Open Access
Add to BibSonomyAbstract
In this paper, we propose and investigate an optical multiplexing technique, called orthogonal time-frequency domain multiplexing (OTFDM) with multilevel signaling, that enables ultrafast, high-spectral-efficiency transmission. On the transmitter side, optical rectangular combs generated from electro-optic modulators are data modulated and multiplexed into the time-frequency domain. On the receiver side, the OTFDM signal is demultiplexed and coherently demodulated by coherent matched detection in which multi-frequency homodyne mixing with a locally generated comb down-converts a target OTFDM tributary channel into baseband frequencies. These multiplexing and demultiplexing processes are fully performed in the optical domain using optoelectronic devices, without the use of fast Fourier transform circuits or optical channel selection filters. It is analytically and numerically proved that multilevel signals such as nPSK and nQAM can be OTFDM-multiplexed and demultiplexed while retaining orthogonality between tributaries. The spectral efficiency of this method reaches as high as 1 Baud/Hz per single polarization, i.e., the Nyquist limit, enabling high-bandwidth operation unrestricted by an electronic response in the transmitter or receiver.
© 2014 Optical Society of America
1. Introduction
Orthogonal frequency division multiplexing (OFDM) is a method that could potentially address increasing demands for highly spectrally efficient optical fiber transmission. OFDM primarily involves (1) electrical [1, 2, 3] or (2) optical multiplexing/demultiplexing approaches [4]. In the electrical approach, tributaries are multiplexed and demultiplexed in the electrical domain using fast Fourier transform (FFT) circuits implemented in a digital signal processor (DSP); optical modulators are used for up-converting the multiplexed signals into optical frequencies, while photodetectors down-convert them back. In optical OFDM, optical FFT circuits directly multiplex and demultiplex the OFDM signals in the optical domain. A major difficulty facing both approaches lies in the construction of the FFT or equivalent functions for implementing the multiplexing and demultiplexing processes. The electrical approach requires considerable digital signal processor (DSP) resources to implement real-time FFT functions, and the throughput achievable is restricted by the processing speed of the DSP [3]. Although the total throughput of the multiplexed signal in the optical approach is not restricted by electronics, the development of optical FFT circuits remains challenging because these rely on large-scale integration of precise optical filters [5, 6, 7, 8].
In this paper, we propose and investigate a new optical multiplexing technique called orthogonal time-frequency domain multiplexing (OTFDM) [9] that enables ”ultra-high-speed” and ”high-spectral-efficiency” transmission. In OTFDM, the signal is optically multiplexed and demultiplexed by means of optoelectronic signal processing technologies that rely on neither optical/electrical FFT circuits nor optical filters for channel selection. This makes the approach (1) highly spectrally efficient (i.e., as efficient as OFDM) because no guard band is required between the channels (guard bands are usually reserved for demultiplexing wavelength channels); (2) simpler than OFDM approaches because neither optical nor electrical FFT circuits are required; (3) advantageous for ultrafast operation at 100 Gbaud, 1 Tbaud, or higher because the optical multiplexing/demultiplexing approach is not restricted by the response of electrical or optoelectronic circuits; and (4) applicable for use with multilevel signaling techniques such as n-ary phase-shift keying (nPSK) and quadrature amplitude modulation (nQAM).
We propose two key techniques for achieving OTFDM multiplexing/demultiplexing: (1) multiple-parallel modulation to enable OTFDM multiplexing on the transmitter side and (2) coherent matched detection to enable OTFDM demultiplexing on the receiver side. In our previous conference paper, we demonstrated OTFDM multiplexing of QPSK signals as a proof of the concept [9]. However, it is not clear enough that the multiplexing and demultiplexing process can ideally keep orthogonality among the channels because the results involved some experimental imperfection. This paper focuses on analytical and numerical investigation, aiming for clearly showing that these multiplexing and demultiplexing processes are linearly orthogonal, enabling OTFDM with higher-order multilevel signaling: OTFDM-nPSK and -nQAM are achieved, where spectral efficiencies reaches as high as log2n [bit/s/Hz] per single polarization without sacrificing receiver sensitivity. It is also shown that the OTFDM multiplexing and demultiplexing is practically achieved using simple electro-optic (EO) modulator-based optical comb generator as a multi-carrier signal source.
2. Multiple-parallel modulation for OTFDM multiplexing
In OTFDM systems, tributary signals are optically multiplexed into the time-frequency domain. Fig. 1 (a) shows the basic layout of an OTFDM transmitter that employs the multiple-parallel modulation technique. The transmitter has a multiple-parallel modulator structure [10] that generates N sets of tributary signals to be multiplexed. Firstly, an optical rectangular comb with a frequency spacing of B [Hz] and a bandwidth of NB [Hz] input to the modulator is split in N and led to tributary arms. In the i th tributary arm, all of the frequency components of the optical comb are data modulated with a same data stream at a symbol rate of B [Baud]; the frequency spacing of the comb is equal to the symbol rate of each tributary, while the number of comb lines is equal to the degree of multiplexing (number of tributaries). For data modulation, an inphase- quadrature- (IQ) modulator can be used for signaling in nPSK, nAPSK, nQAM, or any other linear modulation format. Following data modulation, a delay of i/B [s] is applied to each tributary arm, and then the arm outputs are superposed with an N × 1 optical combiner.
Fig. 1 (a) OTFDM transmitter based on multiple-parallel modulation; (b) OTFDM receiver based on coherent matched detection (For simplicity, in the explanation, we assume that each tributary consists of linearly chirped optical comb.)
The modulation spectrum resulting from the multiplexing process is rectangular and has a bandwidth of NB [Hz]; thus, an OTFDM signal with a bandwidth much higher than that of its tributaries (on the order of ∼100 G – 1 Tb/s) can be generated by using only electro-optic modulators without using FFT circuits or optical channel selection filters. Furthermore, as the OTFDM signal is transmitted within the bandwidth at a bit rate of NB log2n [b/s], its spectral efficiency reaches as high as log2n [b/s/Hz] per single polarization.
3. Optical coherent matched detection for OTFDM demultiplexing and demodulation
Because the tributaries of an OTFDM signal are not shaped into pulse trains and strongly overlap each other in the time domain, the temporal waveform of the multiplexed signal differs greatly from that of conventionally formatted signal (e.g. the signal is different from the waveforms of optical time-division multiplexed signals); in addition, the data rate is much faster than the response speed of photodiodes. Accordingly, we propose a detection scheme called coherent matched detection for demultiplexing and demodulating the component tributary channels from the OTFDM signal, as shown schematically in Fig. 1 (b).
In the coherent matched detection method, a received OTFDM signal is homodyne-mixed over multiple frequencies with a locally generated comb (local comb) that has the same amplitude and phase characteristics as the comb (multi-carriers) generated at the transmitter side. A target channel of the ultrafast OTFDM signal is orthogonally demultiplexed and demodulated when the local comb is matched with the OTFDM mutli-carriers. In other words, the target tributary channel temporally overlap exactly with the local comb are down-converted to DC frequencies, while other channels are converted to higher frequencies, which are subsequently filtered out by an electrical low-pass filter (LPF) applied to the multi-frequency homodyne-mixed signals. Demultiplexing and demodulation of an OTFDM signal in this manner ideally does not cause excess receiver penalty because the multiplexed signals are mutually orthogonal in the optical time-frequency domain and this orthogonality is retained throughout the coherent matched detection process. To coherently demodulate PSK or QAM signals following the coherent matching process, the carrier phase of the demultiplexed channel can be recovered by using either digital signal processing or any optical phase locking technique. It can be noticed that this demultiplexing and demodulation scheme also does not rely on any optical/electrical FFT circuits or optical channel selection filters.
The signal processing techniques equalizing the demultiplexed OTFDM signal is mostly common with those used in single-carrier transmission systems. For example, optical frequency offset between the OTFDM carriers and local comb might cause some problem; however, it can be compensated for in the DSP and tolerance against the frequency offset should be in the same level as single-carrier transmission case. Wavelength dispersion in a transmission line is another problem which disturbs the orthogonality among the channels. The wavelength dispersion can be also compensated for in the electrical domain, since all the amplitude and phase information of the OTFDM signal is preserved even after the demuleiplexing process if we detect all the received channels with N sets of coherent matched detectors.
4. Analytical description of OTFDM multiplexing and demultiplexing
Through the analysis in this section, we prove that OTFDM signals can be orthogonally multiplexed by the multiple-parallel modulator; then demultiplexed and demodulated by the coherent matched detector.
The optical fields of the OTFDM signal S(t) and the local comb, L(t) can be expressed as follows:
where δω is the angular frequency spacing of the comb lines, sk(t) represents a data stream at a symbol rate of B = δω/(2π) applied to the k-th tributary channel; al and bm are the complex amplitudes of the frequency components that form the signal and local combs, respectively; θS and θL are the optical carrier phases of the signal and local combs at the center frequency; ϕk is the randomly chosen phase offset between the tributary channels; and Δt and t0 are the temporal separation between the tributaries and the temporal center position of the local comb, respectively; in addition, number of comb lines is related as lmin = mmin, lmax = mmax, lmax − lmin = mmax − mmin = N − 1.If the center position of the local comb is tuned at t0 = 0 in the coherent matched detector, the detected signal after multi-frequency homodyne mixing becomes
where η is the conversion efficiency of the photodiodes. After filtering l ≠ m components with an LPF, the signal becomes A raised-cosine filter (Nyquist filter) is suitable for the LPF because it can clearly filter out the l ≠ m components, without inducing interference between symbols in the received signal. From this equation, it is seen that the terms for k ≠ 0 are always zero if Δt satisfies where N is the number of comb lines and i is a non-zero integer. Substituting Eq. (4) to Eq. (3), we can confirm it as follows. where ξk ≡ −kω0Δt −θS +θL −ϕk. It should be noted that, for each k, the second term becomes zero because the N sets of frequency components are cancelled out each other when they are vectorially summed up with a phase difference of 2πikl/N. This means that the neighboring channels at k ≠ 0 are not downconverted to the baseband frequencies under the condition. The first condition in Eq. (4) is satisfied using the optical delay lines in the multiple-parallel modulator. The second condition is satisfied if an optical comb with a flat spectral profile is applied to the signal and local combs. A Mach-Zehnder modulator-based flat comb generator (MZ-FCG), a type of electro-optic modulator-based optical comb generator, is suitable for this purpose, as it can stably and flatly produce an optical comb with a rectangular spectral profile and fixed-phase relationships between frequency components [11]. (The structure of MZ-FCG is shown in Fig. 2(b).) The generated comb is flattened if we drive an Mach-Zehnder modulator (MZM) in the MZ-FCG under the following condition: where ΔA and Δθ are the amplitude difference of the driving signal and phase offset (i.e., DC bias) of the MZM, respectively, normalized to one radian [11]. Under the condition, the amplitude and phase relationships between the generated harmonics (i.e., comb lines) yields where k is the order of the harmonics and Ā is the average amplitude of the signals driving the MZM.Setting the amplitudes of the combs at |al| = |bl| = Ak in Eq. (5), it is found that the target signal at k = 0 is demultiplexed as
where P0 ≡ |E0|2. With carrier-phase estimation in the DSP, ξ0 will cancel out to zero; as a result, the original signal s0 is recovered without any crosstalk from neighboring channels. (It can be also noticed that the demultiplexing process requires paired combs that have the equal amplitude and phase relationships; however the process is independent of the value of Φk) In a similar way, the signals at other channels, sk can be demultiplexed and recovered if we align t0 at t0 = (2πk)/(δωN), where t0 is the temporal separation between the tributaries and the temporal center position of the local comb shown in Eq. (1). For example, the first and second-neighboring channels are demultiplexed with receivers operated under the condition of t0 = (2π)/(δωN), t0 = (4π)/(δωN), respectively. By using N sets of coherent matched detectors, all channels, sk can be demultiplexed.Fig. 2 Simulation model; BPF: optical bandpass filter, ATT: optical attenuator, EDFA: Erbium-doped fiber amplifier, MZ-FCG: Mach-Zehnder modulator-based flat comb generator
5. OTFDM with multilevel signaling
The OTFDM multiplexing and demultiplexing are linear processes and orthogonality between the tributaries should be retained if a linear modulation format is adopted. In this section, we numerically prove that multilevel signaling is achieved in the OTFDM systems, investigating OTFDM-BPSK, -QPSK, and −16QAM signals at 80-Gbaud symbol rates.
Fig. 2 shows the setup of the simulation model. In the transmitter side, a set of 8-ch, 10-Gbaud OTFDM tributaries is multiplexed with an 8-arm multiple-parallel modulator. The optical comb utilized to create the multi-carriers that carry the OTFDM signal is generated with an MZ-FCG operated under the condition of Ā = 4π and ΔA = Δθ = π/4, which satisfies the flat spectrum conditions in Eq. (6). The comb is split in eight, each of which is modulated into either BPSK, QPSK, or 16QAM formats using an optical IQ modulator driven with various multilevel data streams, which are generated by combining binary non-return-to-zero data streams in the format of pseudorandom binary data sequences (PRBSs) of length 215 − 1. Sufficient delay is given to each PRBS sequence for adequately decorrelating all channels, and the driving signals are band-limited using Bessel filters with a cut-off frequency of 7.5 GHz. The eight sets of data-modulated combs are then re-combined using an optical combiner. The output signal is shaped with an optical bandpass filter (BPF) with an applied rectangular passband of bandwidth 80 GHz and a roll-off factor in its slope region of 1.6 dB/GHz, resulting in 16-dB loss to the first outside components neighboring the passband. On the receiver side, a local comb is generated using another MZ-FCG operated under the same conditions as the transmitter-side comb; the generated comb is shaped with a BPF with the same passband profile as the transmitter-side one. The received OTFDM signal and local comb are input into the signal and local ports of a 90-degree optical hybrid coupler, respectively, followed by balanced photodiodes (BPDs). A raised-cosine filter with a cut-off frequency of 5 GHz and roll-off factor of 0.9 is applied to the photocurrent output from the BPDs in order to discriminate the target channel received with the coherent matched detector, and the carrier phase is recovered by a DSP that implements the fourth-power algorithm, in the same way as single-carrier homodyne detection. The numerical simulation is conducted using Monte Carlo method to include the factor of amplified spontaneous (ASE) noise emitted from Erbium-doped fiber amplifiers (EDFAs) in the system.
Fig. 3 shows constellations of demultiplexed and demodulated OTFDM signals calculated at an optical signal-to-noise ratio (OSNR @0.1 nm) = 30 dB. (a), (b) and (c) correspond to the constellations for OTFDM-BPSK, -QPSK, and -16QAM, respectively. Below the plots, eye patterns for the in-phase and quadrature signals are plotted. Clear constellations and eye-opening are observed, in each case. Fig. 4 shows bit error rates (BERs) plotted against OSNR@0.1 nm for the various OTFDM signals, with the squares, dots, and triangles representing OTFDM-BPSK, -QPSK, and −16QAM, respectively. OTFDM-BPSK and -QPSK have almost no OSNR penalty from the theoretical traces (single-carrier transmitted ones); whereas, OTFDM-16QAM has slight penalty, ∼0.5 dB at BER = 10−3, which is mainly originated from residual spectral ripples in OTFDM multi-carriers and the local comb, as discussed below.
Fig. 3 Constellations of demultiplexed 80-Gbaud OTFDM signals: (a) OTFDM-BPSK, (b) OTFDM-QPSK, (c) OTFDM-16QAM; Eye patterns: (d) OTFDM-BPSK, (e) OTFDM-QPSK, (f) OTFDM-16QAM (measured at OSNR @ 0.1 nm = 30 dB)
Fig. 4 Bit-error-rate characteristics; red squares: 80-Gbaud OTFDM-BPSK, green dots: OTFDM-QPSK, blue triangles: OTFDM-16QAM, red dotted : 80-Gbaud single-carrier (SC) BPSK (theoretical), green dashed-dotted: 80-Gbaud SC-QPSK (theoretical), blue dashed-dotted: 80-Gbaud SC-16QAM (theoretical)
6. Impact of mismatched comb
Practically, however, the paired combs for OTFDM multi-carriers and local comb cannot have perfectly identical spectral profiles because the generated comb has a residual spectral ripple caused by factors such as misalignment of the bias and/or amplitudes of the driving signals. Such mismatching degrades the orthogonality between the multiplexed channels, which in turn increases the crosstalk between them. Here, we investigate the impact of residual spectral ripple in the local comb on OTFDM multiplexing and demultiplexing performance; to do so, we intentionally detune the bias condition of the comb generator from the flat spectrum condition described in Eq. (6).
Fig. 5 (a) shows the calculated spectral ripple of the local comb plotted against bias misalignment, with the spectral ripple δI defined as δI ≡ 10log10(Imax − Imin) [dB], and the bias misalignment defined as Δθ − Δθ0, where Imax and Imin are the maximum and minimum intensity of the comb lines. For this analysis, we set the driving conditions as ΔA = π/4 and Δθ0 = π/4. It is seen that the residual spectral ripple increases with increasing bias misalignment; this differs from the flat spectrum condition, in which it is minimized to 0.4 dB. Fig. 5 (b) shows the calculated error vector magnitude (EVM) plotted against bias misalignment. It is seen from these results that keeping the bias misalignment lower than or equal to ±0.1 [rad] results in an EVM below 8.3%.
7. Conclusion
In this paper, we proposed orthogonal time-frequency domain multiplexing (OTFDM) with multilevel signaling, which enables high-speed and high-spectral-efficiency transmission. We have shown that optoelectronic processing techniques based on multiple-parallel modulation on the transmitter side and coherent matched detection on the receiver side simply enable OTFDM multiplexing and demultiplexing, without the use of optical or electrical FFT circuits. It was analytically and numerically shown that OTFDM with multilevel signaling is practically achieved applying EO modulator-based comb sources to the OTFDM multiplexing and demultiplexing.
Acknowledgments
This work was supported by Grant-in-Aid for Young Scientists (A), 22686039, Japan Society for the Promotion of Science (JSPS). The author would like to say thanks to Dr. S.J.B. Yoo and colleagues at University of California, Davis, and to Dr. T. Kawanishi and colleagues at National Institute of Information and Communications Technology for fruitful discussion.
References and links
1. A. Lowery, L. Du, and J. Armstrong, “Orthogonal frequency division multiplexing for adaptive dispersion compensation in long haul WDM systems,” in 2006 Optical Fiber Communication Conference (OFC2006) (2006), PDP39.
2. W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,” Electron. Lett. 42(10), 587–589 (2006). [CrossRef]
3. S. Jansen, I. Morita, T. Schenk, N. Takeda, and H. Tanaka, “Coherent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,” J. Lightwave Technol. 26(1), 6–15 (2008). [CrossRef]
4. A. Sano, H. Masuda, E. Yoshida, T. Kobayashi, E. Yamada, Y. Miyamoto, F. Inuzuka, Y. Hibino, Y. Takatori, K. Hagimoto, T. Yamada, and Y. Sakamaki, “30×100 Gb/s all-optical OFDM transmission over 1300 km SMF with 10 ROADM nodes,” in 33th European Conference on Optical Communication (ECOC 2007) (2007), PDP1.7.
5. M. Marhic, “Discrete Fourier transforms by single-mode star networks,” Opt. Lett. 12(1), 63–65 (1987). [CrossRef] [PubMed]
6. H. Sanjoh, E. Yamada, and Y. Yoshikuni, “Optical orthogonal frequency division multiplexing using frequency/time domain filtering for high spectral efficiency up to 1 bit/s/Hz,” in 2002 Optical Fiber Communication Conference (OFC2002) (2002), pp. 401–402, THD1.
7. K. Takiguchi, T. Kitoh, A. Mori, M. Oguma, and H. Takahashi, “Optical orthogonal frequency division multiplexing demultiplexer using slab star coupler-based optical discrete Fourier transform circuit,” Opt. Lett. 36(7), 1140–1142 (2011). [CrossRef] [PubMed]
8. K. Lee, C. Thai, and J. Rhee, “All optical discrete Fourier transform processor for 100 Gbps OFDM transmission,” Opt. Express 16(6), 4023–4028 (2008). [CrossRef] [PubMed]
9. T. Sakamoto, A. Kanno, T. Kawanishi, N. Fontaine, D. Geisler, R. Scott, and S. Yoo, “160-Gb/s orthogonal time-frequency domain multiplexed QPSK for ultra-high-spectral-efficient transmission,” in 37th European Conference on Optical Communication (ECOC2011), Geneva, Switzerland, We.10.P1.77, 2011.
10. T. Sakamoto, A. Chiba, and T. Kawanishi, “50-Gb/s 16 QAM by Quad-Parallel Mach-Zehnder Modulator,” in 33th European Conference on Optical Communication (ECOC2007), Berlin, Germany, PDP2.8, 2007.
11. T. Sakamoto, T. Kawanishi, and M. Izutsu, “Asymptotic formalism for ultraflat optical frequency comb generation using a Mach-Zehnder modulator,” Opt. Lett. 32(11), 1515–1517 (2007). [CrossRef] [PubMed]
