noise noiseinterference interferenceininthe theOFDM OFDM receivers. selecting a suitablethreshold thresholdcan canremove remove most most of of the receivers. The The CDT1 channel has a small amount of side paths. The IMMSE method suppresses the noise while CDT1 channel has a small amount of side paths. The IMMSE method suppresses the noise while not notrestraining restrainingthe theenergy energy of of the the main main path; channel estimation path; thereby, thereby,the theIMMSE IMMSEmethod methodhas hasa good a good channel estimation effect. The SER curve of of thethe confidence level is similar to to that of of thethe Chi-square distribution method effect. The SER curve confidence level is similar that Chi-square distribution method under static CDT1 since the false alarms obey the Chi-square distribution strictly. Therefore, the SER under static CDT1 since the false alarms obey the Chi-square distribution strictly. Therefore, the SER curves of the proposed confidence level method and Chi-square distribution method can suppress the curves of the proposed confidence level method and Chi-square distribution method can suppress noise the effectively. noise effectively. 6.2. The Performance in Dynamic Multipath Channels 6.2. The Performance in Dynamic Multipath Channels Figures 6 and 7 present the SER performance in 16 QAM-modulated CP-OFDM systems over Figures 6 and 7 present the SER performance in 16 QAM-modulated CP-OFDM systems over dynamic Brazil B and Brazil D, respectively. As shown in Figure 6, the gap of the SNR gain among dynamic Brazil B and Brazil D, respectively. As shown in Figure 6, the gap of the−SNR gain among T1 = 5, T2 = 7, T3 = 9 and T4 = 11 is about 3 dB, 2 dB and 1.2 dB at the SER of 5 × 10 2 , respectively. −2 T1 = 5, T2 = 7 , T3 = 9 and T4 = 11 is about 3 dB, 2 dB and 1.2 dB at the SER of 5 × 10 , respectively. In In Figure 7, the gap of the SNR gain among T1 = 5, T2 = 7, T3 = 9 and T4 = 11 is about 4 dB, 1.8 dB 2 , respectively. = 11 is about , T2 = 7 , T3T=1 9= and dB, 1.8can dBbe and Figure the gap of of the8 SNR among T1 = 5 and 0.5 dB7,at the SER × 10−gain Therefore, 5 is aTsuitable value,4which 4 chosen for the dynamic multipath channels. 0.5 dB at the SER of 8 × 10−2, respectively. Therefore, T = 5 is a suitable value, which can be chosen 1

for the dynamic multipath channels.

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1

101 10

0

SER SER

100 10

-1

10-1 10

-2

10-2 10 0 0

T1 = T1 = T2 = T2 = T3 = T3 = T4 = T4 =

5, fd = 20 Hz 5, fd = 20 Hz 7, fd = 20 Hz 7, fd = 20 Hz 9, fd = 20 Hz 9, fd = 20 Hz 11, fd = 20 Hz 11, fd = 20 Hz 5 10 15 5 10 SNR (dB) 15 SNR (dB)

20 20

25 25

Figure 6. SER performance of the 16 QAM-modulated CP-OFDM system over Brazil B with a Doppler Figure SER performance performance of of the the 16 16 QAM-modulated QAM-modulated CP-OFDM CP-OFDM system with aa Doppler Doppler Figure 6. 6. SER system over over Brazil Brazil B B with spread of 20 Hz. spread of 20 Hz. spread of 20 Hz. 1

101 10

0

SER SER

100 10

-1

10-1 10

-2

10-2 10 0 0

T1 = T1 = T2 = T2 = T3 = T3 = T4 = T4 =

5, f d = 20 Hz 5, f d = 20 Hz 7, f d = 20 Hz 7, f d = 20 Hz 9, f d = 20 Hz 9, f d = 20 Hz 11, f d = 20 Hz 11, f d = 20 Hz 5 10 15 5 10 SNR (dB) 15 SNR (dB)

20 20

25 25

Figure 7.7.SER of of thethe 16 QAM-modulated CP-OFDM system over Brazil with aDDoppler SERperformances performances 16 QAM-modulated CP-OFDM system over DBrazil with a Figure 7. SER performances of the 16 QAM-modulated CP-OFDM system over Brazil D with a spread 20 Hz. of 20 Hz. Dopplerofspread Doppler spread of 20 Hz.

In Figure 8, under the the maximum maximum Doppler Doppler spread spread of 20 Hz, Hz, the the proposed proposed confidence confidence level level method method In Figure 8, under of 20 In Figure 8,dB, under the maximum Doppler spread of 20compared Hz, the proposed confidence level method can provide 0.4 1.0 dB and 1.2 dB SNR improvements with the IMMSE method, can provide 0.4 dB, 1.0 dB and 1.2 dB SNR improvements compared with the IMMSE method, the the LS LS can provide 0.4 dB, 1.0 dB and 1.2 dB SNR improvements compared with IMMSE method, the LS −−2 2 ,the method and the Chi-distribution method at the target SER of 2 × 10 respectively. The IMMSE method and the Chi-distribution method at the target SER of 2 × 10−2, respectively. The IMMSE method has and theSER Chi-distribution method at the is target SER of 2 ×dB. 10 , respectively. The IMMSE method method has bad bad SER performance performance when when the the SNR SNR is higher higher than than 19 19 dB. The The confidence confidence level level method method method has bad SER performance when the SNR is higher than 19 dB. The confidence level method has the best SER performance except the ideal estimation and threshold value methods. As shown has the best SER performance except the ideal estimation and threshold value methods. As shown in in has the8, best SER performance except the ideal estimation and threshold value methods. As shown in Figure Figure 8, the the proposed proposed confidence confidence level level method method and and threshold threshold value value method method have have almost almost the the same same Figure 8, the proposed confidence level method and threshold value method have almost the same SER performance in inthe thelower lowerSNR SNRrange. range.Compared Compared with ideal channel estimation method, SER performance with thethe ideal channel estimation method, the SERproposed performance in the lower SNR range. Compared with the idealatchannel estimation method, −2 . the −2 the confidence level method has 2.2 dB SNR degradation the target SER of 2 × 10 proposed confidence level method has 2.2 dB SNR degradation at the target SER of 2 × 10−2. proposed confidence level method has 2.2 dB SNR degradation at the target SER of 2 × 10 .

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0

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-2

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LS, fd = 20 Hz LS, fd = 20 Hz Threshold value, fd = 20 Hz Threshold value, f = 20 Hz Confidence level, fd =d20 Hz Confidence level, fd = 20 Hz Ideal estimation, fd = 20 Hz Ideal estimation, fd = 20 Hz IMMSE, fd = 20 Hz IMMSE, fd = 20 Hz Chi-square distribution, fd = 20 Hz Chi-square distribution, fd = 20 Hz 5 10 15 SNR (dB) 5 10 15 SNR (dB)

-2

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10

0 -3 10

0

20

25 20

25

Figure 8. SER performance of the 16 QAM-modulated CP-OFDM system over Brazil A under T1 = 5 . Figure 8. SER performance of the 16 QAM-modulated CP-OFDM system over Brazil A under T1 =T 5. Figure 8. SER performance of the 16 QAM-modulated CP-OFDM system over Brazil A under = 5. 1

Under the the Brazil Brazil B B channel channel with with aa Doppler Doppler spread spread of of 60 60 Hz, Hz, as as shown shown in in Figure Figure 9, 9, the the proposed proposed Under Under the Brazil B channel with a Doppler spread of 60 Hz, as shown in Figure 9, the proposed −−2 2 confidence level level method method provides provides the the SNR SNR gains gains of of0.6 0.6dB, dB,2.0 2.0dB dBand and4.5 4.5dB dBatatthe theSER SERofof2 2× ×1010 confidence −2 confidence level method provides the SNR gains of 0.6 dB, 2.0 dB and 4.5 dB at the SER of 2 × 10 compared with withthe the IMMSE Chi-square distribution methods, respectively. The method IMMSE compared LS,LS, IMMSE andand Chi-square distribution methods, respectively. The IMMSE compared with theperformance LS, IMMSEwhen and Chi-square distribution respectively. The IMMSE method has bad SER SNR isthan higher thanThe 19methods, dB. The confidence level method has bad SER performance when the SNRthe is higher 19 dB. confidence level method has the has bad SER performance whenideal the SNR is higher 19 dB. value The confidence level method hasmethod the SER performance except estimation andthan threshold methods. Compared best SERbest performance except the idealthe estimation and threshold value methods. Compared with the has the best SER performance except the ideal estimation and threshold value methods. Compared with the threshold value the method, the proposed confidence levelhas method 0.4degradation dB SNR degradation threshold value method, proposed confidence level method 0.4 dBhas SNR at SER of with the threshold value method, the proposed confidence level method has 0.4 dB SNR degradation −2 − 2 SER × 10 . Compared with thechannel ideal channel estimation, the proposed confidence level method 2at× 10 of.2Compared with the ideal estimation, the proposed confidence level method has −2. Compared with the ideal channel estimation, the proposed confidence level method SER 2 × 10 hasatdB 1.9 dBofSNR degradation at the target ×− 102−2 Furthermore,the theSNR SNRgap gap between between the the SER SER 1.9 SNR degradation at the target SERSER of 2of×210 . .Furthermore, −2. Furthermore, the SNR gap between the SER has 1.9 dB SNR degradation at the estimation target SER and of 2 ×the 10proposed performance curves of ideal ideal channel channel confidence level level methods methods is is about about performance curves of estimation and the proposed confidence performance curves of ideal channel estimation and the proposed confidence level methods is about −2 − 2 1.8 dB dB at at the the SER SER of of 22 × × 10 1.8 10 . −2. 1.8 dB at the SER of 2 × 10 . 0

10

0

10

-1

10

-1

SER

SER

10

-2

10

-2

10

-3

10

0 -3 10

0

LS, f d = 60 Hz LS, f d = 60 Hz Threshold value, f d = 60 Hz Threshold value, f = 60 Hz Confidence level, f d =d60 Hz Confidence level, f d = 60 Hz Ideal estimation, f d = 60 Hz Ideal estimation, f = 60 Hz IMMSE, fd = 60 Hz d IMMSE, fd = 60 Hz Chi-square distribution, f d = 60 Hz Chi-square distribution, f d = 60 Hz 5 10 15 SNR (dB) 5 10 15 SNR (dB)

20

25 20

25

Figure 9. SER performance of the 16 QAM-modulated CP-OFDM system over Brazil B under T1 = 5. Figure 9. SER performance of the 16 QAM-modulated CP-OFDM system over Brazil B under T1 = 5 . Figure 9. SER performance of the 16 QAM-modulated CP-OFDM system over Brazil B under T1 = 5 .

As shown in Figure 10, compared with the IMMSE method, the Chi-square distribution method in Figure 10, compared withlevel the IMMSE the Chi-square method and theAs LSshown method, the proposed confidence methodmethod, provides the SNR gainsdistribution of 1.3 dB, 1.5 dB and the LS method, the proposed confidence level method provides the SNR gains of 1.3 dB, 1.5 dB

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As 2018, shown Figure 10, compared with the IMMSE method, the Chi-square distribution method Appl. Sci. 8, x in FOR PEER REVIEW 15 of 17 and the LS method, the proposed confidence level method provides the SNR gains of 1.3 dB, 1.5 dB and −2 when anddB 2.5atdB the of SER the maximum Doppler spread equals 80The Hz.confidence The confidence 2.5 theatSER 3 ×of103−×2 10 when the maximum Doppler spread equals 80 Hz. level level method SER performance the ideal estimation. IMMSEmethod estimation method has thehas bestthe SERbest performance except theexcept ideal estimation. The IMMSEThe estimation has method hasperformance worse SER performance in the highand SNRthe region, and the Chi-squaremethod distribution method worse SER in the high SNR region, Chi-square distribution has the worst has performance. the worst SER performance. with the idealthechannel estimation, proposed SER Compared with theCompared ideal channel estimation, proposed confidencethe level method −2. Moreover, confidence leveldegradation method hasat 2.3 SNR degradation the targetcompared SER of 3with × 10the has 2.3 dB SNR the dB target SER of 3 × 10−2at . Moreover, threshold compared withthe theproposed thresholdconfidence value method, proposed confidence level method SNR value method, levelthe method provides the SNR gains of 0.05provides dB at thethe SER of − 2 −2 gainswith of 0.05 at the SER of 10 spread with the maximum Doppler spread equal to 80 Hz. 10 thedB maximum Doppler equal to 80 Hz. 0

10

-1

SER

10

-2

LS, f d = 80 Hz Threshold value, fd = 80 Hz Confidence level, fd = 80 Hz

10

Ideal estimation, f d = 80 Hz IMMSE, fd = 80 Hz Chi-square distribution, f d = 80 Hz

-3

10

0

5

10

15

20

25

SNR (dB)

Figure 10. SER performance performance of of the the 16 16QAM-modulated QAM-modulatedCP-OFDM CP-OFDMsystem systemover overBrazil BrazilDDunder underT1 T= = 5. 5. 1

The proposed confidence level method can suppress the noise effectively based on the statistical The proposed confidence level method can suppress the noise effectively based on the statistical frames buffer, which reduces the noise. However, the SER curves are not smooth with Doppler spread frames buffer, which reduces the noise. However, the SER curves are not smooth with Doppler equal to 20 Hz, 60 Hz and 80 Hz since the Doppler spread brings interference between adjacent OFDM spread equal to 20 Hz, 60 Hz and 80 Hz since the Doppler spread brings interference between adjacent signals. The 16 QAM utilizing sixteen signals constellations for mapping may cause interference OFDM signals. The 16 QAM utilizing sixteen signals constellations for mapping may cause between constellation points under deep fading channels. As the SNR increases, the SER curves still interference between constellation points under deep fading channels. As the SNR increases, the SER represent a declining trend. The SER performance curves show that the proposed confidence level curves still represent a declining trend. The SER performance curves show that the proposed channel estimation method for the CP-OFDM system is able to provide significant SNR gains under confidence level channel estimation method for the CP-OFDM system is able to provide significant dynamic frequency selective channels. SNR gains under dynamic frequency selective channels. 7. Conclusions 7. Conclusions This paper proposes a novel OFDM channel estimation method based on statistical frames and This paper proposes a novel OFDM channel estimation method based on statistical frames and the confidence level. In this paper, it is proven that the proposed channel estimation method can the confidence level. In this paper, it is proven that the proposed channel estimation method can provide good SER performance whenever under the static multipath channels or dynamic multipath provide good SER performance whenever under the static multipath channels or dynamic multipath channels. When the statistical frame is five, the confidence level channel estimation method has the channels. When the statistical frame is five, the confidence level channel estimation method has the best SER performance compared to the SER performance with the statistical frame equal to seven, best SER performance compared to the SER performance with the statistical frame equal to seven, nine and eleven. nine and eleven. Compared with the conventional block-type pilot-based LS, IMMSE, threshold value method and Compared with the conventional block-type pilot-based LS, IMMSE, threshold value method Chi-square distribution method, the proposed confidence level channel estimation method has the best and Chi-square distribution method, the proposed confidence level channel estimation method has SER performance. The proposed confidence level channel estimation method is easy to implement in the best SER performance. The proposed confidence level channel estimation method is easy to hardware and has broad market prospects that can be applied in underwater acoustic communication implement in hardware and has broad market prospects that can be applied in underwater acoustic communication with multiple-input multiple-output (MIMO) technology [19], RAKE receiving technology [20] and frequency hopping technology [21,22].

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with multiple-input multiple-output (MIMO) technology [19], RAKE receiving technology [20] and frequency hopping technology [21,22]. Author Contributions: X.Z. and C.W. conceived of the algorithm and designed the experiments. X.Z. and R.T. performed the experiments. X.Z. and C.W. analyzed the results. X.Z. and C.W. drafted the manuscript. X.Z., C.W., R.T. and M.Z. revised the manuscript. All authors read and approved the final manuscript. Funding: This research was funded by the National Natural Science Foundation of China (Grant No. 61702303) and the Shandong Provincial Natural Science Foundation, China (Grant Nos. ZR2017MF020 and ZR2015PF004). Conflicts of Interest: The authors declare no conflict of interest.

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