1. Introduction

1.1 Background

Digital Signal Processing (DSP) for modern communication systems has attracted overwhelming scientific and industrial interest due to its great capability of improving the transmission performance and system’s flexibility, offering system adaptivity, and reducing the cost of future photonic networks [1, 2]. As a very successful paradigm of the practical implementation of DSP in communication systems, Orthogonal Frequency Division Multiplexing (OFDM) has been rapidly and widely adopted in wireless, wireline and broadcast systems for efficiently dealing with linear signal distortions encountered when transmitting over dispersive fading channels [3]. OFDM is a form of multi-carrier modulation, where a single high-speed information bearing stream is transmitted over a number of harmonically related narrowband sub-carriers. Recently, OFDM was introduced into the optical domain, leading to the generation of an Optical OFDM (OOFDM) technique [4].

Two main variants of OOFDM have been extensively investigated, including incoherent OOFDM such as Intensity-Modulation and Direction-Detection (IMDD) OOFDM [5,6] and coherent OOFDM [7,8]. IMDD OOFDM has demonstrated great potential for practical implementation in cost-sensitive application scenarios such as Local Area Networks (LANs) and Metropolitan Area Networks (MANs); Whilst CO-OOFDM has been widely regarded as a promising candidate for future long-haul high capacity transmission systems. The scope of this paper is to investigate a novel technique for IMDD OOFDM for applications in LANs and MANs.

In LANs, it is well known [5,6] that, to upgrade the present 1Gb/s Multimode Fibre (MMF)-based backbones to 10Gb/s and above with the installed fibre infrastructure being preserved, the primary difficulty is the highly-variable modal dispersion present in the graded index fibre, which, in turn, causes the large bandwidth variation. To address this technical challenge, a wide range of approaches are currently being investigated, including low-cost coarse Wavelength Division Multiplexing (WDM) [9], offset launch [10], multilevel coding [11] and adaptive optics [12]. In MANs, considerable effort has been expended on exploring low-cost Chromatic Dispersion (CD) compensation schemes for Single-Mode Fibre (SMF)-based transmission systems operating at >10Gb/s, a number of compensation techniques in the electrical domain have been reported, including, for example, the combination of electrical Feed-Forward Equalizers (FFEs) and Decision Feedback Equalizers (DFEs) [13], as well as nonlinear electrical equalization [14].

It is very interesting to note that, a recently proposed signal modulation technique known as Adaptively Modulated OOFDM (AMOOFDM) has demonstrated great potential for providing a high-speed, cost-effective solution for practical implementation in both LANs and MANs [5-6,15-18], as it has the unique features listed as followings: a) very high signal capacity versus reach performance. Statistical investigations have shown [17] that the AMOOFDM technique can support >50Gb/s signal transmission over 300m in 99.5% of already installed MMF links with loss margins of >7dB; b) excellent performance flexibility and robustness to fibre types, variation in launch conditions and signal bit rates [15-18]; c) efficient use of link spectral characteristics. AMOOFDM has the salient capability of exploiting the fibre bandwidth to its full potential, instead of using the spectral characteristics in the vicinity of the reference frequency only; d) as already mentioned above, re-utilisation of legacy fibres, and finally, e) cost-effective in system installation and maintenance. The primary reason underpinning the above-mentioned AMOOFDM features is that, individual sub-carriers within a symbol can be manipulated in the frequency domain by using different signal modulation formats according to the frequency response of a given transmission link. Such sub-carrier modulation manipulation provides AMOOFDM with an unique opportunity for exploiting, in a cost-effective manner, the transmission link bandwidth to its full potential, instead of using the link spectral characteristics in the vicinity of the reference frequency only.

In all the AMOOFDM work reported previously [5-6, 15-18], a Cyclic Prefix (CP) of fixed time duration has been utilised to combat Differential Mode Delays (DMDs) occurring in MMFs and CDs associated with SMFs. A CP is essentially a copy of the last fraction of each time domain OFDM symbol and added to the front of the corresponding symbol in the transmitter. This treatment produces quasi-periodically extended time domain OFDM symbols, leading to the maintenance of the orthogonality between sub-carriers within the symbol. More importantly, due to the CP insertion, the channel dispersive effect becomes equivalent to a cyclic convolution. If the CP length is larger than the expected maximum delay spread to be encountered, after transmitting through the channel, the dispersive effect is localized within the prefix region only. Prior to performing the Fast Fourier Transform (FFT) in the receiver, the distorted CP is removed, thus the OFDM symbol carrying useful information can be recovered without interference between different symbols. As the CP duration can be chosen by design, in principle, AMOOFDM can be made free from any arbitrary delay spread. It is worth emphasizing that a CP does not convey any useful information.

From the above analysis, it is clear that, if a CP time duration is smaller than the DMD (CD) associated with a MMF (SMF) link, the imperfectly compensated DMD (CD) effect limits considerably the maximum achievable transmission performance of the AMOOFDM signals [5, 15]. In addition, a small CP may also affect the sub-carrier orthogonality, resulting in a significant increase in the minimum required Signal-to-Noise Ratio (SNR) for a specific signal modulation format being taken on a sub-carrier [19]. On the other hand, if the CP is longer than the DMD (CD) of a MMF (SMF) link, for a fixed signal sampling speed, the CP wastes a large percentage of the transmitted signal power, giving rise to a degraded effective signal SNR. Furthermore, an excessive length of CP also prevents us from making full use of the available link bandwidth.

Therefore, it is greatly advantageous if the CP lengths can be made variable, according to the properties of different optical transmission links, to ensure that the selected CP lengths are just sufficiently long to compensate for DMDs (CDs) and other effects in MMF (SMF)-based links. For simplification, here the adjustable CP length technique is referred to as Adaptive Cyclic Prefix (ACP) and the AMOOFDM modem using ACP as AMOOFDM-ACP. It should be noted that the concept of ACP was first proposed in [5] by the same research group of this paper. Very recently, for long-haul transmission systems, the transmission link dependent CP length has been shown in a single figure of [20], in which an incoherent OOFDM modem using an identical modulation format crossing all sub-carriers is considered.

1.2 Scope of this paper

The thrust of this paper is to explore thoroughly, for the first time, the impact of ACP on the transmission performance of the AMOOFDM-ACP technique for various application scenarios including MMF-based LANs and SMF-based MANs. It is shown that, in comparison with the conventional AMOOFDM technique, AMOOFDM-ACP can improve the signal transmission capacity versus reach performance by a factor of at least 2 (1.3) for transmission distances of >1000m MMFs (<80km SMFs), together with 1dB enhancements in link loss margin and better performance robustness. In addition, for achieving a specific transmission performance, AMOOFDM-ACP can also relax significantly the requirement on the frequency bandwidth of the Directly Modulated DFB Lasers (DMLs) employed in the transmitter.

As the other salient feature of this paper, three ACP mechanisms are identified, which are referred to, throughout this paper, as ACP mechanism I, ACP mechanism II and ACP mechanism III. ACP mechanism I is to compensate completely any amount of dispersion by adopting sufficiently long CPs required by the link. As demonstrated in Sections 3, 4 and 5, this mechanism is effective for dispersion-limited transmission links; ACP mechanism II is to make efficient use of the OFDM signal powers and the link bandwidths by employing relatively short CP lengths, provided that the link is free from dispersion. This mechanism plays a crucial role in determining the transmission performance of the technique for dispersion-compensated links having spectral bandwidths larger than those corresponding to the transmitted signals. Finally, ACP mechanism III is similar to ACP mechanism II, except that it plays a role when the link spectral bandwidths are comparable to (or smaller than) those corresponding to the transmitted signals, the resulting noise margins are too low to accommodate the signal SNR growth induced by the short CP lengths. This mechanism sets a minimum CP length that may be adopted for a given transmission system. Clearly, the effectiveness of these mechanisms depends upon the transmission link properties.

2. Transmission link model, signal characteristics and simulation parameters

As already addressed in Section 1, AMOOFDM is a signal modulation technique that enables individual sub-carriers within a symbol to be manipulated in the frequency domain by using different modulation formats according to the frequency response of a given transmission link. Generally speaking, a high (low) modulation format is used on a sub-carrier suffering a low (high) transmission loss. Any sub-carrier suffering a very high loss may be dropped completely to avoid the occurrence of a large number of errors on the sub-carrier.

2.1 Transmission link model

In this paper, a typical single-channel, optical amplifier-free, IMDD transmission link based on a DML operating at 1550nm is considered. The link consists of only the transmitter and the receiver linked by MMFs [5] or SMFs [15]. In the transmitter, the generated real-valued AMOOFDM signal in the electrical domain is used to drive directly a DML to produce an optical AMOOFDM waveform, which is then coupled into a transmission link. The transmitted optical signal is detected by a photodetector, and compared against that in the transmitter, the inverse procedure of electrical signal processing is utilised in the receiver to recover the received data. The detailed link diagrams can be found in [5, 15], where the block diagrams of the transmitter and the receiver are also illustrated. Numerical simulations are undertaken, based on the comprehensive theoretical AMOOFDM model developed in [5,15] for MMF and SMF links.

It should be noted that, to produce a real-valued AMOOFDM signal to drive directly the DML in the transmitter, the encoder located at the input of the Inverse Fast Fourier Transform (IFFT) is modified by creating the truncated original complex parallel data in the positive frequency bins and the complex conjugate of the data in the negative frequency bins. In addition, no power is contained in the first sub-carrier (close to the signal baseband) of the positive frequency bins. The data contained in these two frequency bins are arranged specially to satisfy Hermitian symmetry. Sub-carriers in all these frequency bins are able to convey useful information. In this paper, only is information transmitted in the positive frequency bins recovered in the receiver.

In the receiver, all the optical signal power emerging from the link is coupled into and subsequently detected by a square-law photodetector. The received electrical signal, A_E(t), is given by

where A_O(t) is the optical signal coupled into the link; R(t) is the impulse response of the transmission link in the electrical domain; v(t) represents the receiver related noise and signal distortions due to intermixing amongst sub-carriers and the carrier wave. The noise in the receiver is simulated following procedures similar to those presented in [21]. Both shot and thermal noises are considered, whilst signal-spontaneous noise and spontaneousspontaneous beat noise are excluded because of the absence of optical amplifiers in the transmission link. Upon photon detection in the receiver, intermixing takes an effect. It should be noted that, based on the electrical signal waveform in the transmitter, A_O(t) is simulated by using a lump DFB laser model discussed below. Therefore, A_O(t) includes the DML-induced nonlinear effects. In addition, as described below, use is also made of a comprehensive SMF theoretical model to simulate the optical propagation down the SMF transmission links.

The procedures of maximizing signal modulation format levels for individual sub-carriers and of choosing appropriate CP lengths are described as followings: In the initial stage of establishing a connection over a link, negotiations between the transmitter and the receiver take place to identify the highest signal modulation format that should be used on each sub-carrier, based on a CP length estimated initially by using the DMD or CD value of a given transmission link. The signal modulation format can vary from DBPSK, DQPSK, and 16 to 256QAM depending upon the frequency response of the link. Generally speaking, a high (low) modulation format is used on a sub-carrier suffering a low (high) transmission loss. The total channel Bit Error Rate (BER), BER_T, is written as

where N_s is the number of sub-carriers used in the positive frequency bins; En_k is the number of detected errors and Bit_k is the number of transmitted binary bits. Both En_k and Bit_k are for the k-th sub-carrier, whose sub-channel BER_k is defined as BER_k=En_k/Bit_k. Based on BER_T and BER_k, the modulation format used on a specific sub-carrier can be adjusted through the negotiations. It is worth addressing that, a high modulation format is always preferred if BER_T remains at 1.0×10^-3 or better, and that any sub-carrier suffering a very high loss may be dropped completely if the corresponding BER_k k={1, 2,....N_s-1} is still very large even when DBPSK is used.

After completing the first round of signal modulation format manipulation for all the sub-carriers, attempts are then made to alter the initially estimated CP length to examine if the previously obtained signal capacity may be increased. The CP length alteration may vary both the signal modulation formats and/or their distribution across the sub-carriers, therefore, for any changes made to CP, the aforementioned negotiation procedures are repeated, until a maximum signal transmission capacity is achieved by using a minimum CP length. Once the link has been established, the modulation format on each sub-carrier and the selected CP length remain unchanged.

It is well known that direct modulation of a laser drive current introduces a nonlinear frequency chirp to the optical field, which varies with both the drive current and the optical characteristics. To simulate the nonlinear properties of a DFB-based DML, here a lumped DFB laser model developed in [5] is adopted, taking into account a wide range of nonlinear effects such as longitudinal-mode spatial hole-burning, linear and nonlinear carrier recombination and nonlinear gain. The influence of the laser linewidth on the link performance is negligible because IMDD transmission is considered in this paper. The feasibility of the DFB model has been confirmed by good agreement with experimental measurements [4].

To simulate MMF links, measured impulse responses of an installed worst-case MMF [5] are adopted, whose frequency responses corresponding to a 300m link subject to central launch and small offset launch have been presented in [5]. It is assumed that the 3-dB bandwidth of the link is proportional to the inverse of transmission distance. The impact of modal noise is assumed to be negligible. The validity of such an assumption has been verified extensively by using a statistical approach developed in [18].

Here the widely adopted split-step Fourier method is employed to model the propagation of the optical signal down a SMF [22]. It is well known that for a sufficiently small fibre split-step length, this theoretical treatment yields an accurate approximation to the real effects. In the SMF model, the effects of loss, CD and optical power dependence of the refractive index are included. The effect of fibre nonlinearity-induced phase noise to intensity noise conversion is also considered upon the photon detection in the receiver. This model has been successfully used in [15].

2.2 Signal characteristics

To gain a better understanding of the simulated results presented in the following sections of this paper, the AMOOFDM-ACP signal characteristics are summarized below. The total transmitted signal bandwidth, BW_T, is given by

where r_s is the signal sampling speed; T_b is the entire symbol period, and C_p is the ACP parameter, which is defined as

with T_p being the CP time duration. The symbol period used for carrying real information is T_b-T_p. From Eq. (3), the entire symbol period can be written as

It should be pointed out that, due to the use of Analogue-to-Digital Converters (ADCs) in the AMOOFDM transceivers, in practice, the signal sampling speeds are fixed. Therefore, it can be easily understood from Eq. (5) that T_b increases linearly with C_p.

Due to the insertion of a CP into each symbol, the bandwidth occupied only by the signal, BW_S, is given by

Clearly, for a fixed signal sampling speed, an increase in CP length decreases BW_S. In addition, the insertion of a CP can also decrease the effective signal SNR. Considering the noise-like nature of an OFDM signal having a fixed power, the CP-induced SNR reduction, Δ_SNR, can be expressed as

where S_nr is the signal SNR without considering the CP. It should be emphasized that, Eq. (7) is not valid for very short CP lengths as the strong inter-sub-carrier mixing effect brings about significant signal distortions [19].

Considering the operating principles of a CP, and the relationship between the dispersion tolerance of a specific signal and its bandwidth [21], the dispersion tolerance, D_dispersion, of the AMOOFDM-ACP signals is proportional to T_p/BW ² _T, which can be expressed as

It can be found from Eq. (8) that, for a given r_s parameter, the dispersion tolerance increases linearly with CP length in a dispersion limited system. Finally, the signal line rate, R_b, is calculated by using

where n_kb is the number of binary bits conveyed by the k-th sub-carrier within one symbol period. It should be pointed out, in particular, that only when the condition of BER_T=1.0×10^-3 is satisfied, the signal line rate is considered to be valid.

2.3 Simulation parameters

In simulating the AMOOFDM-ACP modem, in the transmitter, 2N_s=64 sub-carriers are employed, of which 31 carry real information and 1 contains no power. The remaining 32 are the complex conjugate of the aforementioned sub-carriers. The powers of all the non-dropped sub-carriers are considered to be identical regardless of their modulation formats. For QAM signals, gray-coded bit mapping is utilized for enhancing the performance of the AMOOFDM-ACP modem. ADCs are adopted with 7-bit resolution at sampling speeds of 12.5 GS/s. The signal clipping levels are fixed at 13dB. The main purpose of adopting these parameters listed above is to ease the performance comparison made with results published in previously papers [5,15] to demonstrate the impact of ACP and explore its operation mechanisms. Of course, use can also be made of a set of the optimized modem parameters identified in [17].

For simulating the performance of the DFB-based DML operating at 1550nm, here all the DFB parameters presented in [5] are considered, based on which the DFB laser can operate in a typical bias current range of 20-60mA (a threshold bias current of 4.2mA) and a typical peak-to-peak drive current range of 10-30mA, and produces output optical powers in a range of 5-10dBm. If the DFB operating condition of a 30mA bias current and a 15mA peak-to-peak drive current is chosen, the resulting output optical signal has a power of 6.3dBm, a signal extinction ratio of 2dB and an adiabatic frequency chirp of 5GHz. It should be pointed out, in particular, that under such operating conditions, the DML frequency chirp effect has been found to be negligible (minimum) on the transmission performance of the AMOOFDM signals in MMFs [5] (SMFs [15]). As discussed in [5,15], the occurrence of the minimum DML effect on the AMOOFDM transmission performance is because of the coexistence of the AMOOFDM dispersion tolerance for a specific CP, the DML operating condition-dependent frequency chirp effect and the DML operating condition dependent-signal extinction ratio. In the following sections, the 30mA bias current and the 15mA peak-to-peak drive current are treated as optimum operating conditions.

In the receiver, a p-i-n photo-detector is used, which has a quantum efficiency of 0.8 and a sensitivity of -19dBm (corresponding to a 10Gb/s nonreturn-to-zero (NRZ) with a BER of 1.0×10^-9).

The 3-dB bandwidths (DMDs) of the adopted MMF link are of 202.5 MHz ·km (2.0 ns/km) and 241.5 MHz km (1.3 ns/km) for central and small offset launch, respectively [5]. For simulating SMF links, Non-Dispersion Shifted Fibres (NDSFs) are considered, whose parameters are listed in [15].

It should be emphasized that all the above-mentioned parameters are treated as default ones, unless addressed explicitly in the corresponding text when necessary.

3. Performance of AMOOFDM-ACP signals over MMFs

3.1. Capacity versus reach transmission performance

The AMOOFDM-ACP transmission performance subject to central and small offset launch [10] is shown in Fig. 1 and Fig. 2, respectively, together with the minimum CP length required for achieving the signal transmission capacity. For performance comparison, the transmission performance supported by the conventional AMOOFDM modem using a fixed CP parameter of C_p=25% is also plotted in the same figures. In obtaining these two figures, the DMLs are set to operate at the optimum conditions discussed in Section 2.3, and optical attenuators inserted between the DMLs and the transmission links are adjusted to ensure that the optical powers coupled into the MMF links are fixed at 0dBm.

 

Fig. 1. Transmission capacity (left) and minimum required cyclic prefix (right) versus transmission distance over the MMF link subject to central launch.

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As expected from Eq. (8), Fig. 1 and Fig. 2 show that the minimum CP lengths required for completely compensating the DMDs of the MMF links increase linearly with transmission distance. In particular, in comparison with the case where AMOOFDM is considered, AMOOFDM-ACP can improve the signal transmission capacity by a factor of at least 2 for transmission distances of >1000m, over which the link DMDs are the dominant factor limiting the maximum achievable transmission performance of the technique [15]. This operation scenario can be regarded as a typical example of how ACP affects the transmission performance through ACP mechanism I.

 

Fig. 2. Transmission capacity (left) and minimum required cyclic prefix (right) versus transmission distance over the MMF link subject to small offset launch.

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As observed in Fig. 1 and Fig. 2, within the above-mentioned transmission distance region, the existence of the slow decay of the AMOOFDM-ACP transmission performance with increasing transmission distance, is because a long CP length associated with a long transmission distance decreases the signal power used for conveying useful information. This leads to a reduced effective signal SNR and subsequently low signal modulation formats taken on sub-carriers. In addition, the long distance-induced increase in link transmission loss also contributes to the decay [5].

As illustrated in Fig. 1 and Fig. 2, for transmission distances of <600m, the minimum required CP parameter is smaller than C_p=25%, implying that the DMDs are compensated completely by the AMOOFDM modems, and that ACP mechanism I does not contribute to the transmission performance observed in this region. Within such a transmission distance region, the transmission performance of the AMOOFDM-ACP modems is almost identical to that achieved by the conventional AMOOFDM modems, suggesting that ACP mechanism II does not play a role for this case either. This can be explained by considering ACP mechanism III. To maintain a sufficient noise margin before the transmitted data is corrupted, due to the dependence of signal modulation format on CP length [19], a short CP length allows relatively low signal modulation formats to be taken on sub-carriers. This constraint is very strong for MMF links (or long SMF links, as discussed in Section 4), as the majority of sub-carriers locating at the flat passband region of the MMF frequency responses, suffer large transmission losses of approximately 10dB below the reference frequency point [17,18]. By considering Eq. (9), it can be understood that the small CP length-induced short symbol time duration, together with the simultaneous reduction in the number of the binary bits contained in the symbol, gives rise to the almost identical transmission performance for both the AMOOFDM-ACP and AMOOFDM modems.

By comparing the ACP-enabled transmission performances shown in Fig. 1 and Fig. 2, it is very interesting to note that, the use of AMOOFDM-ACP can also improve the performance robustness to different launch conditions over the entire transmission range.

3.2. Link loss margin

Another very prominent feature of AMOOFDM-ACP is its ability to enhance the link loss margin, as demonstrated in Fig. 3 and Fig. 4 for different launch conditions. The link loss margin is defined as the variation range of the optical signal power, corresponding to which a BER_T=1.0×10^-3 can be maintained without varying the adopted signal modulation formats [5, 15]. In order to alter the optical power coupled into the link, an optical attenuator is inserted between the DML and the MMF links. All other parameters are identical to those employed in simulating Fig. 1 and Fig. 2, except that the transmission distances are fixed at 1000m and 1100m for Fig. 3 and Fig. 4, respectively.

As seen in Fig. 3 and Fig. 4, in comparison with AMOOFDM, apart from the above-mentioned significant improvement in signal transmission capacity, AMOOFDM-ACP can also enhance the link loss margin by about 1dB, which is independent upon different launch conditions. This is a direct result of ACP mechanism I, which ensures that all types of the MMF links are DMD free, regardless of different launch conditions.

It should be emphasized, in particular, that the performances similar to those shown in Fig. 1-Fig. 4 are also observed in a large number of MMF links having impulse responses constructed statistically by using an approach developed in [17]. This indicates that AMOOFDM-ACP is very effective not only for the MMF link considered here, but also for the vast majority of MMF links. The detailed statistical evaluation of the effectiveness of the AMOOFDM-ACP technique will be reported elsewhere in due course.

 

Fig. 3. Total channel BER as a function of optical power launched into the 1000m MMF link subject to central launch for the cases of using CP=25% and ACP.

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Fig. 4. Total channel BER as a function of optical power launched into the 1100m MMF link subject to small offset launch for the cases of using CP=25% and ACP.

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4. Performance of AMOOFDM-ACP signals over SMFs

4.1. Capacity versus reach transmission performance

Similar to those illustrated in Fig. 1 and Fig. 2, the signal line rate, the minimum required CP length and the corresponding transmission performance supported by the conventional AMOOFDM technique for SMF links are shown in Fig. 5, where a DML and an ideal intensity modulator are considered. The inclusion of the DML is because the DML-induced nonlinear effects are no longer negligible for SMF links [15]. In simulating Fig. 5, an optical power of 6.3dBm is assumed to be coupled into the SMF-link.

For the case where the DML model is considered, Fig. 5 shows that, compared to that achieved by AMOOFDM, AMOOFDM-ACP is capable of improving the transmission performance by a factor of approximately 1.3 for transmission distances of <80km. Over such a transmission distance region, the minimum required CP length grows linearly with transmission distance. This agrees very well with the results obtained in [15,20]. The minimum required CP lengths are smaller than the fixed CP value of 25%, indicating that the present systems are free from the ACP mechanism I effect.

The observed signal transmission capacity improvement results from ACP mechanism II. Since the SMF frequency response for <80km is broad, which is capable of providing the majority of sub-carriers with relatively low transmission losses. Sufficiently large noise margins are, therefore, available to enable that individual sub-carriers can accommodate a SNR growth caused by the reduced CP length, causing that the signal modulation formats are independent of the variation in the CP length. On the other hand, a small CP length produces a short OFDM symbol period. As a direct result of the co-existence of these two processes, the improvement in signal transmission capacity occurs, as shown in Fig. 5.

It can also be seen in Fig. 5 that, the transmission performance of the AMOOFDM-ACP signals using the DML model is very similar to that achieved by the AMOOFDM signals for transmission distances of >80km, over which the link loss and the receiver noise dominate the transmission performance [15]. To partially overcome the noise effect, use can be made of a relatively small CP length to increase the effective signal SNR. This is verified in Fig. 5, where a slight increase in signal capacity occurs for a reduced CP length in a transmission distance range of 80-100km. However, such a capacity improvement is considerably low, compared to that observed for <80km. ACP mechanism III is responsible for such a signal transmission capacity developing trend, because the SMF frequency response becomes narrow with increasing transmission distance, and deep frequency response nulls occur in the signal spectral region. From the above analysis, it is clear that ACP mechanism III sets a minimum CP length for a given transmission link, as shown in Fig. 5.

For the case where an ideal intensity modulator is considered, Fig. 5 shows that, over the entire transmission distance range, the transmission performance of the AMOOFDM-ACP signals is increased by a factor of about 1.2, compared against that achieved by AMOOFDM. ACP mechanism II is the physical reason behind such behaviours. However, this improvement is not as significant as that observed for the DML case for <80km. This can be explained by considering the processes described as follows: The ideal intensity modulator produces a double sideband optical signal in the transmitter, upon the photon detection in the receiver, intermixing between the carrier wave and each of these sidebands distort severely the received signal, giving rise to the observed transmission performance degradation. On the other hand, the performance improvement for transmission distances beyond this region, is mainly due to an increase in the effective signal SNR. The transmission link loss and the receiver noise play key roles in determining the transmission performance for >80km. The signal extinction ratio corresponding to the ideal intensity modulator is very higher than that corresponding to the DML. For a fixed input optical power, the signal produced by the ideal intensity modulator has a high effective signal SNR, which enhances the tolerance to the link loss and the receiver noise, as well as the reduced bandwidth of the SMF frequency response for long transmission distances.

 

Fig. 5. Transmission capacity (left) and cyclic prefix (right) versus transmission distance in the SMF link including and excluding the DML model.

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4.2. Link loss margin

In Fig. 6, the link loss margin is plotted as a function of transmission distance. Here numerical simulations are undertaken for a SMF link involving the DML operating at optimum conditions. It can be found from Fig. 6 that, for transmission distances of <80km, apart from the significant signal capacity improvement discussed previously, AMOOFDM-ACP can also increase the link loss margin by about 1dB, compared to that achieved by AMOOFDM. As already discussed in Fig. 5, the observed link loss margin improvement mainly results from ACP mechanism II. Whilst for transmission distances beyond 80km, the obtained link loss margins are almost identical to those offered by AMOOFDM, because the transmission links are transmission loss-limited.

 

Fig. 6. Link loss margin and signal line rate as a function of transmission distance in a SMF fibre link for the AMOOFDM-ACP and AMOOFDM modems.

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5. ACP-enabled DFB bandwidth relaxation

Given the fact that the frequency chirp induced by a DFB laser-based DML is closely related to the DFB bandwidth, a large DFB bandwidth is thus preferred in practical system design. However, a commercially available DFB laser has a bandwidth of typically 10GHz, which is comparable to the transmitted signal bandwidth. Therefore, it is greatly advantageous if a simple and cost-effective approach can be identified to relax the requirement on the DFB bandwidth without compromising the transmission performance. Fortunately, the use of ACP can fulfil this goal.

The signal line rate as a function of DFB bandwidth for different CP lengths is shown in Fig. 7 for a 1000m MMF link subject to central launch condition. Since a large bias current gives a high DFB bandwidth, the variation in DFB bandwidth is obtained by altering the bias current with a peak-to-peak drive current being fixed at 15mA. All other parameters are the same as those adopted in Fig. 1.

 

Fig. 7. Signal line rate as a function of DFB bandwidth for different CP lengths over a 1000m MMF link subject to central launch.

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Fig. 8. Signal line rate as a function of DFB bandwidth for different CP lengths over a 20km SMF link.

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It can be seen from Fig. 7 that, for achieving a specific signal transmission capacity, ACP can significantly relax the requirement on the DFB bandwidth, ACP can always compensate completely for the DMDs associated with the link. It is interesting to note that, for a given CP length, there exists an optimum DFB bandwidth, corresponding to which a maximum signal transmission capacity can be found. For DFB bandwidths smaller than the optimum value, the signal capacity reduction shown in Fig. 7 is due to the imperfect DMD compensation for the adopted CP length; whilst for DFB bandwidths larger than the optimum value, the decreased signal extinction ratio contributes to the sharp fall in signal transmission capacity, as shown in Fig. 7. In addition, with shortening the CP length, a high DFB bandwidth is necessary to compensate completely for the DMD, resulting in the optimum DFB bandwidth shifting towards the high bandwidth region, as illustrated in Fig. 7.

As seen from Fig. 8, ACP is also very effective for relaxing the requirement on the DFB bandwidth for SMF links. In calculating Fig. 8, a 20km SMF link is utilised and all other parameters are identical to those adopted in Fig. 6. Since ACP mechanism II is responsible for the transmission performance improvement over this transmission distance region, a short CP length in Fig. 8 is, on the contrary to Fig. 7, preferable to effectively lower the DFB bandwidth requirement for achieving a given signal transmission performance. Furthermore, compared with Fig. 7, the signal line rate shown in Fig. 8 drops sharply with decreasing the DFB bandwidth, this is because the small DFB bandwidth enhances the DFB-induced frequency chirp effect.

6. Conclusions

By introducing ACP into the conventional AMOOFDM technique, a new AMOOFDM-ACP technique has been proposed. Detailed investigations of the impact of ACP on the transmission performance of the AMOOFDM-ACP technique have been undertaken in a single channel, DML-based, IMDD MMF/SMF links without optical amplification and dispersion compensation. It has been shown that, in comparison with AMOOFDM having a fixed CP parameter of 25%, AMOOFDM-ACP can improve the signal transmission capacity by a factor of at least 2 (1.3) for transmission distances of >1000m MMFs (<80km SMFs), together with 1dB improvement in link loss margin. Furthermore, ACP can also enhance the flexibility and robustness of the systems. Finally, numerical simulations have also shown that the AMOOFDM-ACP technique can significantly relax the requirement on the DFB bandwidth for achieving a specific signal transmission capacity. It is also worth mentioning that the experimental verification of the effectiveness of the proposed ACP technique is currently being undertaken, and results will be reported elsewhere in due course.

Three mechanisms have been identified, through which ACP affects significantly the transmission performance of the technique. The effectiveness of these mechanisms depends upon the transmission link properties. It is expected that both ACP mechanism I and ACP mechanism II are also effective for coherent OOFDM systems, in which, however, the ACP mechanism III effect is negligible because of the existence of flat SMF frequency responses.