DFT-based offset-QAM OFDM for optical communications

Jian Zhao

doi:10.1364/OE.22.001114

1. Introduction

Multicarrier techniques have attracted much interest for high-speed optical communication systems [1–8], due to their higher spectral efficiency and enhanced tolerance to dispersion. Two common multicarrier systems are conventional orthogonal frequency division multiplexing (C-OFDM) [1–4] and Nyquist frequency (or wavelength) division multiplexing (N-FDM/N-WDM) [5–8]. The former utilizes a sinc-function spectrum to achieve sub-channel orthogonality while the latter employs filters at transmitters/receivers to create a rectangular spectral profile (see Fig. 1). However, with either technique, there is a long oscillating tail in the frequency or time domain, resulting in disadvantages such as vulnerability to intercarrier interference (ICI) in C-OFDM and a long memory length for pulse shaping in N-FDM.

Fig. 1 Spectra of conventional OFDM, N-FDM, and offset-QAM OFDM

Download Full Size | PDF

Offset quadrature amplitude modulation (offset-QAM) is a group of modulation formats in general communications [9], and has been investigated in multicarrier systems [10–12]. Recently, this concept was introduced to optical communications [13–17]. The concept can be implemented in either the optical [13, 16] or electrical domain [14, 15]. It has been theoretically proved that the required signal spectra for sub-channel orthogonality can be greatly relaxed [13]. For example, the square-root-raised-cosine (SRRC) function (see Fig. 1), well known for inter-symbol interference (ISI) free operation in the single-channel case, cannot achieve sub-channel orthogonality in multicarrier systems unless offset-QAM formats are used. Consequently, when compared to C-OFDM and N-FDM, offset-QAM OFDM exhibits greatly improved performance and enhanced tolerance to filter bandwidth in the all-optical domain [13]. However, previous studies in optical communications [13–16] are based on the configuration where sub-channels are modulated and detected on a sub-channel by sub-channel basis. This implementation is difficult to scale to a large number of subcarriers. Similar to C-OFDM, discrete-Fourier-transform (DFT) based implementation is more computationally efficient. Additionally, channel equalization can be achieved at lower complexity using one-tap equalizers, and phase estimation can be realized via pilot tones. However, this implementation has not been investigated in optical communications.

In this paper, we demonstrate and investigate DFT-based implementation of offset-QAM OFDM with both experiments and simulations. We discuss the design of the pulse-shaping filter and dispersion compensation, and implement the system employing signal spectral profiles of the SRRC functions whose roll-off coefficient is defined as α, and the super-Gaussian functions with different order numbers. It is shown that the proposed scheme can support various signal spectral profiles with negligible performance penalty. We compare this system to C-OFDM and N-FDM. The results show that DFT-based offset-QAM OFDM can greatly relax the need of guard interval (GI) for dispersion compensation. When compared to N-FDM, the required memory length of the filter for pulse shaping can be reduced to two regardless of the transmission distance.

2. Principle of DFT-based offset-QAM OFDM

Figure 2 depicts the principle of multiplexing and de-multiplexing of offset-QAM OFDM. In single-carrier offset-QAM, the quadrature signal is delayed by T/2 with respect to the in-phase signal, where T is the symbol period. Offset-QAM OFDM multiplexes multiple sub-channels carrying offset-QAM data, with π/2 phase difference between adjacent sub-channels. This scheme has been shown to exhibit greatly reduced crosstalk levels due to the relaxed requirements for sub-channel orthogonality in either the optical and electrical domain [13–15].

Fig. 2 Principle of multiplexing and de-multiplexing of offset-QAM OFDM. N is assumed to be an even number.

Download Full Size | PDF

In Fig. 2, modulation and detection are performed on a sub-channel by sub-channel basis. Although this implementation is suitable to all-optical offset-QAM OFDM due to the bandwidth limitation of optoelectronic devices, it is not efficient for DSP-generated schemes, especially when the number of subcarriers and/or the memory length of the pulse-shaping filter are large. Additionally, a multi-tap time-domain equalizer is required for each de-multiplexed sub-channel at the receiver to compensate the channel response while DFT-based implementation enables channel equalization at lower complexity using one-tap equalizers.

In this paper, we investigate a DFT-based offset-16QAM OFDM system, as illustrated in Fig. 3. Two bi-polar four-amplitude-shift-keying (4-ASK) data are encoded with Gray coding. For the in-phase tributary, the phases of even subcarriers are set to be 0 (or π) while those of odd subcarriers are set to be π/2 (or 3π/2). Conversely, for the quadrature tributary, the phases of odd subcarriers are set to be 0 (or π) while those of even subcarriers are set to be π/2 (or 3π/2). The quadrature tributary is then delayed by T/2 with respect to the in-phase tributary. An inverse fast Fourier transform (IFFT) is applied to generate time-domain samples from the in-phase tributary at times mT, and from the quadrature tributary at times (m + 1/2)T, where m is an integer. The generated parallel outputs pass through finite impulse response (FIR) filters for pulse shaping before parallel-to-serial (P/S) conversion. Assuming that a_i,n and s_i,k are the frequency-domain n^th subcarrier data and the time-domain k^th signal sample in the i^th OFDM symbol, the time-domain signal in C-OFDM can be obtained by:

s (i \cdot N + k) = \sum_{n = 0}^{N - 1} a_{i, n} \exp (2 π j (i \cdot N + k) \cdot n / N) = s_{i, k} k = 0,1 ... N-1

where N is the number of subcarriers. In offset-QAM OFDM where the impulse response of the pulse-shaping filter in Fig. 2 is represented by h(k), the time-domain signal of OFDM symbols may overlap so Eq. (1) has to be generalized as:

\begin{array}{l} s^{r e a l} (i \cdot N + k) = \sum_{p = - \infty}^{+ \infty} \sum_{n = 0}^{N - 1} a_{p, n}^{r e a l} \exp (j π n / 2) \cdot \exp (2 π j (p \cdot N + k) \cdot n / N) \cdot h (i \cdot N + k - p \cdot N) \\ = \sum_{p = - \infty}^{+ \infty} h (i \cdot N + k - p \cdot N) \cdot \sum_{n = 0}^{N - 1} a_{p, n}^{r e a l} \exp (j π n / 2) \cdot \exp (2 π j (p \cdot N + k) \cdot n / N) \\ = \sum_{p = - \infty}^{+ \infty} h (i \cdot N + k - p \cdot N) \cdot s_{p, k}^{r e a l} k = 0, 1... N - 1 \end{array}

Here, we only provide the time-domain signal

s^{r e a l} (i \cdot N + k)

that is generated from the in-phase tributary,

a_{i, n}^{r e a l}

. The time-domain signal generated from the quadrature tributary can be readily obtained based on the same principle. Note that

s^{r e a l} (i \cdot N + k)

is commonly a complex signal although

a_{i, n}^{r e a l}

is real. exp(jπn/2) in Eq. (2) represents the phase shifts on the sub-channels. From the equation, it can be seen that the impulse response of the FIR filter k in Fig. 3 is the k^th tributary demultiplexed, by a factor of N, from that of the filter in Fig. 2, h(i⋅N + k-p⋅N), -∞ < p < + ∞. The complexity for pulse shaping is also reduced by a factor of N when compared to the implementation in Fig. 2.

Fig. 3 Principle of DFT-based implementation for offset-16QAM OFDM

Download Full Size | PDF

At the receiver, the received signal is serial-to-parallel (S/P) converted with the access time of T/2, that is, the in-phase tributary accesses the sampled points from times mT while the quadrature tributary accesses the sampled points from times (m + 1/2)T, where m is an integer. The outputs pass through FIR filters that are matched to those at the transmitter. An FFT is applied to transform the signals to the frequency domain. Without loss of generality, we illustrate the principles for the in-phase tributary. Assuming that h(t) is designed based on the criterion in [13], in an ideal channel (without phase noise, dispersion etc.), the frequency-domain n^th subcarrier signal for the i^th symbol at the FFT output, $b_{i, n}^{r e a l}$ , can be written as [13]:

b_{i, n}^{r e a l} \propto (a_{i, n}^{r e a l} + j \cdot c_{i, n}^{r e a l}) \cdot \exp (j π n / 2)

where

c_{i, n}^{r e a l}

is a real value and represents the overall effects of the quadrature tributary of the n^th sub-channel and the crosstalk from adjacent sub-channels (the (n-1)^th and (n + 1)^th sub-channels) in the i^th OFDM symbol. Therefore, the data can be correctly decoded if the phase shifts applied to the different subcarriers at the transmitters, exp(jπn/2), are reversed and the real part is then extracted. When phase noise and a dispersive channel are considered, Eq. (3) is extended as:

b_{i, n}^{r e a l} \propto (a_{i, n}^{r e a l} + j \cdot c_{i, n}^{r e a l}) \cdot \exp (j π n / 2) \cdot \exp (j φ_{i}) \cdot \exp (j β_{2} L_{f i b e r} ω_{n}^{2} / 2) \cdot H_{b} (ω_{n})

where φ_i is the common phase error in the i^th symbol. L_fiber and β₂ are the fiber length and the second-order dispersion value, respectively. H_b(ω_n) represents the gain/loss at ω_n, which is the frequency of the n^th subcarrier. Note that the effect of the dispersion, represented as a frequency-dependent phase shift exp(jβ₂L_fiberω_n²/2), is valid under the restriction that the length of the GI is sufficient to avoid ICI and ISI. The design of the GI will be discussed later and we will firstly focus on phase and channel estimation in Eq. (4). Similar to DFT-based C-OFDM, pilot tone can be employed for phase estimation in the proposed implementation. In principle, pilot tone should be inserted as the DC to eliminate the influence of the dispersion. In the case that the driving amplifiers are AC-coupled, pilot tone is inserted into a subcarrier close to the DC such that exp(jβ₂L_fiberω_n²/2) ≈1. In addition, due to the suppressed spectral tail, only the (n-1)^th and (n + 1)^th sub-channels would introduce ICI and ISI to the target n^th sub-channel. Therefore, adjacent sub-channels of the pilot tone are un-modulated to avoid the

c_{i, n}^{r e a l}

term. The pilot tone for the i^th symbol is then written as:

P_{i, n} \propto \exp (j π n / 2) \cdot \exp (j φ_{i})

where n is set such that ω_n is in the zero-frequency region. In Eq. (5), the value of the pilot tone and H_b(ω_n) are assumed to be 1. The pilot tone is then extracted, conjugated, and used for phase correction.

On the other hand, dispersion estimation can be realized by using training symbols (TSs) where the data on subcarriers are real-valued. In each TS, the data are inserted every two or more subcarriers to avoid the $c_{i, n}^{r e a l}$ term in Eq. (4). By using this design, similar to C-OFDM, the response at a subcarrier frequency can be obtained by dividing the decoded signal by the transmitted data at that frequency. Multiple TSs can be designed individually in various ways [18] to not only mitigate the noise effect but also optimally reconstruct the response at all subcarrier frequencies. In this work, the method with the concept described in [19] is used. This method has been shown to exhibit higher tolerance to noise than the conventional time-domain averaging methods when the number of TSs is small.

Next, we will discuss the design of the GI to enable the validity of Eq. (4). In contrast to C-OFDM, the GI to avoid ISI and ICI in the presence of dispersion is greatly reduced in offset-QAM OFDM. Dispersion in fiber links introduces two effects: 1) the pulse of each sub-channel is broadened; 2) the pulses of different sub-channels transmit at different speed, which results in time delays between sub-channels. The first effect is negligible especially for a large number of sub-channels, as it scales with the bandwidth of each sub-channel. The second effect scales with the bandwidth of the full OFDM spectrum and dominates the performance. In C-OFDM, when there is no GI, the demultiplexing filter for the target sub-channel is no longer orthogonal to other sub-channels. Due to the long spectral tails of the sinc function, all sub-channels would introduce ICI (or ISI) to the target sub-channel (or the target OFDM symbol). In order to avoid the ICI and ISI, the length of the GI should be larger than the time delay between the sub-channels that have the largest distance in frequency. In contrast, in offset-QAM OFDM, the spectral tail can be greatly suppressed. The ICI and ISI due to the absence of GI are only from adjacent sub-channels after the demultiplexing filter. The required GI length, T_GI, is obtained as:

T_{G I} = | L_{f i b e r} \cdot β_{2} \cdot Δ ω |

Δω is equal to the full OFDM bandwidth in C-OFDM and twice the subcarrier spacing in offset-QAM OFDM, respectively. In a system with 10-GHz signal bandwidth and 128 subcarriers, it can be readily calculated that the required GI lengths after 600-km SMF transmission (β₂ = −21.7 ps²/km) are 818 ps and 12.8 ps for C-OFDM and offset-QAM OFDM, respectively. These values, in the discrete domain, correspond to 8 and 0 samples, respectively. It is also expected from Eq. (6) that the larger the number of subcarriers, the shorter the required GI length. Therefore, the proposed scheme may reduce the length of GI for disperison compensation, in particular for a large number of subcarriers. Note that in C-OFDM, reduced-guard-interval methods were also proposed [20–23]. In [20], frequency-domain equalization as similar to that in single-carrier formats was adopted, which however would introduce additional complexity. In [21–23], multi-band OFDM was investigated. This technique is based on the combination of C-OFDM and N-FDM, where C-OFDM is adopted in each sub-band and multiple sub-bands are multiplexed based on (quasi-) N-FDM. However, similar to N-FDM as will be shown in Section 4, a large memory length is required for pulse-shaping filters to create a near rectangular spectral profile for each sub-band and a narrow guard band is still required between sub-bands to avoid spectral overlap. Additionally, the required GI length scales with the bandwidth of each sub-band that commonly consists of 8~32 C-OFDM sub-channels. In contrast, our proposed scheme requires a much shorter GI length that scales with twice the subcarrier spacing.

3. Experimental setup

Figure 4 shows the experimental setup. The IFFT and FFT used 128 points, of which 102 subcarriers were used for 16QAM data modulation. The six subcarriers in the zero-frequency region were not modulated, allowing for AC-coupled amplifiers and insertion of pilot tones for phase estimation. The positions of pilot tones were close to DC in order to reduce the influence of dispersion. The twenty subcarriers in the high-frequency region were zero-padded to avoid aliasing. The start-of-frame symbol of the sequence, designed based on the principle similar to [24], was inserted to enable symbol synchronization. In offset-QAM OFDM, the FIR filter created a set of SRRC functions with different roll-off values, and a set of super-Gaussian functions with orders of two, three, and four. In all investigated cases, the 3-dB bandwidths of the shaped spectra were the same as the subcarrier spacing. It may be shown from [13] that the first set of functions can achieve ICI and ISI free operation whilst the second set has slight residual ICI and ISI. In C-OFDM and N-FDM, the spectral profiles were the sinc function and the rectangular function, respectively. Insets of Fig. 4 show the spectra of these three signals, where the SRRC function with a roll-off coefficient of 0.5 was used in offset-QAM OFDM. It can be seen that offset-QAM OFDM avoided the long spectral tails, and so exhibited greatly suppressed side lobes when compared to C-OFDM. On the other hand, the spectrum of N-FDM was similar to that of offset-QAM OFDM. In all figures, pilot tones in the zero-frequency region were allocated for phase estimation. The generated signal was downloaded to an arbitrary waveform generator with 12-GS/s digital-to-analogue converters (DACs). The signal line rate including forward error correction was 38 Gb/s.

Fig. 4 Experimental setup of coherent optical offset-16QAM OFDM, 16QAM C-OFDM, and 16QAM N-FDM. Insets show the spectra of these three signals.

Download Full Size | PDF

A laser with 6-kHz linewidth was used to generate the optical carrier. Lasers with wider linewidth could also be used but would place higher requirements on phase and frequency offset estimation and the number of subcarriers in OFDM symbols. The electrical OFDM signal was fed into an optical I/Q modulator with a peak-to-peak driving swing of 0.5V_π to avoid nonlinear distortion. The generated optical signal was amplified by an erbium doped fiber amplifier (EDFA), filtered by a 4-nm optical band-pass filter (OBPF), and transmitted over a recirculating loop comprising 60-km single-mode fiber (SMF) with 14-dB fiber loss. The noise figure of the EDFA was 6 dB and another 0.8-nm OBPF was used in the loop to suppress the amplified spontaneous emission noise. The launch power per span was around −7 dBm to avoid the nonlinear effects.

At the receiver, the optical signal was detected with a pre-amplified single-polarization coherent receiver. The use of single polarization was only due to device availability and the proposed DFT-based offset-QAM OFDM scheme could be readily extended to polarization-division-multiplexed (PDM) systems. A variable optical attenuator (VOA) was used to vary the optical signal-to-noise ratio (OSNR) for the bit error rate (BER) measurements. The pre-amplifier was followed by an optical band-pass filter with a 3-dB bandwidth of 0.64 nm, a second EDFA, and another OBPF with a 3-dB bandwidth of 1 nm. A tap of the transmitter laser signal was used as the local oscillator at the receiver. A polarization controller (PC) was used to align the polarization of the filtered OFDM signal before entering the signal path of a 90° optical hybrid. The optical outputs of the hybrid were connected to two balanced photodiodes with 40-GHz 3-dB bandwidths, amplified by 40-GHz electrical amplifiers, and captured using a 50-GS/s real-time oscilloscope. The receiver algorithms included interpolation, down-sampling, precise symbol synchronization [24], and decoding. The total number of measured 16QAM symbols was around 240,000.

4. Experimental results

4.1 Back-to-back performance and sub-channel orthogonality

Figure 5(a) shows BER versus the received OSNR for offset-16QAM OFDM and multicarrier systems using conventional QAM without offset, when the signal spectral profile is the SRRC functions with different roll-off coefficients (defined as α). It can be seen that the performance of offset-QAM OFDM was not sensitive to the α value, and the required OSNRs to achieve a BER of 1 × 10⁻³ were all around 15.5 dB. On the other hand, the system using conventional QAM could still achieve similar performance as offset-QAM OFDM for α = 0. In this case, the system is equivalent to N-FDM. However, as α increased, the orthogonality between sub-channels was destroyed and the BER was degraded significantly. Figure 5(b) illustrates BER versus the received OSNR when the signal spectral profile is super-Gaussian shaped with different order numbers. Super-Gaussian functions cannot achieve ideal ICI and ISI free operation. However, the residual ICI and ISI were not severe, so the performances of offset-QAM OFDM using different order numbers were still similar to those of offset-QAM OFDM in Fig. 5(a). On the other hand, the system using conventional QAM exhibited much poorer performance, with the BER above 1 × 10⁻² at an OSNR of 20.3 dB for all three cases. Higher-order super-Gaussian function was closer to N-FDM, so exhibited slightly better performance due to the reduced ICI level. Figures 5(c)-5(f) illustrate the constellation diagrams for the systems using the SRRC functions when α = 0 and 1. Figures 5(g)-5(j) depict the constellation diagrams for the systems using second- and fourth-order super-Gaussian functions. The figures confirm that offset-QAM OFDM could support various spectral profiles. In contrast, the multicarrier systems without offset exhibited similar performance as offset-QAM OFDM only when the SRRC function with α = 0 was used.

Fig. 5 BER versus the received OSNR for multicarrier systems using offset-QAM and conventional QAM when (a) the SRRC functions and (b) the super-Gaussian functions are employed. Figures 5(c)-5(f): recovered constellation diagrams for the SRRC functions with α of 0 ((c)&(d)) and 1 ((e)&(f)) at 18.5-dB OSNR. Figures 5(g)-5(j): recovered constellation diagrams for the super-Gaussian functions with order number of two ((g)&(h)) and four ((i)&(j)).

Download Full Size | PDF

Figure 6(a) shows BER versus the roll-off coefficient α at 18.5-dB OSNR for systems using the SRRC functions. It is confirmed that the BER was stable (2~4 × 10⁻⁴) as α varied for offset-QAM OFDM. This is because all of these spectral profiles can satisfy the conditions for ICI and ISI free operation [13]. In contrast, with conventional QAM, only the rectangular spectrum (α = 0) could obtain ICI and ISI free operation. As α increased, the ICI level increased significantly. Even when α = 0.1, the BER was 6.7 × 10⁻³. Figure 6(b) shows BER versus the roll-off coefficient of the receiver filter when that of the transmitter filter is 0, 0.5 and 1. In order to ensure ISI and ICI free operation, the FIR filters at the transmitter and the receiver should be matched. It can be clearly seen from the figure that the performance was degraded significantly if the value of α at the receiver was different from that at the transmitter. This property may be potentially used in secure photonic communication systems.

Fig. 6 (a) BER versus the roll-off coefficient for OFDM systems with and without offset. (b) BER versus the roll-off coefficient of the receiver filter for offset-QAM OFDM when the roll-off coefficient of the transmitter filter is 0, 0.5 and 1. (a)-(b): the SRRC functions are used.

Download Full Size | PDF

4.2 Transmission performance and comparison to C-OFDM

Figure 7(a) shows BER versus the received OSNR for offset-QAM OFDM after 0-, 300-, and 600-km transmission. Insets illustrate the recovered constellation diagrams at 0 and 600 km. In the figures, the SRRC function with roll-off coefficient α of 0.5 was used and the GI length was zero. It can be clearly seen that offset-QAM OFDM without any GI exhibited negligible transmission penalty after 300 and 600 km. This matches the theoretical discussions in Section 2. By using the SRRC function, the target sub-channel can be demultiplexed without any ISI and ICI from the sub-channels with more than one sub-channel distance. Consequently, the required GI only scales with twice the subcarrier spacing rather than the full OFDM bandwidth. When the number of subcarriers is large, the GI may be eliminated for dispersion compensation. This is in contrast to C-OFDM where the requirement for the GI length is much more restricted. Figure 7(b) shows OSNR penalty at a BER of 2 × 10⁻³ versus the fiber length for offset-QAM OFDM without GI and C-OFDM with different lengths of GI. It is observed that in C-OFDM, when the GI length was zero, the system exhibited a large OSNR penalty of >8dB even at 360 km. Increasing the GI length to four could improve the performance but around 3-dB OSNR penalty was still observed at 600 km. A GI length of eight was required to support 600-km transmission with negligible penalty. This matches the theoretical analysis in Section 2 that the time delay between the sub-channels with the maximum distance in frequency is ~800 ps. On the other hand, the performance of offset-QAM OFDM without any GI was not sensitive to transmission distances up to 600 km. This confirms the advantage of offset-QAM OFDM over C-OFDM in reducing the GI-induced overhead for long-distance fiber transmissions.

Fig. 7 (a) BER versus received OSNR (dB) for offset-QAM OFDM without GI. Insets show the recovered constellation diagrams at 0 and 600 km. (b) BER versus fiber length for C-OFDM with different GI lengths and offset-QAM OFDM without GI. (a)-(b): the SRRC function with roll-off coefficient of 0.5 is used in offset-QAM OFDM.

Download Full Size | PDF

4.3 Memory length of the FIR filter for pulse-shaping and comparison to N-FDM

The previous studies are based on a sufficient memory length for the pulse-shaping FIR filters to create the desirable spectral profile. Figure 8(a) shows BER versus the memory length of the pulse-shaping filter at 0 km using the SRRC function with different roll-off coefficients. As expected, the time-domain signal was a sinc function when α = 0 (rectangular spectral profile as used in N-FDM), so a long oscillating tail existed, resulting in a required memory length longer than 60 to realize the optimal performance. In contrast, the oscillating tail could be significantly suppressed by increasing the value of α to 0.5 or 1, and a memory length as short as two was sufficient to achieve the optimal performance at 0 km. Figure 8(b) show OSNR penalty at a BER of 2 × 10⁻³ versus the fiber length when the memory length of the FIR filters is two. The case for α = 0 could not achieve 2 × 10⁻³ so was not plotted in the figure. It can be seen that even using a short memory length, the performance of offset-QAM OFDM without GI was still insensitive to the transmission distance, and the OSNR penalty was below 1 dB regardless of the fiber length. This confirms the advantage of offset-QAM OFDM over N-FDM in reducing the pulse shaping induced implementation complexity.

Fig. 8 (a) BER versus the memory length of the pulse-shaping FIR filter for the SRRC function with different roll-off coefficients. α = 0 represents rectangular spectral profile (N-FDM). The fiber length is 0 km; (b) BER versus fiber length for offset-QAM OFDM when the memory length of the pulse-shaping FIR filter is two. (a)-(b): the length of the GI is zero.

Download Full Size | PDF

5. Simulation results

In Section 4, experiments were carried out to verify the feasibility of the proposed implementation and the advantages over C-OFDM and N-FDM. It is shown that when compared to C-OFDM, this technique can enhance the net capacity by avoiding the GI. However, experiments may not be suitable to provide fundamental performance limit due to various practical issues and/or device limitations. In this section, we simulate 112-Gb/s PDM offset-4QAM OFDM and 224-Gb/s PDM offset-16QAM OFDM systems, and compare these systems with C-OFDM to find out the ultimate increase in net capacity. The simulation setup was similar to Fig. 4 except the use of dual-polarization coherent receiver. The sampling rate of the DACs was 40 GS/s. The subcarrier number varied from 32 to 1024. For each case, the number of zero-padded subcarriers in the high-frequency region was controlled such that the signal line rate (including the GI in C-OFDM) was fixed to be 112 Gb/s and 224 Gb/s for offset-4QAM (4QAM in C-OFDM) and offset-16QAM (16QAM in C-OFDM), respectively. Nonlinearity was not considered in order to isolate the effect of dispersion. In offset-QAM OFDM, the FIR filter created a set of SRRC functions with a roll-off coefficient of 0.5. The sampling rate of the oscilloscope at the receiver was 40 GS/s. The total simulated 4QAM (or 16QAM) symbols were around 200,000.

Figure 9 shows the OSNR penalty versus CD for (a) PDM (offset-) 4QAM OFDM and (b) PDM (offset-) 16QAM OFDM when the subcarrier number is 128. It can be seen that when GI was not used in C-OFDM, the performance was degraded rapidly as CD increased. The transmission reach was extended by using a longer GI, which however reduced the net data rate. 16QAM OFDM was more sensitive to ISI so exhibited poorer CD tolerance than 4QAM OFDM. On the other hand, offset-QAM OFDM without GI significantly outperformed C-OFDM with 0% GI. Offset-4QAM and offset-16QAM OFDM could realize transmission reaches the same as those of the C-OFDM with 18.75% and 12.5% GI length, respectively. Offset-16QAM OFDM was employed in the experiments in Section 4 to illustrate the advantages due to higher implementation difficulty. However, offset-4QAM OFDM would be more suitable to find out fundamental limit on dispersion tolerance due to its lower OSNR requirement and higher tolerance to nonlinear effects.

Fig. 9 OSNR penalty versus CD for (a) PDM offset-4QAM OFDM without GI and conventional PDM 4QAM OFDM with different GI lengths; (b) PDM offset-16QAM OFDM without GI and conventional PDM 16QAM OFDM with different GI lengths. The subcarrier number is 128.

Download Full Size | PDF

As discussed in Section 2, the CD tolerance of offset-QAM OFDM scales with twice the subcarrier spacing, so inversely with the subcarrier number at a fixed OFDM bandwidth. Figure 10(a) shows the OSNR penalty versus CD for 112-Gb/s PDM offset-4QAM OFDM with different subcarrier numbers. As expected, the larger the subcarrier number, the better the CD tolerance. For 1024 subcarriers, 112-Gb/s PDM offset-4QAM OFDM could support ~36,000 ps/nm without any GI at the 3-dB penalty, which corresponded to the dispersion value of ~2,100-km fiber. Figure 10(b) illustrates supported CD values at the 3-dB penalty versus the subcarrier number. It can be seen that the transmission reaches scaled linearly with the subcarrier number for both offset-QAM OFDM and C-OFDM. For subcarrier numbers larger than 64, ~18.75% GI was required in C-OFDM to achieve the same performance as offset-QAM OFDM without any GI. This verifies that the presented scheme is more suitable for long-distance transmissions, with 1/(1-0.1875) = 23% increase in net data rate.

Fig. 10 (a) OSNR penalty versus CD for PDM offset-4QAM OFDM without GI and with different subcarrier numbers; (b) Supported CD values at the 3-dB OSNR penalty versus the subcarrier number for offset-4QAM OFDM and conventional 4QAM OFDM.

Download Full Size | PDF

6. Conclusions

We have investigated a DFT-based implementation for offset-QAM OFDM that can achieve sub-channel (quasi-) orthogonality using various spectral profiles. We have experimentally transmitted a 38-Gb/s offset-16QAM OFDM signal over 600-km SMF, and numerically investigated 112-Gb/s PDM offset-4QAM and 224-Gb/s PDM offset-16QAM OFDM. It is shown that offset-QAM OFDM exhibits negligible penalty for signal spectral profiles of the SRRC functions with arbitrary roll-off coefficient and the super-Gaussian functions with different order numbers, in contrast to rectangular-function based N-FDM and sinc-function based C-OFDM. When compared to C-OFDM, this scheme may relax the GI for dispersion compensation, and so is more suitable to high-speed long-distance transmissions. When compared to N-FDM, the required memory length of the pulse-shaping filter in offset-QAM OFDM can be reduced from 60 to 2 regardless of the fiber length, resulting in greatly reduced implementation complexity.

Acknowledgments

This work was supported by Science Foundation Ireland under grant number 11/SIRG/I2124 and 06/IN/I969.

References and links

1. B. Inan, S. Adhikari, O. Karakaya, P. Kainzmaier, M. Mocker, H. von Kirchbauer, N. Hanik, and S. L. Jansen, “Real-time 93.8-Gb/s polarization-multiplexed OFDM transmitter with 1024-point IFFT,” Opt. Express 19(26), B64–B68 (2011). [CrossRef] [PubMed]

2. D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. B. Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26Tbit/s line-rate superchannel transmission utilizing all-optical fast Fourier transform processing,” Nat. Photonics 5(6), 364–371 (2011). [CrossRef]

3. E. Giacoumidis, A. Tsokanos, C. Mouchos, G. Zardas, C. Alves, J. L. Wei, J. M. Tang, C. Gosset, Y. Jaouen, and I. Tomkos, “Extensive comparison of optical fast OFDM and conventional OFDM for local and access networks,” J. Opt. Commun. Netw. 4(10), 724–733 (2012). [CrossRef]

4. J. Zhao and A. D. Ellis, “Advantage of optical fast OFDM over OFDM in residual frequency offset compensation,” IEEE Photon. Technol. Lett. 24(24), 2284–2287 (2012). [CrossRef]

5. X. Zhou, L. Nelson, P. Magill, B. Zhu, and D. Peckham, “8x450-Gb/s, 50-GHz-spaced, PDM-32QAM transmission over 400km and one 50GHz-grid ROADM,” in Proc. Optical Fiber Communications Conference (2012), post-deadline paper PDPB3.

6. G. Bosco, A. Carena, V. Curri, P. Poggiolini, and F. Forghieri, “Performance limits of Nyquist WDM and CO-OFDM in high-speed PM-QPSK systems,” IEEE Photon. Technol. Lett. 22(15), 1129–1131 (2010). [CrossRef]

7. J. Zhao and A. D. Ellis, “Electronic impairment mitigation in optically multiplexed multicarrier systems,” J. Lightwave Technol. 29(3), 278–290 (2011). [CrossRef]

8. Z. Dong, X. Li, J. Yu, and N. Chi, “6×144 Gb/s Nyquist WDM PDM-64QAM generation and transmission on a 12-GHz WDM grid equipped with Nyquist band pre-equalization,” J. Lightwave Technol. 30(23), 3687–3692 (2012). [CrossRef]

9. J. G. Proakis, Digital Communications, (4th Edition), New York, McGraw-Hill (2000).

10. B. R. Saltzberg, “Performance of an efficient parallel data transmission system,” IEEE Trans. Commun. Technol. 15(6), 805–811 (1967). [CrossRef]

11. P. Siohan, C. Siclet, and N. Lacaille, “Analysis and design of OFDM/OQAM systems basd on filterbank theory,” IEEE Trans. Signal Process. 50(5), 1170–1183 (2002). [CrossRef]

12. K. Arya and C. Vijaykumar, “Elimination of cyclic prefix of OFDM systems using filter bank based multicarrier systems,” in TENCON IEEE Region 10 Conference (2008), 1–5.

13. J. Zhao and A. D. Ellis, “Offset-QAM based coherent WDM for spectral efficiency enhancement,” Opt. Express 19(15), 14617–14631 (2011). [CrossRef] [PubMed]

14. S. Randel, A. Sierra, X. Liu, S. Chandrasekhar, and P. J. Winzer, “Study of multicarrier offset-QAM for spectrally efficient coherent optical communications,” in Proc. European Conference on Optical Communication (2011), paper Th.11.A.1. [CrossRef]

15. S. Randel, S. Corteselli, S. Chandrasekhar, A. Sierra, X. Liu, P. J. Winzer, T. Ellermeyer, J. Lutz, and R. Schmid, “Generation of 224-Gb/s multicarrier offset-QAM using a real-time transmitter,” in Proc. Optical Fiber Communications Conference (2012), paper OM2H.2. [CrossRef]

16. F. Horlin, J. Fickers, P. Emplit, A. Bourdoux, and J. Louveaux, “Dual-polarization OFDM-OQAM for communications over optical fibers with coherent detection,” Opt. Express 21(5), 6409–6421 (2013). [CrossRef] [PubMed]

17. Z. Li, T. Jiang, H. Li, X. Zhang, C. Li, C. Li, R. Hu, M. Luo, X. Zhang, X. Xiao, Q. Yang, and S. Yu, “Experimental demonstration of 110-Gb/s unsynchronized band-multiplexed superchannel coherent optical OFDM/OQAM system,” Opt. Express 21(19), 21924–21931 (2013). [CrossRef] [PubMed]

18. L. Liu, X. Yang, and W. Hu, “Chromatic dispersion compensation using two pilot tones in optical OFDM systems,” in Proc. Asia Communications and Photonics Conference (2011), paper 830937. [CrossRef]

19. J. Zhao and H. Shams, “Fast dispersion estimation in coherent optical 16QAM fast OFDM systems,” Opt. Express 21(2), 2500–2505 (2013). [CrossRef] [PubMed]

20. Q. Zhuge, C. Chen, and D. V. Plant, “Dispersion-enhanced phase noise effects on reduced-guard-interval CO-OFDM transmission,” Opt. Express 19(5), 4472–4484 (2011). [CrossRef] [PubMed]

21. A. Tolmachev and M. Nazarathy, “Filter-bank based efficient transmission of reduced-guard-interval OFDM,” Opt. Express 19(26), B370–B384 (2011). [CrossRef] [PubMed]

22. Y. Tang, W. Shieh, and B. S. Krongold, “DFT-spread OFDM for fiber nonlinearity mitigation,” IEEE Photon. Technol. Lett. 22(16), 1250–1252 (2010). [CrossRef]

23. X. Liu, S. Chandrasekhar, B. Zhu, P. J. Winzer, A. H. Gnauck, and D. W. Peckham, “448-Gb/s reduced-guard-interval CO-OFDM transmission over 2000 km of ultra-large-area fiber and five 80-GHz-Grid ORADMs,” J. Lightwave Technol. 29(4), 483–490 (2011). [CrossRef]

24. J. Zhao, S. K. Ibrahim, D. Rafique, P. Gunning, and A. D. Ellis, “Symbol synchronization exploiting the symmetric property in optical fast OFDM,” IEEE Photon. Technol. Lett. 23(9), 594–596 (2011). [CrossRef]

DFT-based offset-QAM OFDM for optical communications

Abstract

1. Introduction

2. Principle of DFT-based offset-QAM OFDM

3. Experimental setup

4. Experimental results

4.1 Back-to-back performance and sub-channel orthogonality

4.2 Transmission performance and comparison to C-OFDM

4.3 Memory length of the FIR filter for pulse-shaping and comparison to N-FDM

5. Simulation results

6. Conclusions

Acknowledgments

References and links

Cited By

Figures (10)

Equations (6)

Optics Express