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Detailed investigations are undertaken, for the first time, of the transmission performance of recently proposed novel Adaptively Modulated Optical OFDM (AMOOFDM) modems using Subcarrier Modulation (AMOOFDM-SCM) in single-channel, SMF-based IMDD links without optical amplification and chromatic dispersion compensation. The cross-talk effect induced by beatings among subcarriers of various types is a crucial factor limiting the maximum achievable AMOOFDM-SCM performance. By applying single sideband modulation and/or spectral gapping to AMOOFDM-SCM, three AMOOFDM-SCM designs of varying complexity are proposed, which achieve >60Gb/s signal transmission over 20km, 40km and 60km. Such performances are >1.5 times higher than those supported by conventional AMOOFDM modems.
©2008 Optical Society of America
1. Introduction
Owing to the explosive growth of end-users’ traffic, great effort has been expended on exploring cost-effective solutions for improving the transmission performance of optical networks of various architectures [1]. A wide range of technical strategies in both the optical and electrical domains [2,3] have been proposed, of which Optical Orthogonal Frequency Division Multiplexing (OOFDM) has attracted overwhelming research interest because of its strong inherent tolerance to fibre chromatic dispersion and polarization mode dispersion, significant system flexibility, relatively high signal transmission capacity, as well as potentially low system cost [4–8]. OOFDM can be classified into two main categories including coherent OOFDM [4] and incoherent OOFDM such as Intensity Modulation and Direct Detection (IMDD) OOFDM [5–8]. In particular, IMDD Adaptively Modulated OOFDM (AMOOFDM) has demonstrated great potential for providing a high speed, low-cost and robust solution for practical implementation in cost-sensitive application scenarios such as Multi-Mode Fibre (MMF)-based Local Area Networks (LANs) [5,6] and Single Mode Fibre (SMF)-based access and Metropolitan Area Networks (MANs) [7,8].
AMOOFDM is a signal modulation technique, whereby the modulation format taken on each AMOOFDM subcarrier can be varied according to the frequency response of a given transmission link, i.e. a high (low) modulation format is used on an AMOOFDM subcarrier suffering a low (high) transmission loss. Any AMOOFDM subcarrier suffering a very high loss may be dropped completely if there are still a large number of errors occurred even when the lowest modulation format is employed. Such a subcarrier modulation operation provides the AMOOFDM technique with a unique feature of utilizing very effectively the frequency response characteristics within the entire transmitted signal spectral region. As a direct consequence of the subcarrier modulation format manipulation, for an arbitrary transmission link, the maximized transmission performance is always achievable through negotiations between the transmitter and the receiver. Investigations have shown that optimised AMOOFDM modems can support >50Gb/s signal transmission over 300m in 99.5% of already installed MMF links [5], and that it is also feasible to enable 30Gb/s over 40km and 10Gb/s over 110km signal transmission in directly modulated DFB laser-based SMF IMDD links without incorporating optical amplification and chromatic dispersion compensation [7,8].
However, the conventional AMOOFDM technique just utilizes the frequency response property of a transmission link in the vicinity of the optical carrier frequency, and is not able to adjust the transmitted signal spectrum over a much broad region to make a full use of the available frequency response beyond the baseband. Such a challenge can be overcome by Subcarrier Modulation (SCM) [9], in which an entire baseband signal is modulated onto an intermediate Radio Frequency (RF) carrier that drives directly an Electrical-to-Optical (E/O) intensity modulator. By appropriately detuning the RF carrier frequency, use can be made of the major portion of the frequency response of an arbitrary transmission link. Unfortunately, SCM does not have the capability of manipulating signal modulation formats within the spectral region of each individual SCM subcarrier. This results in the low transmission performance of the SCM technique.
By introducing SCM into AMOOFDM, a novel AMOOFDM-SCM technique has been proposed [10], which consists of two parallel conventional AMOOFDM modems with one operating at the baseband and the other being modulated onto a RF carrier. For simplicity, throughout this paper, each of the above-mentioned AMOOFDM signals produced by a single AMOOFDM-SCM modem is referred to as a SCM subcarrier. Clearly, AMOOFDM-SCM offers salient opportunities of not only manipulating the signal modulation format taken on each individual AMOOFDM subcarrier involved in a SCM subcarrier, but also positing each individual SCM subcarrier at an optimum link frequency response region. The transmission performance of the proposed AMOOFDM-SCM technique has been explored in amplifier-free, worst-case MMF IMDD links [10]. It has been shown that, in comparison with the conventional AMOOFDM modems, AMOOFDM-SCM almost doubles the capacity versus reach transmission performance, and considerably relaxes the minimum requirement on key components involved in the AMOOFDM-SCM modems [10].
As the existence of much wider and flatter frequency responses associated with SMF IMDD links, compared to those corresponding to MMF links, it is greatly advantageous if detailed explorations of the maximum achievable transmission performance of the previously proposed AMOOFDM-SCM technique can be made in SMF-based IMDD transmission links without incorporating optical amplification and fibre chromatic dispersion compensation. The thrust of this paper is, therefore, to address, for the first time, such a challenging issue for practical implementation in access networks and MANs. In addition, the cross-talk effect induced by AMOOFDM subcarriers of various SCM subcarriers within the same AMOOFDM-SCM signal spectrum is identified to be a crucial physical factor limiting the maximum achievable transmission performance of the technique. The physical origin of such an effect is the generation of unwanted subcarrier × subcarrier beating products in the useful signal spectral region, upon square-law direct detection in the receiver.
To maximise the link performance by mitigating the cross-talk effect, in this paper, three AMOOFDM-SCM modem designs are proposed for different application scenarios that may be encountered in access networks and MANs. Here these designs are referred to as AMOOFDM-SCM scheme I, AMOOFDM-SCM scheme II and AMOOFDM-SCM scheme III. The configuration of AMOOFDM-SCM scheme I is identical to that presented in [10], in which two real-valued Double Sideband (DSB) SCM subcarriers are involved with the first SCM subcarrier operating at the baseband and the other being modulated onto an intermediate RF carrier. Whilst the configuration of AMOOFDM-SCM scheme II is similar to AMOOFDM-SCM scheme I, except that, in AMOOFDM-SCM scheme II, a spectral gap in the electrical domain is introduced between the optical carrier and the first SCM subcarrier. The only configuration difference between AMOOFDM-SCM scheme III and AMOOFDM-SCM scheme II is that the two SCM subcarriers in AMOOFDM-SCM scheme III are real-valued Single Sideband (SSB) electrical signals generated by using the phase-shift method [11]. It is worth emphasizing that the optical SSB operation is retained in all the aforementioned three AMOOFDM-SCM modem designs.
It will be shown that, in comparison with the conventional AMOOFDM technique, AMOOFDM-SCM modems of all the proposed designs can improve the capacity versus reach performance by a factor of at least 1.5 for transmission distances up to 60km. In addition, of the proposed three modem designs, AMOOFDM-SCM scheme III (AMOOFDM-SCM scheme I) always offers the highest (lowest) signal transmission performance for transmission distances up to 80km (60km). However, having the simplest modem structure and the highest bandwidth efficiency, AMOOFDM-SCM scheme I may be preferred in practice for short transmission distances of say <20km. In addition, for transmission distances in a range of 20km-40km, use may be made of AMOOFDM-SCM scheme II, since in comparison with AMOOFDM-SCM scheme III, it offers a very similar signal transmission performance of 67Gb/s over 40km, but has a modem structure of much less complexity. For transmission distances in a range from 40km to 80km, AMOOFDM-SCM scheme III may be the best choice and it is able to offer 48Gb/s over 80km signal transmission.
It should be noted that, in [12] a different SSB modulation technique has been reported, which, however, requires a complex coherent transmitter and is not inherently compatible with direct detection. To implement that technique in direct detection systems, a square-root operation has to be applied to the received electrical signals to compensate for the square operation in the photodetector [12].
2. Theoretical models for AMOOFDM-SCM modems and transmission links
The schematic transceiver diagrams of AMOOFDM-SCM scheme I, II and III are illustrated in Fig. 1(a), Fig. 1(b) and Fig. 1(c), respectively. The operating principles for AMOOFDM-SCM scheme III are described in Section 2.1, whilst the operating principles for AMOOFDM-SCM scheme I and II are not presented here, as all the relevant information can be derived easily by taking into account Fig. 1 and Section 2.1. A single-channel, SMF-based IMDD transmission link operating at 1550nm is considered throughout this paper. In Fig. 1(c), a representative frequency response of the link is also shown, in which an AMOOFDM-SCM signal spectrum is inserted. It should be noted that the transmission link is free from both optical amplifiers and chromatic dispersion compensators.
2.1 AMOOFDM-SCM scheme III model
In the AMOOFDM-SCM scheme III transmitter, an input binary data sequence is split into two streams, each of which is encoded independently to serial complex data by using different modulation formats. The complex data is processed separately by each AMOOFDM modem following procedures similar to those presented in [5–7]. The procedures are outlined as followings: a serial-to-parallel converter is utilised to truncate the encoded complex data sequence into a large number of sets of closely and equally spaced narrowband data, the so called AMOOFDM subcarriers. Then an inverse fast Fourier transform (IFFT) is applied to generate real-valued parallel AMOOFDM symbols. Here at the input of the IFFT, a complex conjugate of the original encoded data is introduced, and the original data and its conjugate counterpart are arranged to satisfy the Hermitian symmetry. In addition, no power is contained in the first AMOOFDM subcarrier. To overcome the fibre chromatic dispersion effect, a cyclic prefix, which is a copy of last fraction of each symbol, is added to the front of the corresponding symbol. By utilising a parallel-to-serial converter, the parallel symbols are serialized and a long digital sequence is formed. Finally, after passing through a Digital-to-Analog Converter (DAC) followed by a Low-Pass Filter (LPF), a real-valued DSB baseband signal from each of the two AMOOFDM modems is generated, which is called here as the SCM subcarrier. The two real-valued DSB SCM subcarriers are denoted as A DSB1(t) and A DSB2(t).
As SSB modulation has been widely considered as an effective approach to reduce the subcarrier × subcarrier beating-induced cross-talk effect, the phase-shift method based on the Hilbert transform [11] is applied to A DSB1(t) and A DSB2(t) to perform the SSB signal generation without requiring complex coherent transmitters. The generated real-valued SSB SCM subcarrier can be expressed as
where H{A DSBm(t)} is the Hilbert transform of A DSBm(t). ω RFm is the intermediate RF carrier frequency, and m is the index number of the SCM subcarriers involved in a single AMOOFDM-SCM modem. It should be pointed out that, apart from the necessity for the generation of the real-valued SSB SCM subcarriers, the use of the intermediate RF frequencies is also important to enable the technique to have a capability of fully exploiting the frequency response characteristics of a transmission link. In addition, a reduction in the cross-talk effect is also achievable by appropriately adjusting these RF frequencies, as discussed in Section 4.
Fig. 1. Schematic illustrations of the modem designs for AMOOFDM-SCM scheme I, II and III, together with the transmission link structure considered. A representative link frequency response and an AMOOFDM-SCM scheme III signal spectrum are also shown in Fig. 1(c). LPF: low-pass filter; USB: upper sideband spectrum of the SCM subcarrier.
For simplicity without losing generality, S SSB1(t) and S SSB2(t) are scaled linearly to ensure that they have identical electrical powers. Finally, an intensity modulator is driven directly by
with I dc being the added DC component to ensure that S e(t) is always positive. If use is made of an ideal intensity modulator, the output optical signal is given by
It is worth addressing that, a Quantum Dot Semiconductor Optical Amplifier (QD-SOA) [13] with a typical carrier lifetime of approximately 10ps, is able to achieve a modulation bandwidth as large as about 100GHz. This value is much larger than the bandwidth of the AMOOFDM-SCM signals of interest of this paper. This suggests that a QD-SOA may be used to perform the desired intensity modulation. In such an operation, S e(t) is used to drive directly the QD-SOA with a CW optical wave being injected. The power of the CW optical wave mimics the optical gain variation induced by the electrical waveform of S e(t). Investigations of the transmission performance of the AMOOFDM-SCM technique employing QD-SOAs as intensity modulators are currently being undertaken, and results will be reported elsewhere in due course.
In the AMOOFDM-SCM receiver, the transmitted optical signal is converted into an electrical signal by using a square-law photodetector. Two baseband SCM signals can be obtained by independently performing RF down-conversion followed by a LPF. Finally, the data can be recovered by each of the two AMOOFDM modems in a process of inverse of the transmitters described above.
In the initial stage of establishing a SMF link, negotiations between the transmitter and the receiver take place to identify the highest possible modulation format that should be used on each AMOOFDM subcarrier of individual SCM subcarriers.
It should be pointed out that, orthogonal band multiplexing reported for coherent OOFDM systems [14] can not be employed to reduce the aforementioned cross-talk effect for the IMDD cases considered here, as IMDD systems do not preserve the phase information of transmitted signals, thus the achievement of perfect orthogonality between different SCM subcarriers is impossible, even the following relationship is satisfied:
where Δf SCM and Δf AMOOFDM are the frequency spacing between the adjacent SCM and AMOOFDM subcarriers, respectively, and n is the integer number.
2.2 Models of other components involved in the transmission link
The widely adopted split-step Fourier method is used to model the propagation of the optical signal down an SMF [15]. It is well known that for a sufficient small fiber step length, this treatment yields an accurate approximation to the real effects. In the SMF model, the effects of loss, chromatic dispersion and the optical dependence of the refractive index are included. The effect of fiber nonlinearity-induced phase noise to intensity noise conversion is also considered upon photon detection in the receiver. This SMF model has been successfully used in [6,7].
As mentioned in Section 2.1, a square-law photodetector is utilized in the receiver to detect the optical signals emerging from the transmission links. Shot noise and thermal noise are considered, which are simulated following the procedures similar to that presented in [16], noise generated by beating among signal spontaneous noises are not considered due to the absence of optical amplification in the transmission link.
It should be noted that, all the filters used in simulations are assumed to have ideal square shapes in the frequency domain. Optical carrier suppression is not considered in generating optical SSB signals because of the use of the ideal optical filters. An optical attenuator is inserted between the optical filter and the input facet of the SMF link to adjust the optical power launched into the transmission link.
3. Simulation parameters
Having described the AMOOFDM-SCM scheme III modem and the transmission link, in this section, detailed discussions are made of parameters adopted in numerical simulations. All the parameters listed below are used as default ones unless addressed explicitly in the corresponding text when necessary.
In numerical simulations, for each AMOOFDM modem generating a SCM subcarrier, 64 AMOOFDM subcarriers are considered, in which 31 having identical powers carry real data, one has no power, and the remaining 32 are the complex conjugation of the above-mentioned AMOOFDM subcarriers. The modulation formats used on each AMOOFDM subcarrier vary from Differential Binary Phase Shift Keying (DBPSK), Differential Quadrature Phase Shift Keying (DQPSK), and 16 to 256 Quadrature Amplitude Modulation (QAM), depending on the frequency response of a given transmission link. To improve the transmission performance, gray coding is adopted in mapping binary data into QAM. The cyclic prefix parameter defined in [5–7] is chosen to be 25%. The ADC used here operates at 7 bits quantization and 12.5 GS/s sampling speed. According to the aforementioned parameters, the SCM subcarrier has a bandwidth of 6.25 GHz. In order to reduce the peak-to-average power ratio, signal clipping is applied separately for each SCM subcarrier, and the clipping level defined in [17] is fixed at 13 dB.
An ideal intensity modulator is employed in the transmitter, and a fixed optical power of 6.3dBm is launched into the transmission link. In the receiver, a p-i-n photodetector with a sensitivity of -19 dBm (corresponding to 10 Gb/s nonreturn-to-zero with a BER of 1.0×10-9) and a quantum efficiency of 0.8 is used.
For simulating SMF-based link operating at 1550 nm, Non-Dispersion Shifted Fibers (NDSFs) are adopted, which have the parameters as followings: an effective area of 80 µm2, a dispersion parameter of 17.0 ps/(km·nm), a dispersion slope of 0.07 ps/(km·nm2), a loss of 0.20 dB/km and the Kerr coefficient is taken to be 2.35×10-20 m2/W.
Fig. 2. Signal transmission capacity and RF carrier frequency as a function of transmission distance for AMOOFDM-SCM scheme I.
4. Simulation results
In obtaining the signal transmission performance presented in this section, the signal line rate, Rs, is computed by using the definition given below:
where m is the index of SCM subcarriers involved in a single AMOOFDM-SCM modem of any types. M mk is the number of binary bits carried by the k-th AMOOFDM subcarrier in the m-th SCM subcarrier. N sub is the total number of AMOOFDM subcarriers. N cp is the number of sampling periods occupied by the cyclic prefix. M mk, N sub and N cp are taken to be the values for a single AMOOFDM symbol. T s is the ADC sampling period, which is fixed at 80 ps, according to the simulation parameters listed in Section 3. M mk/⌊(N sub+N cp)T s⌋ is the data rate conveyed by the k-th AMOOFDM subcarrier in the m-th SCM subcarrier. A R s is considered to be valid only when the total channel Bit Error Rate (BER) defined in [5–7] remains at 1.0×10-3 or better, as such a BER leads to error-free operation when combined with Forward Error Correction (FEC).
4.1 Transmission performance of AMOOFDM-SCM scheme I and the cross-talk effect
As already described in Sections 1 and 2, AMOOFDM-SCM scheme I consists of two real-valued DSB SCM subcarriers with the first SCM subcarrier operating at the baseband and the other being modulated onto an intermediate RF carrier. For such a modem, the signal transmission capacity and the corresponding optimum RF carrier frequency are plotted in Fig. 2 as a function of transmission distance. In simulating Fig. 2, both the RF carrier frequency and the signal modulation format taken on each AMOOFDM subcarrier are adjusted until a maximum signal transmission capacity is obtained for a specific transmission distance. To demonstrate the effectiveness of the AMOOFDM-SCM technique, the transmission performance of a conventional AMOOFDM modem is also given in Fig. 2.
It can be seen from Fig. 2 that, in comparison with the conventional AMOOFDM modem, AMOOFDM-SCM scheme I improves considerably the signal transmission performance, especially for short transmission distances. >66.5Gb/s AMOOFDM-SCM signal transmission over 20km is feasible, which almost doubles the transmission performance achieved by the conventional AMOOFDM modem. On the other hand, the frequency response narrowing effect induced by a long SMF causes an increase in transmission loss for AMOOFDM subcarriers contained in the passband SCM subcarrier, such a loss increase can be compensated partially when the RF carrier frequency is decreased appropriately to ensure that the passband SCM subcarrier spectrum locates at a relatively low transmission loss region of the link frequency response. However, as discussed below, the reduced RF carrier frequency also strengthens the cross-talk effect occurring between the two SCM subcarriers. As a direct result of the co-existence of the above-mentioned two effects, the optimum RF carrier frequency reduces with increasing transmission distance and a stair-like optimum RF frequency developing curve occurs, as observed in Fig. 2. All the above-mentioned characteristics agree very well with those reported in [10], confirming the validity of the AMOOFDM-SCM model developed here.
Figure 2 also shows that, the effectiveness of AMOOFDM-SCM scheme I declines quickly with increasing transmission distance. Such a developing trend is underpinned by the frequency response narrowing effect, and the cross-talk encountering between different AMOOFDM subcarriers of various SCM subcarriers. To obtain an in-depth understanding of the significance of the impact of the cross-talk effect on the signal transmission performance of the technique, Fig. 3 is presented, where the signal line rate of the passband SCM subcarrier is plotted as a function of transmission distance for the cases of excluding and including the baseband SCM subcarrier. It should be noted that, to perform a fair comparison between Fig. 3 and Fig. 2, the optimum RF carrier frequencies obtained in Fig. 2 are also adopted in calculating Fig. 3. The exclusion of the baseband SCM subcarrier in AMOOFDM-SCM scheme I can omit completely the cross-talk effect experienced by the passband SCM subcarrier. By considering Fig. 2 and comparing the two lineshapes shown in Fig. 3, it implies that the cross-talk effect can lower the signal transmission capacity of the passband SCM subcarrier by a factor of approximately 2. In addition, the cross-talk effect is less pronounced for short transmission distances, as expected from discussions in [10].
Fig. 3. Signal line rate of passband SCM subcarrier of AMOOFDM-SCM scheme I as a function of transmission distance for the cases of including and excluding the baseband SCM subcarrier.
Having demonstrated the crucial role of the cross-talk effect in determining the maximum achievable transmission performance of the AMOOFDM-SCM technique, special attention is given to identify practical solutions to minimize the impact of such an effect. Considering the fact that the physical origin of the cross-talk effect is subcarrier × subcarrier beatings upon direct detection in the receiver, an effective approach is, therefore, to apply SSB modulation to all the SCM subcarriers involved. The feasibility of such an approach is examined in Fig. 4 and Fig. 5. In Fig. 4, a frequency down-converted electrical spectrum of the DSB passband SCM subcarrier received after passing through a 60km SMF (with the DSB baseband SCM subcarrier being present) is illustrated, which shows the existence of a significantly distorted spectrum, especially for the AMOOFDM subcarriers locating close to the edge of the spectrum. In sharp contrast with Fig. 4, Fig. 5 shows a rectangular spectral shape appearing when SSB modulation is applied to both SCM subcarriers. As a direct result of that, AMOOFDM-SCM scheme III is proposed and discussed in Section 4.3 and Section 4.4.
Fig. 4. Frequency down-converted spectrum of the DSB passband SCM subcarrier after passing through 60 km SMF. The RF carrier frequency is 19GHz.
Fig. 5. Frequency down-converted spectrum of the SSB passband SCM subcarrier after passing through 60km SMF. The RF carrier frequency is 19GHz.
4.2 Transmission performance of AMOOFDM-SCM scheme II
Based on the analysis in Section 4.1, it is envisaged that, upon direction detection in the receiver, beatings between different AMOOFDM subcarriers of the same SCM subcarrier also causes the occurrence of an unwanted spectral distortion region in the vicinity of the optical carrier. This statement is confirmed in Fig. 6, where a spectral distortion region having a bandwidth equal to the SCM subcarrier bandwidth is observed around the zero frequency point. To enable the separation of such an unwanted spectral region from the useful SCM subcarrier spectrum, here AMOOFDM-SCM scheme II is proposed, in which a spectral gap having a bandwidth of the SCM subcarrier bandwidth is introduced between the optical carrier and the spectral band of the first SCM subcarrier. In addition, similar to AMOOFDM-SCM scheme I, the two SCM subcarriers are DSB signals in AMOOFDM-SCM scheme II. It is interesting to note that use has also been made of the spectral gap approach in experimental investigations of long-haul OOFDM transmission [18].
Fig. 6. Received signal spectrum of AMOOFDM-SCM scheme II after transmitting 40 km. The two SCM subcarriers operate at RF carrier frequencies of 18.75GHz and 43.75GHz.
Figure 7 shows the signal capacity versus reach performance of AMOOFDM-SCM scheme II. For comparing different modem designs, the transmission performance of AMOOFDM-SCM scheme I is also plotted in Fig. 7. Taking into account the discussions in Fig. 6 and the simulation parameters listed in Section 3, it is very easy to work out that the RF carrier frequency of the first SCM subcarrier should be fixed at 18.75GHz. On the other hand, the RF carrier frequency of the second SCM subcarrier is taken to be 43.75GHz, which is an optimized value corresponding to a transmission distance of 40km. The validity of the adoption of such a constant RF carrier frequency for the second SCM subcarrier is discussed in Section 4.3.
Fig. 7. Transmission capacity versus reach performance of AMOOFDM-SCM scheme II. The two SCM subcarriers are taken to be 18.75GHz and 43.75GHz.
It is shown in Fig. 7 that, in comparison with AMOOFDM-SCM scheme I, a notable enhancement in signal transmission performance is observed for AMOOFDM-SCM scheme II when transmission distances are shorter than about 60km. As an example, AMOOFDM-SCM scheme II is capable of transmitting 69.4Gb/s and 67.2Gb/s signals over 20km and 40km, respectively. However, for transmission distances of >60km, the AMOOFDM-SCM scheme II enabled-performance worsens rapidly. This arises due to the co-existence of the link frequency response narrowing effect and the cross-talk effect. The first effect becomes even severe for the SCM subcarrier locating far away from the optical carrier frequency, and the later effect becomes strong when the transmission distance increases due to fibre chromatic dispersion and nonlinearity.
4.3 RF carrier frequency dependent transmission performance of AMOOFDM-SCM scheme III
Having demonstrated the importance of SSB modulation and spectral gapping in enhancing the transmission performance of AMOOFDM-SCM modems of two different designs, in Section 4.3 and Section 4.4, an integration of these two individual approaches into a single AMOOFDM-SCM modem is undertaken, which brings about a new modem design called as AMOOFDM-SCM scheme III. In such a scheme, SSB modulation is applied to all the involved SCM subcarriers with a spectral gap of desired width being inserted between the optical carrier and the first SCM subcarrier.
To examine the validity of the assumption adopted in modelling Fig. 7 and, more importantly, the RF carrier frequency-dependent transmission performance of AMOOFDM-SCM scheme III, a contour plot of the maximum achievable signal line rate versus RF carrier frequencies of both the SCM subcarrier 1, ω RF1, and the SCM subcarrier 2, ω RF2, is presented in Fig. 8 for a 40km SMF transmission link. It can be seen from Fig. 8 that, there exists an optimum RF carrier frequency region, corresponding to which a maximum signal transmission performance is achievable. A 5GHz (3GHz) alteration of ω RF2 (ω RF1) gives rise to a <3% variation in signal transmission capacity of the technique. In addition, simulations also show that, the optimum ω RF1 is independent of transmission distance, as expected from the discussions in Section 4.2, and that an extension of the transmission distance from 40km to 80km just reduces the optimum ω RF2 value by approximately 2GHz. All the above-mentioned characteristics indicate that the transmission performance of AMOOFDM-SCM scheme III is very robust to transmission distance and RF carrier frequency. Therefore, for practical cases including the conditions used in Fig. 7, it is sufficiently accurate to fix both RF carrier frequencies at their values optimized for a specific link operating condition. Such robustness may not only speed up considerably the modem design processes, but also reduce significantly the modem cost.
Fig. 8. Contour plot of signal transmission capacity as a function of RF carrier frequencies of the first and second SCM subcarriers for AMOOFDM-SCM scheme III. Numerical simulations are undertaken for a 40 km transmission link.
It should also be noted, in particular, that the optimum ωRF1 value of approximately 12GHz, as shown in Fig. 8, is almost twice of the SSB SCM subcarrier bandwidth, and almost equal to the DSB SCM subcarrier bandwidth discussed in Section 4.2. The physical reason behind such a behavior is that the phase-shift method using the Hilbert transform creates a SSB output by phasing its corresponding DSB sidebands in a way that the DSB sidebands cancel out on one side of the RF carrier frequency and add on the other side [11]. Clearly, such a cancellation operation can not be maintained perfectly if the spectral gap identical to the SSB SCM subcarrier bandwidth is introduced, as one sideband of the DSB signal overlaps with the newly generated spectral distortion region, as illustrated in Fig. 6 and Fig. 9.
It is also very interesting to see from Fig. 8 that, for a given ω RF2, similar transmission performance is obtainable in two ω RF1 regimes. This can be explained by considering Fig. 9, where two residual spectral distortion regions are still present in the SSB signal spectrum after direct detection. The first spectral distortion region close to the zero frequency point occurs because of beatings of various AMOOFDM subcarriers within the same SCM subcarrier. Whilst the second spectral distortion region present between the two SCM subcarriers occurs due to the co-existence of both the above-mentioned physical mechanism and beatings between various AMOOFDM subcarriers of different SCM subcarriers within the same modem. Shifting ω RF1 towards the low (high) frequency side results in the first SCM subcarrier experiences increased distortions induced by the first (second) spectral distortion region, and simultaneously experiences decreased distortions induced by the second (first) spectral distortion region. The co-existence of all these effects gives rise to the occurrence of the two ω RF1 regions, over which the same transmission performances can be observed.
Fig. 10. Signal transmission capacity versus reach performance of AMOOFDM-SCM scheme III. For comparison, the transmission performances for AMOOFDM-SCM scheme I, AMOOFDM-SCM scheme II and conventional AMOOFDM are also illustrated.
4.4 Transmission performance of AMOOFDM-SCM scheme III and modem design criteria
The transmission performance of AMOOFDM-SCM scheme III is presented in Fig. 10 for the operating conditions of adopting two optimum RF carrier frequencies of ω RF1=12GHz and ω RF2=37.5GHz, as identified in Fig. 8. To undertake performance comparisons between different modem designs, the signal capacity versus reach performances are also plotted for AMOOFDM-SCM scheme I, AMOOFDM-SCM scheme II and conventional AMOOFDM. It can be found from Fig. 10 that, of the proposed three types of modem designs, AMOOFDM-SCM scheme III is capable of always offering the highest transmission performance for SMF link lengths of up to 80km. As an example, the AMOOFDM-SCM scheme III-enabled signal transmission of 71Gb/s over 20km, 63Gb/s over 60km and 48Gb/s over 80km is feasible. It is also worth emphasizing that all the performances specified above are at least 1.5 times higher than those supported by the conventional AMOOFDM technique over the same SMF transmission links.
As also seen in Fig. 10, for SMF link lengths in a range from 20km to 40km, the transmission performances of AMOOFDM-SCM scheme II and AMOOFDM-SCM scheme III are very similar, both of which are, however, higher than those offered by AMOOFDM-SCM scheme I. This indicates that the impact of the reduction in the cross-talk effect due to applying SSB modulation to SCM subcarriers is negligible on the signal transmission performance of AMOOFDM-SCM scheme III. On the other hand, such a cross-talk reduction is crucial for transmission distances of >60km, because over such a distance region, AMOOFDM-SCM scheme III can improve considerably the signal transmission performance compared to AMOOFDM-SCM scheme II. Finally, for transmission distances beyond 90km, the link frequency response becomes very narrow and is not able to provide AMOOFDM-SCM scheme III with a sufficiently broad bandwidth required, thus resulting in the rapidest performance degradation with increasing transmission distance among all the modem types proposed in this paper.
Use may be made of each of the three modem designs to satisfy requirements of different application scenarios that may be encountered in access networks and MANs. Firstly, given the fact that AMOOFDM-SCM scheme I has the simplest modem structure and the highest bandwidth efficiency, it may be preferred for practical implementation in very short transmission links of, say 20km, to enable 66.5Gb/s signal transmission. Secondly, AMOOFDM-SCM scheme II consists of a structure less complex than AMOOFDM-SCM scheme III, it may be employed to extend the above-mentioned transmission links to approximately 40km, with the signal transmission capacity being improved slightly. Finally, the AMOOFDM-SCM scheme II- enabled transmission links can be extended further to about 60km with a 10% enhancement of signal transmission capacity, compared to that offered by AMOOFDM-SCM scheme II at 40km.
5. Conclusions
Detailed investigations have been undertaken, for the first time, of the transmission performance of a recently proposed novel AMOOFDM-SCM modem in single-channel, SMF-based IMDD transmission links without optical amplification and chromatic dispersion compensation for practical applications in access networks and MANs. It has been shown that the cross-talk effect induced by beatings among subcarriers of various types is a crucial factor limiting the maximum achievable AMOOFDM-SCM performance. To mitigate such an effect, SSB modulation and spectral gapping are applied to AMOOFDM-SCM. As a direct result, three AMOOFDM-SCM modem designs of varying electrical complexity have been proposed, which include, for example, AMOOFDM-SCM scheme I, AMOOFDM-SCM scheme II and AMOOFDM-SCM scheme III.
Numerical simulations have shown that, in comparison with conventional AMOOFDM modems, all the proposed three modem designs can improve significantly the signal transmission capacity versus reach performance by a factor of at least 1.5 for transmission distances of up to 60km. AMOOFDM-SCM scheme I has the least modem complexity and the highest bandwidth efficiency, it may be preferred for use in very short transmission links of up to 20km to enable 66.5Gb/s signal transmission. With an approximately 1Gb/s increase to such a signal capacity, AMOOFDM-SCM scheme II having a structure less complex than AMOOFDM-SCM scheme III, may be employed to extend the transmission link to 40km. Once again, the AMOOFDM-SCM scheme II-supported transmission links may be upgraded even further to 63Gb/s over 60km, when use is made of AMOOFDM-SCM scheme III.
Given the fact that the fibre nonlinearity-induced wavelength division multiplexing (WDM) effect is not significant for transmission distances of <80km when the optical launch power of each channel is optimised [7], it is, therefore, expected that the above-mentioned transmission performances of the three proposed modems still retain for WDM channel cases. It is also worth mentioning that the experimental verification of the proposed three AMOOFDM-SCM schemes is currently being undertaken, and results will be reported elsewhere in due course.
Acknowledgment
This work was partly supported by the European Community’s Seventh Framework Programme (FP7/2007-2013) within the project ICT ALPHA under grant agreement n° 212 352, in part by the U.K. Engineering and Physics Science Research Council (EPSRC) under Grant EP/D036976, and in part by The Royal Society Brian Mercer Feasibility Award. The work of X. Zheng and J. L. Wei was also supported by the School of Electronic Engineering and the Bangor University.
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