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Performance comparison of optical single-sideband modulation in RoF link
Optics Communications 463 (2020) 125409
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Performance comparison of optical single-sideband modulation in RoF link Yuancheng Cai, Xiang Gao, Yun Ling ∗, Bo Xu, Kun Qiu Key Laboratory of Optical Fiber Sensing and Communications (Ministry of Education), University of Electronic Science and Technology of China, Chengdu, 611731, China
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Keywords: Radio over fiber (RoF) Single-sideband (SSB) Signal-to-signal beating interference (SSBI) Modulation
ABSTRACT In this paper, three different single-sideband (SSB) modulation schemes, based on the dual drive Mach–Zehnder modulator (DD-MZM), IQ-MZM operating in push–push and push–pull modes respectively, are theoretically analyzed and validated by simulation in 60 GHz RoF link. The simulation results are well in accordance with the theoretical predictions. For the low-cost DD-MZM SSB scheme, a high optimal carrier signal power ratio (CSPR) results in low receiving sensitivity and the evident susceptibility of SSB form to the direct current (DC) drift are the main shortcomings. Instead, although suffering from the same high optimal CSPR issue for the push–push IQ-MZM SSB scheme, a wide tolerance to the DC drift as well as a low power loss of the modulator can be provided at the expense of cost. In addition, by adjusting the DC bias difference applied to the MZMs in conjunction with the Kramers–Kronig algorithm for signal-to-signal beating interference cancellation, the push–pull IQ-MZM SSB scheme can reduce the optimal CSPR by more than 3 dB and also provide 5 dB improvement in receiver sensitivity, as compared with the previous two SSB schemes. The analyses and results presented in this paper can provide a deep insight on improving the performance for the SSB RoF links.
1. Introduction With the explosive growth of wireless communication capacity, the frequency of radio communication continues to increase. In the recent decade, 60 GHz radio over fiber (RoF) solution has been highlighted for high data transmission capacity because of the 7-GHz license-free bandwidth from 57 to 64 GHz [1–4]. In order to improve the transmission performance of high-frequency (such as 60 GHz and above) radio frequency (RF) signals, the optical fiber enabling the characteristics of high bandwidth, low delay and immunity to electromagnetic interference, is consistently advocated to replace the conventional coaxial cable for RF signals transmission. However, for traditional doublesideband (DSB) signal in RoF system, the frequency selective power fading caused by the interaction of fiber chromatic dispersion and the square-law detection, is a serious problem that must be dealt with [5]. As has been proven, single-sideband (SSB) transmission exhibits excellent resistance to power fading effect, as well as high spectral efficiency, hence it has attracted much attention of researchers [6–9]. For the optical SSB transmission systems, three different electrooptic modulators are commonly used for optical SSB signal generation. One is the general intensity modulator (IM) in conjunction with an optical filter. The IM is used to yield an optical DSB signal, then the optical SSB signal is produced by suppressing the undesired sideband via an optical filter [10–12]. The main advantage of the setup resides in its simple principle, whereas drawbacks come in that either an appropriate guard band (GB) between the optical carrier and the sideband signal or
a sharp optical filter is required to ensure SSB filtering performance. Unlike the IM based SSB scheme which relies on additional device, the dual drive Mach–Zehnder modulator (DD-MZM) or the MZM-based IQ modulator driven by a pair of Hilbert transform (HT) signals can directly generate a quasi-ideal gapless optical SSB signal under small signal modulation condition, just by controlling the modulator’s direct current (DC) bias voltage [9,13,14]. Many literatures have presented comprehensive mathematical analyses [13,15,16] and experimental verifications [17,18] on the two optical SSB modulation schemes. Nevertheless, research works on the optical SSB generation via IQ-MZM are mainly focused on push–pull mode, whereas rare relevant results for the push–push mode [19]. On the other hand, the signal-to-signal beating interference (SSBI) is an important limitation for the performance of such systems. Though the SSBI can be overcome via a sufficient GB [14, 15,18] or special SSBI elimination techniques [13,17], no detailed investigations on the difference between the three types of SSB schemes and how much impact of their respective SSBIs on system performance have been conducted? In this paper, three types of SSB modulation schemes and the corresponding performances in 60 GHz RoF link are studied and compared in detail. One is the DD-MZM SSB scheme and the other two are the IQ-MZM (which is composed of two DD-MZMs instead of the two single-electrode MZMs) SSB schemes operating in either push–push or push–pull modes [19]. The thorough analyses on the condition of SSB generation, the carrier signal power ratio (CSPR) control measures,
∗ Corresponding author. E-mail address: [email protected] (Y. Ling).
https://doi.org/10.1016/j.optcom.2020.125409 Received 17 December 2019; Received in revised form 26 January 2020; Accepted 28 January 2020 Available online 31 January 2020 0030-4018/© 2020 Elsevier B.V. All rights reserved.
Y. Cai, X. Gao, Y. Ling et al.
Optics Communications 463 (2020) 125409
Fig. 1. Simplified schematic architecture of the optical SSB RoF link based on optical heterodyne detection technique (Ignore fiber and wireless transmission links here for simplicity). LD, laser diode; Mod., modulator; OC, optical coupler; PC, polarization controller; LO, local oscillator; PD, photodiode; BPF, band-pass filter. Red lines indicate the optical links and purple lines indicate the electrical links. . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the impact of modulator’s DC drift and SSBI are performed based on the above three SSB schemes. The optimal parameters of three SSB schemes, such as DC bias difference applied to the modulator and CSPR of the SSB signal, are analyzed and given. This optimal parameters are obtained by a compromise between the nonlinear distortion (NLD) terms caused by the modulator, SSBI resulted from the square-law detection, and additive Gaussian white noise (AWGN) originated from the transmission channel. What’s more, the similarities and differences between the three SSB schemes and how much impact does SSBI have on the performance of the respective systems are compared in detail. They are theoretically analyzed and validated by simulations in 60-GHz RoF link. The simulation results are well in accordance with the theoretical predictions. Numerical analyses and simulation verifications show that: (1) the DD-MZM SSB scheme offers low cost, but its high optimal CSPR results in low receiving sensitivity and the SSB form is susceptible to DC drift. (2) The push–push IQ-MZM SSB scheme suffers from the same high optimal CSPR problem, however, not only a low power loss of the modulator but also a good tolerance to the DC drift, can be provided at the expense of cost. (3) Unlike the above two SSB schemes whose CSPRs are exclusively adjusted by the optical modulation index (OMI), the CSPR of the push–pull IQ-MZM SSB scheme can be jointly controlled via the OMI and the DC bias difference applied to the MZM, which effectively helps to reduce the optimal CSPR. Moreover, the push–pull IQ-MZM SSB scheme combined with the Kramers–Kronig (KK) algorithm [20] for SSBI cancellation, the performance is significantly improved. As compared with the other two SSB schemes, this scheme can reduce the optimal CSPR from above 10 dB to about 7 dB, and also provides 5 dB improvement in the required received optical power (ROP) at the bit error rate (BER) of 3.8 × 10−3 for 5 Gbaud 16-QAM signal after 100 km fiber transmission. The analyses and results presented in this paper can provide a deep insight on improving the performance for the SSB RoF links. The rest of this paper is organized as follows. Section 2 introduces the theoretical models and analyses of the three SSB schemes in RoF link. Simulation verification and results discussion are shown in Section 3. In the last Section, the main conclusions are given accordingly.
performed using a power detector which consists of a square-law device and a low-pass filtering (LPF). Subsequently, the obtained signal is demodulated through digital signal processing (DSP) after sampled by the analog–digital converter (ADC). Suppose that s(t ) is the information-bearing complex baseband signal shaped by the Nyquist pulse with a full bandwidth of B. An electric SSB signal can be obtained by frequency shifting operation, i.e., 𝑠𝑆𝑆𝐵 (𝑡) = 𝑠 (𝑡) exp (𝑗𝜋𝐵𝑡), whose imaginary part is the HT of the real part of the signal [21]. Note that no frequency gap is reserved. The pair of HT signals can be given as [ ] 𝐼 (𝑡) = 𝑟𝑒𝑎𝑙 𝑠𝑆𝑆𝐵 (𝑡) , [ ] (1) 𝑄 (𝑡) = 𝑖𝑚𝑎𝑔 𝑠𝑆𝑆𝐵 (𝑡) = 𝐻𝑇 [𝐼 (𝑡)] , where real[X ] and imag [X ] are the operations that take the real part and imaginary parts of X, respectively. Assume that the transmitter and local oscillator (LO) light are respectively √ [ ( )] (2) 𝐸𝑐 (𝑡) = 𝑃𝑐 exp 𝑗 2𝜋𝑓𝑐 𝑡 + 𝜑𝑐 (𝑡) , √ [ ( )] 𝐸𝐿𝑂 (𝑡) = 𝑃𝐿𝑂 exp 𝑗 2𝜋𝑓𝐿𝑂 𝑡 + 𝜑𝐿𝑂 (𝑡) , (3) where 𝑃𝑐 , 𝑓𝑐 and 𝜑𝑐 (t) are the optical power, central frequency and phase noise of the lightwave from the transmitter laser source and 𝑃𝐿𝑂 , 𝑓𝐿𝑂 and 𝜑𝐿𝑂 (t) are the optical power, central frequency and phase noise of the LO lightwave, respectively. Driven by a pair of HT signals, a single DD-MZM or IQ-MZM is used to generate the quasi-ideal optical SSB-C signal. Later, the modulated optical signal is coupled with the LO light followed by a single-ended PD which can model as 𝐼𝑃 𝐷 (𝑡) = 𝑅 ⋅ ||𝐸𝑠 (𝑡) + 𝐸𝐿𝑂 (𝑡)|| = 𝐼𝐵𝑎𝑠𝑒𝑏𝑎𝑛𝑑 (𝑡) + 𝐼𝑅𝐹 (𝑡) , 2
(4)
2 2 where 𝐼𝐵𝑎𝑠𝑒𝑏𝑎𝑛𝑑 (𝑡) = 𝑅 ⋅ ||𝐸𝐿𝑂 (𝑡)|| + 𝑅 ⋅ ||𝐸𝑠 (𝑡)|| and 𝐼𝑅𝐹 (𝑡) = 2𝑅 ⋅ [ ] 𝑟𝑒𝑎𝑙 𝐸𝑠 (𝑡) 𝐸𝐿𝑂 ∗ (𝑡) are located at the baseband and the RF band, respectively. R denotes the responsivity of the PD. Since the main purpose in this paper is to study the RF signal for RoF link, the baseband signal is not the key point to be discussed in subsequent analysis. It is worth noting that a polarization controller (PC) is required to adjust the polarization direction of the LO light to be consistent with the signal light, so as to obtain the best performance from the beating of two beams [22,23]. The central frequency of the obtained RF component is equal to the difference between the two lasers’ central frequencies. Note that the generated RF signal contains the sum of two laser phase noises. Therefore, the square-law-based power detection can be used at the receiving end to complete the frequency down-conversion while removing the phase noise through modulo operation. Since the mathematical expression of the optical SSB-C signal 𝐸𝑠 (t) depends on the modulation method, the theoretical models of SSB generation via the DD-MZM and IQ-MZM are given in what follows.
2. Theoretical model and analysis The simplified schematic architecture of the optical SSB RoF link based on optical heterodyne detection technique is shown in Fig. 1. For concision purpose, the fiber and wireless transmission links are omitted here. The optical SSB with carrier (SSB-C) modulation is performed via an electro-optic modulator, whose schematic diagram will be given later. After fiber transmission, the transmitted quasi-ideal optical SSB-C signal is converted into an electrical signal by optical heterodyne beating detection, which can also complete the frequency up-conversion to RF. The desired up-converted RF signal can be obtained via a bandpass filter (BPF) from the detected photocurrent of the photodiode (PD). After the RF signal arriving the receiving end through a pair of antennas and the wireless channel, frequency down-conversion is
2.1. DD-MZM SSB modulation Fig. 2(a) shows the schematic diagram of the DD-MZM. It consists of two phase modulators, two RF inputs and two DC bias inputs. When 2
Y. Cai, X. Gao, Y. Ling et al.
Optics Communications 463 (2020) 125409
Fig. 2. Schematic diagrams of the DD-MZM and IQ-MZM. (a) DD-MZM. (b) IQ-MZM operating in push–push mode. (c) IQ-MZM operating in push–pull mode. PM, phase modulator; inv, inverse.
the form of 𝑠𝑆𝑆𝐵 (𝑡) = 𝐼 (𝑡) + 𝑗𝑄 (𝑡) (Only considering the right sideband signal [25] in this paper). For simplicity, let 𝑉𝑏𝑖𝑎𝑠1 = −𝑉𝜋 ∕2, 𝑉𝑏𝑖𝑎𝑠2 = 0, which means the DD-MZM is biased at the quadrature transmission point (QTP), then Eq. (5) can be rewritten as [ ( ( )) ] 1 𝐸𝑠 (𝑡) = 𝐸𝑐 (𝑡) ⋅ exp 𝑗𝑚 𝐼 (𝑡) − 𝑉𝜋 ∕2 + exp (𝑗𝑚 (𝑄 (𝑡))) 2 (6) [ ( )] 1 1 ≈ 𝐸𝑐 (𝑡) ⋅ (1 − 𝑗) + 𝑚 ⋅ 𝑠𝑆𝑆𝐵 (𝑡) − 𝑚2 ⋅ 𝑂 𝑋 2 . 2 2 It can be seen that when small signal modulation allows all NLDs to be ignored, the electric SSB signal is linearly mapped to the optical domain with an extra carrier term 1 − j. The CSPR of the obtained quasi-ideal optical SSB-C can be given as 𝐶𝑆𝑃 𝑅 = 10 × log
𝑃𝑐𝑎𝑟𝑟𝑖𝑒𝑟 |1 − 𝑗|2 2 = 10 × log . = 10 × log 𝑃𝑠𝑖𝑔𝑛𝑎𝑙 𝜋 2 ⋅ 𝑂𝑀𝐼 2 |𝑚𝜎|2
(7)
Eq. (7) shows that the only way to control the CSPR for the DD-MZM SSB scheme is to adjust the OMI. Although a smaller OMI guarantees a more ideal optical SSB signal, it results in a larger CSPR, where the carrier occupies most of the energy leading to low AWGN tolerance and low receiver sensitivity. By substituting Eq. (6) to Eq. (4), the resultant RF component can be expressed as
Fig. 3. Typical transmission function curves for the DDMZM operating in push– pull mode. V (t ) is the phase shift caused by the driving voltage. MATP, maximum transmission point; MITP, minimum transmission point; QTP, quadrature transmission point;.
the upper and lower arms of the DD-MZM are driven by the abovementioned HT signal pair, the output of the DD-MZM can be expressed as [24]
𝐼𝑅𝐹 (𝑡) = 𝑀 ⋅ [sin (𝛥𝜓 (𝑡) + 𝑚𝐼 (𝑡)) + cos (𝛥𝜓 (𝑡) + 𝑚𝑄 (𝑡))] , (8) √ ( ) where 𝑀 = 𝑅 𝑃𝑐 𝑃𝐿𝑂 , 𝛥𝜓 (𝑡) = 2𝜋 𝑓𝑐 − 𝑓𝐿𝑂 𝑡 + 𝜑𝑐 (𝑡) − 𝜑𝐿𝑂 (𝑡) corresponds to RF carrier from heterodyne beating but contains laser phase noise from two unrelated laser sources. Finally, the output of power detector is given as follows
[ ( ( )) ( ( ))] 1 𝐸 (𝑡) ⋅ exp 𝑗𝑚 𝐼 (𝑡) + 𝑉𝑏𝑖𝑎𝑠1 + exp 𝑗𝑚 𝑄 (𝑡) + 𝑉𝑏𝑖𝑎𝑠2 2 𝑐 { [ ] 1 ≈ 𝐸𝑐 (𝑡) ⋅ 𝐴1 + 𝐴2 + 𝑚 𝑗𝐴1 ⋅ 𝐼 (𝑡) + 𝐴2 ⋅ 𝑗𝑄 (𝑡) 2 ( )} 1 − 𝑚2 ⋅ 𝑂 𝑋 2 , 2
𝐸𝑠 (𝑡) =
⎫ ⎧1 + sin [𝑚 (𝐼 (𝑡) − 𝑄 (𝑡))] ⎪ + sin [2𝛥𝜓 (𝑡) + 𝑚𝐼 (𝑡) + 𝑚𝑄 (𝑡)] |𝐼𝑅𝐹 (𝑡)|2 = 𝑀 2 ⋅ ⎪ ⎬ ⎨ | | 1 1 ⎪− cos [2𝛥𝜓 (𝑡) + 2𝑚𝐼 (𝑡)] + cos [2𝛥𝜓 (𝑡) + 2𝑚𝑄 (𝑡)]⎪ ⎭ ⎩ 2 2 ∝ 𝑀 2 ⋅ {1 + sin [𝑚 (𝐼 (𝑡) − 𝑄 (𝑡))]} { ( )} 1 ≈ 𝑀 2 ⋅ 1 + 𝑚 [𝐼 (𝑡) − 𝑄 (𝑡)] − 𝑚3 ⋅ 𝑂 𝑋 3 . 6
(5) ( ) ( ) where 𝐴1 = exp 𝑗𝑚𝑉𝑏𝑖𝑎𝑠1 , 𝐴2 = exp 𝑗𝑚𝑉𝑏𝑖𝑎𝑠2 , 𝑚 = 𝜋∕𝑉𝜋 is a constant with 𝑉𝜋 denoting the half-wave voltage of the DD-MZM. ( ) 𝑂 𝑋 2 describes the second-order NLD after using Taylor expansion, the third-order and above NLDs have been omitted. The NLDs are derived from the nonlinear transmission function of the DD-MZM. The typical transmission function curves for the DDMZM operating in push– pull mode are shown in Fig. 3. It can be seen that the closer to the minimum transmission point (MITP) where has the smallest output power, the more linear field signal modulation which means the smaller NLDs can be obtained. Suppose 𝜎 is the standard deviation of the ( ) zero-mean electric SSB signal, 𝑠𝑆𝑆𝐵 (𝑡), it is equal to 𝑉𝑖𝑛 𝑅𝑀𝑆 , the root-mean-square (RMS) amplitude of the electrical input to the DD( ) MZM. Then the OMI, defined as 𝑂𝑀𝐼 = 𝑉𝑖𝑛 𝑅𝑀𝑆 ∕𝑉𝜋 = 𝜎∕𝑉𝜋 , actually reflects the signal modulation depth. From Eq. (5), it can be inferred that two conditions must be met to produce an optical SSB signal. One is that the OMI must be small enough to guarantee that the higher-order NLDs which scale with (𝑚𝜎)𝑛 (𝑛 = 2, 3, 4, …) can be ignored. The other is keeping 𝑗𝐴1 = 𝐴2 , i.e., 𝑉𝑏𝑖𝑎𝑠1 +𝑉𝜋 ∕2 = 𝑉𝑏𝑖𝑎𝑠2 to produce a SSB signal in
(9) It can be seen that a LPF can be used to remove the high frequency terms from square-law detection containing the laser phase noise. In the remaining signal, only the third-order and above SSBIs exist after Taylor expansion. In the case of m < 1 and small OMI for small signal modulation, the third-order SSBI can almost be ignored because of its much smaller coefficient than that of the desired first-order term. Afterwards, the Hilbert superposition cancellation (HSC) method [26] can be used to restore the I (t ) and Q(t ). Therefore, using DD-MZM biased at the QTP to generate SSB signal, a situation almost no SSBI is presented after the square-law detection. However, in order to achieve more ideal SSB form, a small OMI should be used to reduce the NLDs of the DD-MZM, hence inevitably leads to a large CSPR according to Eq. (7), which will limit the system performance. 3
Y. Cai, X. Gao, Y. Ling et al.
Optics Communications 463 (2020) 125409
SSBI terms can be neglected with small signal modulation. Of course, the same disadvantages such as high optimal CSPR which will limit the system performance still exist.
2.2. Push–push IQ-MZM SSB modulation Fig. 2(b) shows the schematic diagram of the IQ-MZM operating in push–push mode. It consists of one 90-degree phase shifter and two DD-MZMs, as well as two RF inputs and two DC bias inputs. According to the output expression of the DD-MZM in Ref. [24], the output of the push–push IQ-MZM which driven by a pair of HT signals can be expressed as √ ) 2( 𝐸𝑢𝑝𝑝𝑒𝑟−𝐷𝐷𝑀𝑍𝑀 + 𝑗𝐸𝑙𝑜𝑤𝑒𝑟−𝐷𝐷𝑀𝑍𝑀 𝐸𝑠 (𝑡) = 2 [ ] (10) = 𝐵1 𝐵2 ⋅ 𝐸𝑐 (𝑡) ⋅ exp (𝑗𝑚𝐼 (𝑡)) + 𝑗 exp (𝑚𝑄 (𝑡)) [ ] ( ) 1 ≈ 𝐵1 𝐵2 ⋅ 𝐸𝑐 (𝑡) ⋅ (1 + 𝑗) + 𝑗𝑚 ⋅ 𝑠𝑠𝑠𝑏 (𝑡) − 𝑚2 ⋅ 𝑂 𝑋 2 , 2 ( ) ( ) where 𝐵1 = cos 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 , 𝐵2 = exp 𝑗𝑚𝑉𝑠𝑢𝑚 ∕2 . 𝑉𝑑𝑖𝑓 𝑓 = 𝑉𝑏𝑖𝑎𝑠1 − 𝑉𝑏𝑖𝑎𝑠2 and 𝑉𝑠𝑢𝑚 = 𝑉𝑏𝑖𝑎𝑠1 +𝑉𝑏𝑖𝑎𝑠2 are the difference and sum of the two DC biases applied to the DD-MZM, respectively. The second-order and above NLDs can also be ignored under small signal modulation condition. It can be found that the electric SSB signal is linearly mapped to the optical domain with a carrier term 1 + j, as long as the IQ-MZM is not biased at the MITP, where 𝑉𝑑𝑖𝑓 𝑓 = ±𝑉𝜋 , 𝐵1 = 0. The CSPR of the obtained approximate optical SSB-C can be given as
2.3. Push–pull IQ-MZM SSB modulation Fig. 2(c) shows the schematic diagram of the IQ-MZM operating in push–pull mode, which is different from the push–push mode in that the RF inputs of the lower arm of each DD-MZM are inverted [19]. Also driven by a pair of HT signals, the output of the push–pull IQ-MZM can be expressed as [24] √ ) 2( 𝐸𝑠 (𝑡) = 𝐸𝑢𝑝𝑝𝑒𝑟−𝐷𝐷𝑀𝑍𝑀 + 𝑗𝐸𝑙𝑜𝑤𝑒𝑟−𝐷𝐷𝑀𝑍𝑀 2 [ ( ) ( )] = 𝐵2 𝐸𝑐 (𝑡) ⋅ cos 𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 + 𝑗 ⋅ cos 𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 [ ] ( ) 1 ≈ 𝐵2 𝐸𝑐 (𝑡) ⋅ 𝐵1 (1 + 𝑗) + 𝐶1 𝑚 ⋅ 𝑠𝑠𝑠𝑏 (𝑡) − 𝑚2 𝐵1 ⋅ 𝑂 𝑋 2 , 2 (14) ( ) where 𝐶1 = − sin 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 . Note that the optical carrier and the sideband signal now have different coefficients. A quasi-ideal optical SSB signal can also be obtained with small signal modulation, as long as the IQ-MZM is not biased at the MATP where 𝐶1 = 0. The corresponding CSPR of the obtained approximate optical SSB-C from Eq. (14) can be given as
𝑃𝑐𝑎𝑟𝑟𝑖𝑒𝑟 |1 + 𝑗|2 = 10 × log 𝑃𝑠𝑖𝑔𝑛𝑎𝑙 |𝑗𝑚𝜎|2 2 = 10 × log . (11) 𝜋 2 ⋅ 𝑂𝑀𝐼 2 Compared with Eq. (7), the two SSB schemes have the same CSPR, hence the same problems such as high optimal CSPR and low receiver sensitivity also remains for this scheme. However, the DD-MZM can only generate an optical SSB signal by biasing at its QTP. On the contrary, for IQ-MZM operating in push–push mode, regardless of how the DC bias voltage changes as long as it is far from the MITP, an approximate optical SSB signal with the same CSPR can be produced. By substituting Eq. (10) to Eq. (4), then the resultant RF component and the output of the power detector are found to be √ [ ( ) 𝐼𝑅𝐹 (𝑡) = 2𝐵1 𝑀 ⋅ cos 𝛥𝜓 (𝑡) + 𝑚𝐼 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ∕2 ( )] − sin 𝛥𝜓 (𝑡) + 𝑚𝑄 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ∕2 , (12)
𝐶𝑆𝑃 𝑅 = 10 × log
|𝐼𝑅𝐹 |
|𝐵1 (1 + 𝑗)|2 𝑃𝑐𝑎𝑟𝑟𝑖𝑒𝑟 | = 10 × log | 𝑃𝑠𝑖𝑔𝑛𝑎𝑙 |𝐶1 𝑚𝜎 |2 | )] | [ ( 2 1 + cos 𝑚𝑉𝑑𝑖𝑓 𝑓 = 10 × log [ ( )] . 𝜋 2 ⋅ 𝑂𝑀𝐼 2 ⋅ 1 − cos 𝑚𝑉𝑑𝑖𝑓 𝑓
𝐶𝑆𝑃 𝑅 = 10 × log
(15)
Eq. (15) shows that the CSPR relies on the interplay between the OMI and the DC bias difference. Consequently, when keeping the same OMI case as Eq. (7) or (11), the optimal CSPR can be further decreased via the DC bias difference. By substituting Eq. (14) to Eq. (4), the composite RF component and the output of the power detector can be expressed as √ [ ( ) ( ) 𝐼𝑅𝐹 (𝑡) = 2𝑀 ⋅ cos 𝛥𝜓 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ∕2 ⋅ cos 𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 ( ) ( )] − sin 𝛥𝜓 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ∕2 ⋅ cos 𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 , (16) |𝐼𝑅𝐹 (𝑡)|2 = 1 𝑀 2 | | 2 ( ) ( ) ⎧2 + cos 2𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 + cos 2𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ⎫ [ ( ) ( )] ⎪ ⎪ ⎪+ cos 2𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 − cos 2𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ⎪ ⎪ ⎪⋅ cos (2𝛥𝜓 (𝑡) + 𝑚𝑉 ) 𝑠𝑢𝑚 ⋅⎨ ) ( )⎬ ( 𝑚 𝑚 ⎪ ⎪ ⎪−4 × cos 𝑚𝐼 (𝑡) + 2 𝑉𝑑𝑖𝑓 𝑓 ⋅ cos 𝑚𝑄 (𝑡) + 2 𝑉𝑑𝑖𝑓 𝑓 ⎪ ( ) ⎪ ⎪ ⎩⋅ sin 2𝛥𝜓 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ⎭ ( ) ( )] 1 2 [ ∝ 𝑀 ⋅ 2 + cos 2𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 + cos 2𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 2 { ( ) ( )} ≈ 𝑀 2 ⋅ 𝐵3 + 𝐶2 ⋅ [𝐼 (𝑡) + 𝑄 (𝑡)] + 𝐶3 ⋅ 𝑂 𝑋 2 + 𝐶4 ⋅ 𝑂 𝑋 3 ,
⎧2 + 2 sin [𝑚 (𝐼 (𝑡) − 𝑄 (𝑡))] ⎫ ⎪ ⎪ ⎪− [sin (2𝑚𝐼 (𝑡)) − sin (2𝑚𝑄 (𝑡)) + 2 cos (𝑚𝐼 (𝑡) ⎪ ⎪ ⎪ ( ) 1 2 (𝑡)|| = 𝐵3 𝑀 2 ⋅ ⎨ +𝑚𝑄 (𝑡))] ⋅ sin 2𝛥𝜓 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ⎬ 2 ⎪ ⎪ + − cos − 2 sin [cos (2𝑚𝐼 (𝑡)) (2𝑚𝑄 (𝑡)) (𝑚𝐼 (𝑡) ⎪ ⎪ ( ) ⎪ ⎪ +𝑚𝑄 (𝑡))] ⋅ cos 2𝛥𝜓 (𝑡) + 𝑚𝑉 𝑠𝑢𝑚 ⎩ ⎭ ∝ 𝐵3 𝑀 2 ⋅ {1 + sin [𝑚 (𝐼 (𝑡) − 𝑄 (𝑡))]} { ( )} 1 ≈ 𝐵3 𝑀 2 ⋅ 1 + 𝑚 [𝐼 (𝑡) − 𝑄 (𝑡)] − 𝑚3 ⋅ 𝑂 𝑋 3 . 6
(13) ( ) where 𝐵3 = 1 + cos 𝑚𝑉𝑑𝑖𝑓 𝑓 . The low-pass filtered signal in Eq. (13) is only different in coefficient as compared with Eq. (9). As mentioned above, it is not able to restore the information-bearing signal at the MITP. Instead two other typical biases at the QTP and maximum transmission point (MATP) are considered. For the former, 𝑉𝑑𝑖𝑓 𝑓 = ±𝑉𝜋 ∕2, 𝐵3 = 1, and for the latter, 𝑉𝑑𝑖𝑓 𝑓 = 0, 𝐵3 = 2. For the push–push IQ-MZM biased at the MATP, from the comparison of Eqs. (6) and (10), it is found that the optical power of the obtained SSB-C signal is twice that of the DD-MZM biased at the QTP. That is, with the same optical power of the transmitter laser, the push–push IQ-MZM SSB scheme has a higher output optical power up to 3 dB compared to the DD-MZM SSB scheme. In other words, it reduces the power loss of the modulator and increases the power efficiency of the link. Meanwhile, just like the DD-MZM SSB scheme, no second-order SSBI exists and the high-order
(17) ( ) ( ) 2 3 2 where 𝐶2 = −𝑚 ⋅ sin 𝑚𝑉𝑑𝑖𝑓 𝑓 , 𝐶3 = −𝑚 ⋅ cos 𝑚𝑉𝑑𝑖𝑓 𝑓 , 𝐶4 = 3 𝑚 ⋅ ( ) sin 𝑚𝑉𝑑𝑖𝑓 𝑓 . The signal obtained by a LPF is a function of the DC bias difference. However, for both MITP and MATP cases where 𝐶2 = 𝐶4 = 0, 𝐶3 = ±𝑚2 , only second-order SSBI term remains but does not have desired first-order term, hence it is hardly to recover the desired signal. If the QTP case is considered where 𝐶2 = ±m, 𝐶3 = 0, 𝐶4 = ±2m3 /3, there is no second-order SSBI term but the high CSPR issue like the above two SSB schemes remains. Therefore, the optimum DC bias depends on a trade-off between the CSPR and SSBI. In summary, in order to generate a SSB-C signal, the DD-MZM must be exclusively biased at the QTP while the push–push IQ-MZM is fine as long as it is not biased at MITP, and with respect to the push–pull IQMZM, the bias is not allowed at neither MATP nor MITP. Moreover, for 4
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Fig. 4. Simulation setup of the optical SSB transmission for 60 GHz RoF link. ECL, external cavity laser; PRBS, pseudo random binary sequence; VOA, variable optical attenuator; SSMF, standard single mode fiber; EDFA, erbium-doped optical fiber amplifier; OSNR, optical signal-to-noise ratio; DAC, digital–analog converter; ADC, analog–digital converter; ECDC, electrical chromatic dispersion compensation; Tx, transmitter; Rx, receiver; DSP, digital signal processing.
generating a more ideal SSB signal, a small OMI is required to suppress the NLD terms caused by the modulator’s nonlinearity for all of the three schemes. In addition, the SSBI terms resulting from the squarelaw detection can be almost ignored for the DD-MZM and push–push IQ-MZM SSB schemes. However, both the two SSB schemes suffer from a high optimal CSPR due to the small OMI required, and thus lead to the reductions in AWGN tolerance and receiver sensitivity. Whereas for the push–pull IQ-MZM SSB scheme, the SSBI may seriously impact the system performance, especially when biased at between the QTP and MITP. Due to a lower CSPR than those of the previous two SSB schemes, the SSBI may outperform the AWGN to dominate the system performance for this case.
(ECDC), baseband recovery, matched filtering, downsampling, equalization, symbol demodulation and BER calculation were performed in sequence. As a rule of thumb, the DC bias in the actual system easily causes DC drift as the environment changes (such as the DC power supply operating temperature rises with time). Unfortunately, the DC drift has a serious impact on the performance of electro-optic modulation [28]. In order to study this impact, 𝑉𝑏𝑖𝑎𝑠1 was fixed at −𝑉𝜋 /2, then 𝑉𝑏𝑖𝑎𝑠2 was scanned from −𝑉𝜋 /2 to 𝑉𝜋 /2 (that is, from MATP to MITP) under the cases of the DD-MZM, push–pull IQ-MZM and push–push IQ-MZM with the same OMI of 0.12, respectively. The changes of the received signals’ Q-factors are shown in Fig. 5. It can be observed that the DDMZM and push–pull IQ-MZM have similar response curves as the DC drifts, but the theoretical mechanisms behind them are different. For the former, a quasi-ideal optical SSB-C signal can be generated only at the QTP, otherwise the optical SSB signal form is destroyed leading to a reduction of the Q-factor. Whereas for the latter, although a quasi-ideal optical SSB-C signal is always generated as long as the push–pull IQMZM is not biased at the MATP and MITP, its CSPR changes with the DC bias difference and dominates the system performance. The optimal DC bias for this scheme is not at QTP but at some point between the QTP and MITP due to a compromise between the CSPR and SSBI. When the DC bias changes from the optimum to MATP, the increased CSPR reduces the AWGN tolerance leading to lower receiver sensitivity. On the contrary, as the DC bias increases from QTP to MITP, the SSBIs increases with the reduced CSPR and gradually outperforms the AWGN to dominate the system performance. Nevertheless, with respect to the push–push IQ-MZM, as long as the DC bias difference keeps away from the MITP where both the sideband signal and the carrier are zero, a good tolerance to DC drift can be achieved due to the fact that the CSPR is independent of the DC bias difference. In particular, when the push–push IQ-MZM is biased at the MATP (that is, keeping the two arms of the DD-MZMs with the same DC value), a quite flat Q-factor curve can be obtained regardless of how the DC drifts. In a real system, this situation is easier to implement than the DD-MZM scheme that needs to be kept at QTP and the push–pull IQ-MZM which needs to be biased at a particular point between QTP and MITP to achieve optimal performance. In addition, as described in Section 2.2, the push–push IQMZM SSB scheme can actually reduce the power loss of the modulator to achieve higher power efficiency as compared with other schemes, which is not reflected in Fig. 5 because sufficient optical power was guaranteed in the simulation. The above results were obtained without SSBI cancellation. As described in Section 2, the low-pass filtered signal after power detection has SSBI terms which will deteriorate the system performance, especially for push–pull IQ-MZM SSB scheme. Recently, as an effective SSBI elimination technique, KK algorithm has attracted extensive research interest [20,29,30]. Accordingly, this approach is adopted in this paper to eliminate the SSBIs resulting from the square-law detection of the
3. Simulation verification and results discussion The simulation setup is show in Fig. 4. In the transmitter DSP, a pseudo-random bit sequence (PRBS) with a length of 214 was mapped into 16 quadrature amplitude modulation (QAM) and the symbol rate was set to 5 Gbaud. The 16-QAM signal was firstly pulse shaped by the raised cosine filter with a rolloff of 0.1, and then right-shifted its center frequency by 2.75 GHz to produce a gapless electrical SSB signal after upsampling. Afterwards, the real and imaginary parts of the electrical SSB signal, respectively, were used to drive the DD-MZM or IQ-MZM with the same half-wave voltage of 3.6 V to generate a quasi-ideal optical SSB-C signal. Then the obtained signal was transmitted over a 100 km standard single mode fiber (SSMF). After coupled with an LO light for optical heterodyne beating detection based on a singleended PD, the optical SSB-C signal was converted to the electrical RF component according Eq. (4). A PC was used to align the polarization directions of the two beams. Both the transmitter laser and the LO used the external cavity lasers (ECL) with a linewidth of 100 kHz. Note that different linewidths have little impact on system performance due to the phase noise cancellation by power detection [27], as discussed in Section 2. In order to generate the desired RF band, the difference of the two lasers’ center frequencies were set at 60 GHz. The attenuation coefficient, dispersion coefficient and nonlinear index of the SSMF were 0.2 dB/km, 16 ps/nm/km and 2.6 × 10−20 m2 /W, respectively. Two variable optical attenuators (VOA), respectively, were used to control the launch power and ROP. The erbium-doped optical fiber amplifier (EDFA) provided 20 dB power amplification with a noise figure of 4 dB. The optical signal-to-noise ratio (OSNR) was fixed at 35 dB. The PD had a responsivity of 0.84 A/W and a dark current of 0.43 nA. In the simulation setup, the wireless link was omitted, the photocurrent from the PD was directly fed to the ADC for sampling, and then was processed in the receiving DSP, where the desired 60 GHz RF signal was selected by an ideal brick-wall BPF and detected via a power detector in the digital domain. In addition, first-order interference cancellation based on the HSC method [26] or high-order SSBIs cancellation based on KK algorithm [20], electrical chromatic dispersion compensation 5
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tradeoff between the AWGN, NLDs and SSBIs three effects is necessary. For the IQ-MZM operating in push–push mode at MATP scheme, the SSBI term is quite small according to Eq. (13), thus the optimal OMIs are both 0.12 whether KK algorithm is used or not. On the contrary, for IQ-MZM operating in push–pull mode at STP scheme, the SSBIs outperforms NLDs to dominate system performance as OMI grows large. Thereby, the optimal OMI is shifted from 0.07 to 0.10 after adopting KK algorithm for SSBI cancellation. Additionally, benefiting from the effective elimination of SSBIs, this scheme combined with the KK algorithm improves the SNR performance by about 4.3 dB compared to without KK algorithm case. It also achieves an SNR advantage over 3.5 dB attributed to the low operating CSPR compared with the push–push IQ-MZM at the MATP scheme. The measured and theoretical CSPR versus OMI curves for the two SSB schemes are shown in Fig. 7(b). The measured CSPRs are calculated through the sampled RF SSB-C signals in the receiving DSP, while the theoretical CSPRs are obtained according to Eqs. (11) and (15), respectively. It is found that the measured CSPRs are well in accordance with the theoretical prediction. In addition, with the same OMI, the IQ-MZM in push–pull mode case achieves a pronounced reduction in CSPR compared to the push–push mode case. This mainly attributes to the fact that the DC bias is set not at QTP but STP, as supported by Eq. (15). Moreover, in the case of optimal OMI, the optimal CSPR for push–pull mode with KK algorithm is 7.3 dB. It has been reduced by an amount of 3.1 dB and 4 dB, respectively, compared to the schemes without KK algorithm case and the push–push mode case. At last, in the case of optimal DC bias and OMI, the 5 Gbaud 16QAM signal BER versus ROP curves with and without KK algorithm for the IQ-MZM operating in push–push mode at MATP and push–pull mode at STP are given as Fig. 8. Without using KK algorithm, the performance of the push–pull IQ-MZM at STP scheme is much worse than that of push–push mode at MATP scheme. This is mainly because that for the former scheme, a larger SSBI due to smaller CSPR (7.3 dB) compared with the later scheme (11.3 dB), as shown in Fig. 7. Moreover, the performance improvement brought by KK algorithm for the push–push mode at MATP scheme is not obvious due to the relatively small SSBI. The effect is more pronounced as the symbol rate increases or the fiber distance grows, because the SSBI is aggravated with accumulated dispersion [32]. Instead, after using KK algorithm, an improvement of the BER-floor of nearly three orders of magnitude can be observed for the push–pull mode at STP scheme. Compared to the former scheme, the later scheme with the aid of the KK algorithm can achieve a reduction in the required ROP by about 5 dB at the 7% hard-decision forward error correction (HD-FEC) threshold (3.8 × 10−3 ), which is obviously presented at the Insets. The improved receiver sensitivity mainly attributes to a low CSPR enhancing the AWGN tolerance as well as the SSBI cancellation by the KK algorithm. An important aspect of evaluating a scheme is the analysis of system cost and operational complexity. Since only one MZM is used for the DD-MZM SSB scheme, its cost is less than half as much as IQ-MZM SSB scheme, which requires two MZMs and a phase shifter. With respect to the operational complexity, the push–push IQ-MZM SSB scheme is the same as the DD-MZM SSB scheme. Because the SSBIs in both two SSB schemes can be ignored for 5 Gbaud 16-QAM signal after 100 km fiber transmission, thus no SSBI elimination technique is required. However, for the push–pull IQ-MZM SSB scheme, although the KK algorithm can effectively remove SSBI so as to bring significant performance improvement, a somewhat additional complexity of the postdetection processing mainly due to the upsampling and HT operations required by the KK algorithm is introduced [20]. Fortunately, there are already people working on how to reduce the complexity of the KK algorithm [33–35]. We believe that the further improvements are likely once more dedicated efforts are invested into the complexity issue of KK algorithm.
Fig. 5. Q-factor is a function of the DC bias applied to the MZM’s lower arm for different SSB schemes with the same OMI. For the first three schemes, 𝑉𝑏𝑖𝑎𝑠1 is fixed at −𝑉𝜋 ∕2, and setting 𝑉𝑏𝑖𝑎𝑠1 = 𝑉𝑏𝑖𝑎𝑠2 for the last one. 𝑉𝜋 is equal to 3.6 V. MATP, maximum transmission point.
Fig. 6. SNR versus the DC bias of the MZM’s lower arm with (w/) and without (w/o) KK algorithm for SSBI cancellation in the push–pull IQ-MZM SSB scheme. 𝑉𝑏𝑖𝑎𝑠1 is also fixed at −𝑉𝜋 ∕2 and scanning 𝑉𝑏𝑖𝑎𝑠2 from QTP to MITP. 𝑉𝜋 is equal to 3.6 V. QTP, quadrature transmission point; MITP, minimum transmission point.
power detector. It can be predicted that the optimal bias voltage should move further away from the QTP towards MITP after using the SSBI cancellation technique, leading to further reduction of the optimal CSPR. The corresponding result is shown in Fig. 6 where the optimal lower arm DC bias is shifted from 0.2 V to 0.7 V after using KK algorithm to eliminate the SSBIs. Hereinafter this DC bias condition is referred to as specific transmission point (STP). Benefiting from the optimal CSPR reduction and the SSBI cancellation, the signal-to-noise ratio (SNR), defined as SNR(dB) = −20𝑙𝑜𝑔10 (EVM ) where EVM is the error vector magnitude [31], also achieves an improvement of 3.2 dB, as shown in Fig. 6. To further investigate the influence of OMI on different SSB schemes, the IQ-MZM operating in push–push mode at MATP and push– pull mode at STP, are compared for SNR and CSPR performance with the same OMI. Since the SSB-C signals generated by the DD-MZM and the push–push IQ-MZM at MATP have the same CSPRs and SSBIs, the performance of the two SSB schemes are almost the same when sufficient optical power is available. Therefore, only the result of the push–push IQ-MZM at MATP is given here. As shown in Fig. 7(a), an appropriate OMI should be selected. For low OMI, the performance is dominated by the AWGN. For high OMI, the NLDs resulting from the modulators’ nonlinearity and the SSBIs caused by the square-law detection become the dominant performance degradation. Hence, a 6
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Fig. 7. (a) SNR versus OMI curves with (w/) and without (w/o) KK algorithm for SSBI cancellation in the push–push IQ-MZM at MATP and push–pull IQ-MZM at STP SSB schemes. (b) The measured and theoretical CSPR versus OMI curves for the two SSB schemes. The MATP corresponds to 𝑉𝑏𝑖𝑎𝑠1 = 𝑉𝑏𝑖𝑎𝑠2 = −𝑉𝜋 ∕2 and STP corresponds to 𝑉𝑏𝑖𝑎𝑠1 = −𝑉𝜋 ∕2, 𝑉𝑏𝑖𝑎𝑠2 = 0.7 V. 𝑉𝜋 is equal to 3.6 V. MATP, maximum transmission point; STP, specific transmission point.
Fig. 8. BER versus ROP curves with (w/) and without (w/o) KK algorithm for the IQ-MZM operating in push–push mode at MATP and push–pull mode at STP cases. Insets (i)-(iv) are the corresponding constellation diagrams of the 16-QAM signals in the two SSB schemes with and without KK algorithm at the ROP of −20 dBm.
4. Conclusions
CRediT authorship contribution statement
Three types of SSB generation schemes, based on the DD-MZM, IQMZM operating in the push–push and push–pull modes respectively, are numerically analyzed and validated with system simulations in 60 GHz RoF link. For the low-cost DD-MZM SSB scheme, a high optimal CSPR results in low receiving sensitivity and the evident susceptibility of SSB form to the DC drift are the main shortcomings. Instead, although suffering from the same high optimal CSPR issue for the push–push IQMZM SSB scheme, a wide tolerance to the DC drift as well as a low power loss of the modulator can be provided at the expense of cost. In addition, by adjusting the DC bias difference applied to the MZM, the push–pull IQ-MZM SSB scheme can solve the high optimal CSPR issue. The KK algorithm can be used to eliminate the large SSBI resulted from low CSPR, so as to enhance the overall system performance. As compared with the previous two SSB schemes, this scheme can reduce the optimal CSPR by more than 3 dB, and also provides 5 dB improvement in receiver sensitivity at the 7% HD-FEC threshold for 5 Gbaud 16-QAM signal with 100 km fiber transmission. Those benefits come at the cost of increased DSP complexity. In all, the analyses and results presented in this paper provide a deep insight on both reducing the SSBI’s impact and improving the performance for the SSB RoF links.
Yuancheng Cai: Methodology, Validation, Writing - original draft. Xiang Gao: Investigation, Formal analysis. Yun Ling: Conceptualization, Writing - review & editing. Bo Xu: Writing - review & editing. Kun Qiu: Resources. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 61420106011) and the Fundamental Research Funds for the Central Universities, China (Grant No. ZYGX2016J014). References [1] C.T. Lin, C.H. Ho, H.T. Huang, Y.H. Cheng, Ultrahigh capacity 2 x 2 MIMO rof system at 60 GHz employing single-sideband single-carrier modulation, Opt. Lett. 39 (6) (2014) 1358–1361. [2] X. Wang, J. Yu, Z. Cao, J. Xiao, L. Chen, SSBI mitigation at 60 GHz OFDM-ROF system based on optimization of training sequence, Opt. Express 19 (9) (2011) 8839–8846. [3] W.J. Fang, X.G. Huang, G. Li, A full duplex radio-over-fiber transmission of OFDM signals at 60 GHz employing frequency quintupling optical up-conversion, Opt. Commun. 294 (2013) 118–122. 7
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Performance comparison of optical single-sideband modulation in RoF link Yuancheng Cai, Xiang Gao, Yun Ling ∗, Bo Xu, Kun Qiu Key Laboratory of Optical Fiber Sensing and Communications (Ministry of Education), University of Electronic Science and Technology of China, Chengdu, 611731, China
ARTICLE
INFO
Keywords: Radio over fiber (RoF) Single-sideband (SSB) Signal-to-signal beating interference (SSBI) Modulation
ABSTRACT In this paper, three different single-sideband (SSB) modulation schemes, based on the dual drive Mach–Zehnder modulator (DD-MZM), IQ-MZM operating in push–push and push–pull modes respectively, are theoretically analyzed and validated by simulation in 60 GHz RoF link. The simulation results are well in accordance with the theoretical predictions. For the low-cost DD-MZM SSB scheme, a high optimal carrier signal power ratio (CSPR) results in low receiving sensitivity and the evident susceptibility of SSB form to the direct current (DC) drift are the main shortcomings. Instead, although suffering from the same high optimal CSPR issue for the push–push IQ-MZM SSB scheme, a wide tolerance to the DC drift as well as a low power loss of the modulator can be provided at the expense of cost. In addition, by adjusting the DC bias difference applied to the MZMs in conjunction with the Kramers–Kronig algorithm for signal-to-signal beating interference cancellation, the push–pull IQ-MZM SSB scheme can reduce the optimal CSPR by more than 3 dB and also provide 5 dB improvement in receiver sensitivity, as compared with the previous two SSB schemes. The analyses and results presented in this paper can provide a deep insight on improving the performance for the SSB RoF links.
1. Introduction With the explosive growth of wireless communication capacity, the frequency of radio communication continues to increase. In the recent decade, 60 GHz radio over fiber (RoF) solution has been highlighted for high data transmission capacity because of the 7-GHz license-free bandwidth from 57 to 64 GHz [1–4]. In order to improve the transmission performance of high-frequency (such as 60 GHz and above) radio frequency (RF) signals, the optical fiber enabling the characteristics of high bandwidth, low delay and immunity to electromagnetic interference, is consistently advocated to replace the conventional coaxial cable for RF signals transmission. However, for traditional doublesideband (DSB) signal in RoF system, the frequency selective power fading caused by the interaction of fiber chromatic dispersion and the square-law detection, is a serious problem that must be dealt with [5]. As has been proven, single-sideband (SSB) transmission exhibits excellent resistance to power fading effect, as well as high spectral efficiency, hence it has attracted much attention of researchers [6–9]. For the optical SSB transmission systems, three different electrooptic modulators are commonly used for optical SSB signal generation. One is the general intensity modulator (IM) in conjunction with an optical filter. The IM is used to yield an optical DSB signal, then the optical SSB signal is produced by suppressing the undesired sideband via an optical filter [10–12]. The main advantage of the setup resides in its simple principle, whereas drawbacks come in that either an appropriate guard band (GB) between the optical carrier and the sideband signal or
a sharp optical filter is required to ensure SSB filtering performance. Unlike the IM based SSB scheme which relies on additional device, the dual drive Mach–Zehnder modulator (DD-MZM) or the MZM-based IQ modulator driven by a pair of Hilbert transform (HT) signals can directly generate a quasi-ideal gapless optical SSB signal under small signal modulation condition, just by controlling the modulator’s direct current (DC) bias voltage [9,13,14]. Many literatures have presented comprehensive mathematical analyses [13,15,16] and experimental verifications [17,18] on the two optical SSB modulation schemes. Nevertheless, research works on the optical SSB generation via IQ-MZM are mainly focused on push–pull mode, whereas rare relevant results for the push–push mode [19]. On the other hand, the signal-to-signal beating interference (SSBI) is an important limitation for the performance of such systems. Though the SSBI can be overcome via a sufficient GB [14, 15,18] or special SSBI elimination techniques [13,17], no detailed investigations on the difference between the three types of SSB schemes and how much impact of their respective SSBIs on system performance have been conducted? In this paper, three types of SSB modulation schemes and the corresponding performances in 60 GHz RoF link are studied and compared in detail. One is the DD-MZM SSB scheme and the other two are the IQ-MZM (which is composed of two DD-MZMs instead of the two single-electrode MZMs) SSB schemes operating in either push–push or push–pull modes [19]. The thorough analyses on the condition of SSB generation, the carrier signal power ratio (CSPR) control measures,
∗ Corresponding author. E-mail address: [email protected] (Y. Ling).
https://doi.org/10.1016/j.optcom.2020.125409 Received 17 December 2019; Received in revised form 26 January 2020; Accepted 28 January 2020 Available online 31 January 2020 0030-4018/© 2020 Elsevier B.V. All rights reserved.
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Optics Communications 463 (2020) 125409
Fig. 1. Simplified schematic architecture of the optical SSB RoF link based on optical heterodyne detection technique (Ignore fiber and wireless transmission links here for simplicity). LD, laser diode; Mod., modulator; OC, optical coupler; PC, polarization controller; LO, local oscillator; PD, photodiode; BPF, band-pass filter. Red lines indicate the optical links and purple lines indicate the electrical links. . (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the impact of modulator’s DC drift and SSBI are performed based on the above three SSB schemes. The optimal parameters of three SSB schemes, such as DC bias difference applied to the modulator and CSPR of the SSB signal, are analyzed and given. This optimal parameters are obtained by a compromise between the nonlinear distortion (NLD) terms caused by the modulator, SSBI resulted from the square-law detection, and additive Gaussian white noise (AWGN) originated from the transmission channel. What’s more, the similarities and differences between the three SSB schemes and how much impact does SSBI have on the performance of the respective systems are compared in detail. They are theoretically analyzed and validated by simulations in 60-GHz RoF link. The simulation results are well in accordance with the theoretical predictions. Numerical analyses and simulation verifications show that: (1) the DD-MZM SSB scheme offers low cost, but its high optimal CSPR results in low receiving sensitivity and the SSB form is susceptible to DC drift. (2) The push–push IQ-MZM SSB scheme suffers from the same high optimal CSPR problem, however, not only a low power loss of the modulator but also a good tolerance to the DC drift, can be provided at the expense of cost. (3) Unlike the above two SSB schemes whose CSPRs are exclusively adjusted by the optical modulation index (OMI), the CSPR of the push–pull IQ-MZM SSB scheme can be jointly controlled via the OMI and the DC bias difference applied to the MZM, which effectively helps to reduce the optimal CSPR. Moreover, the push–pull IQ-MZM SSB scheme combined with the Kramers–Kronig (KK) algorithm [20] for SSBI cancellation, the performance is significantly improved. As compared with the other two SSB schemes, this scheme can reduce the optimal CSPR from above 10 dB to about 7 dB, and also provides 5 dB improvement in the required received optical power (ROP) at the bit error rate (BER) of 3.8 × 10−3 for 5 Gbaud 16-QAM signal after 100 km fiber transmission. The analyses and results presented in this paper can provide a deep insight on improving the performance for the SSB RoF links. The rest of this paper is organized as follows. Section 2 introduces the theoretical models and analyses of the three SSB schemes in RoF link. Simulation verification and results discussion are shown in Section 3. In the last Section, the main conclusions are given accordingly.
performed using a power detector which consists of a square-law device and a low-pass filtering (LPF). Subsequently, the obtained signal is demodulated through digital signal processing (DSP) after sampled by the analog–digital converter (ADC). Suppose that s(t ) is the information-bearing complex baseband signal shaped by the Nyquist pulse with a full bandwidth of B. An electric SSB signal can be obtained by frequency shifting operation, i.e., 𝑠𝑆𝑆𝐵 (𝑡) = 𝑠 (𝑡) exp (𝑗𝜋𝐵𝑡), whose imaginary part is the HT of the real part of the signal [21]. Note that no frequency gap is reserved. The pair of HT signals can be given as [ ] 𝐼 (𝑡) = 𝑟𝑒𝑎𝑙 𝑠𝑆𝑆𝐵 (𝑡) , [ ] (1) 𝑄 (𝑡) = 𝑖𝑚𝑎𝑔 𝑠𝑆𝑆𝐵 (𝑡) = 𝐻𝑇 [𝐼 (𝑡)] , where real[X ] and imag [X ] are the operations that take the real part and imaginary parts of X, respectively. Assume that the transmitter and local oscillator (LO) light are respectively √ [ ( )] (2) 𝐸𝑐 (𝑡) = 𝑃𝑐 exp 𝑗 2𝜋𝑓𝑐 𝑡 + 𝜑𝑐 (𝑡) , √ [ ( )] 𝐸𝐿𝑂 (𝑡) = 𝑃𝐿𝑂 exp 𝑗 2𝜋𝑓𝐿𝑂 𝑡 + 𝜑𝐿𝑂 (𝑡) , (3) where 𝑃𝑐 , 𝑓𝑐 and 𝜑𝑐 (t) are the optical power, central frequency and phase noise of the lightwave from the transmitter laser source and 𝑃𝐿𝑂 , 𝑓𝐿𝑂 and 𝜑𝐿𝑂 (t) are the optical power, central frequency and phase noise of the LO lightwave, respectively. Driven by a pair of HT signals, a single DD-MZM or IQ-MZM is used to generate the quasi-ideal optical SSB-C signal. Later, the modulated optical signal is coupled with the LO light followed by a single-ended PD which can model as 𝐼𝑃 𝐷 (𝑡) = 𝑅 ⋅ ||𝐸𝑠 (𝑡) + 𝐸𝐿𝑂 (𝑡)|| = 𝐼𝐵𝑎𝑠𝑒𝑏𝑎𝑛𝑑 (𝑡) + 𝐼𝑅𝐹 (𝑡) , 2
(4)
2 2 where 𝐼𝐵𝑎𝑠𝑒𝑏𝑎𝑛𝑑 (𝑡) = 𝑅 ⋅ ||𝐸𝐿𝑂 (𝑡)|| + 𝑅 ⋅ ||𝐸𝑠 (𝑡)|| and 𝐼𝑅𝐹 (𝑡) = 2𝑅 ⋅ [ ] 𝑟𝑒𝑎𝑙 𝐸𝑠 (𝑡) 𝐸𝐿𝑂 ∗ (𝑡) are located at the baseband and the RF band, respectively. R denotes the responsivity of the PD. Since the main purpose in this paper is to study the RF signal for RoF link, the baseband signal is not the key point to be discussed in subsequent analysis. It is worth noting that a polarization controller (PC) is required to adjust the polarization direction of the LO light to be consistent with the signal light, so as to obtain the best performance from the beating of two beams [22,23]. The central frequency of the obtained RF component is equal to the difference between the two lasers’ central frequencies. Note that the generated RF signal contains the sum of two laser phase noises. Therefore, the square-law-based power detection can be used at the receiving end to complete the frequency down-conversion while removing the phase noise through modulo operation. Since the mathematical expression of the optical SSB-C signal 𝐸𝑠 (t) depends on the modulation method, the theoretical models of SSB generation via the DD-MZM and IQ-MZM are given in what follows.
2. Theoretical model and analysis The simplified schematic architecture of the optical SSB RoF link based on optical heterodyne detection technique is shown in Fig. 1. For concision purpose, the fiber and wireless transmission links are omitted here. The optical SSB with carrier (SSB-C) modulation is performed via an electro-optic modulator, whose schematic diagram will be given later. After fiber transmission, the transmitted quasi-ideal optical SSB-C signal is converted into an electrical signal by optical heterodyne beating detection, which can also complete the frequency up-conversion to RF. The desired up-converted RF signal can be obtained via a bandpass filter (BPF) from the detected photocurrent of the photodiode (PD). After the RF signal arriving the receiving end through a pair of antennas and the wireless channel, frequency down-conversion is
2.1. DD-MZM SSB modulation Fig. 2(a) shows the schematic diagram of the DD-MZM. It consists of two phase modulators, two RF inputs and two DC bias inputs. When 2
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Optics Communications 463 (2020) 125409
Fig. 2. Schematic diagrams of the DD-MZM and IQ-MZM. (a) DD-MZM. (b) IQ-MZM operating in push–push mode. (c) IQ-MZM operating in push–pull mode. PM, phase modulator; inv, inverse.
the form of 𝑠𝑆𝑆𝐵 (𝑡) = 𝐼 (𝑡) + 𝑗𝑄 (𝑡) (Only considering the right sideband signal [25] in this paper). For simplicity, let 𝑉𝑏𝑖𝑎𝑠1 = −𝑉𝜋 ∕2, 𝑉𝑏𝑖𝑎𝑠2 = 0, which means the DD-MZM is biased at the quadrature transmission point (QTP), then Eq. (5) can be rewritten as [ ( ( )) ] 1 𝐸𝑠 (𝑡) = 𝐸𝑐 (𝑡) ⋅ exp 𝑗𝑚 𝐼 (𝑡) − 𝑉𝜋 ∕2 + exp (𝑗𝑚 (𝑄 (𝑡))) 2 (6) [ ( )] 1 1 ≈ 𝐸𝑐 (𝑡) ⋅ (1 − 𝑗) + 𝑚 ⋅ 𝑠𝑆𝑆𝐵 (𝑡) − 𝑚2 ⋅ 𝑂 𝑋 2 . 2 2 It can be seen that when small signal modulation allows all NLDs to be ignored, the electric SSB signal is linearly mapped to the optical domain with an extra carrier term 1 − j. The CSPR of the obtained quasi-ideal optical SSB-C can be given as 𝐶𝑆𝑃 𝑅 = 10 × log
𝑃𝑐𝑎𝑟𝑟𝑖𝑒𝑟 |1 − 𝑗|2 2 = 10 × log . = 10 × log 𝑃𝑠𝑖𝑔𝑛𝑎𝑙 𝜋 2 ⋅ 𝑂𝑀𝐼 2 |𝑚𝜎|2
(7)
Eq. (7) shows that the only way to control the CSPR for the DD-MZM SSB scheme is to adjust the OMI. Although a smaller OMI guarantees a more ideal optical SSB signal, it results in a larger CSPR, where the carrier occupies most of the energy leading to low AWGN tolerance and low receiver sensitivity. By substituting Eq. (6) to Eq. (4), the resultant RF component can be expressed as
Fig. 3. Typical transmission function curves for the DDMZM operating in push– pull mode. V (t ) is the phase shift caused by the driving voltage. MATP, maximum transmission point; MITP, minimum transmission point; QTP, quadrature transmission point;.
the upper and lower arms of the DD-MZM are driven by the abovementioned HT signal pair, the output of the DD-MZM can be expressed as [24]
𝐼𝑅𝐹 (𝑡) = 𝑀 ⋅ [sin (𝛥𝜓 (𝑡) + 𝑚𝐼 (𝑡)) + cos (𝛥𝜓 (𝑡) + 𝑚𝑄 (𝑡))] , (8) √ ( ) where 𝑀 = 𝑅 𝑃𝑐 𝑃𝐿𝑂 , 𝛥𝜓 (𝑡) = 2𝜋 𝑓𝑐 − 𝑓𝐿𝑂 𝑡 + 𝜑𝑐 (𝑡) − 𝜑𝐿𝑂 (𝑡) corresponds to RF carrier from heterodyne beating but contains laser phase noise from two unrelated laser sources. Finally, the output of power detector is given as follows
[ ( ( )) ( ( ))] 1 𝐸 (𝑡) ⋅ exp 𝑗𝑚 𝐼 (𝑡) + 𝑉𝑏𝑖𝑎𝑠1 + exp 𝑗𝑚 𝑄 (𝑡) + 𝑉𝑏𝑖𝑎𝑠2 2 𝑐 { [ ] 1 ≈ 𝐸𝑐 (𝑡) ⋅ 𝐴1 + 𝐴2 + 𝑚 𝑗𝐴1 ⋅ 𝐼 (𝑡) + 𝐴2 ⋅ 𝑗𝑄 (𝑡) 2 ( )} 1 − 𝑚2 ⋅ 𝑂 𝑋 2 , 2
𝐸𝑠 (𝑡) =
⎫ ⎧1 + sin [𝑚 (𝐼 (𝑡) − 𝑄 (𝑡))] ⎪ + sin [2𝛥𝜓 (𝑡) + 𝑚𝐼 (𝑡) + 𝑚𝑄 (𝑡)] |𝐼𝑅𝐹 (𝑡)|2 = 𝑀 2 ⋅ ⎪ ⎬ ⎨ | | 1 1 ⎪− cos [2𝛥𝜓 (𝑡) + 2𝑚𝐼 (𝑡)] + cos [2𝛥𝜓 (𝑡) + 2𝑚𝑄 (𝑡)]⎪ ⎭ ⎩ 2 2 ∝ 𝑀 2 ⋅ {1 + sin [𝑚 (𝐼 (𝑡) − 𝑄 (𝑡))]} { ( )} 1 ≈ 𝑀 2 ⋅ 1 + 𝑚 [𝐼 (𝑡) − 𝑄 (𝑡)] − 𝑚3 ⋅ 𝑂 𝑋 3 . 6
(5) ( ) ( ) where 𝐴1 = exp 𝑗𝑚𝑉𝑏𝑖𝑎𝑠1 , 𝐴2 = exp 𝑗𝑚𝑉𝑏𝑖𝑎𝑠2 , 𝑚 = 𝜋∕𝑉𝜋 is a constant with 𝑉𝜋 denoting the half-wave voltage of the DD-MZM. ( ) 𝑂 𝑋 2 describes the second-order NLD after using Taylor expansion, the third-order and above NLDs have been omitted. The NLDs are derived from the nonlinear transmission function of the DD-MZM. The typical transmission function curves for the DDMZM operating in push– pull mode are shown in Fig. 3. It can be seen that the closer to the minimum transmission point (MITP) where has the smallest output power, the more linear field signal modulation which means the smaller NLDs can be obtained. Suppose 𝜎 is the standard deviation of the ( ) zero-mean electric SSB signal, 𝑠𝑆𝑆𝐵 (𝑡), it is equal to 𝑉𝑖𝑛 𝑅𝑀𝑆 , the root-mean-square (RMS) amplitude of the electrical input to the DD( ) MZM. Then the OMI, defined as 𝑂𝑀𝐼 = 𝑉𝑖𝑛 𝑅𝑀𝑆 ∕𝑉𝜋 = 𝜎∕𝑉𝜋 , actually reflects the signal modulation depth. From Eq. (5), it can be inferred that two conditions must be met to produce an optical SSB signal. One is that the OMI must be small enough to guarantee that the higher-order NLDs which scale with (𝑚𝜎)𝑛 (𝑛 = 2, 3, 4, …) can be ignored. The other is keeping 𝑗𝐴1 = 𝐴2 , i.e., 𝑉𝑏𝑖𝑎𝑠1 +𝑉𝜋 ∕2 = 𝑉𝑏𝑖𝑎𝑠2 to produce a SSB signal in
(9) It can be seen that a LPF can be used to remove the high frequency terms from square-law detection containing the laser phase noise. In the remaining signal, only the third-order and above SSBIs exist after Taylor expansion. In the case of m < 1 and small OMI for small signal modulation, the third-order SSBI can almost be ignored because of its much smaller coefficient than that of the desired first-order term. Afterwards, the Hilbert superposition cancellation (HSC) method [26] can be used to restore the I (t ) and Q(t ). Therefore, using DD-MZM biased at the QTP to generate SSB signal, a situation almost no SSBI is presented after the square-law detection. However, in order to achieve more ideal SSB form, a small OMI should be used to reduce the NLDs of the DD-MZM, hence inevitably leads to a large CSPR according to Eq. (7), which will limit the system performance. 3
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SSBI terms can be neglected with small signal modulation. Of course, the same disadvantages such as high optimal CSPR which will limit the system performance still exist.
2.2. Push–push IQ-MZM SSB modulation Fig. 2(b) shows the schematic diagram of the IQ-MZM operating in push–push mode. It consists of one 90-degree phase shifter and two DD-MZMs, as well as two RF inputs and two DC bias inputs. According to the output expression of the DD-MZM in Ref. [24], the output of the push–push IQ-MZM which driven by a pair of HT signals can be expressed as √ ) 2( 𝐸𝑢𝑝𝑝𝑒𝑟−𝐷𝐷𝑀𝑍𝑀 + 𝑗𝐸𝑙𝑜𝑤𝑒𝑟−𝐷𝐷𝑀𝑍𝑀 𝐸𝑠 (𝑡) = 2 [ ] (10) = 𝐵1 𝐵2 ⋅ 𝐸𝑐 (𝑡) ⋅ exp (𝑗𝑚𝐼 (𝑡)) + 𝑗 exp (𝑚𝑄 (𝑡)) [ ] ( ) 1 ≈ 𝐵1 𝐵2 ⋅ 𝐸𝑐 (𝑡) ⋅ (1 + 𝑗) + 𝑗𝑚 ⋅ 𝑠𝑠𝑠𝑏 (𝑡) − 𝑚2 ⋅ 𝑂 𝑋 2 , 2 ( ) ( ) where 𝐵1 = cos 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 , 𝐵2 = exp 𝑗𝑚𝑉𝑠𝑢𝑚 ∕2 . 𝑉𝑑𝑖𝑓 𝑓 = 𝑉𝑏𝑖𝑎𝑠1 − 𝑉𝑏𝑖𝑎𝑠2 and 𝑉𝑠𝑢𝑚 = 𝑉𝑏𝑖𝑎𝑠1 +𝑉𝑏𝑖𝑎𝑠2 are the difference and sum of the two DC biases applied to the DD-MZM, respectively. The second-order and above NLDs can also be ignored under small signal modulation condition. It can be found that the electric SSB signal is linearly mapped to the optical domain with a carrier term 1 + j, as long as the IQ-MZM is not biased at the MITP, where 𝑉𝑑𝑖𝑓 𝑓 = ±𝑉𝜋 , 𝐵1 = 0. The CSPR of the obtained approximate optical SSB-C can be given as
2.3. Push–pull IQ-MZM SSB modulation Fig. 2(c) shows the schematic diagram of the IQ-MZM operating in push–pull mode, which is different from the push–push mode in that the RF inputs of the lower arm of each DD-MZM are inverted [19]. Also driven by a pair of HT signals, the output of the push–pull IQ-MZM can be expressed as [24] √ ) 2( 𝐸𝑠 (𝑡) = 𝐸𝑢𝑝𝑝𝑒𝑟−𝐷𝐷𝑀𝑍𝑀 + 𝑗𝐸𝑙𝑜𝑤𝑒𝑟−𝐷𝐷𝑀𝑍𝑀 2 [ ( ) ( )] = 𝐵2 𝐸𝑐 (𝑡) ⋅ cos 𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 + 𝑗 ⋅ cos 𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 [ ] ( ) 1 ≈ 𝐵2 𝐸𝑐 (𝑡) ⋅ 𝐵1 (1 + 𝑗) + 𝐶1 𝑚 ⋅ 𝑠𝑠𝑠𝑏 (𝑡) − 𝑚2 𝐵1 ⋅ 𝑂 𝑋 2 , 2 (14) ( ) where 𝐶1 = − sin 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 . Note that the optical carrier and the sideband signal now have different coefficients. A quasi-ideal optical SSB signal can also be obtained with small signal modulation, as long as the IQ-MZM is not biased at the MATP where 𝐶1 = 0. The corresponding CSPR of the obtained approximate optical SSB-C from Eq. (14) can be given as
𝑃𝑐𝑎𝑟𝑟𝑖𝑒𝑟 |1 + 𝑗|2 = 10 × log 𝑃𝑠𝑖𝑔𝑛𝑎𝑙 |𝑗𝑚𝜎|2 2 = 10 × log . (11) 𝜋 2 ⋅ 𝑂𝑀𝐼 2 Compared with Eq. (7), the two SSB schemes have the same CSPR, hence the same problems such as high optimal CSPR and low receiver sensitivity also remains for this scheme. However, the DD-MZM can only generate an optical SSB signal by biasing at its QTP. On the contrary, for IQ-MZM operating in push–push mode, regardless of how the DC bias voltage changes as long as it is far from the MITP, an approximate optical SSB signal with the same CSPR can be produced. By substituting Eq. (10) to Eq. (4), then the resultant RF component and the output of the power detector are found to be √ [ ( ) 𝐼𝑅𝐹 (𝑡) = 2𝐵1 𝑀 ⋅ cos 𝛥𝜓 (𝑡) + 𝑚𝐼 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ∕2 ( )] − sin 𝛥𝜓 (𝑡) + 𝑚𝑄 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ∕2 , (12)
𝐶𝑆𝑃 𝑅 = 10 × log
|𝐼𝑅𝐹 |
|𝐵1 (1 + 𝑗)|2 𝑃𝑐𝑎𝑟𝑟𝑖𝑒𝑟 | = 10 × log | 𝑃𝑠𝑖𝑔𝑛𝑎𝑙 |𝐶1 𝑚𝜎 |2 | )] | [ ( 2 1 + cos 𝑚𝑉𝑑𝑖𝑓 𝑓 = 10 × log [ ( )] . 𝜋 2 ⋅ 𝑂𝑀𝐼 2 ⋅ 1 − cos 𝑚𝑉𝑑𝑖𝑓 𝑓
𝐶𝑆𝑃 𝑅 = 10 × log
(15)
Eq. (15) shows that the CSPR relies on the interplay between the OMI and the DC bias difference. Consequently, when keeping the same OMI case as Eq. (7) or (11), the optimal CSPR can be further decreased via the DC bias difference. By substituting Eq. (14) to Eq. (4), the composite RF component and the output of the power detector can be expressed as √ [ ( ) ( ) 𝐼𝑅𝐹 (𝑡) = 2𝑀 ⋅ cos 𝛥𝜓 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ∕2 ⋅ cos 𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 ( ) ( )] − sin 𝛥𝜓 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ∕2 ⋅ cos 𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ∕2 , (16) |𝐼𝑅𝐹 (𝑡)|2 = 1 𝑀 2 | | 2 ( ) ( ) ⎧2 + cos 2𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 + cos 2𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ⎫ [ ( ) ( )] ⎪ ⎪ ⎪+ cos 2𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 − cos 2𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 ⎪ ⎪ ⎪⋅ cos (2𝛥𝜓 (𝑡) + 𝑚𝑉 ) 𝑠𝑢𝑚 ⋅⎨ ) ( )⎬ ( 𝑚 𝑚 ⎪ ⎪ ⎪−4 × cos 𝑚𝐼 (𝑡) + 2 𝑉𝑑𝑖𝑓 𝑓 ⋅ cos 𝑚𝑄 (𝑡) + 2 𝑉𝑑𝑖𝑓 𝑓 ⎪ ( ) ⎪ ⎪ ⎩⋅ sin 2𝛥𝜓 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ⎭ ( ) ( )] 1 2 [ ∝ 𝑀 ⋅ 2 + cos 2𝑚𝐼 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 + cos 2𝑚𝑄 (𝑡) + 𝑚𝑉𝑑𝑖𝑓 𝑓 2 { ( ) ( )} ≈ 𝑀 2 ⋅ 𝐵3 + 𝐶2 ⋅ [𝐼 (𝑡) + 𝑄 (𝑡)] + 𝐶3 ⋅ 𝑂 𝑋 2 + 𝐶4 ⋅ 𝑂 𝑋 3 ,
⎧2 + 2 sin [𝑚 (𝐼 (𝑡) − 𝑄 (𝑡))] ⎫ ⎪ ⎪ ⎪− [sin (2𝑚𝐼 (𝑡)) − sin (2𝑚𝑄 (𝑡)) + 2 cos (𝑚𝐼 (𝑡) ⎪ ⎪ ⎪ ( ) 1 2 (𝑡)|| = 𝐵3 𝑀 2 ⋅ ⎨ +𝑚𝑄 (𝑡))] ⋅ sin 2𝛥𝜓 (𝑡) + 𝑚𝑉𝑠𝑢𝑚 ⎬ 2 ⎪ ⎪ + − cos − 2 sin [cos (2𝑚𝐼 (𝑡)) (2𝑚𝑄 (𝑡)) (𝑚𝐼 (𝑡) ⎪ ⎪ ( ) ⎪ ⎪ +𝑚𝑄 (𝑡))] ⋅ cos 2𝛥𝜓 (𝑡) + 𝑚𝑉 𝑠𝑢𝑚 ⎩ ⎭ ∝ 𝐵3 𝑀 2 ⋅ {1 + sin [𝑚 (𝐼 (𝑡) − 𝑄 (𝑡))]} { ( )} 1 ≈ 𝐵3 𝑀 2 ⋅ 1 + 𝑚 [𝐼 (𝑡) − 𝑄 (𝑡)] − 𝑚3 ⋅ 𝑂 𝑋 3 . 6
(13) ( ) where 𝐵3 = 1 + cos 𝑚𝑉𝑑𝑖𝑓 𝑓 . The low-pass filtered signal in Eq. (13) is only different in coefficient as compared with Eq. (9). As mentioned above, it is not able to restore the information-bearing signal at the MITP. Instead two other typical biases at the QTP and maximum transmission point (MATP) are considered. For the former, 𝑉𝑑𝑖𝑓 𝑓 = ±𝑉𝜋 ∕2, 𝐵3 = 1, and for the latter, 𝑉𝑑𝑖𝑓 𝑓 = 0, 𝐵3 = 2. For the push–push IQ-MZM biased at the MATP, from the comparison of Eqs. (6) and (10), it is found that the optical power of the obtained SSB-C signal is twice that of the DD-MZM biased at the QTP. That is, with the same optical power of the transmitter laser, the push–push IQ-MZM SSB scheme has a higher output optical power up to 3 dB compared to the DD-MZM SSB scheme. In other words, it reduces the power loss of the modulator and increases the power efficiency of the link. Meanwhile, just like the DD-MZM SSB scheme, no second-order SSBI exists and the high-order
(17) ( ) ( ) 2 3 2 where 𝐶2 = −𝑚 ⋅ sin 𝑚𝑉𝑑𝑖𝑓 𝑓 , 𝐶3 = −𝑚 ⋅ cos 𝑚𝑉𝑑𝑖𝑓 𝑓 , 𝐶4 = 3 𝑚 ⋅ ( ) sin 𝑚𝑉𝑑𝑖𝑓 𝑓 . The signal obtained by a LPF is a function of the DC bias difference. However, for both MITP and MATP cases where 𝐶2 = 𝐶4 = 0, 𝐶3 = ±𝑚2 , only second-order SSBI term remains but does not have desired first-order term, hence it is hardly to recover the desired signal. If the QTP case is considered where 𝐶2 = ±m, 𝐶3 = 0, 𝐶4 = ±2m3 /3, there is no second-order SSBI term but the high CSPR issue like the above two SSB schemes remains. Therefore, the optimum DC bias depends on a trade-off between the CSPR and SSBI. In summary, in order to generate a SSB-C signal, the DD-MZM must be exclusively biased at the QTP while the push–push IQ-MZM is fine as long as it is not biased at MITP, and with respect to the push–pull IQMZM, the bias is not allowed at neither MATP nor MITP. Moreover, for 4
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Fig. 4. Simulation setup of the optical SSB transmission for 60 GHz RoF link. ECL, external cavity laser; PRBS, pseudo random binary sequence; VOA, variable optical attenuator; SSMF, standard single mode fiber; EDFA, erbium-doped optical fiber amplifier; OSNR, optical signal-to-noise ratio; DAC, digital–analog converter; ADC, analog–digital converter; ECDC, electrical chromatic dispersion compensation; Tx, transmitter; Rx, receiver; DSP, digital signal processing.
generating a more ideal SSB signal, a small OMI is required to suppress the NLD terms caused by the modulator’s nonlinearity for all of the three schemes. In addition, the SSBI terms resulting from the squarelaw detection can be almost ignored for the DD-MZM and push–push IQ-MZM SSB schemes. However, both the two SSB schemes suffer from a high optimal CSPR due to the small OMI required, and thus lead to the reductions in AWGN tolerance and receiver sensitivity. Whereas for the push–pull IQ-MZM SSB scheme, the SSBI may seriously impact the system performance, especially when biased at between the QTP and MITP. Due to a lower CSPR than those of the previous two SSB schemes, the SSBI may outperform the AWGN to dominate the system performance for this case.
(ECDC), baseband recovery, matched filtering, downsampling, equalization, symbol demodulation and BER calculation were performed in sequence. As a rule of thumb, the DC bias in the actual system easily causes DC drift as the environment changes (such as the DC power supply operating temperature rises with time). Unfortunately, the DC drift has a serious impact on the performance of electro-optic modulation [28]. In order to study this impact, 𝑉𝑏𝑖𝑎𝑠1 was fixed at −𝑉𝜋 /2, then 𝑉𝑏𝑖𝑎𝑠2 was scanned from −𝑉𝜋 /2 to 𝑉𝜋 /2 (that is, from MATP to MITP) under the cases of the DD-MZM, push–pull IQ-MZM and push–push IQ-MZM with the same OMI of 0.12, respectively. The changes of the received signals’ Q-factors are shown in Fig. 5. It can be observed that the DDMZM and push–pull IQ-MZM have similar response curves as the DC drifts, but the theoretical mechanisms behind them are different. For the former, a quasi-ideal optical SSB-C signal can be generated only at the QTP, otherwise the optical SSB signal form is destroyed leading to a reduction of the Q-factor. Whereas for the latter, although a quasi-ideal optical SSB-C signal is always generated as long as the push–pull IQMZM is not biased at the MATP and MITP, its CSPR changes with the DC bias difference and dominates the system performance. The optimal DC bias for this scheme is not at QTP but at some point between the QTP and MITP due to a compromise between the CSPR and SSBI. When the DC bias changes from the optimum to MATP, the increased CSPR reduces the AWGN tolerance leading to lower receiver sensitivity. On the contrary, as the DC bias increases from QTP to MITP, the SSBIs increases with the reduced CSPR and gradually outperforms the AWGN to dominate the system performance. Nevertheless, with respect to the push–push IQ-MZM, as long as the DC bias difference keeps away from the MITP where both the sideband signal and the carrier are zero, a good tolerance to DC drift can be achieved due to the fact that the CSPR is independent of the DC bias difference. In particular, when the push–push IQ-MZM is biased at the MATP (that is, keeping the two arms of the DD-MZMs with the same DC value), a quite flat Q-factor curve can be obtained regardless of how the DC drifts. In a real system, this situation is easier to implement than the DD-MZM scheme that needs to be kept at QTP and the push–pull IQ-MZM which needs to be biased at a particular point between QTP and MITP to achieve optimal performance. In addition, as described in Section 2.2, the push–push IQMZM SSB scheme can actually reduce the power loss of the modulator to achieve higher power efficiency as compared with other schemes, which is not reflected in Fig. 5 because sufficient optical power was guaranteed in the simulation. The above results were obtained without SSBI cancellation. As described in Section 2, the low-pass filtered signal after power detection has SSBI terms which will deteriorate the system performance, especially for push–pull IQ-MZM SSB scheme. Recently, as an effective SSBI elimination technique, KK algorithm has attracted extensive research interest [20,29,30]. Accordingly, this approach is adopted in this paper to eliminate the SSBIs resulting from the square-law detection of the
3. Simulation verification and results discussion The simulation setup is show in Fig. 4. In the transmitter DSP, a pseudo-random bit sequence (PRBS) with a length of 214 was mapped into 16 quadrature amplitude modulation (QAM) and the symbol rate was set to 5 Gbaud. The 16-QAM signal was firstly pulse shaped by the raised cosine filter with a rolloff of 0.1, and then right-shifted its center frequency by 2.75 GHz to produce a gapless electrical SSB signal after upsampling. Afterwards, the real and imaginary parts of the electrical SSB signal, respectively, were used to drive the DD-MZM or IQ-MZM with the same half-wave voltage of 3.6 V to generate a quasi-ideal optical SSB-C signal. Then the obtained signal was transmitted over a 100 km standard single mode fiber (SSMF). After coupled with an LO light for optical heterodyne beating detection based on a singleended PD, the optical SSB-C signal was converted to the electrical RF component according Eq. (4). A PC was used to align the polarization directions of the two beams. Both the transmitter laser and the LO used the external cavity lasers (ECL) with a linewidth of 100 kHz. Note that different linewidths have little impact on system performance due to the phase noise cancellation by power detection [27], as discussed in Section 2. In order to generate the desired RF band, the difference of the two lasers’ center frequencies were set at 60 GHz. The attenuation coefficient, dispersion coefficient and nonlinear index of the SSMF were 0.2 dB/km, 16 ps/nm/km and 2.6 × 10−20 m2 /W, respectively. Two variable optical attenuators (VOA), respectively, were used to control the launch power and ROP. The erbium-doped optical fiber amplifier (EDFA) provided 20 dB power amplification with a noise figure of 4 dB. The optical signal-to-noise ratio (OSNR) was fixed at 35 dB. The PD had a responsivity of 0.84 A/W and a dark current of 0.43 nA. In the simulation setup, the wireless link was omitted, the photocurrent from the PD was directly fed to the ADC for sampling, and then was processed in the receiving DSP, where the desired 60 GHz RF signal was selected by an ideal brick-wall BPF and detected via a power detector in the digital domain. In addition, first-order interference cancellation based on the HSC method [26] or high-order SSBIs cancellation based on KK algorithm [20], electrical chromatic dispersion compensation 5
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tradeoff between the AWGN, NLDs and SSBIs three effects is necessary. For the IQ-MZM operating in push–push mode at MATP scheme, the SSBI term is quite small according to Eq. (13), thus the optimal OMIs are both 0.12 whether KK algorithm is used or not. On the contrary, for IQ-MZM operating in push–pull mode at STP scheme, the SSBIs outperforms NLDs to dominate system performance as OMI grows large. Thereby, the optimal OMI is shifted from 0.07 to 0.10 after adopting KK algorithm for SSBI cancellation. Additionally, benefiting from the effective elimination of SSBIs, this scheme combined with the KK algorithm improves the SNR performance by about 4.3 dB compared to without KK algorithm case. It also achieves an SNR advantage over 3.5 dB attributed to the low operating CSPR compared with the push–push IQ-MZM at the MATP scheme. The measured and theoretical CSPR versus OMI curves for the two SSB schemes are shown in Fig. 7(b). The measured CSPRs are calculated through the sampled RF SSB-C signals in the receiving DSP, while the theoretical CSPRs are obtained according to Eqs. (11) and (15), respectively. It is found that the measured CSPRs are well in accordance with the theoretical prediction. In addition, with the same OMI, the IQ-MZM in push–pull mode case achieves a pronounced reduction in CSPR compared to the push–push mode case. This mainly attributes to the fact that the DC bias is set not at QTP but STP, as supported by Eq. (15). Moreover, in the case of optimal OMI, the optimal CSPR for push–pull mode with KK algorithm is 7.3 dB. It has been reduced by an amount of 3.1 dB and 4 dB, respectively, compared to the schemes without KK algorithm case and the push–push mode case. At last, in the case of optimal DC bias and OMI, the 5 Gbaud 16QAM signal BER versus ROP curves with and without KK algorithm for the IQ-MZM operating in push–push mode at MATP and push–pull mode at STP are given as Fig. 8. Without using KK algorithm, the performance of the push–pull IQ-MZM at STP scheme is much worse than that of push–push mode at MATP scheme. This is mainly because that for the former scheme, a larger SSBI due to smaller CSPR (7.3 dB) compared with the later scheme (11.3 dB), as shown in Fig. 7. Moreover, the performance improvement brought by KK algorithm for the push–push mode at MATP scheme is not obvious due to the relatively small SSBI. The effect is more pronounced as the symbol rate increases or the fiber distance grows, because the SSBI is aggravated with accumulated dispersion [32]. Instead, after using KK algorithm, an improvement of the BER-floor of nearly three orders of magnitude can be observed for the push–pull mode at STP scheme. Compared to the former scheme, the later scheme with the aid of the KK algorithm can achieve a reduction in the required ROP by about 5 dB at the 7% hard-decision forward error correction (HD-FEC) threshold (3.8 × 10−3 ), which is obviously presented at the Insets. The improved receiver sensitivity mainly attributes to a low CSPR enhancing the AWGN tolerance as well as the SSBI cancellation by the KK algorithm. An important aspect of evaluating a scheme is the analysis of system cost and operational complexity. Since only one MZM is used for the DD-MZM SSB scheme, its cost is less than half as much as IQ-MZM SSB scheme, which requires two MZMs and a phase shifter. With respect to the operational complexity, the push–push IQ-MZM SSB scheme is the same as the DD-MZM SSB scheme. Because the SSBIs in both two SSB schemes can be ignored for 5 Gbaud 16-QAM signal after 100 km fiber transmission, thus no SSBI elimination technique is required. However, for the push–pull IQ-MZM SSB scheme, although the KK algorithm can effectively remove SSBI so as to bring significant performance improvement, a somewhat additional complexity of the postdetection processing mainly due to the upsampling and HT operations required by the KK algorithm is introduced [20]. Fortunately, there are already people working on how to reduce the complexity of the KK algorithm [33–35]. We believe that the further improvements are likely once more dedicated efforts are invested into the complexity issue of KK algorithm.
Fig. 5. Q-factor is a function of the DC bias applied to the MZM’s lower arm for different SSB schemes with the same OMI. For the first three schemes, 𝑉𝑏𝑖𝑎𝑠1 is fixed at −𝑉𝜋 ∕2, and setting 𝑉𝑏𝑖𝑎𝑠1 = 𝑉𝑏𝑖𝑎𝑠2 for the last one. 𝑉𝜋 is equal to 3.6 V. MATP, maximum transmission point.
Fig. 6. SNR versus the DC bias of the MZM’s lower arm with (w/) and without (w/o) KK algorithm for SSBI cancellation in the push–pull IQ-MZM SSB scheme. 𝑉𝑏𝑖𝑎𝑠1 is also fixed at −𝑉𝜋 ∕2 and scanning 𝑉𝑏𝑖𝑎𝑠2 from QTP to MITP. 𝑉𝜋 is equal to 3.6 V. QTP, quadrature transmission point; MITP, minimum transmission point.
power detector. It can be predicted that the optimal bias voltage should move further away from the QTP towards MITP after using the SSBI cancellation technique, leading to further reduction of the optimal CSPR. The corresponding result is shown in Fig. 6 where the optimal lower arm DC bias is shifted from 0.2 V to 0.7 V after using KK algorithm to eliminate the SSBIs. Hereinafter this DC bias condition is referred to as specific transmission point (STP). Benefiting from the optimal CSPR reduction and the SSBI cancellation, the signal-to-noise ratio (SNR), defined as SNR(dB) = −20𝑙𝑜𝑔10 (EVM ) where EVM is the error vector magnitude [31], also achieves an improvement of 3.2 dB, as shown in Fig. 6. To further investigate the influence of OMI on different SSB schemes, the IQ-MZM operating in push–push mode at MATP and push– pull mode at STP, are compared for SNR and CSPR performance with the same OMI. Since the SSB-C signals generated by the DD-MZM and the push–push IQ-MZM at MATP have the same CSPRs and SSBIs, the performance of the two SSB schemes are almost the same when sufficient optical power is available. Therefore, only the result of the push–push IQ-MZM at MATP is given here. As shown in Fig. 7(a), an appropriate OMI should be selected. For low OMI, the performance is dominated by the AWGN. For high OMI, the NLDs resulting from the modulators’ nonlinearity and the SSBIs caused by the square-law detection become the dominant performance degradation. Hence, a 6
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Fig. 7. (a) SNR versus OMI curves with (w/) and without (w/o) KK algorithm for SSBI cancellation in the push–push IQ-MZM at MATP and push–pull IQ-MZM at STP SSB schemes. (b) The measured and theoretical CSPR versus OMI curves for the two SSB schemes. The MATP corresponds to 𝑉𝑏𝑖𝑎𝑠1 = 𝑉𝑏𝑖𝑎𝑠2 = −𝑉𝜋 ∕2 and STP corresponds to 𝑉𝑏𝑖𝑎𝑠1 = −𝑉𝜋 ∕2, 𝑉𝑏𝑖𝑎𝑠2 = 0.7 V. 𝑉𝜋 is equal to 3.6 V. MATP, maximum transmission point; STP, specific transmission point.
Fig. 8. BER versus ROP curves with (w/) and without (w/o) KK algorithm for the IQ-MZM operating in push–push mode at MATP and push–pull mode at STP cases. Insets (i)-(iv) are the corresponding constellation diagrams of the 16-QAM signals in the two SSB schemes with and without KK algorithm at the ROP of −20 dBm.
4. Conclusions
CRediT authorship contribution statement
Three types of SSB generation schemes, based on the DD-MZM, IQMZM operating in the push–push and push–pull modes respectively, are numerically analyzed and validated with system simulations in 60 GHz RoF link. For the low-cost DD-MZM SSB scheme, a high optimal CSPR results in low receiving sensitivity and the evident susceptibility of SSB form to the DC drift are the main shortcomings. Instead, although suffering from the same high optimal CSPR issue for the push–push IQMZM SSB scheme, a wide tolerance to the DC drift as well as a low power loss of the modulator can be provided at the expense of cost. In addition, by adjusting the DC bias difference applied to the MZM, the push–pull IQ-MZM SSB scheme can solve the high optimal CSPR issue. The KK algorithm can be used to eliminate the large SSBI resulted from low CSPR, so as to enhance the overall system performance. As compared with the previous two SSB schemes, this scheme can reduce the optimal CSPR by more than 3 dB, and also provides 5 dB improvement in receiver sensitivity at the 7% HD-FEC threshold for 5 Gbaud 16-QAM signal with 100 km fiber transmission. Those benefits come at the cost of increased DSP complexity. In all, the analyses and results presented in this paper provide a deep insight on both reducing the SSBI’s impact and improving the performance for the SSB RoF links.
Yuancheng Cai: Methodology, Validation, Writing - original draft. Xiang Gao: Investigation, Formal analysis. Yun Ling: Conceptualization, Writing - review & editing. Bo Xu: Writing - review & editing. Kun Qiu: Resources. Acknowledgments This work is supported by the National Natural Science Foundation of China (No. 61420106011) and the Fundamental Research Funds for the Central Universities, China (Grant No. ZYGX2016J014). References [1] C.T. Lin, C.H. Ho, H.T. Huang, Y.H. Cheng, Ultrahigh capacity 2 x 2 MIMO rof system at 60 GHz employing single-sideband single-carrier modulation, Opt. Lett. 39 (6) (2014) 1358–1361. [2] X. Wang, J. Yu, Z. Cao, J. Xiao, L. Chen, SSBI mitigation at 60 GHz OFDM-ROF system based on optimization of training sequence, Opt. Express 19 (9) (2011) 8839–8846. [3] W.J. Fang, X.G. Huang, G. Li, A full duplex radio-over-fiber transmission of OFDM signals at 60 GHz employing frequency quintupling optical up-conversion, Opt. Commun. 294 (2013) 118–122. 7
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