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BPSK optical mm-wave signal generation by septupling frequency via a single optical phase modulator
Optics Communications 374 (2016) 69–74
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
BPSK optical mm-wave signal generation by septupling frequency via a single optical phase modulator Peng Wu, Jianxin Ma n State Key Laboratory of Information Photonics and Optical Communications, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
art ic l e i nf o
a b s t r a c t
Article history: Received 23 March 2016 Received in revised form 22 April 2016 Accepted 22 April 2016
In this paper, we have proposed a novel and simple scheme to generate the BPSK optical millimeter wave (MMW) signal with frequency septupling by using an optical phase modulator (PM) and a wavelength selective switch (WSS). In this scheme, the PM is driven by a radio frequency (RF) BPSK signal at the optimized modulation index of 4.89 to assure the 4th and 3rd-order sidebands have equal amplitudes. An wavelength selective switch (WSS) is used to abstract the 4th and þ 3rd-order sidebands from the spectrum generated by RF BPSK signal modulating the lightwave to form the BPSK optical MMW signal with frequency septupling the driving RF signal. In these two tones, only the þ3rd-order sideband bears the BPSK signal while the 4th-order sideband is unmodulated since the phase information is canceled by the even times multiplication of the phase of BPSK signal. The MMW signal can avoid the pulse walkoff effect and the amplitude fading effect caused by the fiber chromatic dispersion. By adjusting the modulation index to assure the two tones have equal amplitude, the generated optical MMW signal has the maximal opto-electrical conversion efficiency and good transmission performance. & 2016 Elsevier B.V. All rights reserved.
Keywords: Radio-over-fiber (RoF) Millimeter-wave (MMW) Phase modulator (PM) Frequency septupling
1. Introduction With the advent of the era of mobile internet, the need for the high-speed wireless access has increased quickly [1], low frequency microwave band becomes more and more congested and the millimeter-wave (MMW) becomes the most potential option to carry the high-speed data [2]. The inherent wide bandwidth of MMW enable it to carry the multi-gigabit signal [3], and enables the rapid growth of the broadband services in future. However, the coverage of the base station (BS) in the MMW wireless system is extremely limited for its serious propagation loss in the air and metal waveguide [4]. RoF technology transmits the MMW signal over the optical fiber by modulating it on the lightwave, and recovers it back to the electrical domain by PD in the remote base station. Due to the ultralow loss of the fiber, RoF extends the transmission distance greatly [5]. This makes RoF a promising support technology for the broadband wireless communication in MMW band. In the traditional RoF system with lithium niobium trioxide electro-optical modulator, the MMW vector signal is transported on the first-order sidebands linearly without frequency multiplication. Although deep modulation can realize the frequency n
Corresponding author. E-mail address: [email protected] (J. Ma).
http://dx.doi.org/10.1016/j.optcom.2016.04.057 0030-4018/& 2016 Elsevier B.V. All rights reserved.
multiplication, the amplitude and phase of the vector signal on higher-order sidebands are distorted and multiplicated, respectively, and this nonlinear transform makes the vector signal unable to directly recover linearly, and so pre-coding technology [6–12] is necessary to overcome these issues but at the cost of transmitter complexity. In [6–12], dual tone optical MMW signal are generated and transmitted over the SSMF, but the link is more vulnerable to the fiber dispersion since both tones carry the signal [13,14], and the pulse width of the signal carried by the MMW in photocurrent becomes narrow with the increase of the transmission length. In this paper, we propose a simple scheme to generate the BPSK optical mm-wave signal with frequency septupling via a single optical PM based on the nonlinear modulation of the lightwave along with a wavelength selective switch (WSS). After the lightwave is modulated by the RF BPSK signal with an optimized modulation index to maximize the 4th-order and þ 3rd-order sidebands, only the odd-order sidebands carry the BPSK signal while the even-order sidebands are unmodulated due to the phase information cancellation during the frequency multiplication. In the scheme, only the 4th-order sideband and þ3rd-order sideband are abstracted to form the optical mm-wave signal. Because only þ3rd-order sideband bears the BPSK signal, the optical mmwave signal suffers no pulse walk-off effect caused by the fiber chromatic dispersion as it is transmitted over the standard single mode fiber (SSMF) and the ROF link maintains good performance. The paper is organized as follows: in the Section 2, the
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principle of our proposed optical MMW signal generation scheme is described and the transmission performance along the single mode fiber is analyzed theoretically. In the Section 3, the simulation link is built up and the simulation results, including eye diagrams and BER curves, are given and discussed. Finally, a conclusion is drawn in Section 4.
phase cancellation. To generate a frequency multiplied BPSK optical MMW signal immune to both the fading effect and bit walkoff effect caused by the fiber dispersion, one odd-order and one even-order sideband are abstracted. In the proposed scheme, the þ3rd-order sideband and the 4th-order sideband are abstracted by wavelength selective switch (WSS) to generate the BPSK MMW signal with frequency septupling. The generated optical MMW signal can be expressed as
2. Principle
E s (t ) = Elaser
Fig. 1 shows the principle of the generation scheme of BPSK MMW signal with frequency septupling via a single optical PM. The BPSK signal carried by the LO at fs can be expressed as
It can be seen that the optical power of the generated optical MMW signal is proportional to J32(ξ)þJ42(ξ). According to the curve of [J32(ξ)þ J42(ξ)] shown in Fig. 2(b), the BPSK optical MMW signal gets the maximum power when ξ ¼4.6. But the maximum optical power of the optical MMW signal does not mean the MMW signal downconverted from it gets maximal since the magnitude of the generated MMW photocurrent depends on the beating product J3(ξ)J4(ξ) if the optical amplifier is not used. For the generated optical MMW signal with the modulation index of ξ, if a high-speed PD is used to detected the optical mm-wave signal, the photocurrent can be expressed as
VRF (t ) = VRF cos ⎡⎣ 2πfs t + φ (t ) ⎤⎦
(1)
where VRF and ϕ(t) are the amplitude and phase of the RF BPSK signal, respectively. For the BPSK signal, ϕ(t) ¼0 or π. The lightwave at fc from the CWLD can be expressed as
Elaser (t ) = Elaser exp ( j2πfc t ),
(2)
here Elaser is the amplitude of the lightwave. The lightwave is modulated by this RF BPSK signal via an optical PM with the halfwave voltage of Vπ. The modulated lightwave can be expressed as
Eout (t ) = Elaser k =∞
= Elaser
⎛ VRF cos ⎡⎣ 2πfs t + φ (t ) ⎤⎦ ⎞ ⎟⎟ exp ⎜⎜ j2πfc t + jπ Vπ ⎝ ⎠
jk Jk (ξ ) exp ⎡⎣ j2π ( fc + kfs ) t + jkφ (t ) ⎤⎦,
∑
(3)
k =−∞
where Jk( ) is the first kind Bessel function of order k and ξ ¼ πVRF/Vπ is the modulation index of the PM. It can be seen that the amplitude of the nth-order sideband depends on the Bessel function of order k, as given in Fig. 2(a), its frequency is shift from the optical carrier with the spacing of kfs, and its phase is k-fold of the driving RF signal. For the BPSK signal, since ϕ(t)¼0 or π, the even-order sidebands have phases of 0 or 2nπ, which means that the phase information of the BPSK signal is canceled; while the odd-order sidebands have the phase information of (2kþ1)ϕ(t) and still bears the BPSK signal since (2kþ1)ϕ(t) is equivalent to 0 for ϕ(t)¼0 and is equivalent to π for ϕ (t)¼ π, and the odd-sidebands carry the same phase as the driving RF BPSK signal. The modulated lightwave becomes ∞
j k Jk (ξ ) exp ⎡⎣ j2π fc + kfs t + jkφ (t ) ⎤⎦ k =−∞ ⎫ ∞ ⎧ j 2n J (ξ ) exp ⎡ j2π f + 2nf t + j2nφ (t ) ⎤ ⎪ ⎪ ⎣ ⎦ c s 2n ⎬ = Elaser ∑ ⎨ + ⎡ ⎤ n 2 1 ⎪ ⎪+ j J2n + 1 (ξ ) exp ⎣ j2π fc + (2n + 1) fs t + j (2n + 1) φ (t ) ⎦⎭ n =−∞ ⎩ ∞ ⎡ ⎤ ⎡ n = Elaser ∑ (−1) J2n (ξ ) exp ⎣ j2π fc + 2nfs t ⎦ + jJ2n + 1 (ξ ) exp ⎣ j2π fc + (2n + 1) fs t + jφ (t ) ⎤⎦ n =−∞ E out (t ) = Elaser
(
∑
)
(
)
(
{
(
)
)
(
)
} (4)
It is easy to see that only the odd-order sidebands bear the BPSK signal while the even-order sidebands do not due to the
Fig. 1. The principle of generation scheme of BPSK MMW signal by a single PM with frequency septupling. BPSK: binary phase shift keying; LO: local oscillator; CWLD: continuous wave light diode; PM: phase modulator; WSS: wavelength selective switch; EDFA: erbium doped fiber amplifier; SSMF: standard single mode fiber; PD: photoelectric detector.
{ −jJ3 (ξ) exp ⎡⎣ j 2π ( fc + 3fs ) t + jφ (t ) ⎤⎦ + J4 (ξ) exp ⎡⎣ j 2π ( fc − 4fs ) t ⎤⎦ }
2 IMMW (t ) = Elaser RJ3 (ξ ) J4 (ξ ) exp ⎡⎣ j2π⋅7fs t + jφ (t ) ⎤⎦
(5)
(6)
Where R is the sensitivity of the PD, and the magnitude of the MMW signal in the photocurrent is proportional to J3(ξ)J4(ξ) and gets maximum as ξ ¼ 4.7 according to the curve of the product |J3(ξ) J4(ξ)| in Fig. 2(c). The opto-electrical conversion efficiency of the RoF link depends on both the optical power and the beating product of the two optical tones, and is proportional to
η (ξ ) =
J3 (ξ )⋅J4 (ξ ) J32 (ξ ) + J42 (ξ )
.
(7)
Here we assure the sensitivity of the PD is 1. It can be seen that although the generated MMW signal gets maximum at 4.7, the optoelectrical conversion efficiency may be not if the two tones have different amplitudes. In the real RoF link, the absolute optical power of the optical MMW signal output from the optical modulator is not important since we can enhance it easily by an optical amplifier. What we take more care is the optoelectrical conversion efficiency, which means that the MMW signal photocurrent is maximized at a given power of the optical MMW signal. According to the optoelectrical conversion efficiency curve of the generated MMW signal photocurrent in Fig. 2(d), the maximum conversion efficiency is obtained as ξ ¼4.89, 6.98, and 8.70 where the two tones of the optical MMW signal, the 3rd-and 4th-order sidebands, have equal amplitude. But the two tones have relatively large while the other sidebands are relatively smaller only at ξ ¼4.89 according to the curve shown in the Fig. 2(d), namely VRF ¼1.56Vπ. However, in the real system, it is difficult to strictly set the modulation index at a precise value. The deviation of the modulation index from the optimum value would results in difference between the 4th-order sideband and þ3rd-order sideband, thus reduces the optoelectrical conversion efficiency due to the reduction of the amplitude of the generated MMW signal for a given received optical power. According to Fig. 2(d), it can be seen that the optoelectrical conversion efficiency is relatively flat aside the optimal modulation index of 4.89. When the modulation index is deviated from the optimal value to 5.39 and 4.39 with 70.5 deviation, the optoelectrical conversion efficiency is reduces by 0.5 dB and 0.27 dB only with the reduction from 0.5 to 0.472 and 0.485, respectively. So the performance of the generated vector mm-wave signal suffer little from the deviation of the modulation index and the system has good tolerance to the deviation of the modulation index.
P. Wu, J. Ma / Optics Communications 374 (2016) 69–74
J0(x) J1(x) J2(x)
(a) 4.89
0.8
J3(x) J4(x)
Jn (
)
J5(x)
0.4
(b)
0.2
0.1
0.0
0.0
-0.4 0
2
4
6
0
8
Modulation Index ( ) 0.15
4.6
0.3 J32 ( )+J42 ( )
1.2
71
4.7
(c)
(d)
2 4 6 Modulation Index ( ) 4.89
0.27dB
0.5dB
8
6.98
( )(A/W)
|J3( )*J4( )|
0.4 0.10
0.05
0.00
4.39-5.39
0.2
0.0 0
2
4
6
8
Modulation Index ( )
0
2
4
6
8
Modulation Index ( )
Fig. 2. (a) Bessel function of the first kind, (b) J32(ξ) þJ42(ξ) versus the modulation index, (c) |J3(ξ) J4(ξ)| versus the modulation index, (d) optoelectrical conversion efficiency versus the modulation index.
The generated BPSK optical MMW signal is amplified by an erbium doped fiber amplifier (EDFA) to enhance the launch optical power to the standard single mode fiber (SSMF). After being transmitted over the optical fiber with the amplitude attenuation coefficient of α and propagation constant of β(ω) at the frequency of fc, the signal can be expressed as ⎤ ⎡ ⎡ ⎥ ⎢ 3 ⎢ ⎥ ⎢ Elaser j J3 (ξ ) exp ⎢ j2π ( fc + 3fs ) ⎣ ⎥ ⎢ ⎥ ⎢ ⎛ E (z , t ) = e −αz ⎢ β ( fc + 3fs ) ⎞ ⎤ ⎥ ⎥ ⎜⎜ t − ⎟⎟ β φ t j f f z j z − + + 3 ( ) c s ⎥ ⎢ fc + 3fs ⎠ ⎥⎦ ⎝ ⎥ ⎢ ⎢ −4 ⎡ ⎤⎥ ⎢⎣ + Elaser j J−4 (ξ ) exp ⎣ j2π ( fc − 4fs ) t − jβ ( fc − 4fs ) z ⎦ ⎥⎦
(8)
Two tones of the transmitted signal beat with each other in the square-law PD, after filtering, the MMW photocurrent from the PD is abstracted and can be expressed as ⎡ 2π⋅7f t − β ( f + 3f ) z + β ( f − 4f ) z ⎤ s c s c s ⎥ ⎢ 2 ⎥ ⎛ iMMW (z, t ) = e−2αzElaser μJ3 (ξ ) J−4 (ξ ) cos ⎢ β ( fc + 3fs ) ⎞ ⎥ ⎢ + φ ⎜⎜ t − z ⎟⎟ ⎥⎦ ⎢⎣ fc + 3fs ⎠ ⎝
(9)
where μ is the sensitivity of the PD. It can be seen that the down converted BPSK MMW signal suffers no bit walk-off effect due to the fiber chromatic dispersion, and only the power reduces with the increase of the transmission distance due to the fiber loss.
3. Simulation setup and results To verify our theoretical analysis, the RoF link with the frequency-septupling BPSK MMW signal generation is built on the simulation platform, as shown in Fig. 1. The lightwave from the CWLD at the frequency of 193.1 THz with an optical power of 8.5 dBm and the linewidth of 1 MHz, Then the linewidth will be set at 0.1 MHz and 10 MHz to verify the influence of the linewidth. The lightwave is modulated by the 10 GHz MMW with 3 Gbps
BPSK signal mapped from pseudo-random binary sequence (PRBS) with the word length of 212 1 via a PM with the half-wave voltage of 4 V. According to our theoretical deduction above, the amplitude of MMW BPSK signal is set to 6.22 V to assure that the modulation index of PM is 4.89, the optical spectrum of the output lightwave is shown in Fig. 3(a). it can be seen that the 73rd and 74th order sidebands have a relative larger power than the other and the 74th order sidebands has a much narrow linewidth since the BPSK signal is canceled by their phase four-folded. Then, an interleaver at the frequency of 193.06 THz with the frequency spacing of 35 GHz and bandwidth of 6 GHz, is used to abstract the þ3rd-order and 4th-order sidebands, the spectrum of the generated optical MMW signal is shown in Fig. 3(b). It can be seen that the other tones are at least 25 dB smaller than the two main tones after filtering. Before injecting into the SSMF, the optical MMW signal is amplified to 4.65 dBm by an EDFA with optical signal to noise ratio (OSNR) of 35 dB. The SSMF with the attenuation coefficient of 0.2 dB/km, the chromatic dispersion of 16.75 ps/nm km, dispersion slope of 0.075 ps/nm2 km and PMD coefficient of 0.5 ps/km1/2. After fiber transmission, the optical MMW signal are injected into the square-law PD with the sensitivity of 1 A/W, and the two tones beat with each other and generate the MMW BPSK signal at 70 GHz and a direct current (DC) with the spectrum shown in Fig. 3(c). The other harmonics at 10 GHz, 20 GHz, 40 GHz, 60 GHz, 80 GHz, and 90 GHz have much small amplitude with at least 10 GHz away from the main tone, and can be further suppressed as the 70 GHz MMW BPSK signal is coherently demodulated by a 70 GHz local oscillator with a low pass filter. To verify the influence of the modulation index on the received optical power of the PD without optical amplifier. The BER versus the modulation index from 3 to 6 is calculated at the BtB case with the laser linewidth of 0.1 MHz and the power of 8.5 dBm, and then the generated optical MMW signal is attenuated fixedly by 15 dB via an attenuator, the relationships between the BER and the received optical power and the modulation index without optical amplification are shown in the Fig. 4(a). It can be seen that the
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Fig. 3. (a) Optical spectrum after phase modulator, (b) optical spectrum after filtering by an IL, and (c) RF spectrum of the generated mm-wave signal after PD.
received optical power curve is in accord with that of J32(ξ)þ J42(ξ) in the Fig. 2(b). The BER gets its minimum due to the maximum signal to noise ratio (SNR) since the MMW photocurrent gets its maximum at the modulation index of 4.7 although the received optical power gets maximal at the modulation index of 4.6. But the minimum BER appears at the modulation index of 4.7 since the SNR is maximized at the point. The simulation results match well with our theoretical deduction. Whereafter, the influence of the optoelectrical conversion efficiency on this system is tested, the BER versus the modulation index from 3 to 6 is calculated at the BtB case with the laser linewidth of 0.1 MHz. A tunable optical attenuator is used to assure the received optical power by the PD is fixed at 10 dBm. The BER versus the modulation index curve along with the received optical power is shown in the Fig. 4(b). It can be seen that the BER gets its minimum as the optoelectrical conversion efficiency gets its maximum at the modulation index of 4.89. For a given received optical power, higher conversion efficiency makes the generated MMW signal get higher in the photocurrent, namely, the SNR gets maximal as the optoelectrical conversion efficiency is maximal for a given received optical power. So the optimum modulation index is 4.89 in the simulation case, where the two tones of the optical MMW signal have equal amplitude according to the theoretical analysis above. According to Fig. 4(b), when the modulation index is deviated from the optimum to 4.39 and 5.39, the BER increases from 4e 10 to 1.3e 9 and 5e 8, respectively. The link performance degradation attributes to the reduction of the mm-wave signal photocurrent. These agree well with our theoretical
-10.0
log10(BER)
-4 -10.5 -6 -11.0
-11.5 -10 3.5
4.0 4.5 5.0 Modulation Index
5.5
6.0
(b)
-6
4.89
-4
-8
-5 -10
-6 4.39-5.39
-7 -8 -9
-10 3.0
3.5
-12
0.5dB
-8
-3
0.27dB
4.7
-14 4.0
4.5
5.0
5.5
Received Optical Power (dBm)
-2
4.6
log10(BER)
(a)
Received Optical Power (dBm)
-2
analysis. Then, the transmission performance of the generated frequency septupling optical BPSK MMW signal are checked. The BERs versus the received optical power is calculated with different laser linewidth and different transmission distance, the BER curves are shown in Fig. 5. From Fig. 5, it is clear to see that the BER curves are overlapped together at OBtB case with the three different laser linewidth and the error free transmission (BER o1e–9) [15–17] are achieved at the received optical power of 10.13 dBm since the laser linewidth has no impact on the generated BPSK optical MMW signal. The transmission penalty of the BPSK optical MMW signal increase with the increase of the fiber length and the laser linewidth. The transmission power penalties of the simulation configuration with different laser linewidth and fiber transmission distance are summarized in Table 1. The BPSK optical MMW signal with the linewidth of less than 1 MHz can maintain the transmission penalty below 1 dBm even after 50 km transmission over SSMF. While larger laser linewidth makes the RoF link more sensitive to the increase of the fiber length, and the transmission penalty increases to 3.57 dB as the transmission distance reaches 50 km with the laser linewidth of 10 MHz, for the heavier phase noise caused by the wider laser linewidth. Meanwhile, the eye diagrams of the BPSK signal coherently demodulated from the 70 GHz MMW signals are observed with 1 MHz linewidth at BtB case, and after 30, 40 and 50 km SSMF transmission at the received optical power of 10 dBm, as shown in the Fig. 5(a)–(d), respectively. It can be seen that although the opening of the eye diagrams reduces with the increase of the
6.0
Modulation Index
Fig. 4. (a) BER versus the modulation index while the received optical power is controlled by the modulation index and (b) the BER versus the modulation index from 3 to 6 at a given received optical power of 10 dBm.
P. Wu, J. Ma / Optics Communications 374 (2016) 69–74
73
-2
log10(BER)
-4 OBtB-0.1MHz OBtB-1.0MHz OBtB-10MHz 30km-0.1MHz 30km-1.0MHz 30km-10MHz 40km-0.1MHz 40km-1.0MHz 40km-10MHz 50km-0.1MHz 50km-1.0MHz 50km-10MHz
-6
-8
-10
-12
-14
-14
(d) (b) (a)
-12
(c)
-10
-8
-6
Received Optical Power (dBm) Fig. 5. The BER versus the received optical power of the BPSK optical mm-wave signal at OBtB case, and after 30, 40 and 50 km SSMF transmissions with different laser linewidth. Insert: the eye diagrams of the BPSK signal demodulated from the optical MMW signal with the laser linewidth of 1 MHz after different SSMF transmissions.
transmission distance, the eye width keeps constant. This attributes to the factor that the influence of the fiber dispersion is greatly reduced for only one tone bearing the BPSK signal. As for the opening height reduction, it is caused by the increasing phase noise and the transmission loss. These agree well with our theoretical analysis. The maximum SSMF transmission distances are further explored. With the increase of the fiber length, the received mmwave signal degrades. The MMW signals with the linewidth of 0.1 MHz, 1 MHz and 10 MHz can obtain their maximum error free SSMF transmission (BER o1e–9) distance of 74.2 km, 73.8 km and 61.7 km with the received optical power of 9.8 dBm, 9.74 dBm and 7.3 dBm, respectively. For the case with the laser linewidth of 10 MHz, the BER reaches after 70 km fiber transmission, which is above the error free limit of 1e–9.
4. Conclusion An optical mm-wave generation scheme by photonic frequency septupling technology with a single PM has been proposed and successfully demonstrated. The tones which transmit over the SSMF are abstracted by an IL from the spectrum generated by RF BPSK signal modulating the lightwave. Since only one tone bears the BPSK signal and another tone is unmodulated for the phase cancellation of the even-order sideband, the generated optical MMW signal has high dispersion tolerance for only one tone bearing the BPSK signal. By adjusting the modulation index, these two tones can have equal amplitude to make a maximal Table 1 The power penalty (dB) of the RoF link with different laser linewidth and fiber transmission distance at BER of 1e–9. Transmission length (km)
30 40 50
Laser linewidth (MHz) 0.1
1.0
10.0
0.2 dBm 0.2 dBm 0.5 dBm
0.2 dBm 0.3 dBm 0.7 dBm
1.2 dBm 1.2 dBm 3.6 dBm
optoelectrical conversion efficiency in the PD. The BER curves, eye diagrams and optoelectrical conversion efficiency curve are obtained by simulation, and the simulation results show the good performance of our proposed scheme.
Acknowledgments This work was supported inpart by Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, Beijing, China) with the Grant: IPOC2015ZT09.
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
BPSK optical mm-wave signal generation by septupling frequency via a single optical phase modulator Peng Wu, Jianxin Ma n State Key Laboratory of Information Photonics and Optical Communications, School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
art ic l e i nf o
a b s t r a c t
Article history: Received 23 March 2016 Received in revised form 22 April 2016 Accepted 22 April 2016
In this paper, we have proposed a novel and simple scheme to generate the BPSK optical millimeter wave (MMW) signal with frequency septupling by using an optical phase modulator (PM) and a wavelength selective switch (WSS). In this scheme, the PM is driven by a radio frequency (RF) BPSK signal at the optimized modulation index of 4.89 to assure the 4th and 3rd-order sidebands have equal amplitudes. An wavelength selective switch (WSS) is used to abstract the 4th and þ 3rd-order sidebands from the spectrum generated by RF BPSK signal modulating the lightwave to form the BPSK optical MMW signal with frequency septupling the driving RF signal. In these two tones, only the þ3rd-order sideband bears the BPSK signal while the 4th-order sideband is unmodulated since the phase information is canceled by the even times multiplication of the phase of BPSK signal. The MMW signal can avoid the pulse walkoff effect and the amplitude fading effect caused by the fiber chromatic dispersion. By adjusting the modulation index to assure the two tones have equal amplitude, the generated optical MMW signal has the maximal opto-electrical conversion efficiency and good transmission performance. & 2016 Elsevier B.V. All rights reserved.
Keywords: Radio-over-fiber (RoF) Millimeter-wave (MMW) Phase modulator (PM) Frequency septupling
1. Introduction With the advent of the era of mobile internet, the need for the high-speed wireless access has increased quickly [1], low frequency microwave band becomes more and more congested and the millimeter-wave (MMW) becomes the most potential option to carry the high-speed data [2]. The inherent wide bandwidth of MMW enable it to carry the multi-gigabit signal [3], and enables the rapid growth of the broadband services in future. However, the coverage of the base station (BS) in the MMW wireless system is extremely limited for its serious propagation loss in the air and metal waveguide [4]. RoF technology transmits the MMW signal over the optical fiber by modulating it on the lightwave, and recovers it back to the electrical domain by PD in the remote base station. Due to the ultralow loss of the fiber, RoF extends the transmission distance greatly [5]. This makes RoF a promising support technology for the broadband wireless communication in MMW band. In the traditional RoF system with lithium niobium trioxide electro-optical modulator, the MMW vector signal is transported on the first-order sidebands linearly without frequency multiplication. Although deep modulation can realize the frequency n
Corresponding author. E-mail address: [email protected] (J. Ma).
http://dx.doi.org/10.1016/j.optcom.2016.04.057 0030-4018/& 2016 Elsevier B.V. All rights reserved.
multiplication, the amplitude and phase of the vector signal on higher-order sidebands are distorted and multiplicated, respectively, and this nonlinear transform makes the vector signal unable to directly recover linearly, and so pre-coding technology [6–12] is necessary to overcome these issues but at the cost of transmitter complexity. In [6–12], dual tone optical MMW signal are generated and transmitted over the SSMF, but the link is more vulnerable to the fiber dispersion since both tones carry the signal [13,14], and the pulse width of the signal carried by the MMW in photocurrent becomes narrow with the increase of the transmission length. In this paper, we propose a simple scheme to generate the BPSK optical mm-wave signal with frequency septupling via a single optical PM based on the nonlinear modulation of the lightwave along with a wavelength selective switch (WSS). After the lightwave is modulated by the RF BPSK signal with an optimized modulation index to maximize the 4th-order and þ 3rd-order sidebands, only the odd-order sidebands carry the BPSK signal while the even-order sidebands are unmodulated due to the phase information cancellation during the frequency multiplication. In the scheme, only the 4th-order sideband and þ3rd-order sideband are abstracted to form the optical mm-wave signal. Because only þ3rd-order sideband bears the BPSK signal, the optical mmwave signal suffers no pulse walk-off effect caused by the fiber chromatic dispersion as it is transmitted over the standard single mode fiber (SSMF) and the ROF link maintains good performance. The paper is organized as follows: in the Section 2, the
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principle of our proposed optical MMW signal generation scheme is described and the transmission performance along the single mode fiber is analyzed theoretically. In the Section 3, the simulation link is built up and the simulation results, including eye diagrams and BER curves, are given and discussed. Finally, a conclusion is drawn in Section 4.
phase cancellation. To generate a frequency multiplied BPSK optical MMW signal immune to both the fading effect and bit walkoff effect caused by the fiber dispersion, one odd-order and one even-order sideband are abstracted. In the proposed scheme, the þ3rd-order sideband and the 4th-order sideband are abstracted by wavelength selective switch (WSS) to generate the BPSK MMW signal with frequency septupling. The generated optical MMW signal can be expressed as
2. Principle
E s (t ) = Elaser
Fig. 1 shows the principle of the generation scheme of BPSK MMW signal with frequency septupling via a single optical PM. The BPSK signal carried by the LO at fs can be expressed as
It can be seen that the optical power of the generated optical MMW signal is proportional to J32(ξ)þJ42(ξ). According to the curve of [J32(ξ)þ J42(ξ)] shown in Fig. 2(b), the BPSK optical MMW signal gets the maximum power when ξ ¼4.6. But the maximum optical power of the optical MMW signal does not mean the MMW signal downconverted from it gets maximal since the magnitude of the generated MMW photocurrent depends on the beating product J3(ξ)J4(ξ) if the optical amplifier is not used. For the generated optical MMW signal with the modulation index of ξ, if a high-speed PD is used to detected the optical mm-wave signal, the photocurrent can be expressed as
VRF (t ) = VRF cos ⎡⎣ 2πfs t + φ (t ) ⎤⎦
(1)
where VRF and ϕ(t) are the amplitude and phase of the RF BPSK signal, respectively. For the BPSK signal, ϕ(t) ¼0 or π. The lightwave at fc from the CWLD can be expressed as
Elaser (t ) = Elaser exp ( j2πfc t ),
(2)
here Elaser is the amplitude of the lightwave. The lightwave is modulated by this RF BPSK signal via an optical PM with the halfwave voltage of Vπ. The modulated lightwave can be expressed as
Eout (t ) = Elaser k =∞
= Elaser
⎛ VRF cos ⎡⎣ 2πfs t + φ (t ) ⎤⎦ ⎞ ⎟⎟ exp ⎜⎜ j2πfc t + jπ Vπ ⎝ ⎠
jk Jk (ξ ) exp ⎡⎣ j2π ( fc + kfs ) t + jkφ (t ) ⎤⎦,
∑
(3)
k =−∞
where Jk( ) is the first kind Bessel function of order k and ξ ¼ πVRF/Vπ is the modulation index of the PM. It can be seen that the amplitude of the nth-order sideband depends on the Bessel function of order k, as given in Fig. 2(a), its frequency is shift from the optical carrier with the spacing of kfs, and its phase is k-fold of the driving RF signal. For the BPSK signal, since ϕ(t)¼0 or π, the even-order sidebands have phases of 0 or 2nπ, which means that the phase information of the BPSK signal is canceled; while the odd-order sidebands have the phase information of (2kþ1)ϕ(t) and still bears the BPSK signal since (2kþ1)ϕ(t) is equivalent to 0 for ϕ(t)¼0 and is equivalent to π for ϕ (t)¼ π, and the odd-sidebands carry the same phase as the driving RF BPSK signal. The modulated lightwave becomes ∞
j k Jk (ξ ) exp ⎡⎣ j2π fc + kfs t + jkφ (t ) ⎤⎦ k =−∞ ⎫ ∞ ⎧ j 2n J (ξ ) exp ⎡ j2π f + 2nf t + j2nφ (t ) ⎤ ⎪ ⎪ ⎣ ⎦ c s 2n ⎬ = Elaser ∑ ⎨ + ⎡ ⎤ n 2 1 ⎪ ⎪+ j J2n + 1 (ξ ) exp ⎣ j2π fc + (2n + 1) fs t + j (2n + 1) φ (t ) ⎦⎭ n =−∞ ⎩ ∞ ⎡ ⎤ ⎡ n = Elaser ∑ (−1) J2n (ξ ) exp ⎣ j2π fc + 2nfs t ⎦ + jJ2n + 1 (ξ ) exp ⎣ j2π fc + (2n + 1) fs t + jφ (t ) ⎤⎦ n =−∞ E out (t ) = Elaser
(
∑
)
(
)
(
{
(
)
)
(
)
} (4)
It is easy to see that only the odd-order sidebands bear the BPSK signal while the even-order sidebands do not due to the
Fig. 1. The principle of generation scheme of BPSK MMW signal by a single PM with frequency septupling. BPSK: binary phase shift keying; LO: local oscillator; CWLD: continuous wave light diode; PM: phase modulator; WSS: wavelength selective switch; EDFA: erbium doped fiber amplifier; SSMF: standard single mode fiber; PD: photoelectric detector.
{ −jJ3 (ξ) exp ⎡⎣ j 2π ( fc + 3fs ) t + jφ (t ) ⎤⎦ + J4 (ξ) exp ⎡⎣ j 2π ( fc − 4fs ) t ⎤⎦ }
2 IMMW (t ) = Elaser RJ3 (ξ ) J4 (ξ ) exp ⎡⎣ j2π⋅7fs t + jφ (t ) ⎤⎦
(5)
(6)
Where R is the sensitivity of the PD, and the magnitude of the MMW signal in the photocurrent is proportional to J3(ξ)J4(ξ) and gets maximum as ξ ¼ 4.7 according to the curve of the product |J3(ξ) J4(ξ)| in Fig. 2(c). The opto-electrical conversion efficiency of the RoF link depends on both the optical power and the beating product of the two optical tones, and is proportional to
η (ξ ) =
J3 (ξ )⋅J4 (ξ ) J32 (ξ ) + J42 (ξ )
.
(7)
Here we assure the sensitivity of the PD is 1. It can be seen that although the generated MMW signal gets maximum at 4.7, the optoelectrical conversion efficiency may be not if the two tones have different amplitudes. In the real RoF link, the absolute optical power of the optical MMW signal output from the optical modulator is not important since we can enhance it easily by an optical amplifier. What we take more care is the optoelectrical conversion efficiency, which means that the MMW signal photocurrent is maximized at a given power of the optical MMW signal. According to the optoelectrical conversion efficiency curve of the generated MMW signal photocurrent in Fig. 2(d), the maximum conversion efficiency is obtained as ξ ¼4.89, 6.98, and 8.70 where the two tones of the optical MMW signal, the 3rd-and 4th-order sidebands, have equal amplitude. But the two tones have relatively large while the other sidebands are relatively smaller only at ξ ¼4.89 according to the curve shown in the Fig. 2(d), namely VRF ¼1.56Vπ. However, in the real system, it is difficult to strictly set the modulation index at a precise value. The deviation of the modulation index from the optimum value would results in difference between the 4th-order sideband and þ3rd-order sideband, thus reduces the optoelectrical conversion efficiency due to the reduction of the amplitude of the generated MMW signal for a given received optical power. According to Fig. 2(d), it can be seen that the optoelectrical conversion efficiency is relatively flat aside the optimal modulation index of 4.89. When the modulation index is deviated from the optimal value to 5.39 and 4.39 with 70.5 deviation, the optoelectrical conversion efficiency is reduces by 0.5 dB and 0.27 dB only with the reduction from 0.5 to 0.472 and 0.485, respectively. So the performance of the generated vector mm-wave signal suffer little from the deviation of the modulation index and the system has good tolerance to the deviation of the modulation index.
P. Wu, J. Ma / Optics Communications 374 (2016) 69–74
J0(x) J1(x) J2(x)
(a) 4.89
0.8
J3(x) J4(x)
Jn (
)
J5(x)
0.4
(b)
0.2
0.1
0.0
0.0
-0.4 0
2
4
6
0
8
Modulation Index ( ) 0.15
4.6
0.3 J32 ( )+J42 ( )
1.2
71
4.7
(c)
(d)
2 4 6 Modulation Index ( ) 4.89
0.27dB
0.5dB
8
6.98
( )(A/W)
|J3( )*J4( )|
0.4 0.10
0.05
0.00
4.39-5.39
0.2
0.0 0
2
4
6
8
Modulation Index ( )
0
2
4
6
8
Modulation Index ( )
Fig. 2. (a) Bessel function of the first kind, (b) J32(ξ) þJ42(ξ) versus the modulation index, (c) |J3(ξ) J4(ξ)| versus the modulation index, (d) optoelectrical conversion efficiency versus the modulation index.
The generated BPSK optical MMW signal is amplified by an erbium doped fiber amplifier (EDFA) to enhance the launch optical power to the standard single mode fiber (SSMF). After being transmitted over the optical fiber with the amplitude attenuation coefficient of α and propagation constant of β(ω) at the frequency of fc, the signal can be expressed as ⎤ ⎡ ⎡ ⎥ ⎢ 3 ⎢ ⎥ ⎢ Elaser j J3 (ξ ) exp ⎢ j2π ( fc + 3fs ) ⎣ ⎥ ⎢ ⎥ ⎢ ⎛ E (z , t ) = e −αz ⎢ β ( fc + 3fs ) ⎞ ⎤ ⎥ ⎥ ⎜⎜ t − ⎟⎟ β φ t j f f z j z − + + 3 ( ) c s ⎥ ⎢ fc + 3fs ⎠ ⎥⎦ ⎝ ⎥ ⎢ ⎢ −4 ⎡ ⎤⎥ ⎢⎣ + Elaser j J−4 (ξ ) exp ⎣ j2π ( fc − 4fs ) t − jβ ( fc − 4fs ) z ⎦ ⎥⎦
(8)
Two tones of the transmitted signal beat with each other in the square-law PD, after filtering, the MMW photocurrent from the PD is abstracted and can be expressed as ⎡ 2π⋅7f t − β ( f + 3f ) z + β ( f − 4f ) z ⎤ s c s c s ⎥ ⎢ 2 ⎥ ⎛ iMMW (z, t ) = e−2αzElaser μJ3 (ξ ) J−4 (ξ ) cos ⎢ β ( fc + 3fs ) ⎞ ⎥ ⎢ + φ ⎜⎜ t − z ⎟⎟ ⎥⎦ ⎢⎣ fc + 3fs ⎠ ⎝
(9)
where μ is the sensitivity of the PD. It can be seen that the down converted BPSK MMW signal suffers no bit walk-off effect due to the fiber chromatic dispersion, and only the power reduces with the increase of the transmission distance due to the fiber loss.
3. Simulation setup and results To verify our theoretical analysis, the RoF link with the frequency-septupling BPSK MMW signal generation is built on the simulation platform, as shown in Fig. 1. The lightwave from the CWLD at the frequency of 193.1 THz with an optical power of 8.5 dBm and the linewidth of 1 MHz, Then the linewidth will be set at 0.1 MHz and 10 MHz to verify the influence of the linewidth. The lightwave is modulated by the 10 GHz MMW with 3 Gbps
BPSK signal mapped from pseudo-random binary sequence (PRBS) with the word length of 212 1 via a PM with the half-wave voltage of 4 V. According to our theoretical deduction above, the amplitude of MMW BPSK signal is set to 6.22 V to assure that the modulation index of PM is 4.89, the optical spectrum of the output lightwave is shown in Fig. 3(a). it can be seen that the 73rd and 74th order sidebands have a relative larger power than the other and the 74th order sidebands has a much narrow linewidth since the BPSK signal is canceled by their phase four-folded. Then, an interleaver at the frequency of 193.06 THz with the frequency spacing of 35 GHz and bandwidth of 6 GHz, is used to abstract the þ3rd-order and 4th-order sidebands, the spectrum of the generated optical MMW signal is shown in Fig. 3(b). It can be seen that the other tones are at least 25 dB smaller than the two main tones after filtering. Before injecting into the SSMF, the optical MMW signal is amplified to 4.65 dBm by an EDFA with optical signal to noise ratio (OSNR) of 35 dB. The SSMF with the attenuation coefficient of 0.2 dB/km, the chromatic dispersion of 16.75 ps/nm km, dispersion slope of 0.075 ps/nm2 km and PMD coefficient of 0.5 ps/km1/2. After fiber transmission, the optical MMW signal are injected into the square-law PD with the sensitivity of 1 A/W, and the two tones beat with each other and generate the MMW BPSK signal at 70 GHz and a direct current (DC) with the spectrum shown in Fig. 3(c). The other harmonics at 10 GHz, 20 GHz, 40 GHz, 60 GHz, 80 GHz, and 90 GHz have much small amplitude with at least 10 GHz away from the main tone, and can be further suppressed as the 70 GHz MMW BPSK signal is coherently demodulated by a 70 GHz local oscillator with a low pass filter. To verify the influence of the modulation index on the received optical power of the PD without optical amplifier. The BER versus the modulation index from 3 to 6 is calculated at the BtB case with the laser linewidth of 0.1 MHz and the power of 8.5 dBm, and then the generated optical MMW signal is attenuated fixedly by 15 dB via an attenuator, the relationships between the BER and the received optical power and the modulation index without optical amplification are shown in the Fig. 4(a). It can be seen that the
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Fig. 3. (a) Optical spectrum after phase modulator, (b) optical spectrum after filtering by an IL, and (c) RF spectrum of the generated mm-wave signal after PD.
received optical power curve is in accord with that of J32(ξ)þ J42(ξ) in the Fig. 2(b). The BER gets its minimum due to the maximum signal to noise ratio (SNR) since the MMW photocurrent gets its maximum at the modulation index of 4.7 although the received optical power gets maximal at the modulation index of 4.6. But the minimum BER appears at the modulation index of 4.7 since the SNR is maximized at the point. The simulation results match well with our theoretical deduction. Whereafter, the influence of the optoelectrical conversion efficiency on this system is tested, the BER versus the modulation index from 3 to 6 is calculated at the BtB case with the laser linewidth of 0.1 MHz. A tunable optical attenuator is used to assure the received optical power by the PD is fixed at 10 dBm. The BER versus the modulation index curve along with the received optical power is shown in the Fig. 4(b). It can be seen that the BER gets its minimum as the optoelectrical conversion efficiency gets its maximum at the modulation index of 4.89. For a given received optical power, higher conversion efficiency makes the generated MMW signal get higher in the photocurrent, namely, the SNR gets maximal as the optoelectrical conversion efficiency is maximal for a given received optical power. So the optimum modulation index is 4.89 in the simulation case, where the two tones of the optical MMW signal have equal amplitude according to the theoretical analysis above. According to Fig. 4(b), when the modulation index is deviated from the optimum to 4.39 and 5.39, the BER increases from 4e 10 to 1.3e 9 and 5e 8, respectively. The link performance degradation attributes to the reduction of the mm-wave signal photocurrent. These agree well with our theoretical
-10.0
log10(BER)
-4 -10.5 -6 -11.0
-11.5 -10 3.5
4.0 4.5 5.0 Modulation Index
5.5
6.0
(b)
-6
4.89
-4
-8
-5 -10
-6 4.39-5.39
-7 -8 -9
-10 3.0
3.5
-12
0.5dB
-8
-3
0.27dB
4.7
-14 4.0
4.5
5.0
5.5
Received Optical Power (dBm)
-2
4.6
log10(BER)
(a)
Received Optical Power (dBm)
-2
analysis. Then, the transmission performance of the generated frequency septupling optical BPSK MMW signal are checked. The BERs versus the received optical power is calculated with different laser linewidth and different transmission distance, the BER curves are shown in Fig. 5. From Fig. 5, it is clear to see that the BER curves are overlapped together at OBtB case with the three different laser linewidth and the error free transmission (BER o1e–9) [15–17] are achieved at the received optical power of 10.13 dBm since the laser linewidth has no impact on the generated BPSK optical MMW signal. The transmission penalty of the BPSK optical MMW signal increase with the increase of the fiber length and the laser linewidth. The transmission power penalties of the simulation configuration with different laser linewidth and fiber transmission distance are summarized in Table 1. The BPSK optical MMW signal with the linewidth of less than 1 MHz can maintain the transmission penalty below 1 dBm even after 50 km transmission over SSMF. While larger laser linewidth makes the RoF link more sensitive to the increase of the fiber length, and the transmission penalty increases to 3.57 dB as the transmission distance reaches 50 km with the laser linewidth of 10 MHz, for the heavier phase noise caused by the wider laser linewidth. Meanwhile, the eye diagrams of the BPSK signal coherently demodulated from the 70 GHz MMW signals are observed with 1 MHz linewidth at BtB case, and after 30, 40 and 50 km SSMF transmission at the received optical power of 10 dBm, as shown in the Fig. 5(a)–(d), respectively. It can be seen that although the opening of the eye diagrams reduces with the increase of the
6.0
Modulation Index
Fig. 4. (a) BER versus the modulation index while the received optical power is controlled by the modulation index and (b) the BER versus the modulation index from 3 to 6 at a given received optical power of 10 dBm.
P. Wu, J. Ma / Optics Communications 374 (2016) 69–74
73
-2
log10(BER)
-4 OBtB-0.1MHz OBtB-1.0MHz OBtB-10MHz 30km-0.1MHz 30km-1.0MHz 30km-10MHz 40km-0.1MHz 40km-1.0MHz 40km-10MHz 50km-0.1MHz 50km-1.0MHz 50km-10MHz
-6
-8
-10
-12
-14
-14
(d) (b) (a)
-12
(c)
-10
-8
-6
Received Optical Power (dBm) Fig. 5. The BER versus the received optical power of the BPSK optical mm-wave signal at OBtB case, and after 30, 40 and 50 km SSMF transmissions with different laser linewidth. Insert: the eye diagrams of the BPSK signal demodulated from the optical MMW signal with the laser linewidth of 1 MHz after different SSMF transmissions.
transmission distance, the eye width keeps constant. This attributes to the factor that the influence of the fiber dispersion is greatly reduced for only one tone bearing the BPSK signal. As for the opening height reduction, it is caused by the increasing phase noise and the transmission loss. These agree well with our theoretical analysis. The maximum SSMF transmission distances are further explored. With the increase of the fiber length, the received mmwave signal degrades. The MMW signals with the linewidth of 0.1 MHz, 1 MHz and 10 MHz can obtain their maximum error free SSMF transmission (BER o1e–9) distance of 74.2 km, 73.8 km and 61.7 km with the received optical power of 9.8 dBm, 9.74 dBm and 7.3 dBm, respectively. For the case with the laser linewidth of 10 MHz, the BER reaches after 70 km fiber transmission, which is above the error free limit of 1e–9.
4. Conclusion An optical mm-wave generation scheme by photonic frequency septupling technology with a single PM has been proposed and successfully demonstrated. The tones which transmit over the SSMF are abstracted by an IL from the spectrum generated by RF BPSK signal modulating the lightwave. Since only one tone bears the BPSK signal and another tone is unmodulated for the phase cancellation of the even-order sideband, the generated optical MMW signal has high dispersion tolerance for only one tone bearing the BPSK signal. By adjusting the modulation index, these two tones can have equal amplitude to make a maximal Table 1 The power penalty (dB) of the RoF link with different laser linewidth and fiber transmission distance at BER of 1e–9. Transmission length (km)
30 40 50
Laser linewidth (MHz) 0.1
1.0
10.0
0.2 dBm 0.2 dBm 0.5 dBm
0.2 dBm 0.3 dBm 0.7 dBm
1.2 dBm 1.2 dBm 3.6 dBm
optoelectrical conversion efficiency in the PD. The BER curves, eye diagrams and optoelectrical conversion efficiency curve are obtained by simulation, and the simulation results show the good performance of our proposed scheme.
Acknowledgments This work was supported inpart by Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications, Beijing, China) with the Grant: IPOC2015ZT09.
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