1. Introduction

Long reach passive optical networks (LR-PONs) which extend the coverage span of the access networks from the traditional 20-km range to up to 100-km have gained considerable research interests, since the LR-PONs would replace the current separate metro and access networks with a single, integrated network [1], and therefore can significantly reduce the cost and simplify the architecture [2]. To reach the target of a higher data rate in LR-PONs, optical intensity modulation and direct-detection (IM/DD) scheme is still preferred due to its simple implementation and low cost compared with coherent schemes. For IM/DD LR-PONs, chromatic dispersion (CD) induced power fading is a challenge which would significantly limit the transmission distance. One solution is to use single side-band (SSB) modulation. The SSB schemes [3–5 ], however, have relatively low receiver sensitivity since half of the signal power is lost. Meanwhile, the optical SSB scheme may also result in additional complexity [3] and reduced electrical spectrum efficiency [5]. It is therefore desirable to use DSB modulation for high spectral efficiency while eliminating the dispersion induced power fading. Several CD compensation schemes have been proposed in DSB modulated IM/DD systems [6–9 ]. However, they may either require a feedback channel providing the knowledge of the amount of CD [8,9 ], or may require complicated transmitter configurations with less efficient data transmission [6,7 ], since 50% of the transmission symbols were used for CD compensation.

Optical orthogonal frequency-division multiplexing (O-OFDM) [10] is a promising modulation scheme due to its high spectral efficiency, its robustness towards inter-symbol interference (ISI), and its modulation flexibility when combined with adaptive bit and power loading schemes [11,12 ]. Recently, we proposed to use super-Nyquist image induced aliasing to compensate the chromatic dispersion induced power fading [13] in optical OFDM systems. Super-Nyquist spectrum components (images) are generated along with the in-band spectrum in sampled systems using digital-to-analog converters (DACs) [14]. The super-Nyquist images are usually removed using a so-called anti-aliasing filter after the DAC output [4,5 ]. We showed in [13] that by taking advantage of the aliasing caused when down sampling the received signal, the super-Nyquist image can actually be used for compensation of CD induced power fading. In this paper, we elaborate the topic of super-Nyquist image based dispersion compensation technique. We show that diversity is introduced by deliberate aliasing using the 1st order super-Nyquist images. We then propose to use fractional sampling and a per-subcarrier MRC scheme to harvest this diversity. We experimentally show that the signal-to-noise ratio (SNR) of the fractionally sampled signals can be significantly improved using our proposed scheme. We also consider 3 kinds of QPSK modulated 10-GHz OFDM signals, i.e. conventional OFDM signals, discrete Fourier transform spread (DFT-S) OFDM signals and code-division multiplexing (CDM) OFDM signals, and show that DFT-S OFDM signaling along with the super-Nyquist image induced aliasing can provide the best performance, extending the reach of the 10-GHz QPSK modulated signals to up to 100 km. In addition, we show that by compensating the power of the higher frequency spectrum components, the achievable data rate can also be increased when adaptive bit and power loading schemes are applied. An 83.2-km, 40-Gb/s IM/DD OFDM-PON is successfully demonstrated.

2. Operating principle

2.1 The principle of super-Nyquist image induced aliasing

Figure 1(a) shows the spectrum of a cosine signal with a frequency $f_{out}$ generated from a DAC with a sampling clock $f_{clock}=20\text{(GHz)}$. The sin(x)/x envelope is due to the zero-order hold operation of the DAC [12]. Typically, a 5th order Bessel filter is applied after the DAC output to remove the higher order super-Nyquist images, leaving only the first order image which appears at$f_{clock}-f_{out}$. At the receiver, an analog-to-digital converter (ADC) with a bandwidth larger than $f_{clock}-f_{out}$ and a sampling rate of $m\times f_{clock}$ (m = 2, 3, 4 …) is used to digitize the signal along with the 1st order image. The fractional sampling operation here is equivalent to having $m$ receptions at the receiver, each with a different sampling phase. Note that since the frequency of the 1st order image $f_{clock}-f_{out}>f_{clock}/2$, spectrum aliasing will occur when down-sampling to$f_{clock}$[see Fig. 1(b)] according to Nyquist–Shannon sampling theorem. From Fig. 1(b) one can see that the conjugated of the 1st order image is superimposed with the fundamental frequency$f_{out}$. It should be noted that the conjugate of the 1st order image is exactly a replica of the fundamental frequency with its amplitude attenuated by filtering [14].

 

Fig. 1 (a) Frequency representation of the DAC output spectrum; (b) illustration of spectrum aliasing occurred during down-sampling without anti-aliasing filtering using sample rate$f_{clock}=20\text{(GHz)}$.

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Therefore, the power of the signal $f_{out}$ can be enhanced if we combine the m receptions in away that maximizes its output power, or equivalently, its signal-to-noise ratio (SNR) [15]. In a DSB modulated optical OFDM system, this power enhancement effect can be considered as a kind of diversity, as shown in Fig. 2(b) . There is no diversity introduced without aliasing, thus all of the m sampling points exhibit the same SNR [black line in Fig. 2(b)]; however, when deliberate aliasing is introduced using the super-Nyquist images, diversity can be observed [see the dashed lines in Fig. 2(b)]. This diversity can be harvested by using fractional sampling [16] and a per-subcarrier MRC algorithm. Accordingly, the proposed SNR enhancement technique can be performed by taking the following steps: 1) keeping the super-Nyquist images unfiltered at the transmitter, i.e., no anti-aliasing filter is added after the AWG; 2) using an ADC with a bandwidth larger than that of the signal at the receiver (fractional sampling); 3) applying a digital filter with a bandwidth larger than that of the signal to remove the unwanted noise; 4) resampling to m × (m = 2, 3, 4, …) of its original sample rate (2 × the Nyquist bandwidth) ; 5) down-sampling by keeping every m ^th sample starting with the l ^th (l = 1, 2, 3, …, m) sampling point, thereby obtaining m signals; 6) minimum mean square error (MMSE) based channel equalization and per-subcarrier SNR acquisition for each of the m signals and 7) demodulating using per-subcarrier MRC. The resultant signal after per-subcarrier MRC can be expressed as:

 

Fig. 2 Block diagram of MRC for DSB modulated optical OFDM systems with super-Nyquist image induced aliasing. Inset A, B, C, and D are the electrical spectra of their corresponding test points. AWG: arbitrary waveform generator; ADC: analog-to-digital convertor; Bw: Nyquist bandwidth of the received signal.

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Fig. 3 (a) Simulated channel SNR using MRC for 5 × oversampled signals; (b) measured electrical back-to-back SNR of the AWG generated 16-QAM modulated OFDM signals with 20 Gsa/s sample rate using MRC; (c) received 16-QAM constellation for a 10-GHz receiver (no aliasing); (d) received 16-QAM constellation for a 15-GHz receiver (w/ aliasing).

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Table 1. Parameters Used for Experiments and Simulations

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2.2 Spreading schemes using DFT (DFT-S) and CDM

For conventional OFDM signals, each subcarrier is modulated independently in parallel, rendering them susceptible to CD induced frequency nulls. Therefore, in this work, two spectrum spreading schemes, i.e., DFT-S and CDM are introduced to evaluate our proposed CD compensation scheme.

DFT-S OFDM has been well studied in wireless communications [17] and have recently been revisited in optical communications community [18,19 ]. For DFT-S OFDM signals used in this work, 256 QPSK samples are firstly converted into frequency domain using DFT. The resulting 256 frequency bins are then mapped to selected subcarriers. Hermitian symmetry (conjugate symmetry) is imposed to the 544 frequency subcarriers to generate real-valued time-domain signals after inverse fast Fourier transform (IFFT). The remaining procedures in the transmitter are the same as the conventional OFDM signaling (shown in Fig. 4 ). At the receiver, after timing and frequency synchronization [20], the 8-point cyclic prefix (CP) is removed and a 544-point FFT is used to convert the DFT-S OFDM signal into frequency domain. After channel equalization, The 256 data-carrying subcarriers are selected and a 256-point IFFT is used to reconvert the data samples. Information-carrying data symbols are spread among the frequency subcarriers using DFT-S OFDM signaling; hence they can be more tolerant towards CD induced power fading compared with OFDM signals. DFT-S OFDM is also known to have improved peak-to-average power ratio (PAPR) performance. A signal with a lower PAPR can lead to a larger power density (and enhanced SNR) using the same peak amplitude, which can be beneficial in our IM/DD system with a limited optical modulation index (OMI).

 

Fig. 4 Experimental setup. DFB: distributed feedback; PC: polarization controller; MZM: Mach-Zehnder modulator; VOA: variable optical attenuator; EDFA: Erbium doped fiber amplifier; BPF: band pass filter.

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CDM-OFDM has also been extensively studied in wireless literatures [21]. The coding (spreading) process in CDM-OFDM signaling is similar to that of DFT-S OFDM, with the difference in that a 256$\times$256 Walsh matrix W is used for spreading and despreading operation, instead of using FFT and IFFT. The Walsh matrix can be generated using

3. Experimental setup

The experimental setup of the DSB modulated IM/DD OFDM-PON using super-Nyquist image based CD compensation is shown in Fig. 4. Three cascaded OFDM frames, i.e. conventional OFDM, CDM-OFDM and DFT-S OFDM, were used for evaluation each run. The detailed parameters used in the experiments and simulations are summarized in Table 1.

The total number of subcarriers used for fast Fourier transform (FFT) is 544. The 2nd −257th subcarriers were modulated, while the 1st, 258th – 273rd subcarriers were zero padded. In order that the OFDM signals after IFFT can be real-valued, the complex conjugates of the 2nd – 272nd subcarriers were placed to the 544th – 274th subcarriers, respectively. For conventional OFDM signals, the 256-channel QPSK modulated signals were directly mapped to the 2nd - 257th subcarriers. For CDM-OFDM signals, the 256-channel QPSK modulated signal vector x was firstly multiplied by a 256 × 256 Walsh matrix W before being sent for mapping, which has been detailed in section 2. For DFT-S OFDM signals, similarly, a 256-point FFT was performed on the 256-channel QPSK modulated signals before subcarrier mapping, as shown in Fig. 4. After IFFT, the time-domain signal was then padded with an 8-point cyclic prefix (CP), parallel/serial converted, and then digital/analog (D/A) converted using an arbitrary waveform generator (AWG 7122C) operating at 20 Gsa/s. The calculated data rate was18.53 Gb/s. The output signals from the AWG were then amplified and sent to a Mach-Zehnder modulator for DSB modulation. A distributed feedback (DFB) laser with a center wavelength of 1550.12 nm were used here as the light source. For each transmission, the first symbol was added for timing synchronization [20], the next 30 symbols were added as training symbols for channel estimation, and the last 3 × 300 symbols were effective OFDM, CDM-OFDM, and DFT-S OFDM payloads. Although 30 symbols were used for channel estimation, this over-head is typically ignored for direct-detected (DD) OFDM in laboratory conditions [4], since the channel impulse response (CIR) is stable in DD-OFDM systems [5]. The optical signals were then sent into a spool of standard single mode fiber (SSMF) for transmission. At the receiver, a variable optical attenuator (VOA) was used to change the received optical power (ROP) prior to a pre-amplified receiver which consists of an Erbium doped fiber amplifier (EDFA) with a noise figure of about 4.3 dB and an optical band pass filter (OBPF) with a 0.8 nm bandwidth. The pre-amplified optical signals were then detected via a photo detector (PD) with a bandwidth of 43 GHz. The electrical signals after PD were digitized using a 100Gsa/s real time oscilloscope (DPO73324D) and then processed off-line. The off-line DSP procedures include pre-filtering, down sampling, timing synchronization, serial-to-parallel(S/P) conversion, FFT, MMSE channel equalization, SNR probing, per-subcarrier MRC, demodulation, and error counting. For CDM-OFDM and DFT-S OFDM signals, a decoding and an IFFT operation, respectively, were required before demodulation, as shown in Fig. 4.

4. Results and discussion

We firstly investigate the feasibility of the CD compensation scheme using super-Nyquist image induced aliasing by simulation. The simulation parameters were shown in Table 1. Again, three kinds of OFDM signal, i.e. OFDM, CDM-OFDM, and DFT-S OFDM, were considered. For each run, 300 symbols of payloads were tested. The results were then averaged over 20 runs. Figure 5(a) shows the simulated required received optical power (ROP) at FEC limit (BER = 3.8E-3) as a function of the transmission distance, from which the following observations could be made: 1) using spectrum spreading via CDM and DFT (red and green curves) improves the system performance, as compared with conventional OFDM signals (blue curves); 2) the DFT-S OFDM signal has the best performance of the three, which could be attributed to its lower PAPR [see Fig. 5(d)]: a lower PAPR can lead to a larger power density for signals with the same peak amplitude; 3) the distance can be extended from less than 40 km to around 90 km for conventional OFDM signals when our proposed scheme is applied, with a forbidden window at around 70 km, where both the in-band subcarriers and their 1st order super-Nyquist images are suppressed due to CD induced power fading. This can also be seen from the SNR vs. frequency curves shown in Fig. 5(b). A possible workaround for this forbidden window issue is to use adaptive modulation schemes [11,12 ], which will be discussed shortly; 4) for CDM-OFDM and DFT-S OFDM signals, the receiver sensitivity can be significantly improved by using our proposed scheme [see the solid red and green curves in Fig. 5(a)]. The reason why the OFDM signal had the worst performance among the three is that since all subcarriers were modulated independently in OFDM signals, the data streams in the deep nulled subcarriers due to CD induced powerfading cannot be recovered, which would result in a serious error floor; while for CDM-OFDM and DFT-S OFDM signals, the data samples were spread across all sub-carriers using CDM and DFT, respectively. Therefore, the frequency nulls caused by CD will only result in a flat SNR degradation for all data streams. It should be noted that, as the transmission length increases, the needed excessive bandwidth also increases, as the first available window becomes smaller [11]. One can refer to Fig. 5(e) for the required receiver bandwidth for a given fiber length, which is calculated according to the1st order super-Nyquist image position of the frequency point with 3-dB attenuation due to CD induced power fading. We also investigated the impact of oversampling ratio on the system performance by changing the oversampling factor m from 2 to 6. Figure 5(c) shows the SNR performance when different values of m are used after 50-km of SSMF transmission and at a received optical power (ROP) of −10 dBm. It can be seen from Fig. 5(c) that improved SNR performance can be obtained as the oversampling ratio increases, at the cost of increased processing complexity. The performance improvement becomes marginal, however, when the oversampling factor$m>3$.

 

Fig. 5 (a) Required ROP at FEC limit vs. fiber length; (b) SNR performance after 70-km SSMF transmission; (c) SNR performance for various over-sampling factors; (d) PAPR performance of the OFDM signals; (e) estimated bandwidth requirement as a function of transmission distance. ROP: received optical power; FEC: forward error correction; PAPR: peak-to-average power ratio.

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We then experimentally evaluated the super-Nyquist image based CD compensation technique. We measured the BER as a function of the ROP at back-to-back and after 83.2 km of SSMF transmissions, as shown in Fig. 6 . From Fig. 6, the following observations could be made: 1) DFT-S OFDM signals have the best BER performance for all cases; 2) after 83.2 km SSMF transmission, the BER of all three OFDM signals succeeded to drop below FEC limit when using our proposed CD compensation technique with a 14-GHz receiver bandwidth; 3) when without the super-Nyquist image induced aliasing (10-GHz cases), the power penalties were more than 8 dB for CDM-OFDM and DFT-S OFDM signals; for conventional OFDM signals, however, a minimum BER of around 2E-2 was observed, as shown in Fig. 6(a). This is due to the severely deteriorated SNR (below 5 dB in some of the subcarriers) caused by CD, as shown in Fig. 6(b).

 

Fig. 6 (a) Measured BER vs. ROP for back-to-back (B-2-B, dashed lines) and after 83.2-km of SSMF transmission (solid lines); (b) probed SNR for OFDM signals w/ and w/o aliasing after 83.2-km of SSMF transmission.

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As shown in Fig. 3 and Fig. 7(b) , the SNR of the received signals were significantly improved after deliberate aliasing was introduced via 1st order super-Nyquist image. It is therefore possible to increase the available bit rate for the conventional OFDM signals by using super-Nyquist image induced aliasing when an adaptive bit and power loading algorithm [22] is employed. We considered optical B-2-B, 48.3-km and 83.2-km SSMF transmission cases for measurement of the achievable bit rate at FEC limit. The initial channel SNR curves for each receiver bandwidth were measured before bit loading. A set of BER vs. total number of loaded bits ($N_{bits}$) were then measured for each receiver bandwidth, from which we obtain the achievable data rate (DR) at FEC limit vs. the receiver bandwidth for the four cases, as shown in Fig. 7(a). The transmitted data rate DR was calculated using$DR=f_{clock}\times N_{bits}/\left(N_{FFT}+N_{cp}\right)$, where$N_{bits}$is the number of total allocated bits. Figure 7(b) shows the sampled signal constellations at FEC limit. Figure 7(c) is the measured channel SNR after transmitting 48.3 km, showing a more than 12 dB SNR improvement for 48.3-km casewhen super-Nyquist image induced aliasing is utilized. Figure 7(d) shows the loaded bit at each subcarrier according to its measured initial SNR. One can see that for an OFDM-PON system with a fixed 10-GHz bandwidth, introducing deliberate aliasing does improve the achievable data rate: about 10% improvement was obtained in optical B-2-B case when a 13.5 GHz receiver was used, achieving a peak bit rate of 57 Gb/s. For 48.3 km and 83.2 km SSMF transmission cases, the data rate improvements are about 10.5% and 5.2%, respectively. A bit rate of 40 Gb/s could be achieved after 83.2 km SSMF transmission using a 14-GHz receiver, meaning that using adaptive modulation schemes can significantly increase the system capacity compared with previous experiments using QPSK modulation where only an 18.53 Gb/s was achieved. It should be noted that the proposed scheme only takes advantage of the residual super-Nyquist image to enhance the SNR; no modifications are made at the transmitter. Therefore, no power overhead is needed in order to implement this scheme.

 

Fig. 7 (a) Measured achievable bit rate as a function of receiver bandwidth; (b) sampled signal constellations at FEC limit; (c) measured channel SNR after 48.3 km of SSMF transmission w/ (12.5-GHz bandwidth) and w/o (10-GHz bandwidth) aliasing; (d) bit allocation for a 46 Gb/s OFDM signal transmission through 48.3 km of SSMF.

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5. Conclusions

We have experimentally demonstrated a CD compensation scheme using super-Nyquist image induced aliasing for DSB modulated OFDM-PONs. Simulation and experimental results showed that the proposed aliasing based CD compensation technique can significantly extend the reach of DSB modulated PON systems at the cost of only a slight increase in the receiver bandwidth. We showed that diversity is introduced to the higher frequency components by deliberate aliasing using the 1st order super-Nyquist images. We have proposed to use fractional sampling plus per-subcarrier MRC to harvest this diversity. It has been confirmed that DFT-S OFDM signal outperforms both OFDM and CDM-OFDM signal in DSB modulated PON systems due to spectrum spreading and its low PAPR. By using super-Nyquist image induced aliasing, an 83.2-km, 18.53-Gb/s QPSK OFDM-PON system has been successfully demonstrated. Meanwhile, it was also observed that using super-Nyquist image induced aliasing can effectively enhance the channel SNR, and thus increase the achievable bit rate when adaptive modulation schemes were applied, depending on the transmission distance. A 10.5% and 5.2% increase in achievable bit rate was obtained using super-Nyquist image induced aliasing after 48.3 km and 83.2 km SSMF transmission cases, respectively, achieving a data rate of 40 Gb/s after 83.2 km SSMF transmission. The data rate improvement may be negligible when both the in-band subcarriers and their corresponding images are suppressed, which happens when the transmission distance is around 70-km.