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A Golay complementary TS-based symbol synchronization scheme in variable rate LDPC-coded MB-OFDM UWBoF system
Optics Communications 350 (2015) 189–195
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
A Golay complementary TS-based symbol synchronization scheme in variable rate LDPC-coded MB-OFDM UWBoF system Jing He n, Xuejie Wen, Ming Chen, Lin Chen College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan, China
art ic l e i nf o
a b s t r a c t
Article history: Received 21 January 2015 Received in revised form 15 March 2015 Accepted 4 April 2015 Available online 7 April 2015
In this paper, a Golay complementary training sequence (TS)-based symbol synchronization scheme is proposed and experimentally demonstrated in multiband orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband over fiber (UWBoF) system with a variable rate low-density parity-check (LDPC) code. Meanwhile, the coding gain and spectral efficiency in the variable rate LDPC-coded MBOFDM UWBoF system are investigated. By utilizing the non-periodic auto-correlation property of the Golay complementary pair, the start point of LDPC-coded MB-OFDM UWB signal can be estimated accurately. After 100 km standard single-mode fiber (SSMF) transmission, at the bit error rate of 1 10 3, the experimental results show that the short block length 64QAM-LDPC coding provides a coding gain of 4.5 dB, 3.8 dB and 2.9 dB for a code rate of 62.5%, 75% and 87.5%, respectively. & 2015 Published by Elsevier B.V.
Keywords: Multiband orthogonal frequency-divisionmultiplexing (MB-OFDM) Ultra-wideband over fiber (UWBoF) system Low-density parity-check (LDPC) Golay complementary sequence
1. Introduction Due to the rapid growth of the communication capacity demand for wireless and mobile users, bandwidth requirements have been ever-increasing. Ultra-wideband (UWB) technology has some advantages such as low power and co-existence with other wireless services [1]. Thus it is recognized as a potential solution in wireless personal network and in-home network [2,3]. At present, orthogonal frequency division multiplexing (OFDM) [4] is a promising solution because of its robustness of multipath channels [5] and easily implementation based on fast Fourier transform (FFT) algorithms [6]. Therefore, multiband orthogonal frequency division multiplexing (MB-OFDM) UWB has paid more attention due to its high spectral efficiency, robust against multi-path effects and low power consumption [7]. However, the power spectral density of a MB-OFDM UWB signal regulated by the Federal Communications Commission (FCC) is constrained, so that the transmission distance of a MB-OFDM UWB signal is limited a few meters. To extend the area of coverage, MB-OFDM UWB signals over fiber (UWBoF) system are proposed and experimental investigated [8,9]. The MB-OFDM UWB signals based on external modulation can transmit over 40 km single-mode fiber (SMF) [9]. However, the received optical power is relatively higher. Recently, in the IEEE 802.15.3.c standard [10], the short block length low-density parityn
Corresponding author. E-mail addresses: [email protected], [email protected] (J. He).
http://dx.doi.org/10.1016/j.optcom.2015.04.012 0030-4018/& 2015 Published by Elsevier B.V.
check (LDPC) codes are proposed as a low complexity solution for impulse response (IR) UWB systems [11]. The short block length codes have good prospects of on chip implementation and commercialization. In addition, the short block length LDPC code based on the WiMAX 802.16e standard is proposed in the MB-OFDM UWB over fiber systems [12]. In this paper, for the first time to our knowledge, a Golay complementary training sequence (TS)-based symbol synchronization scheme is proposed in a variable rate LDPC-coded MBOFDM UWB over fiber system. By utilizing the non-periodic autocorrelation complementary property of the Golay complementary pair, the start point of LDPC-coded MB-OFDM UWB signal can be estimated accurately. After 100 km standard single-mode fiber (SSMF) transmission, at the bit error rate of 1 10 3, the short block length LDPC coding provides a coding gain of 4.5 dB, 3.8 dB and 2.9 dB for a code rate of 62.5%, 75% and 87.5%, respectively, when compared with un-coded MB-OFDM UWBoF system.
2. Principle 2.1. A Golay complementary TS-based symbol synchronization scheme In our previous work [12], a TS-based symbol synchronization scheme is proposed in LDPC-coded MB-OFDM UWBoF system. However, there are two sidelobes around the strong peak of the timing synchronization metric. In the paper, a Golay
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complementary TS-based symbol synchronization scheme is used to implement the symbol synchronization in a variable rate LDPCcoded MB-OFDM UWBoF system. The generation of Golay complementary pair of length 2″ is implemented [13]. Let A0 and B0 are Golay complementary pair of length N ¼2n, respectively. After interleaving between A0 and B0 , A and B can be generated as follows:
where k = 0, 1, 2, … , D − 1 is the delay time index, y (m) is the mth sample at the receiver, a [⋅] and b [⋅] are the transmitted Golay complementary pair A and B, respectively. To obtain the synchronization point, the timing metric is defined as
A = [a 0, ⋯, ar − 1 , b0 , ⋯, br − 1 , ar , ⋯, a2r − 1, br , ⋯, b2r − 1,
Z (m) =
⋯⋯, aN − r , ⋯, aN − 1 , bN − r , ⋯, bN − 1 ]
(1)
B = [a 0, ⋯, ar − 1 , − b0 , ⋯, − br − 1 , ar , ⋯, a2r − 1, − br , ⋯, − b2r − 1, ⋯⋯, aN − r , ⋯, aN − 1 , − bN − r , ⋯, − bN − 1 ]
(3)
D − 1− k
∑
a (j) ⁎a (j + k) (4)
j=0 D − 1− k
ACb, b (k) =
∑
b (j) ⁎b (j + k) (5)
j=0
Here, we utilize the non-periodic auto-correlation property of the Golay complementary pair [14]. The proposed preamble can be given by [15]
GolayTS = [ A O B O ]
(6)
where A and B are Golay complementary pair of length D, O is the zero-value sequence of length D. By using double slide windows spaced D, at the receiver, the non-periodic cross-correlation with Golay sequence A in the window 1 and B in the window 2 are performed at time m, it can be expressed as D − 1− k
A (m, k) =
∑ j=0
y (m + 2D + j) b (j + k) (8)
j=0
P (m) R (m)
(9)
where
P (m) = r (m, 0) 2
where ACa, a (k) and ACb, b (k) are the non-periodic auto-correlation of A and B, and it is given respectively by
ACa, a (k) =
∑
(2)
where r ∈ (1, 2, ⋯N), ak and bk are the kth value in the Golay complementary pair A0 and B0 , respectively. Assuming that A and B are Golay complementary pair of length D, respectively, they have the property [13]
⎧ 2D , k=0 ACa, a (k) + ACb, b (k) = ⎨ ⎩ 0, 1 ≤ k ≤ D − 1
D − 1− k
B (m, k) =
R (m) =
1 D−1
(10)
D−1
∑
r (m, k) 2
r (m, k) = A (m, k) + B (m, k)
(7)
(12)
As the sample point is corresponding to the maximum value of Z (m), and it is selected as timing synchronization point, then, the estimation of timing metric offset can be written as ∧
ε = arg max⋅(Z (m))
(13)
m
At the receiver, the digitalized signal is down-converted to the baseband signal with the corresponding TFC. Then, the blocks of MB-OFDM UWB symbols are send to the synchronization module. In the synchronization module, the synchronized signal is captured to pinpoint the start of FFT window and separate the training symbols and data symbols. The symbol synchronization scheme for MB-OFDM UWBoF system is shown in Fig. 1. Assuming that Golay complementary pair A and B are corresponding to window 1 and window 2, respectively, it can be expressed as
r (m, k) = A (m, k) + B (m, k) = h (k) ⊗ [x (m + k) ⊗ a ( − k) + x (m + 2D + k) ⊗ b ( − k)] + w (k) ⎡ D − 1− k = h (k) ⊗ ⎢ ∑ a (j) a (j + k) + ⎢⎣ j = 0
D − 1− k
∑ j=0
⎤ b (j) b (j + k) ⎥ ⎥⎦
+ w (k) = h (k) ⊗ [ACa, a (k) + ACb, b (k)] + w (k) = 2Dh (k) + w (k)
y (m + j) a (j + k)
(11)
k=1
(14)
where ⊗ denotes convolution operation, a ( − k) and b ( − k) are
Fig. 1. Symbol synchronization scheme of MB-OFDM UWBoF system.
J. He et al. / Optics Communications 350 (2015) 189–195
that HcT ¼0, where H is an(n − k) × nparity check matrix. Each of the parity-check matrices can be partitioned into square subblocks (sub-matrices) of size z × z (z = 21). These sub-matrices are either cyclic-permutations of the identity matrix or null (all-zero) sub-matrices. The cyclic-permutation matrix pi is obtained from the z × z identity matrix. It can be implemented by cyclically shifting the columns to the left by i elements. The matrix p0 is the z × z identity matrix. For example, the matrix permutation indices of parity-check matrices for 75% LDPC code rates are shown as follows:
the reflection of Golay sequence a (k) and b (k) respectively, h (k) is channel impulse response of the kth delay channel tap. w (k) is noise samples. Andx (m) is the mth sample at the transmitter. In this way, the timing metric have the impulsive value at the timing point.
2.2. The variable rate LDPC-coded MB-OFDM UWB transceiver Fig. 2 shows the block diagram of a variable rate LDPC-coded MB-OFDM UWB transmitter and receiver. At the MB-OFDM UWB transmitter, as shown in Fig. 2(a), a pseudo-random binary
⎡0 ⎢ ⎢− ⎢5 ⎢− H=⎢ ⎢− ⎢6 ⎢ ⎢− ⎢⎣18
− 18 0 − 5 − −
− 6 − 18 0 − 5
5 − − 6 − 18 0
− 7 − 0 16 − 18
18 − − 7 − 0 16
16 − 18 − − 7 −
− 0 16 − 18 − −
− 10 6 − 3 − −
− 2 − 10 6 − 3
3 − − 2 − 10 6
6
−
−
−
−
0
7
2
−
− 10 16 9
6 10 − − 0 − − − 16 9 − 20 3 0 10 − − 5 − − − 16 9 − − − 0 10 − − 2 9 − − 16 9 − − − 0 10 7 −
−
sequences (PRBSs) pattern is generated by offline Matlab. After the interleaver, the PRBSs are encoded based on the LDPC codes with the different code rate. The variable rate LDPC codes are based on the IEEE 802.15.3.c standard [10]. The LDPC code rates with forward error correction (FEC), LDPC information block lengths and LDPC codeword block lengths are described in Table 1. The LDPC encoder is systematic, i.e., it encodes an information block of size k, i ¼(i0, i1, …, i(k–1)), into a codeword c of size n, c ¼(i0, i1, …, i(k–1), p0, p1, …, p(n–k–1)), by adding n–k parity bits so
191
−
7 − − 20 5 − −
− 9 7 − − 20 5
5 − − 9 7 − −
− − 4 4 − 4 12 − − 4 4 − − 4 5 − 4 12 − − 4 4 − − − − − 4 12 19 − 4 4 − 10
9
− 20 12 −
−
4
10 − − 4 5 − −
− 19 10 − − − 5
5 − − 19 − − −
− 19 −
4
⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 19 − ⎥ − 17 − 10 ⎥⎦
− − 19 − − − 7
− − − 10 − − −
− − − − − −
− − − − − −
where the integer i denotes the cyclic-permutation matrix pi. The ‘–’ denote null (all zero) sub-matrices. In this way, the PRBSs are encoded based on the variable rate LDPC codes by using the parity-check matrices H in IEEE 802.15.3.c standard. Then the LDPC coded sequences are fed to the mappers with 64-quadrature amplitude modulation (64-QAM). For the purpose of channel tracking, 12 sub-carriers are used to transmit pilot symbols in the transmitter. Then, 128-point inverse fast Fourier transforms (IFFT) function is used to realize OFDM modulation. After OFDM
Fig. 2. The block diagrams of the variable rate LDPC-coded MB-OFDM UWB transceiver: (a) transmitter and (b) receiver.
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3. Experimental setup and results
Table 1 The parameters of the irregular LDPC codes. LDPC code rate (%), RFEC
LDPC information block length (bits), Linf
LDPC codeword block length (bits), LFEC
62.5 75 87.5
420 504 588
672 672 672
modulation, the outputs of IFFT are scaled and clipped. In addition, a cyclic prefix of 16 samples is appended to the beginning of each 128 IFFT output samples. Subsequently, the baseband OFDM signal with LDPC code is digital up-conversion with time-frequency code (TFC) [7] to generate a LDPC-coded MB-OFDM UWB signal. In this way, at the transmitter, an MB-OFDM UWB frame consists of one Golay complementary TS and 462 MB-OFDM UWB symbols. Meanwhile, the Golay complementary TS is located at the beginning of OFDM signal frame. And it is used to realize symbol synchronization. At the MB-OFDM UWB receiver, as shown in Fig. 2(b), after SSMF transmission and optical/electrical conversion, the received electrical MB-OFDM UWB signal is converted into the digital signals by an analog-to-digital converter (ADC). The digitalized signal is further down-converted to the baseband signal with the corresponding TFC. Then the baseband signal is sent to the Golay complementary TS-based symbol synchronization module. Once symbol synchronization is implemented, a cyclic prefix at the beginning of the OFDM symbol is removed. In addition, 128-point FFT function is used to realize OFDM signal demodulation. The channel responses on every data sub-carriers can be estimated and compensated by using inserted pilot symbols [16]. Subsequently, the outputs of the 64-QAM demodulator are fed to a LDPC decoder and it is implemented based on the sum-product algorithm [17]. Meanwhile, the recovered bits are transmitted to the BER calculate function. And the count error bits are over a total of 100 462 6 ¼277,200 bits.
The experimental setup of the variable rate LDPC-coded optical MB-OFDM UWBoF system is shown in Fig. 3. At the transmitter, continuous wave (CW) light is generated from a commercial external cavity laser (ECL) source with 100 kHz line-width. Then, the CW light is injected into a single-drive Mach–Zehnder modulator (MZM), and a polarization controller (PC) is rotated to maximize the MZM output optical power. Meanwhile, the variable rate LDPCcoded MB-OFDM UWB signal is generated by offline Matlab, and then uploaded into a Tektronix Arbitrary Waveform Generator (AWG) operating at 10.561 GSps sampling rate, 10-bit digital-toanalog converter (DAC) resolution. The output MB-OFDM UWB signal with a peak-to-peak voltage (Vp-p) of about 560 mV is amplified to 1.6Vp-p by an electrical amplifier (EA) with 14 GHz bandwidth. Subsequently, the MZM is driven by the amplified electrical MB-OFDM UWB signal. The DC bias of MZM at negative quadrature point is 2.1 V. In this way, the optical MB-OFDM UWB signal is generated and then transmitted over 100 km SSMF. At the receiver, the EDFA is used to amplify the optical MBOFDM UWB signal. And a variable optical attenuator (VOA) is applied to adjust the received optical power for the measurement. The optical-to-electrical (O/E) conversion is implemented via PD with 3-dB bandwidth of 10-GHz. After the electrical low-pass filter (LPF) with a bandwidth of 5.5 GHz, a direct-current (DC) block is utilized to remove the DC component. In addition, the electrical MB-OFDM UWB signal is captured by a digital storage oscilloscope (DSO) with 20GSps sampling rate, 8-GHz bandwidth and 8-bit analog-to-digital converter (ADC) resolution. After the DSO, the electrical spectrum of MB-OFDM UWB signal is shown in Fig. 3. Subsequently, the captured signal is further processed by off-line digital signal processing. The off-line digital signal processing is as follows: firstly, the captured signal is resampled to 10.561 GSps and then digitally down-converted. Secondly, the electrical intermediate frequency MB-OFDM UWB signal is demodulated as MBOFDM UWB Receiver shown in Fig. 2(b). Finally, the LDPC-coded sequences are demapped into binary bits for bit error rate (BER) counting. In the experiment, some key parameters in the variable rate LDPC-coded MB-OFDM UWB transceiver are given in Table 2.
Fig. 3. Experimental setup of the variable rate LDPC-coded MB-OFDM UWBoF system.
J. He et al. / Optics Communications 350 (2015) 189–195
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Table 2 Some key parameters of LDPC-coded MB-OFDM UWB transceiver. Parameter
Value
Bandwidth (for one bands) LDPC code rate Modulation format IFFT/FFT size Cyclic prefix length Data/pilot/null subcarriers The location of pilot subcarriers Data bits per symbol Pilot bits per symbol The length of training sequence The number of MB-OFDM UWB symbols per frame The number of training sequence per MB-OFDM UWB frame DAC and ADC sampling rate Total bits per frame 64-QAM-Uncoded raw signal bit rate 64-QAM-Uncoded net signal bit rate
528 MHz 62.5%, 75%, 87.5% 64-QAM 128 Points 16 Points 100/12/6 [ 55 45 35 25 15 5 5 15 25 35 45 55] 100 6 Bits 12 2 Bits 144 Points 462 1
10.561 GSps (20 times oversampling) and 20 GSps
Fig. 5. The BER of three MB-OFDM UWB sub-bands for a fixed SSMF length of 100 km.
277,200 Bits log2(64-QAM) (1/312.5) 100¼1.92 Gbps 277,200/(463 165 20/10.561) ¼1.915 Gbps
In the paper, a Golay complementary TS-based symbol synchronization scheme is used to implement the symbol synchronization. According to Eq. (13), the timing synchronization metric of LDPC-coded MB-OFDM UWB signal is shown in Fig. 4(a). It can be seen that one strong peak of the timing synchronization metric is very obvious. The detailed impulse-shaped timing synchronization metric is shown in Fig. 4(b). As we can see from it, there is no any sidelobe interference around the strong peak of the timing synchronization metric. Moreover, the shape of the timing synchronization metric is very sharp. Therefore, the start point of LDPC-coded MB-OFDM UWB signal can be estimated accurately by using the Golay complementary TS-based symbol synchronization scheme. Fig. 5 shows the BER of three 64QAM-Uncoded MB-OFDM UWB sub-bands. At a BER of 1 10 3, for the three MB-OFDM UWB subbands, the required receiver optical power after 100 km SSMF transmission are –17.3 dBm for Band #1, 20.0 dBm for Band #2
Fig. 6. The BER of MB-OFDM UWB system using variable code rate LDPC versus received optical power after 100 km SSMF.
Fig. 4. Timing synchronization metric based on the Golay complementary TS scheme after 100 km SSMF: (a) the MB-OFDM UWB signal timing metric of the experiment data frame and (b) the detailed impulse-shaped timing metric.
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J. He et al. / Optics Communications 350 (2015) 189–195
64QAM-Uncoded, 21.6 dBm for 64QAM-LDPC with 87.5% code rate, –22.5 dBm for 64QAM-LDPC with 75% code rate and 23.2 dBm for 64QAM-LDPC with 62.5% code rate, respectively. Thus, the short block length LDPC coding provides a coding gain of 4.5 dB, 3.8 dB and 2.9 dB for a code rate of 62.5%, 75% and 87.5%, respectively. The experimental results show that short block length LDPC is effective for the MB-OFDM UWBoF system. The spectral efficiency (SE) based on the variable rate LDPC code with 64QAM and 16QAM modulation is shown in Fig. 7. According to Table 2, the SE can be expressed as [18]
SE =
Fig. 7. The spectral efficiency of 64QAM/16QAM MB-OFDM UWB system versus variable LDPC code rate.
and 20.6 dBm for Band #3, respectively. Comparing with Band #1, the power penalty of Band #3 is 3.3 dB. The loss of high frequency component in Band #3 is due to the low-pass filter effects. It is mainly caused by the electrical or optical devices, such as the roll-off of DAC and the limited bandwidth of AWG. The experimental results for different LDPC code rates in the MB-OFDM UWBoF system is shown in Fig. 6. At the BER of 1 10 3, after 100 km SSMF transmission, the required receive optical power of different LDPC code rates is 18.7 dBm for
Bit rateraw ⁎ log2M data subcarriers
Bandwidth⁎ OFDM subcarriers
⁎Code rate (15)
where the Bit rateraw is the raw signal rate, M is the modulation level. The bandwidth of the MB-OFDM UWB signal is528 MHz. In addition, the data sub-carriers and OFDM sub-carriers are 100 and 128, respectively. For the 64QAM, as the LDPC code rate are 62.5%, 75% and 87.5%, the corresponding SE are 2.903 bit/s/Hz, 3.484 bit/ s/Hz and 4.064 bit/s/Hz, respectively. For the 16QAM, as the LDPC code rate are 62.5%, 75% and 87.5%, the corresponding SE are 1.935 bit/s/Hz, 2.322 bit/s/Hz and 2.709 bit/s/Hz, respectively. Comparing to the 16QAM-LDPC [12], the SE of the MB-OFDM UWB signal with 64QAM-LDPC coded is about 1.5 times than that of the 16QAM-LDPC coded at the same coding rate. Moreover, 64QAMLDPC MB-OFDM UWB with 87.5% code rate has a high SE up to 4.064 bit/s/Hz. Fig. 8 shows the constellations of the 64QAM-Uncoded and 64QAM-LDPC with 75% code rate MB-OFDM UWB signals after 100 km SSMF transmission. For the 64QAM-Uncoded and 64QAMLDPC with 75% code rate MB-OFDM UWB signals, the
Fig. 8. The constellations of MB-OFDM UWB system after transmission over 100 km SSMF. (a) ROP ¼ –16 dBm, 64QAM-Uncoded, (b) ROP ¼ –20 dBm, 64QAM-Uncoded, (c) ROP¼–24 dBm, 64QAM-Uncoded, (d) ROP ¼ –16 dBm, 64QAM-LDPC (75%), (e) ROP ¼ –20 dBm, 64QAM-LDPC (75%), and (f) ROP ¼ -24 dBm, 64QAM-LDPC (75%).
J. He et al. / Optics Communications 350 (2015) 189–195
corresponding received optical power are –16 dBm, –20 dBm and –24 dBm, respectively. In addition, as the received optical power decreases, the constellation of the 64QAM-Uncoded and 64QAMLDPC with 75% code rate MB-OFDM UWB signals are obvious to deterioration. Meanwhile, the constellations of the 64QAM-Uncoded are shown in Fig. 8(a), (b) and (c). It can be seen that the EVMs [19] are 25.02 dB, 22.36 dB and 16.36 dB respectively. Moreover, as shown in Fig. 8(d), (e) and (f), for the constellations of 64QAM-LDPC with 75% code rate, the EVMs are 25.22 dB, 22.67 dB and 16.57 dB respectively. It shows that the degrade EVM performances are mainly due to the fiber dispersion-induced effects and the noise figure of EDFA.
4. Conclusion In this paper, a Golay complementary TS-based symbol synchronization scheme was proposed in the variable rate LDPC-coded MB-OFDM UWBoF system. Meanwhile, the coding gain and spectral efficiency in the variable rate LDPC-coded MB-OFDM UWBoF system were experimental investigated. After 100 km SSMF transmission, at the bit error rate of 1 10–3, the experimental results show that the short block length 64QAM-LDPC coding provides a coding gain of 4.5 dB, 3.8 dB and 2.9 dB for a code rate of 62.5%, 75% and 87.5%, respectively. In addition, for the 64QAM-LDPC, as the LDPC code rate are 62.5%, 75% and 87.5%, the corresponding spectral efficiency are 2.903 bit/s/Hz, 3.484 bit/s/Hz and 4.064 bit/s/Hz, respectively.
Acknowledgments This work is supported by the National Natural Science Foundation of China (61307087 and 61377079), and by the Fundamental Research Funds for the Central Universities and Young Teachers Program of Hunan University.
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
A Golay complementary TS-based symbol synchronization scheme in variable rate LDPC-coded MB-OFDM UWBoF system Jing He n, Xuejie Wen, Ming Chen, Lin Chen College of Computer Science and Electronic Engineering, Hunan University, Changsha, Hunan, China
art ic l e i nf o
a b s t r a c t
Article history: Received 21 January 2015 Received in revised form 15 March 2015 Accepted 4 April 2015 Available online 7 April 2015
In this paper, a Golay complementary training sequence (TS)-based symbol synchronization scheme is proposed and experimentally demonstrated in multiband orthogonal frequency division multiplexing (MB-OFDM) ultra-wideband over fiber (UWBoF) system with a variable rate low-density parity-check (LDPC) code. Meanwhile, the coding gain and spectral efficiency in the variable rate LDPC-coded MBOFDM UWBoF system are investigated. By utilizing the non-periodic auto-correlation property of the Golay complementary pair, the start point of LDPC-coded MB-OFDM UWB signal can be estimated accurately. After 100 km standard single-mode fiber (SSMF) transmission, at the bit error rate of 1 10 3, the experimental results show that the short block length 64QAM-LDPC coding provides a coding gain of 4.5 dB, 3.8 dB and 2.9 dB for a code rate of 62.5%, 75% and 87.5%, respectively. & 2015 Published by Elsevier B.V.
Keywords: Multiband orthogonal frequency-divisionmultiplexing (MB-OFDM) Ultra-wideband over fiber (UWBoF) system Low-density parity-check (LDPC) Golay complementary sequence
1. Introduction Due to the rapid growth of the communication capacity demand for wireless and mobile users, bandwidth requirements have been ever-increasing. Ultra-wideband (UWB) technology has some advantages such as low power and co-existence with other wireless services [1]. Thus it is recognized as a potential solution in wireless personal network and in-home network [2,3]. At present, orthogonal frequency division multiplexing (OFDM) [4] is a promising solution because of its robustness of multipath channels [5] and easily implementation based on fast Fourier transform (FFT) algorithms [6]. Therefore, multiband orthogonal frequency division multiplexing (MB-OFDM) UWB has paid more attention due to its high spectral efficiency, robust against multi-path effects and low power consumption [7]. However, the power spectral density of a MB-OFDM UWB signal regulated by the Federal Communications Commission (FCC) is constrained, so that the transmission distance of a MB-OFDM UWB signal is limited a few meters. To extend the area of coverage, MB-OFDM UWB signals over fiber (UWBoF) system are proposed and experimental investigated [8,9]. The MB-OFDM UWB signals based on external modulation can transmit over 40 km single-mode fiber (SMF) [9]. However, the received optical power is relatively higher. Recently, in the IEEE 802.15.3.c standard [10], the short block length low-density parityn
Corresponding author. E-mail addresses: [email protected], [email protected] (J. He).
http://dx.doi.org/10.1016/j.optcom.2015.04.012 0030-4018/& 2015 Published by Elsevier B.V.
check (LDPC) codes are proposed as a low complexity solution for impulse response (IR) UWB systems [11]. The short block length codes have good prospects of on chip implementation and commercialization. In addition, the short block length LDPC code based on the WiMAX 802.16e standard is proposed in the MB-OFDM UWB over fiber systems [12]. In this paper, for the first time to our knowledge, a Golay complementary training sequence (TS)-based symbol synchronization scheme is proposed in a variable rate LDPC-coded MBOFDM UWB over fiber system. By utilizing the non-periodic autocorrelation complementary property of the Golay complementary pair, the start point of LDPC-coded MB-OFDM UWB signal can be estimated accurately. After 100 km standard single-mode fiber (SSMF) transmission, at the bit error rate of 1 10 3, the short block length LDPC coding provides a coding gain of 4.5 dB, 3.8 dB and 2.9 dB for a code rate of 62.5%, 75% and 87.5%, respectively, when compared with un-coded MB-OFDM UWBoF system.
2. Principle 2.1. A Golay complementary TS-based symbol synchronization scheme In our previous work [12], a TS-based symbol synchronization scheme is proposed in LDPC-coded MB-OFDM UWBoF system. However, there are two sidelobes around the strong peak of the timing synchronization metric. In the paper, a Golay
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complementary TS-based symbol synchronization scheme is used to implement the symbol synchronization in a variable rate LDPCcoded MB-OFDM UWBoF system. The generation of Golay complementary pair of length 2″ is implemented [13]. Let A0 and B0 are Golay complementary pair of length N ¼2n, respectively. After interleaving between A0 and B0 , A and B can be generated as follows:
where k = 0, 1, 2, … , D − 1 is the delay time index, y (m) is the mth sample at the receiver, a [⋅] and b [⋅] are the transmitted Golay complementary pair A and B, respectively. To obtain the synchronization point, the timing metric is defined as
A = [a 0, ⋯, ar − 1 , b0 , ⋯, br − 1 , ar , ⋯, a2r − 1, br , ⋯, b2r − 1,
Z (m) =
⋯⋯, aN − r , ⋯, aN − 1 , bN − r , ⋯, bN − 1 ]
(1)
B = [a 0, ⋯, ar − 1 , − b0 , ⋯, − br − 1 , ar , ⋯, a2r − 1, − br , ⋯, − b2r − 1, ⋯⋯, aN − r , ⋯, aN − 1 , − bN − r , ⋯, − bN − 1 ]
(3)
D − 1− k
∑
a (j) ⁎a (j + k) (4)
j=0 D − 1− k
ACb, b (k) =
∑
b (j) ⁎b (j + k) (5)
j=0
Here, we utilize the non-periodic auto-correlation property of the Golay complementary pair [14]. The proposed preamble can be given by [15]
GolayTS = [ A O B O ]
(6)
where A and B are Golay complementary pair of length D, O is the zero-value sequence of length D. By using double slide windows spaced D, at the receiver, the non-periodic cross-correlation with Golay sequence A in the window 1 and B in the window 2 are performed at time m, it can be expressed as D − 1− k
A (m, k) =
∑ j=0
y (m + 2D + j) b (j + k) (8)
j=0
P (m) R (m)
(9)
where
P (m) = r (m, 0) 2
where ACa, a (k) and ACb, b (k) are the non-periodic auto-correlation of A and B, and it is given respectively by
ACa, a (k) =
∑
(2)
where r ∈ (1, 2, ⋯N), ak and bk are the kth value in the Golay complementary pair A0 and B0 , respectively. Assuming that A and B are Golay complementary pair of length D, respectively, they have the property [13]
⎧ 2D , k=0 ACa, a (k) + ACb, b (k) = ⎨ ⎩ 0, 1 ≤ k ≤ D − 1
D − 1− k
B (m, k) =
R (m) =
1 D−1
(10)
D−1
∑
r (m, k) 2
r (m, k) = A (m, k) + B (m, k)
(7)
(12)
As the sample point is corresponding to the maximum value of Z (m), and it is selected as timing synchronization point, then, the estimation of timing metric offset can be written as ∧
ε = arg max⋅(Z (m))
(13)
m
At the receiver, the digitalized signal is down-converted to the baseband signal with the corresponding TFC. Then, the blocks of MB-OFDM UWB symbols are send to the synchronization module. In the synchronization module, the synchronized signal is captured to pinpoint the start of FFT window and separate the training symbols and data symbols. The symbol synchronization scheme for MB-OFDM UWBoF system is shown in Fig. 1. Assuming that Golay complementary pair A and B are corresponding to window 1 and window 2, respectively, it can be expressed as
r (m, k) = A (m, k) + B (m, k) = h (k) ⊗ [x (m + k) ⊗ a ( − k) + x (m + 2D + k) ⊗ b ( − k)] + w (k) ⎡ D − 1− k = h (k) ⊗ ⎢ ∑ a (j) a (j + k) + ⎢⎣ j = 0
D − 1− k
∑ j=0
⎤ b (j) b (j + k) ⎥ ⎥⎦
+ w (k) = h (k) ⊗ [ACa, a (k) + ACb, b (k)] + w (k) = 2Dh (k) + w (k)
y (m + j) a (j + k)
(11)
k=1
(14)
where ⊗ denotes convolution operation, a ( − k) and b ( − k) are
Fig. 1. Symbol synchronization scheme of MB-OFDM UWBoF system.
J. He et al. / Optics Communications 350 (2015) 189–195
that HcT ¼0, where H is an(n − k) × nparity check matrix. Each of the parity-check matrices can be partitioned into square subblocks (sub-matrices) of size z × z (z = 21). These sub-matrices are either cyclic-permutations of the identity matrix or null (all-zero) sub-matrices. The cyclic-permutation matrix pi is obtained from the z × z identity matrix. It can be implemented by cyclically shifting the columns to the left by i elements. The matrix p0 is the z × z identity matrix. For example, the matrix permutation indices of parity-check matrices for 75% LDPC code rates are shown as follows:
the reflection of Golay sequence a (k) and b (k) respectively, h (k) is channel impulse response of the kth delay channel tap. w (k) is noise samples. Andx (m) is the mth sample at the transmitter. In this way, the timing metric have the impulsive value at the timing point.
2.2. The variable rate LDPC-coded MB-OFDM UWB transceiver Fig. 2 shows the block diagram of a variable rate LDPC-coded MB-OFDM UWB transmitter and receiver. At the MB-OFDM UWB transmitter, as shown in Fig. 2(a), a pseudo-random binary
⎡0 ⎢ ⎢− ⎢5 ⎢− H=⎢ ⎢− ⎢6 ⎢ ⎢− ⎢⎣18
− 18 0 − 5 − −
− 6 − 18 0 − 5
5 − − 6 − 18 0
− 7 − 0 16 − 18
18 − − 7 − 0 16
16 − 18 − − 7 −
− 0 16 − 18 − −
− 10 6 − 3 − −
− 2 − 10 6 − 3
3 − − 2 − 10 6
6
−
−
−
−
0
7
2
−
− 10 16 9
6 10 − − 0 − − − 16 9 − 20 3 0 10 − − 5 − − − 16 9 − − − 0 10 − − 2 9 − − 16 9 − − − 0 10 7 −
−
sequences (PRBSs) pattern is generated by offline Matlab. After the interleaver, the PRBSs are encoded based on the LDPC codes with the different code rate. The variable rate LDPC codes are based on the IEEE 802.15.3.c standard [10]. The LDPC code rates with forward error correction (FEC), LDPC information block lengths and LDPC codeword block lengths are described in Table 1. The LDPC encoder is systematic, i.e., it encodes an information block of size k, i ¼(i0, i1, …, i(k–1)), into a codeword c of size n, c ¼(i0, i1, …, i(k–1), p0, p1, …, p(n–k–1)), by adding n–k parity bits so
191
−
7 − − 20 5 − −
− 9 7 − − 20 5
5 − − 9 7 − −
− − 4 4 − 4 12 − − 4 4 − − 4 5 − 4 12 − − 4 4 − − − − − 4 12 19 − 4 4 − 10
9
− 20 12 −
−
4
10 − − 4 5 − −
− 19 10 − − − 5
5 − − 19 − − −
− 19 −
4
⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ 19 − ⎥ − 17 − 10 ⎥⎦
− − 19 − − − 7
− − − 10 − − −
− − − − − −
− − − − − −
where the integer i denotes the cyclic-permutation matrix pi. The ‘–’ denote null (all zero) sub-matrices. In this way, the PRBSs are encoded based on the variable rate LDPC codes by using the parity-check matrices H in IEEE 802.15.3.c standard. Then the LDPC coded sequences are fed to the mappers with 64-quadrature amplitude modulation (64-QAM). For the purpose of channel tracking, 12 sub-carriers are used to transmit pilot symbols in the transmitter. Then, 128-point inverse fast Fourier transforms (IFFT) function is used to realize OFDM modulation. After OFDM
Fig. 2. The block diagrams of the variable rate LDPC-coded MB-OFDM UWB transceiver: (a) transmitter and (b) receiver.
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3. Experimental setup and results
Table 1 The parameters of the irregular LDPC codes. LDPC code rate (%), RFEC
LDPC information block length (bits), Linf
LDPC codeword block length (bits), LFEC
62.5 75 87.5
420 504 588
672 672 672
modulation, the outputs of IFFT are scaled and clipped. In addition, a cyclic prefix of 16 samples is appended to the beginning of each 128 IFFT output samples. Subsequently, the baseband OFDM signal with LDPC code is digital up-conversion with time-frequency code (TFC) [7] to generate a LDPC-coded MB-OFDM UWB signal. In this way, at the transmitter, an MB-OFDM UWB frame consists of one Golay complementary TS and 462 MB-OFDM UWB symbols. Meanwhile, the Golay complementary TS is located at the beginning of OFDM signal frame. And it is used to realize symbol synchronization. At the MB-OFDM UWB receiver, as shown in Fig. 2(b), after SSMF transmission and optical/electrical conversion, the received electrical MB-OFDM UWB signal is converted into the digital signals by an analog-to-digital converter (ADC). The digitalized signal is further down-converted to the baseband signal with the corresponding TFC. Then the baseband signal is sent to the Golay complementary TS-based symbol synchronization module. Once symbol synchronization is implemented, a cyclic prefix at the beginning of the OFDM symbol is removed. In addition, 128-point FFT function is used to realize OFDM signal demodulation. The channel responses on every data sub-carriers can be estimated and compensated by using inserted pilot symbols [16]. Subsequently, the outputs of the 64-QAM demodulator are fed to a LDPC decoder and it is implemented based on the sum-product algorithm [17]. Meanwhile, the recovered bits are transmitted to the BER calculate function. And the count error bits are over a total of 100 462 6 ¼277,200 bits.
The experimental setup of the variable rate LDPC-coded optical MB-OFDM UWBoF system is shown in Fig. 3. At the transmitter, continuous wave (CW) light is generated from a commercial external cavity laser (ECL) source with 100 kHz line-width. Then, the CW light is injected into a single-drive Mach–Zehnder modulator (MZM), and a polarization controller (PC) is rotated to maximize the MZM output optical power. Meanwhile, the variable rate LDPCcoded MB-OFDM UWB signal is generated by offline Matlab, and then uploaded into a Tektronix Arbitrary Waveform Generator (AWG) operating at 10.561 GSps sampling rate, 10-bit digital-toanalog converter (DAC) resolution. The output MB-OFDM UWB signal with a peak-to-peak voltage (Vp-p) of about 560 mV is amplified to 1.6Vp-p by an electrical amplifier (EA) with 14 GHz bandwidth. Subsequently, the MZM is driven by the amplified electrical MB-OFDM UWB signal. The DC bias of MZM at negative quadrature point is 2.1 V. In this way, the optical MB-OFDM UWB signal is generated and then transmitted over 100 km SSMF. At the receiver, the EDFA is used to amplify the optical MBOFDM UWB signal. And a variable optical attenuator (VOA) is applied to adjust the received optical power for the measurement. The optical-to-electrical (O/E) conversion is implemented via PD with 3-dB bandwidth of 10-GHz. After the electrical low-pass filter (LPF) with a bandwidth of 5.5 GHz, a direct-current (DC) block is utilized to remove the DC component. In addition, the electrical MB-OFDM UWB signal is captured by a digital storage oscilloscope (DSO) with 20GSps sampling rate, 8-GHz bandwidth and 8-bit analog-to-digital converter (ADC) resolution. After the DSO, the electrical spectrum of MB-OFDM UWB signal is shown in Fig. 3. Subsequently, the captured signal is further processed by off-line digital signal processing. The off-line digital signal processing is as follows: firstly, the captured signal is resampled to 10.561 GSps and then digitally down-converted. Secondly, the electrical intermediate frequency MB-OFDM UWB signal is demodulated as MBOFDM UWB Receiver shown in Fig. 2(b). Finally, the LDPC-coded sequences are demapped into binary bits for bit error rate (BER) counting. In the experiment, some key parameters in the variable rate LDPC-coded MB-OFDM UWB transceiver are given in Table 2.
Fig. 3. Experimental setup of the variable rate LDPC-coded MB-OFDM UWBoF system.
J. He et al. / Optics Communications 350 (2015) 189–195
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Table 2 Some key parameters of LDPC-coded MB-OFDM UWB transceiver. Parameter
Value
Bandwidth (for one bands) LDPC code rate Modulation format IFFT/FFT size Cyclic prefix length Data/pilot/null subcarriers The location of pilot subcarriers Data bits per symbol Pilot bits per symbol The length of training sequence The number of MB-OFDM UWB symbols per frame The number of training sequence per MB-OFDM UWB frame DAC and ADC sampling rate Total bits per frame 64-QAM-Uncoded raw signal bit rate 64-QAM-Uncoded net signal bit rate
528 MHz 62.5%, 75%, 87.5% 64-QAM 128 Points 16 Points 100/12/6 [ 55 45 35 25 15 5 5 15 25 35 45 55] 100 6 Bits 12 2 Bits 144 Points 462 1
10.561 GSps (20 times oversampling) and 20 GSps
Fig. 5. The BER of three MB-OFDM UWB sub-bands for a fixed SSMF length of 100 km.
277,200 Bits log2(64-QAM) (1/312.5) 100¼1.92 Gbps 277,200/(463 165 20/10.561) ¼1.915 Gbps
In the paper, a Golay complementary TS-based symbol synchronization scheme is used to implement the symbol synchronization. According to Eq. (13), the timing synchronization metric of LDPC-coded MB-OFDM UWB signal is shown in Fig. 4(a). It can be seen that one strong peak of the timing synchronization metric is very obvious. The detailed impulse-shaped timing synchronization metric is shown in Fig. 4(b). As we can see from it, there is no any sidelobe interference around the strong peak of the timing synchronization metric. Moreover, the shape of the timing synchronization metric is very sharp. Therefore, the start point of LDPC-coded MB-OFDM UWB signal can be estimated accurately by using the Golay complementary TS-based symbol synchronization scheme. Fig. 5 shows the BER of three 64QAM-Uncoded MB-OFDM UWB sub-bands. At a BER of 1 10 3, for the three MB-OFDM UWB subbands, the required receiver optical power after 100 km SSMF transmission are –17.3 dBm for Band #1, 20.0 dBm for Band #2
Fig. 6. The BER of MB-OFDM UWB system using variable code rate LDPC versus received optical power after 100 km SSMF.
Fig. 4. Timing synchronization metric based on the Golay complementary TS scheme after 100 km SSMF: (a) the MB-OFDM UWB signal timing metric of the experiment data frame and (b) the detailed impulse-shaped timing metric.
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64QAM-Uncoded, 21.6 dBm for 64QAM-LDPC with 87.5% code rate, –22.5 dBm for 64QAM-LDPC with 75% code rate and 23.2 dBm for 64QAM-LDPC with 62.5% code rate, respectively. Thus, the short block length LDPC coding provides a coding gain of 4.5 dB, 3.8 dB and 2.9 dB for a code rate of 62.5%, 75% and 87.5%, respectively. The experimental results show that short block length LDPC is effective for the MB-OFDM UWBoF system. The spectral efficiency (SE) based on the variable rate LDPC code with 64QAM and 16QAM modulation is shown in Fig. 7. According to Table 2, the SE can be expressed as [18]
SE =
Fig. 7. The spectral efficiency of 64QAM/16QAM MB-OFDM UWB system versus variable LDPC code rate.
and 20.6 dBm for Band #3, respectively. Comparing with Band #1, the power penalty of Band #3 is 3.3 dB. The loss of high frequency component in Band #3 is due to the low-pass filter effects. It is mainly caused by the electrical or optical devices, such as the roll-off of DAC and the limited bandwidth of AWG. The experimental results for different LDPC code rates in the MB-OFDM UWBoF system is shown in Fig. 6. At the BER of 1 10 3, after 100 km SSMF transmission, the required receive optical power of different LDPC code rates is 18.7 dBm for
Bit rateraw ⁎ log2M data subcarriers
Bandwidth⁎ OFDM subcarriers
⁎Code rate (15)
where the Bit rateraw is the raw signal rate, M is the modulation level. The bandwidth of the MB-OFDM UWB signal is528 MHz. In addition, the data sub-carriers and OFDM sub-carriers are 100 and 128, respectively. For the 64QAM, as the LDPC code rate are 62.5%, 75% and 87.5%, the corresponding SE are 2.903 bit/s/Hz, 3.484 bit/ s/Hz and 4.064 bit/s/Hz, respectively. For the 16QAM, as the LDPC code rate are 62.5%, 75% and 87.5%, the corresponding SE are 1.935 bit/s/Hz, 2.322 bit/s/Hz and 2.709 bit/s/Hz, respectively. Comparing to the 16QAM-LDPC [12], the SE of the MB-OFDM UWB signal with 64QAM-LDPC coded is about 1.5 times than that of the 16QAM-LDPC coded at the same coding rate. Moreover, 64QAMLDPC MB-OFDM UWB with 87.5% code rate has a high SE up to 4.064 bit/s/Hz. Fig. 8 shows the constellations of the 64QAM-Uncoded and 64QAM-LDPC with 75% code rate MB-OFDM UWB signals after 100 km SSMF transmission. For the 64QAM-Uncoded and 64QAMLDPC with 75% code rate MB-OFDM UWB signals, the
Fig. 8. The constellations of MB-OFDM UWB system after transmission over 100 km SSMF. (a) ROP ¼ –16 dBm, 64QAM-Uncoded, (b) ROP ¼ –20 dBm, 64QAM-Uncoded, (c) ROP¼–24 dBm, 64QAM-Uncoded, (d) ROP ¼ –16 dBm, 64QAM-LDPC (75%), (e) ROP ¼ –20 dBm, 64QAM-LDPC (75%), and (f) ROP ¼ -24 dBm, 64QAM-LDPC (75%).
J. He et al. / Optics Communications 350 (2015) 189–195
corresponding received optical power are –16 dBm, –20 dBm and –24 dBm, respectively. In addition, as the received optical power decreases, the constellation of the 64QAM-Uncoded and 64QAMLDPC with 75% code rate MB-OFDM UWB signals are obvious to deterioration. Meanwhile, the constellations of the 64QAM-Uncoded are shown in Fig. 8(a), (b) and (c). It can be seen that the EVMs [19] are 25.02 dB, 22.36 dB and 16.36 dB respectively. Moreover, as shown in Fig. 8(d), (e) and (f), for the constellations of 64QAM-LDPC with 75% code rate, the EVMs are 25.22 dB, 22.67 dB and 16.57 dB respectively. It shows that the degrade EVM performances are mainly due to the fiber dispersion-induced effects and the noise figure of EDFA.
4. Conclusion In this paper, a Golay complementary TS-based symbol synchronization scheme was proposed in the variable rate LDPC-coded MB-OFDM UWBoF system. Meanwhile, the coding gain and spectral efficiency in the variable rate LDPC-coded MB-OFDM UWBoF system were experimental investigated. After 100 km SSMF transmission, at the bit error rate of 1 10–3, the experimental results show that the short block length 64QAM-LDPC coding provides a coding gain of 4.5 dB, 3.8 dB and 2.9 dB for a code rate of 62.5%, 75% and 87.5%, respectively. In addition, for the 64QAM-LDPC, as the LDPC code rate are 62.5%, 75% and 87.5%, the corresponding spectral efficiency are 2.903 bit/s/Hz, 3.484 bit/s/Hz and 4.064 bit/s/Hz, respectively.
Acknowledgments This work is supported by the National Natural Science Foundation of China (61307087 and 61377079), and by the Fundamental Research Funds for the Central Universities and Young Teachers Program of Hunan University.
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