electronics Article
Low-Complexity PAPR Reduction Scheme Combining Multi-Band Hadamard Precoding and Clipping in OFDM-Based Optical Communications Pu Miao 1, *, Peng Chen 2 1 2 3
*
ID
and Zhimin Chen 3
School of Electronic and Information Engineering, Qingdao University, 308 Ningxia Road, Qingdao 266071, China School of Information Science and Engineering, Southeast University, Nanjing 210096, China;
[email protected] School of Electronic Information, Shanghai Dianji University, Olive Road, Shanghai 200240, China;
[email protected] Correspondence:
[email protected]; Tel.: +86-532-8595-0706
Received: 24 December 2017; Accepted: 17 January 2018; Published: 23 January 2018
Abstract: In this paper, we propose a low-complexity peak-to-average power ratio (PAPR) reduction scheme that combines both multi-band (MB)-Hadamard precoding and clipping for the optical orthogonal frequency division multiplexing (OFDM) systems. Approximations of PAPR distribution for baseband OFDM signals are analyzed and the effective signal-to-noise ratio (SNR) of the whole transmission link considering both the clipping and quantization noise are presented. After that, the MB-Hadamard precoding is adopted to compresses the peak signals, minimizing the contaminating influence of signal distortions in subsequent clipping operations. In addition, the received SNRs and bit error rate (BER) are calculated theoretically for each split sub-band. The 50-m step-index polymer optical fiber (POF) transmission is adopted as a special case to both evaluate the system performance and then compare the proposed scheme with other well-known PAPR reduction techniques. With this scheme, the PAPR is reduced effectively and the system’s BER performance is improved significantly. The results show that the proposed scheme with appropriate number of sub-bands precoding provides favorable trade-offs among PAPR reduction, power spectral density, transmission rate, BER, and computational complexity, which demonstrates its feasibility and validity. Keywords: orthogonal frequency division multiplexing; peak-to-average power ratio; optical communication; multi-band Hadamard; clipping
1. Introduction Orthogonal frequency division multiplexing (OFDM) is regarded as a promising modulation candidate for optical wireless communication (OWC) and polymer optical fiber (POF) as it provides a high data rate, high spectral efficiency, and high tolerance to multi-path interference [1,2]. A baseband OFDM with Hermitian symmetry property, as in [3,4], is also called discrete multi-tone (DMT). For simple and low cost consideration, the DMT can be employed in optical communications using the intensity modulation with direct detection (IM/DD) technique and bit-loading algorithm to maximize the system capacity [4–6]. However, the DMT suffers from a high peak-to-average power ratio (PAPR) and is more susceptible to nonlinear distortions. Since the light-emitting diode (LED) has a limited linear dynamic range, the DMT signals with high PAPRs drive the LED at the transmitter to saturation, producing a greater number of nonlinear distortions and degrading the overall system performance [7–9]. Therefore, the PAPR of the DMT should be reduced so that the LED can operate linearly and power efficiently [10]. Electronics 2018, 7, 11; doi:10.3390/electronics7020011
www.mdpi.com/journal/electronics
Electronics 2018, 7, 11
2 of 16
Several PAPR reduction techniques have been proposed for wireless communication systems [11–18]. In general, these techniques can be broadly categorized into signal distortion, distortionless, and coding schemes. Clipping, filtering and companding are well-known varieties of signal distortion schemes that directly limit the peak envelope of the transmitting signals to a desired value [13–15]. However, these signal processing schemes result in both in-band distortion and out-of-band high frequency components, which further degrades the bit error rate (BER) performance and reduces the spectral efficiency. Selective mapping (SLM), and partial transmit sequence (PTS) are typical distortionless schemes [16–18] that improve the PAPR distribution statistically and provide pretty good PAPR performance. However, they all have very high computational complexities and require the receivers to know the side information to retrieve the original data blocks. In addition, it is complicated to design the phase vectors for both SLM and PTSs. The coding changes their original codewords to reduce their PAPRs with high operational complexities. Tone reservation and tone injection are effective approaches to mitigate the PAPR problem [11]. However, due to their computational complexity, the challenge is to find the optimal subset and it becomes intractable for OFDM systems with a large number of subcarriers. In addition, the transmission rate is also degraded. Schemes such as active constellation extension introduce redundancy as well [12]. In particular, these methods used in radio wireless communication cannot be directly adopted in optical systems because of the real value property in IM/DD implementation. In contrast, discrete Fourier transform spreading (DFT-S) is an efficient method of reducing the PAPR without causing any distortion noise [8]. Nevertheless, DFT-S-DMT still exhibits a high PAPR because of the Hermitian symmetry requirement of the IM/DD channel. In addition, each subcarrier of DFT-S-DMT obtains the same signal-to-noise ratio (SNR) after the equalization and dispreading procedure, indicating that it is unsuited to apply the bit-loading with DFT-S-DMT in the frequency selective channel to achieve overall system capacity. Moreover, DFT-S-DMT is extremely sensitive to LED nonlinearity, which limits its practical applications. The discrete Hartley transform (DHT)-spread approach exhibits a lower PAPR compared to DFT-spread techniques. However, it is only applicable to real constellations such as pulse amplitude modulation (PAM) and the PAPR reduction capability decreases with an increase in size of the PAM alphabet. In this paper, an efficient low-complexity PAPR reduction scheme combining both multi-band (MB)-Hadamard precoding and clipping is proposed in DMT systems. The modulated symbols of a split sub-band are pre-coded by MB-Hadamard matrix to compress the peak signals of the DMT, which would mitigate the signal distortions of the following clipping operation. The received SNRs and BERs are also calculated for each split bands. The results demonstrated that the proposed scheme reduces the PAPR significantly and improves the BER performance effectively. Moreover, it matches well with the bit-loading technique to enhance the system capacity. In addition, some other famous PAPR reduction approaches are also compared and discussed. The remainder of this paper is organized as follows. In Section 2, we briefly present the PAPR characteristics of the DMT. In Section 3, the effective SNR of the whole IM/DD channel considering both the clipping and the quantization is analyzed. In Section 4, a hybrid PAPR reduction scheme is proposed to compress the peak signals and then limit the PAPR to a given threshold level. Section 5 presents the results and discusses them, and Section 6 concludes the paper. Notations: the time and frequency domain vectors are represented by lower and upper boldface italic letters (e.g., x and X), respectively. The (n + 1)th element of the column vector x is denoted as x (n). Upper-case boldface letters (e.g., F) denote matrices, and E{·}, (·) T , (·)∗ , |·|, R(·) and Z (·) are the expectation, the transpose, complex conjugate, absolute value, real component, and symmetric conjugate operator, respectively. Let N µ, σ2 denotes the Gaussian distribution with a mean of µ and a variance of σ2 .
Electronics 2018, 7, 11
3 of 16
2. DMT and PAPR With respect to a DMT symbol with N sub-carriers, the data stream is mapped onto X based on the quadrature amplitude modulation (QAM) constellation. Then, the time domain DMT signal x is generated by a 2N-point inverse discrete Fourier transform (IDFT), given by [4–7]: x (n) = √
2N −1
1 2N
∑
C (k)e
j2πnk 2N
, n = 0, 1, · · · , 2N − 1
(1)
k =0
h iT where C = XT , (Z (X)) T conforms to Hermitian symmetry [4] to produce the real-valued time-domain signal x. According to the central limit theorem, for N → ∞ , x can be modeled as a Gaussian distribution with N 0, σx2 . The PAPR of x is defined as the ratio between the maximum peak power and the average power during one symbol period, which can be written as [5,19] n o max | x (n)|2 0≤k ≤2N −1 n o Υd = = E | x (n)|2
n
max
0≤k ≤2N −1
| x (n)|2
o .
σx2
Based on the central limit theorem, we can obtain ! r √ √ x (n) r0 | x (n)|2 ≤ r0 ≈ er f ≤ r0 = Pr − r0 ≤ , Pr σx 2 σx2
(2)
(3)
√ Rψ 2 where er f (ψ) = 2/ π 0 e−t dt, Pr (·) denotes the probability, and r0 denotes the threshold. Therefore, the complementary cumulative distribution function (CCDF) can be calculated as CCDFd = Pr (Υd > r0 ) = 1 − er f
2N
r
r0 . 2
(4)
Continuous-time DMT signal x (t) can be represented approximately by the L0 times oversampled x. Based on the extreme value theory, the corresponding CCDF can be calculated by −2N − r0 2 CCDFc = Pr (Υc > r0 ) = 1 − exp √ e , 3
(5)
where Υc is the PAPR of x (t). Study [11] demonstrates that selecting L0 ≥ 4 is sufficient for approximating the peak value of x (t). Taking the discrete-time DMT as an example, the instantaneous power of x (n) can be calculated by
| x (n)|2
2N −1 2N −1
j2π ( p − q)n/2N ∑ C ( p)C ∗ (q)e p =0 q =0 2N −1 2πqn 2N −1−q , ∗ 1 j 2N + NR ∑ e C p + q C p ( ) ( ) ∑ q =1 p =0 | {z }
=
1 2N
=
1 2
∑
ρC (q )
(6)
Electronics 2018, 7, 11
4 of 16
where ρC (q) is defined as the aperiodic autocorrelation function (ACF) of C. For an arbitrary complex N −1 N −1 Xn , the following inequalities hold R{Xn } ≤|Xn | and ∑ Xn ≤ ∑ |Xn |. Thus, a PAPR with a unit n =0
mean power (σx2 = 1) satisfies max
Υd =
n
0≤k ≤2N −1
| x (n)|2
n =0
o
≤
σx2
1 1 2N −1 1 1 + |ρC (q)| = + ξ C , 2 N q∑ 2 N =1
(7)
2N −1
where ξ C = ∑ |ρC (q)|. Therefore, a close relationship exists between Υd and ξ C . When the input q =1 n o symbols C (n) are all equal, max | x (n)|2 is able to reach its maximum value within one symbol 0≤k ≤2N −1
duration. 3. The Effective SNR Due to both the high PAPRs of DMT signals and the finite dynamic ranges of digital-to-analog conversion (DAC) devices, digital clipping for the given upper and lower thresholds is usually performed before DAC. The clipped signal is given as [5] x ( n ), x (n) = Au , A, l
Al ≤ x (n) ≤ Au . x (n) > Au x (n) < Al
(8)
For simplicity, we consider symmetric clipping (Au = − Al = Ath ). The clipping ratio (CR) is defined as Ath A γ = r n th (9) o = σ . x 2 E | x (n)| The output of clipping process can be considered as the sum of x (n) and the clipping noise cclip (n): (10) x (n) = x (n) + cclip (n). Nevertheless, based on the Bussgang theorem [20] for Gaussian inputs x ∼ N 0, σx2 , the clipped signal can also be decomposed statistically into two uncorrelated parts, given by x ( n ) = α x ( n ) + d ( n ),
(11)
where d(n) is the component of clipping distortion that is statistically uncorrelated to x (n) (e.g., E[ x ∗ (n)d(n)] = 0), and α is a linear attenuation factor that can be calculated by α =
E[ x ∗ (n) x (n)] γ h i = 1 − er f c √ , 2 E | x (n)|2
(12)
where er f c(·) = 1 − er f (·). The power of cclip (n) can be obtained by ( 2 σclip =
1 + γ2
γ er f c √ 2
r
−
γ2 2 γ e− 2 π
) σx2 .
(13)
2 is a function of γ and is independent of both the QAM modulation order and Therefore, σclip the size of IFFT/FFT. x (n) is converted into the analog signal x (t) by the DAC component. Due to
Electronics 2018, 7, 11
5 of 16
the finite bit resolution Q1 of the DAC, the quantization noise is then generated. The corresponding power can be calculated as 2 σDAC =
2 · γ2 σx2 max| x (n)|2 = er f Q 3·4 1 3 · 4Q1
γ √ . 2
(14)
To modulate the LED, x (t) is added by DC current IDC and obtain the final driving signals. We assume that the DMT signal is properly clipped, avoiding the LED nonlinearity. After optical channel transmission, the optical signal is detected by the optical detector, a combination of a photo diode (PD) and a trans-impedance amplifier (TIA). In most of the cases, the main sources of noise in the optical detector can be modeled as an additive white Gaussian noise (AWGN) following the distribution as N 0, σw2 . Then, the received electrical signal is captured by analog-to-digital conversion (ADC) components with Q2 bits of resolution. The power of the quantization noise in the ADC is given as γ2 · ρ2h · σx2 2 σADC = , (15) 3 · 4Q2 where ρ2h is the optical path gain coefficient. For simplicity, Q1 = Q2 = Q, ρ2h = 1 and IDC = 1 are adopted in analysis. Finally, the total noise power in IM/DD channel link can be approximately 2 2 2 2 + σ2 . Therefore, the system performance can be measured with σtotal = σADC + σDAC + σclip w evaluated by SNRe f f as the ratio between the power of the useful signal and the effective noise power, expressed as α2 σ 2 SNRe f f = 2 x . (16) σtotal For σx2 = 1,σw2 = 3.1486 × 10−4 and N = 512, the characteristic behavior of SNRe f f with different γ and Q is depicted in Figure 1. It can be observed that the SNRe f f can achieve its maximum value regarding to the optimum clipping γopt for each Q, e.g., γopt = 7 dB for Q = 8. Once the SNRe f f is computed, the BER performance of the DMT system can be easily evaluated with the help of the exact close-form expression of the QAM in AWGN channel [21]. As Figure 1 demonstrates, the SNRe f f degradation caused by the quantization is negligibly small when both Q1 and Q2 are greater than seven. In addition, the clipping effect dominates the system’s SNRe f f as the σw2 and γ threshold is fixed. Therefore, if we perform an appropriate n method o for reducing the ξ C of the input C (n), then, a transmitted signal with a lower
max
0≤k ≤2N −1
| x (n)|2 is obtained and the probability of
2 can be the Υd exceeding a given γ within one symbol duration is reduced. This indicates that the σclip lowered accordingly. Motivated by this way, a novel DMT scheme is proposed in the followings to reduce the value of ξ C , thus indirectly reducing the PAPR and improving the SNRe f f .
Electronics 2018, 7, 11 Electronics2018, 2018,7,7,xxFOR FORPEER PEERREVIEW REVIEW Electronics
6 of 16 of16 16 66of
SNReff(dB) (dB) SNR eff
12 12
20 20
11 11 10 10
15 15
Bits Bits of ofresolution resolution
99 88
10 10
77 66
55
55 00
44 33
-5 -5
22 11
22
44
66
88
(dB) γγ (dB)
10 10
12 12
14 14
Figure1. 1. Distribution Distribution of of the effective signal-to-noise ratio (SNR) forfor different clipping ratio andand bits Figure 1. (SNR) for different clipping ratio and bits Figure Distribution ofthe theeffective effectivesignal-to-noise signal-to-noiseratio ratio (SNR) different clipping ratio resolution. bits resolution. resolution.
4.Proposed ProposedScheme Scheme Proposed Scheme 4.4. Ablock block diagram of proposed the proposed proposed scheme isinshown shown in Compared Figure 2. 2. with Compared with the the A block diagram of the is Figure Compared with A diagram of the schemescheme is shown Figure in 2. the conventional conventional DMT (C-DMT), two additional modules, extra MB-Hadamard precoding and clipping, conventional (C-DMT), modules, two additional modules, extraprecoding MB-Hadamard precoding and clipping, DMT (C-DMT),DMT two additional extra MB-Hadamard and clipping, are implemented are implemented at the the transmitter. transmitter. Hadamard is aa class class of Jacket Jacket matrix matrix [22–24] which are are simple simple are at is of [22–24] which at theimplemented transmitter. Hadamard is a classHadamard of Jacket matrix [22–24] which are simple to calculate and easily to calculate and easily element-wise inverse. to calculate and easily element-wise inverse. element-wise inverse.
Figure2. 2.Diagram Diagramof ofthe theproposed proposedscheme schemeat attransmitter. transmitter. Figure Figure 2. Diagram of the proposed scheme at transmitter.
(( ))
HM == hhmm,l,l Assuming H signifies aa unit unit M Hadamard matrix, matrix, the the inverse inverse Hadamard Hadamard M ××M M Hadamard Assuming signifies Assuming H M M= (hm,l ) MMMsignifies a unit M × M Hadamard matrix, the inverse Hadamard matrix −1 11 can be calculated matrix H−M−Mcalculated directly using using H be directly using matrix can be calculated directly M can H 1 T H− . (17) M−−11= H M T (17) HMM == H HTM (17) H M .. For example, example, For
Electronics 2018, 7, 11
7 of 16
For example, H[1]
1 = √ 2
"
1 1
1 −1
# ,
(18)
where [κ ] = 2κ denotes the matrix order. Note that the Hadamard matrix H[κ ] with an order of the power-of-2 is adopted in this paper. l ( l = 0, · · · , L − 1, m = 0, · · · , M − 1) is Assuming that there are N = M · L sub-carriers, Xm l is spread by an M × M the (m + 1)th data symbol in the (l + 1)th band. The original symbol Xm Hadamard matrix firstly, and then a new set symbols is generated with Skl 0 =
M −1
∑
l Xm hm,k0 , k0 = 0, · · · , M − 1,
(19)
m =0
where hm,k0 is an element of H M and Skl 0 are sub-band mapped onto the N-point symbol vector, expressed by C MB = C0 (0), · · · ,C1 ( M), · · ·, · · · , C L−1 (( L − 1) M ), · · · , (20) | {z } | {z }| {z } 1−th
2−th
L−th
C l (k)
where ∈ C MB are the modulated symbols according to the sub-band constellation mapping, expressed as ( Skl 0 , k = k0 + Ml l C (k) = ,k = 0, · · · , N − 1. (21) 0, others h iT In addition, the vector C MB−n = is obtained by performing (C MB )T , (Z (C MB ))T Hermitian symmetry, and then fed into to the IFFT block to generate the time domain signals x MB−n . By introducing both the ACF expression from Equation (6) and the ACF sum from Equation (7), we can arrive at E ξ C MB−n < E{ξ C }. (22) Note that Equation (22) will be verified by the numerical result which is demonstrated in the Section 5.1. Furthermore, ξ C MB−n approaches an approximate Gaussian distribution as the value of N is large enough. The reduction in E ξ C MB−n implies a lower value of ξ C MB−n . Thus, we obtain ξ C MB−n < ξ C
(23)
According to Equation (7), there is a close relationship between Υd and the correlations of the input frequency-domain data-symbols. Therefore, the more ξ C MB−n can be reduced, the lower the PAPR value and the higher the SNRe f f can be obtained by MB-Hadamard precoding. After that, the precoded DMT is added with cyclic prefix (CP) and then fed into the clipping module to further reduce the peaks. In addition, we can also perform the filtering procedure iteratively to both remove the out-of-band interference and suppress the regrowth of the peak power. The received optical signal is transformed into an electrical signal y MB−n by the PD detector. Note that the quantization noise is negligibly small when the bit resolution is greater than seven. After the FFT and CP removal, the digital received symbol in the frequency domain can be approximately expressed with a matrix form as Y MB−n = HC MB−n + HCclip + W,
(24)
where H is the frequency domain channel response, Cclip is the cclip (n) in the frequency domain and W is channel noise. In what follows, the perfectly known channel response and the perfect
Electronics 2018, 7, 11
8 of 16
synchronization in the demodulation process are assumed for every received frame. After zero-forcing equalization, the equalized symbol can be expressed as Yeq− MB−n = C MB−n + Cclip (n) + H −1 W.
(25)
ˆ MB is With the Hermitian symmetric data of Yeq− MB−n removed, the new received symbol C ˆ MB is fed into the MB-Hadamard decoding module. A diagram of the proposed generated. Then, C decoding operation is depicted in Figure 3, where the demodulation procedure is the reverse of those l used in (19)–(21). After the sub-band demapping is completed, Sˆ k0 is transformed by the inverse l
1 ˆ Hadamard matrix H− M and the final data symbol Xm is obtained. Then, a maximum likelihood (ML) estimator is adopted as ˆ − Xi , Xˆ F = arg min α−1 X (26)
Xi i =1,2,··· ,I
where Xi is constellation point of QAM and I is the constellation size. When bit-loading with the desired BER Pe is employed, the SNR for each split band can be represented by " !#−1 M −1 σ2 Γ l SNR = M ∑ , (27) l 2 l m=0 Hm Pm 2 /N is the average noise power per subcarrier, Γ is the modulation gap, H l and Pl where σ2 = σtotal m m denote the channel response and the allocated power at the (m + 1)th subcarrier in the (l + 1)th band, respectively. As we known, the clipping will introduce the offensive impulse noise among in-band and out-band. Fortunately, as seen in Equation (27), the system noise is spread averagely in each sub-band and the corresponding SNR gains will be achieved by the MB-Hadamard decoding, which is favorable for symbol estimation. When a uniform power allocation is adopted for each sub-band and the total used power is Pt , then Pml can be calculated as Pml = Pt /M. Therefore, for a frequency-selective channel such as a POF, the SNR of the entire transmission band can be written as
iT h SNR MB = SNR0 , SNR1 , · · · , SNR L−1 .
(28)
As shown in Equations (27) and (28), the SNRl values within the same sub-band are equal, whereas those of adjacent sub-bands are different. Under these circumstances, it is appropriate to apply the bit-loading technique to each sub-band, which represents the primary difference between the proposed scheme and the DFT-S-DMT with respect to bit loading. Finally, the BER of the MB-Hadamard decoding in the (l + 1)th band can be approximately calculated as v √ " !#−1 u M − 1 I −1 2 u σ2 Γ 3 log2 (I) M er f ct BERl = √ (29) . ∑ l 2 P l I −1 I log2 (I) H m =0 m m
Electronics 2018, 7, 11 Electronics 2018, 7, x FOR PEER REVIEW Electronics 2018, 7, x FOR PEER REVIEW
9 of 16 9 of 16 9 of 16
Figure Figure3.3. 3.Diagram Diagramof ofproposed proposeddecoding decodingatat atreceiver. receiver. Figure Diagram of proposed decoding receiver.
5.5.Results Resultsand andDiscussion Discussion 5. Results and Discussion In section, the performance of the proposed scheme over an IM/DD optical is In this this optical channel channel In this section, section, the the performance performance of of the the proposed proposed scheme scheme over over an an IM/DD IM/DD optical channel is is investigated and evaluated in terms of its PAPR, power spectral density (PSD), achievable investigated and in terms of its PAPR, (PSD), achievable investigated andevaluated evaluated in terms of its power PAPR,spectral powerdensity spectral density (PSD),transmission achievable transmission rate, BER and complexity. POF transmission is depicted in Figure 4. Ten-bit rate, BER and complexity. The POF The transmission setup is setup depicted in Figure Ten-bit DAC transmission rate, BER and complexity. The POF transmission setup is depicted in 4. Figure 4. Ten-bit DAC and eight-bit ADC are both adopted, resulting in negligible quantization noise. A standard and eight-bit ADC are both resulting in negligible quantization noise. noise. A standard 50-m DAC and eight-bit ADC areadopted, both adopted, resulting in negligible quantization A standard 50-m Polymethyl Metacrylate (PMMA) step index (SI) (150 POFdB/km (150 dB/km @650 nm) is employed. The Polymethyl Metacrylate (PMMA) step index (SI) POF @650 nm) is employed. The DMT 50-m Polymethyl Metacrylate (PMMA) step index (SI) POF (150 dB/km @650 nm) is employed. The DMT signals are pre-generated by a computer and stored in the arbitrary waveform generator signalssignals are pre-generated by a computer and stored the arbitrary waveform generator (AWG) DMT are pre-generated by a computer and in stored in the arbitrary waveform generator (AWG) memory. The analogue electrical signal of the AWG output is then used to drive a 650-nm memory.memory. The analogue electricalelectrical signal ofsignal the AWG output then used to drive (AWG) The analogue of the AWGisoutput is then used ato650-nm drive aRC-LED 650-nm RC-LED with abias 10-mA biasAfter current. After the SI-POF transmission, theoptical received optical signal by is with a 10-mA current. the SI-POF transmission, the received signal is detected RC-LED with a 10-mA bias current. After the SI-POF transmission, the received optical signal is detected by then the PD and then captured by the ADC Finally, components. digital signal processing is the PD and captured by the ADC components. digitalFinally, signal processing is implemented detected by the PD and then captured by the ADC components. Finally, digital signal processing in is implemented in MATLAB. With respect to the received probing symbols, the estimated MATLAB. Withinrespect to theWith received probing symbols, the probing estimatedsymbols, channel information is channel obtained implemented MATLAB. respect to the received the estimated channel information is obtained andPSD the normalized PSD is measured approximately −110 and the normalized noise measured noise at approximately −110 at dB/Hz, which will be dB/Hz, used in information is obtained and theisnormalized noise PSD is measured at approximately −110 dB/Hz, which will be used in the following simulations. The DMT parameters are depicted in Table 1. the following The DMTsimulations. parameters The are depicted in Table 1.are depicted in Table 1. which will be simulations. used in the following DMT parameters
Figure4.4.Transmission Transmissionsetup setupwith withoffline offlineprocessing. processing. Figure Figure 4. Transmission setup with offline processing.
Electronics 2018, 7, 11
10 of 16
Electronics 2018, 7, x FOR PEER REVIEW
10 of 16
Table 1. Modulation parameters. Table 1. Modulation parameters.
DMT Parameter DMT Parameter Sampling frequency (GHz) Sampling frequency (GHz) IFFT/FFT length IFFT/FFT length Subcarrier spacing (MHz) Subcarrier spacing (MHz) Subcarrier number N N Subcarrier number Cyclic prefix ratio Cyclic prefix ratio Sub-band number L L Sub-band number
Value Value 1.0 1.0 2048 2048 0.488 0.488 1–1024 1–1024 1/64 1/64 1, 1, 4,4,8 8
5.1. PAPR Reduction 5.1. PAPR Reduction
N = 512 To assess performance theMB-Hadamard MB-Hadamard precoding in in reducing the the PAPR, the the To assess the the performance ofofthe precoding reducing PAPR, N =512 value is adopted from Table 1, and the signal bandwidth is calculated to be approximately 250 MHz. value is adopted from Table 1, and the signal bandwidth is calculated to be approximately 250 MHz. In our simulations, 4000 DMT symbols are generated randomly. Figure 5 shows the signal In our simulations, 4000 DMT symbols are generated randomly. Figure 5 shows the signal amplitudes amplitudes of our proposed scheme for various sub-band numbers L as well as the signal of ouramplitude proposed scheme for various sub-band numbers L as well as the signal amplitude of C-DMT. of C-DMT. As shown in the figure, the signal amplitude is reduced significantly by the As shown in the figure, the signal amplitude reduced proposed proposed MB-Hadamard precoding for the is cases of L =significantly 1, L = 4 and by 8. In addition,MB-Hadamard the energy L =the precoding for the cases of L =uniform, 1, L = and 4 and L = addition, the energy distribution distribution becomes more most of 8. the In large amplitudes are compressed belowbecomes the moreclipping uniform, and most of the largethat amplitudes compressed below theclipping clipping threshold, threshold, which indicates the signal are distortion in the following could be tothat somethe extent. whichmitigated indicates signal distortion in the following clipping could be mitigated to some extent. 3
3
C-DMT proposed (L=4)
2
2
1
1
Amplitude
Amplitude
C-DMT proposed (L=1)
0
0
-1
-1
-2
-2
-3
50
100
150
200
250
300
350
-3
400
50
100
150
200
250
300
350
400
Sampling points
Sampling points
(b)
(a) 3 C-DMT proposed (L=8) 2
Amplitude
1
0
-1
-2
-3
50
100
150
200
250
300
350
400
Sampling points
(c) Figure 5. Waveforms of proposed scheme with various numbers of split bands: (a) L = 1 (b) L = 4 (c) L
Figure 5. Waveforms of proposed scheme with various numbers of split bands: (a) L = 1 (b) L = 4 (c) = 8. L = 8.
Figure 6 illustrates the CCDF performance of the proposed scheme. As shown in the figure, the C-DMT achieves highest PAPR; however, smaller the band split (e.g., L in ), the = 1the Figure 6scheme illustrates the the CCDF performance of thethe proposed scheme. As shown figure,
the C-DMT scheme achieves the highest PAPR; however, the smaller the band split (e.g., L = 1), the lower the PAPR obtained by the proposed. When the CCDF = 10−3 , the PAPR of the C-DMT is 14.1 dB, whereas those of the proposed are 10.15 dB and 11.53 dB for L = 1 and L = 4, respectively,
Electronics 2018, 7, x FOR PEER REVIEW
11 of 16
Electronics 2018, 7, 11
11 of 16
lower the PAPR obtained by the proposed. When the CCDF = 10−3, the PAPR of the C-DMT is 14.1 dB, whereas those of the proposed are 10.15 dB and 11.53 dB for L = 1 and L = 4, respectively, resultingininrespective respective3.95 3.95dB dBand and2.57 2.57dB dBperformance performanceimprovements. improvements.In Inaddition, addition,the thefigure figurealso also resulting indicatesthat thatthe the CCDF CCDF performance of the because an indicates the proposed proposedscheme schemewith with LL ==8 8improves improveslittle little because insufficient volume of reliable data exists in the split band, which affects the correlations of the an insufficient volume of data exists in the split band, which affects the correlations of the input U denote input symbols. The of CCDF of a well-known PTS in which the parameters , V and denote symbols. The CCDF a well-known PTS in which the parameters U, V and W theW numbers numbers of corresponding modified candidate sequences, disjoint sub-vectors and respectively, phase angles, ofthe corresponding modified candidate sequences, disjoint sub-vectors and phase angles, is also demonstrated. The PAPR of the exceedsbut that of C-DMT but is isrespectively, also demonstrated. The PAPR performance of performance the PTS exceeds thatPTS of C-DMT is inferior to those to thosescheme of the proposed ofinferior the proposed for both Lscheme = 1 andfor L both = 4. L = 1 and L = 4. 0
10
C-DMT proposed (L=1) proposed (L=4) proposed (L=8) PTS(U=16,V=4,W=16)
-1
CCDF
10
-2
10
X: 10.15 Y: 0.001
-3
X: 12.4 Y: 0.001
X: 14.1 Y: 0.001
10
X: 11.53 Y: 0.001
X: 13.37 Y: 0.001
-4
10
7
8
9
10
11
12
13
14
15
PAPR0 (dB)
Figure6.6.Complementary Complementarycumulative cumulativedistribution distributionfunction function(CCDF) (CCDF)performance performancecomparison. comparison. Figure
{
}
n o 2 Thecalculated calculatedE |ρρC(q()| valueswith withrespect respecttotoboth boththe theC-DMT C-DMTand andthe theproposed proposedscheme scheme q 2) values The C under of LofareL shown in Figure 7a, which that thesethat curves move gradually undervarious variousvalues values are shown in Figure 7a,illustrates which illustrates these curves move away from away the C-DMT as LC-DMT decreases. Asdecreases. seen in the figure, the corresponding relationship gradually from the as As seen in the figure, the corresponding L E ξ C MB−n < E{ξ C } can easily be obtained based on the definition of ρC (q) give inρEquation (6). relationship ξCMB − n < {ξC } can easily be obtained based on the definition of C ( q ) give in Taking N = 512 as an example, the calculated probability density function (PDF), in terms of both (6). Taking N = 512 as an example, the calculated probability densitysimilar function (PDF), ξEquation shapes andin C and ξ C MB−n , is shown in Figure 7b. The figure reveals that the curves have ξ ξ terms of both and , is shown in Figure 7b. The figure reveals that the curves have CMBdistributed. are approximatelyC Gaussian Compared to ξ C , ξ C MB−n and E ξ C MB−n are decreased, −n which implies thatand the MB-Hadamard precoding reducesdistributed. the PAPR effectively. In addition, ξCdiscussed similar shapes are approximately Gaussian Compared to ξC , as and MB − n in Section 4, the establishment of inequalities Equations (22) and (23) are also verified by the results ξCMB − n are decreased, which implies that the MB-Hadamard precoding reduces the PAPR shown in Figure 7. effectively. In addition, as discussed in Section 4, the establishment of inequalities Equations (22) 5.2. andPSD (23)Performance are also verified by the results shown in Figure 7.
{
{
}
}
Figure 8 depicts a comparison of the PSD performances for the MB-Hadamard precoding under 5.2. PSDband Performance various numbers L. As shown in the figure, the rectangular PSD characteristics of the DMT are maintained, which indicates that theofMB-Hadamard precodingfor neither affects the signalprecoding PSD nor Figure 8 depicts a comparison the PSD performances the MB-Hadamard damages the spectral the sideband spectrum is reduced, which is advantageous under various bandefficiency. numbers Furthermore, . As shown in the figure, the rectangular PSD characteristics of the L for hybrid signal transmissions in short range POF systems. DMT are maintained, which indicates that the MB-Hadamard precoding neither affects the signal
PSD nor damages the spectral efficiency. Furthermore, the sideband spectrum is reduced, which is advantageous for hybrid signal transmissions in short range POF systems.
Electronics 2018, 7, 11 Electronics 2018, 7, x FOR PEER REVIEW Electronics 2018, 7, x FOR PEER REVIEW
12 of 16 12 of 16 12 of 16 -4
2500
x 10
6
C-DMT
2500
-4
6
C-DMT(L=1) proposed proposed (L=1) proposed (L=4)
2000
5
proposed (L=8)
proposed (L=8) 4
1500
The PDF The PDF
1500
4
3
C
E [ |ρ (q)|2] C E [ |ρ (q)|2]
C-DMT proposed C-DMT(L=1) proposed (L=4) proposed (L=1) proposed (L=8) proposed (L=4)
5
proposed (L=4) proposed (L=8)
2000
x 10
1000 1000
3
2
2
500 500
1 1
0 0
64
128 64
128
192
256
320
384
N384 192subcarrier 256 number 320 The The subcarrier number N
(a) (a)
448 448
0
512 512
{{
4
0
4.5 4
5
4.5
2
}}
5.5 5
6
6.5
7
5.5 The
6 of ACF 6.5 7 sum The sum of ACF
(b) (b)
7.5 7.5
8
8.5 8x 104 8.5 4
x 10
Figure 7. CCDF performance comparison: n (a) ρo C ( q ) 2 values for various subcarriers (b) Figure 7. CCDF performance comparison: various(b) subcarriers Figure 7. CCDF performance comparison: (a) E |(a) ρC (q)|2 ρ C values various for subcarriers probability(b) ( q ) for values probability density functions (PDFs) of aperiodic autocorrelation function (ACF) performance density functions (PDFs) of aperiodic autocorrelation function (ACF) performance comparison probability density functions (PDFs) of aperiodic autocorrelation function (ACF) performance comparison (for 512 subcarrier withmulti-tone 4000 discrete multi-tone (DMT) symbols). (for 512 subcarrier with 4000 discrete (DMT) symbols). comparison (for 512 subcarrier with 4000 discrete multi-tone (DMT) symbols). 0 0
Normalized PSD(dB) Normalized PSD(dB)
-10 -10 -20 -20 -30 -30
C-DMT proposed (L=4) C-DMT proposed (L=4) proposed (L=8) proposed (L=8)
-40 -40
proposed (L=1) proposed (L=1)
-50 -50 -60 0 -60
0
50 100 150 200 250 300 350 400 450 500 50 100 150 Frequency(MHz) 200 250 300 350 400 450 500
Frequency(MHz)
Figure8.8.Power Powerspectral spectraldensity density(PSD) (PSD)performance performancecomparison. comparison. Figure Figure 8. Power spectral density (PSD) performance comparison.
5.3.Achievable AchievableTransmission TransmissionRate Rate 5.3. 5.3. Achievable Transmission Rate Tomaximize maximize capacity of POF the POF system, thesub-band split sub-band first be L must To thethe capacity of the the split numbernumber Lnumber must first be evaluated. To maximize the capacity of thesystem, POF system, the split sub-band L must first be evaluated. a fixedpower electrical power of six decibel-milliwatts andbiasing a 10-mA biasing are Both a fixedBoth electrical of six decibel-milliwatts and a 10-mA current arecurrent used for evaluated. Both a fixed electrical power of six decibel-milliwatts and a 10-mA biasing current are used for the practical transmission. The CR is maintained at a constant dB. In addition, the γ = 12 theused practical transmission. The CR is The maintained at a constant = 12 dB. In12addition, the Chowthe for the practical transmission. CR is maintained at aγconstant dB. In addition, γ = adopted. number of Chow bit-loading algorithm with a BER target of−3Pis 1× 10−3 isThe bit-loading algorithm [25] with [25] a BER target of Pe = 1 × 10 numberThe of sub-carriers e =adopted. Chow bit-loading algorithm [25] with a BER target of Pe = 1× 10−3 is adopted. The number of varies with the fixedwith spacing ∆ f =spacing 0.488 MHz. channel is not used in this study. Δf =Note 0.488that MHz. Notecoding that channel coding is not used in sub-carriers varies the fixed Δf MHz = 0.488 MHz. Notethe that channel codingtransmission is not used in sub-carriers varies with the fixed between spacing 50 For various signal bandwidths and 500 MHz, total achievable this study. thisofstudy. rates C-DMT and the bandwidths proposed scheme with L50= 1, L = 4, and500 L = MHz, 8 are compared Figure 9a. Forthevarious signal between MHz and the totalinachievable For variousscheme signal and bandwidths between 50 MHz and 500transmission MHz, the rates total based achievable Both the proposed the C-DMT can achieve their maximal transmission rates of the C-DMT and the proposed scheme with L = 1, L = 4, and L = 8 on are transmission rates of the C-DMT and varies the proposed scheme 1, LL = L = of = 4,1, and L = 8 are the optimalinsignal bandwidth alongand with L. C-DMT In with the case the maximal optimal u , which compared Figure 9a. Both Bthe proposed scheme the can achieve their comparedrange in Figure 9a. Both the proposed scheme and C-DMT can due achieve maximal bandwidth is limited between approximately 150 MHz and 200 MHz to thetheir achievable Bthe transmission ratesψ based on the optimal signal bandwidth u , which varies along with L . In the B , which varies along with . In the transmission rates based on the optimal signal bandwidth L u transmission sensitive to the signal addition, the performance is severely ψ is limitedIn case of L = 1,rate the is optimal bandwidth range bandwidth. between approximately 150 MHz and 200 case of when theused optimal bandwidth range is limited between MHz and 200 L = 1,the degraded bandwidth exceeds theψψ. The ψ for both L = 4approximately and L = 8 are 150 wider than that MHz due to the achievable transmission rate is sensitive to the signal bandwidth. In addition, the of MHz L = 1.due In addition, compared to the C-DMT, transmission of the proposedIn scheme withthe to the achievable transmission rate the is sensitive to therate signal bandwidth. addition, performance is severely degraded when the used bandwidth exceeds the ψ . The ψ for both L = performance is severely degraded when the used bandwidth exceeds the ψ . The ψ for both L = 4 and L = 8 are wider than that of L = 1. In addition, compared to the C-DMT, the transmission 4 and L = 8 are wider than that of L = 1. In addition, compared to the C-DMT, the transmission
Electronics 2018, 7, x FOR PEER REVIEW
13 of 16
Electronics 2018, 7, 11
13 of 16
rate of the proposed scheme with L = 4 improves by at least eight percent, and its highest transmission rate is achieved at approximately 1.204 Gbps for Bu = 228 MHz. For this case, the Lcorresponding = 4 improves by least power eight percent, and its highest achievedin at approximately bitat and distributions of eachtransmission sub-carrier rate are isdepicted Figure 9b. As 1.204 Gbps for Bu = 228 MHz. For this case, the corresponding bit and power distributions of eachl discussed in the previous section, each subcarrier in the same sub-band obtains the same SNR sub-carrier are depicted in Figure 9b. As discussed in the previous section, each subcarrier in the same value after boththe equalization have takenand place. Therefore, based the sub-band obtains same SNRl and valuedispreading after both equalization dispreading have takenon place. calculations of the Chow algorithm [25], bothalgorithm equal numbers ofequal the modulated and equal Therefore, based on the calculations of the Chow [25], both numbers of bits the modulated amounts of power are allocated sub-carrier the same sub-band, in a frequency bits and equal amounts of power to areeach allocated to eachinsub-carrier in the sameeven sub-band, even in channel such as the such POF. as Asthe shown figure, also exists someexists slightsome distinction aselective frequency selective channel POF.in Asthe shown in there the figure, there also slight of the bit and power allocations in the last sub-band because the target number of total bits has distinction of the bit and power allocations in the last sub-band because the target number of total bits already nearly been allocated by by thethe previous sub-carriers, leading to to fewer bits being assigned to has already nearly been allocated previous sub-carriers, leading fewer bits being assigned thethe last effective SNR SNR distribution distribution to lastsub-carrier sub-carrier(e.g., (e.g.,a asingle singlebit bitcould couldbe be enough). enough). In In addition, the effective amongthe thesub-carriers sub-carriersforfor proposed scheme is depicted in Figure Asinseen in the among thethe proposed scheme (L =( L4)=is4)depicted in Figure 9c. As9c. seen the figure, figure, theSNR overall gain of the is obviously achieved obviously by thescheme proposed schemethe compared the overall gainSNR of the system is system achieved by the proposed compared C-DMT the C-DMT at the same clipping threshold. at the same clipping threshold. 8
C-DMT proposed (L=1) proposed (L=4) proposed (L=8)
7
1100
Bit Allocation
Transmission Rate (Mbps)
1200
1000
900
800
700
600
50
100
150
200
250
300
350
400
450
4 Allocated Bit Allocated Power
6
2
5
1
4
0
3
-1
2
-2
1
-3
0
500
3
0
50
100
150
200
Power Allocation (dB)
1300
250
Frequency (MHz)
Bandwidth (MHz)
(a)
(b) 25 proposed (L=4) C-DMT
The effective SNR (dB)
20
15
10
5
0
-5
0
50
100
150
200
250
Frequency (MHz)
(c) Figure 9. 9. Fifty-metre (a)(a) Transmission rate (at Figure Fifty-metre step step index indexpolymer polymeroptical opticalfiber fiber(SI-POF) (SI-POF)transmission transmission Transmission rate −3, without channel coding) (b) Bit and power distribution of the proposed a bit error rate (BER) of 10 − 3 (at a bit error rate (BER) of 10 , without channel coding) (b) Bit and power distribution of the proposed schemewith withLL== 44 (for (for transmission transmission rate rate of of1.204 1.204Gbps) Gbps)(c) (c)The Theeffective effectiveSNRs SNRsdistribution. distribution. scheme
Stated thusly, a moderate L can guarantee both the validity and the feasibility of the Stated thusly, a moderate L can guarantee both the validity and the feasibility of the proposed proposed scheme as well as maximize the transmission rate, which is more important for a practical scheme as well as maximize the transmission rate, which is more important for a practical transmission transmission system. Note that the proposed scheme chooses the optimal L according to the system. Note that the proposed scheme chooses the optimal L according to the actual signal bandwidth. actual signal bandwidth.
Electronics 2018, 7, 11 Electronics 2018, 7, x FOR PEER REVIEW
14 of 16 14 of 16
5.4. BER Performance 5.4. BER Performance The BER performances of the C-DMT (clipping-only), Golay complementary sequences (GCSs) The BER performances of the C-DMT (clipping-only), Golay complementary sequences [12], and PTS are carefully investigated and discussed in this section. To provide a fair comparison, (GCSs) [12], and PTS are carefully investigated and discussed in this section. To provide a fair the transmitting signals have the same modulation parameters as those depicted in Table 1, and the comparison, the transmitting signals have the same modulation parameters as those depicted in number of sub-carriers N = 512 is used. The Chow algorithm with Pe = 1 × 10 −3 and a desired Table 1, and the number of sub-carriers N = 512 is used. The Chow algorithm with Pe = 1 × 10−3 and rate of 1.0rate Gbps is also adopted. In addition, the CR isthe chosen be γ to dB=and = 10 atransmission desired transmission of 1.0 Gbps is also adopted. In addition, CR isto chosen be γ 10 the dB input electrical signal power is varied from −2–6 decibel-milliwatts. and the input electrical signal power is varied from −2–6 decibel-milliwatts. As shown shownin in Figure the GCStheoffers its excellent As the the Figure 10, the10, GCS offers lowestthe BERlowest becauseBER of itsbecause excellent of error-correction error-correction Clipping in the C-DMT is to thereduce simplest to whereas reduce the ability. Clipping ability. in the C-DMT is the simplest way theway PAPR, thePAPR, BER iswhereas limited γ L = the BER is limited by . The proposed scheme with 4 provides a better BER performance by γ . The proposed scheme with L = 4 provides a better BER performance than the C-DMT, than and −3 . the power is reduced least byisfour decibel-milliwatts for the given BER = 1 ×for10the the required C-DMT,signal and the required signalat power reduced at least by four decibel-milliwatts Compared smaller clipping distortion is generated in the proposed scheme because given BER to = the to the C-DMT, smaller clipping distortion is generated in the 1 × C-DMT, 10 −3 . Compared most of thescheme large signal amplitudes arethe compressed. Theamplitudes PTS also achieves a better BERThe performance. proposed because most of large signal are compressed. PTS also However, sideBER information of PTS must bethe known the receiver. If this information to achieves athe better performance. However, side by information of PTS must be knownfails by the be detected, the information demodulatorfails cannot thethe original signal correctly and the the BERoriginal performance receiver. If this to berecover detected, demodulator cannot recover signal degrades accordingly. correctly and the BER performance degrades accordingly. -1
10
-2
10
-3
BER
10
-4
10
proposed (L=4, γ = 10dB) C-DMT (clipping γ = 10dB) PTS GCS
-5
10
-6
10
-2
-1
0
1
2
3
4
5
6
Input electrical signal power (dBm)
Figure 10. 10. Comparisons Comparisons of of BER BER performance. performance. Figure
5.5. Computational Computational Complexity Complexity 5.5. the total time consumed bythe both the The elapsed elapsedsignal signalprocessing processingtime time The tS , trepresenting the total time consumed by both signal S , representing signal generation the demodulation, is as adopted astoameasure metric to the computational generation and theand demodulation, is adopted a metric themeasure computational complexity complexity performance. this150, study, 150, and 200 DMT each are performed in the performance. In this study,In100, and 100, 200 DMT symbols each symbols are performed in the transmissions. tS forare transmissions. Thevarious value of various schemes are measured and then shown in Figure 11. The value of tS for schemes measured and then shown in Figure 11. The figure illustrates that PTSillustrates and GCS that schemes require longest signal processing times,signal and the corresponding The the figure the PTS andthe GCS schemes require the longest processing times, values of t increase dramatically with an increase in the number of DMT symbols used. In addition, S and the corresponding values of tS increase dramatically with an increase in the number of DMT many times of IFFT computations are required in the PTS scheme to find its combination symbols used. In addition, many times of IFFT computations are required in optimum the PTS scheme to find of phase factors. GCS also has more difficulty in seeking the optimum generated matrix phase its optimum combination of phase factors. GCS also has more difficulty in seeking theand optimum rotation vectors as greater numbers of subcarriers are used. In addition to these overhead loads, generated matrix and phase rotation vectors as greater numbers of subcarriers are used. In addition many more complex adder andmore multiplier have to be performed bothtothe and the to these overhead loads, many complex adder and multiplierinhave be PTS performed in GCS, both which consumes more hardware resources and requires more time. However, the t of the proposed S time. However, the PTS and the GCS, which consumes more hardware resources and requires more scheme and changes little asand thechanges numbervery of symbols increases, that the tS is of shorter the proposed schemevery is shorter little as used the number of meaning symbols used a lower computational complexity is obtained. The additional operations performed in the proposed increases, meaning that a lower computational complexity is obtained. The additional operations
Electronics Electronics 2018, 2018, 7, 7, 11 x FOR PEER REVIEW
15 15 of of 16 16
performed in the proposed scheme consist of H M spreading and H −M1 dispreading, −1 scheme consist entirely of H M spreading and Hentirely M dispreading, which are both easily employed and which are both easily employed and convenient for hardware implementation. convenient for hardware implementation. In summary, the proposed high-speed data transmission from the In summary, the proposed scheme schemeisisbeneficial beneficialtotothe the high-speed data transmission from carefully performance investigation of the PAPR, the the BER, the the transmission rate,rate, the the PSDPSD andand the the carefully performance investigation of the PAPR, BER, transmission computational complexity. the computational complexity. 60
The elapsed time (second)
50
proposed (L=4, γ = 10dB) C-DMT (clipping γ = 10dB) PTS GCS
40
30
20
10
0
100 DMT symbol
150 DMT symbol
200 DMT symbol
Figure 11. 11. Comparisons Comparisons of of computational computational complexity complexity for for different differentscheme. scheme. Figure
6. Conclusions Conclusions 6. In this this paper, paper, an an efficient efficient low-complexity low-complexity scheme scheme using using both both MB-Hadamard MB-Hadamard precoding precoding and and In clipping was proposed to reduce the PAPRs of OFDM-based systems. By implementing this clipping was proposed to reduce the PAPRs of OFDM-based systems. By implementing this methodology, the the peak as as a consequence. In methodology, peak signal signal was was compressed compressedand andthe thePAPR PAPRwas wasreduced reduced a consequence. addition, the nonlinear distortions caused by clipping were effectively mitigated, and the BER In addition, the nonlinear distortions caused by clipping were effectively mitigated, and the BER performance was was improved improved significantly. significantly. Moreover, Moreover, it it improves improves the the robustness robustness of of the the Hadamard Hadamard performance precoding to system nonlinearity and sets the optimal sub-band number according to the signal actual precoding to system nonlinearity and sets the optimal sub-band number according to the actual signal bandwidth. The results demonstrate that the proposed scheme can provide favorable bandwidth. The results demonstrate that the proposed scheme can provide favorable trade-offs among trade-offs among the PAPR,rate, BER, transmission complexity, spectral efficiency. A further the PAPR, BER, transmission complexity, and rate, spectral efficiency.and A further degree of experimental degree of experimental verification will be investigated in the future works. verification will be investigated in the future works. Acknowledgments: The The authors authors acknowledge acknowledge the support support for for this this work work from from the the National National Natural Natural Science Science Acknowledgments: Foundation We would like to express gratitude to Lenan Wu Foundation of of China China (61601281). (61601281). We Wu and and Linning Linning Peng Peng that that constructive constructivesuggestions suggestionsand andassistance assistanceto tothis thisarticle. article. Author Contributions: Pu Miao, Peng Chen and Zhimin Chen conceived and designed the simulations and Author Contributions: Pu Miao, Peng Chen and Zhimin Chen conceived and designed the simulations and experiments; Pu Miao and Peng Chen analyzed the data; Zhimin Chen contributed figures plotting; Pu Miao experiments; Pu Miao and Peng Chen analyzed the data; Zhimin Chen contributed figures plotting; Pu Miao wrote the paper. wrote the paper. Conflicts of Interest: The authors declare no conflict of interest. Conflicts of Interest: The authors declare no conflict of interest.
References References 1. 1. 2. 2. 3. 3. 4. 4.
Okonkwo, C.M.; Tangdiongga, E.; Yang, H.; Visani, D.; Loquai, S.; Kruglov, R.; Charbonnier, B.; Ouzzif, M.; Okonkwo, C.M.; Tangdiongga, E.; Yang, H.;from Visani, S.; Kruglov, R.; Charbonnier, B.; Ouzzif, Greiss, I.; Ziemann, O.; et al. Recent Results theD.; EULoquai, POF-PLUS Project: Multi-Gigabit Transmission M.; Greiss, I.; Ziemann, O.; et Optical al. Recent Results from Technol. the EU2011, POF-PLUS Project: Multi-Gigabit Over 1 mm Core Diameter Plastic Fibers. J. Lightwave 29, 186–193. [CrossRef] Transmission Over 1 mm Core Diameter Plastic Optical Lightwave Technol. 2011, 29, 186–193. Guariglia, E. Entropy and Fractal Antennas. Entropy 2016,Fibers. 18, 84.J.[CrossRef] Guariglia, E. Entropy and Fractal Antennas. Entropy 2016, 18, 84. Chen, L.; Krongold, B.; Evans, J. Performance Analysis for Optical OFDM Transmission in Short-Range Chen, L.; Krongold, B.; Evans, J. Performance Analysis[CrossRef] for Optical OFDM Transmission in Short-Range IM/DD Systems. J. Lightwave Technol. 2012, 30, 974–983. IM/DD J. Lightwave 2012, 30, for 974–983. Peng, L.;Systems. Helard, M.; Haese, S.Technol. On Bit-Loading Discrete Multi-Tone Transmission over Short Range POF Peng, L.; J.Helard, M.;Technol. Haese, 2013, S. On31, Bit-Loading Discrete Multi-Tone Transmission over Short Range Systems. Lightwave 4155–4165.for [CrossRef] POF Systems. J. Lightwave Technol. 2013, 31, 4155–4165.
Electronics 2018, 7, 11
5. 6. 7.
8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
18. 19. 20. 21. 22. 23.
24. 25.
16 of 16
Azim, A.W.; Guennec, Y.L.; Maury, G. Decision-directed iterative methods for PAPR reduction in optical wireless OFDM systems. Opt. Commun. 2017, 389, 318–330. [CrossRef] Stepniak, G. DMT Transmission in SI POF with Minimax Channel Shortening Equalizer. IEEE Photonics Technol. Lett. 2014, 26, 1750–1753. [CrossRef] Zhang, G.; Zhang, J.; Hong, X.; He, S. Low-complexity frequency domain nonlinear compensation for ofdm based high-speed visible light communication systems with light emitting diodes. Opt. Express 2017, 25, 3780–3794. [CrossRef] [PubMed] Karabetsos, S.; Pikasis, E.; Nikas, T.; Nassiopoulos, A.; Syvridis, D. DFT-Spread DMT Modulation for 1-Gb/s Transmission Rate Over 100 m of 1-mm SI-POF. IEEE Photonics Technol. Lett. 2012, 24, 836–838. Karunatilaka, D.; Zafar, F.; Kalavally, V.; Parthiban, R. Led based indoor visible light communications: State of the art. IEEE Commun. Surv. Tutor. 2015, 17, 1649–1678. [CrossRef] Ying, K.; Yu, Z.; Baxley, R.J.; Qian, H.; Chang, G.K.; Zhou, G.T. Nonlinear distortion mitigation in visible light communications. IEEE Wirel. Commun. 2015, 22, 36–45. [CrossRef] Lim, D.W.; Heo, S.J.; No, J.S. An overview of peak-to-average power ratio reduction schemes for OFDM signals. J. Commun. Netw. 2009, 11, 229–239. [CrossRef] Wunder, G.; Fischer, R.F.H.; Boche, H.; Litsyn, S.; No, J.S. The PAPR Problem in OFDM Transmission: New Directions for a Long-Lasting Problem. IEEE Signal Process. Mag. 2012, 30, 130–144. [CrossRef] Dimitrov, S.; Sinanovic, S.; Haas, H. Clipping Noise in OFDM-Based Optical Wireless Communication Systems. IEEE Trans. Commun. 2012, 60, 1072–1081. [CrossRef] Sudha, V.; Syamkumar, M.; Kumar, D.S. A Low Complexity Modified SLM and Companding based PAPR Reduction in Localized OFDMA. Wirel. Pers. Commun. 2017, 96, 3207–3226. [CrossRef] Mazahir, S.; Sheikh, S.A. On Companding Schemes for PAPR Reduction in OFDM Systems Employing Higher Order QAM. IEEE Trans. Broadcast. 2016, 62, 716–726. [CrossRef] Kamal, S.; Meza, C.A.; Tran, N.H. Low-PAPR Hybrid Filter for SC-FDMA. IEEE Commun. Lett. 2017, 21, 905–908. [CrossRef] Ta¸spınar, N.; Yıldırım, M. A Novel Parallel Artificial Bee Colony Algorithm and Its PAPR Reduction Performance Using SLM Scheme in OFDM and MIMO-OFDM Systems. IEEE Commun. Lett. 2015, 19, 1830–1833. [CrossRef] Adegbite, S.A.; McMeekin, S.G.; Stewart, B.G. A low complexity SI sequence estimator for pilot-aided SLM–OFDM systems. AEU-Int. J. Electron. Commun. 2016, 70, 1267–1274. [CrossRef] Zhang, H.; Yuan, Y.; Xu, W. Papr reduction for dco-ofdm visible light communications via semidefinite relaxation. IEEE Photonics Technol. Lett. 2014, 26, 1718–1721. [CrossRef] Yang, L.; Song, K.; Siu, Y.M. Iterative Clipping Noise Recovery of OFDM Signals Based on Compressed Sensing. IEEE Trans. Broadcast. 2017, 63, 706–713. [CrossRef] Lee, A.; Messerschmitt, D.G. Digital Communication; Springer: New York, NY, USA, 1994. Mohammad, N.; Brandt-Pearce, M. Hadamard-Coded Modulation for Visible Light Communications. IEEE Trans. Commun. 2016, 64, 1167–1175. Miao, P.; Jiang, D.; Wu, L.; Chen, P. A Hybrid PAPR Reduction Approach for the IM/DD Optical OFDM Communications. In Proceedings of the 2017 IEEE/CIC International Conference on Communications in China (ICCC), Qingdao, China, 22–24 October 2017; pp. 1–5. Miao, P.; Wu, L.; Chen, Z. An anti-noise modem for visible light communication systems using the improved M-ary position phase shift kfeying. AEU-Int. J. Electron. Commun. 2018, 85, 126–133. [CrossRef] Chow, P.S.; Cioffi, J.M.; Bingham, J. A practical discrete multitone transceiver loading algorithm for data transmission over spectrally shaped channels. IEEE Trans. Commun. 1995, 43, 773–775. [CrossRef] © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
