## Abstract

This paper presents multi-tone parallel coherent matched detection that orthogonally detects superchannels without crosstalk between neighboring channels. The receiver consists of multiple sets of multi-tone coherent matched detector employed in parallel. In each detector, the received superchannels signal is homodyne mixed in multi frequency with locally generated multi-tone optical frequency comb; detected is a signal set that has the amplitude and phase exactly matched with the local comb. By launching orthogonal sets of local comb to the multiple parallel coherent matched detectors, the received superchannels are orthogonally downconverted to the baseband frequencies keeping the amplitude and phase information of all channels included. With an aid of *n* × *n* transform matrix, all channels are separately recovered from the downconverted signal sets. The system does not rely on any optical filters for channel demultiplexing and separation, with increased flexibility in wavelength arrangement. In addition, the parallel configuration equivalently enhance the bandwidth of the coherent matched detector keeping the speed in each tributary channel as high as possible. In this paper, it is experimentally demonstrated that even-odd interleaved 23 × 20-Gb/s QPSK superchannels are orthogonally demultiplexed and detected by two-tone coherent matched detection.

© 2013 OSA

## 1. Introduction

Optical multicarrier transmission enables bundling and transmitting multiple channels in optical fiber links, which is advantageous mainly for (1) enhancing spectral efficiency, (2) reducing complexity of the transmission systems. These days, optical orthogonal-frequency-division-multiplexing (OFDM) and supperchannels are gathering great attention because these approaches are effective for reaching the spectral efficiency as high as Nyquist limit, *i.e.* 1 [Baud/Hz] per single polarization [1–6]. In these technologies, it is essentially important to keep coherence between the neighboring channels for canceling out interferometric crosstalk there, enabling orthogonal multiplexing and demultiplexing of tributary channels. In OFDM systems, a pair of Fast Fourier Transform (FFT) and inverse-FFT (IFFT) are required for multiplexing and demultiplexing, where numbers of channels are multiplexed through FFT processing keeping coherence among channels [1–3]. A major problem in this approach is that the data rate is always restricted by processing speed of a digital signal processor (DSP) with FFT implemented (except for the approach based on optical FFT circuits; however it is still challenging to develop them). To form supperchannels is another solution for highly spectrally efficient transmission, mainly involving two techniques [5, 6]: (1) temporal or spectral waveform shaping, where each channel are shaped into Nyquist waveform to suppress interference among the multiplexed channels, (2) crosstalk cancellation through multiple channel detection, where phase relations between neighboring channels are simultaneously analyzed for the cancellation. Multiplexing/demultiplexing of superchannels also relies on DSP and mostly requests excess electrical bandwidth for signal processing covering neighboring channels or some special algorithm for smoothly connecting the spectra in neighboring channels. Accordingly, a larger number of channels should be bundled into a fiber link because the data rate of each channel in superchannels typically cannot be as high as that of conventional single-channel transmission and/or the complexity in the DSP is increased.

To break the speed limitation and reduce the complexity of the superchannels, in this paper, we propose a multi-tone coherent-matched detection in parallel configuration, where the received signal is coherently matched detected with a multi-frequency local oscillator, enabling simultaneous and orthogonal multi-channel demultiplexing/demodulation of superchannels. An advantage of this approach is that the parallel configuration of the coherent matched detectors can equivalently enhance optical bandwidth in the region upto 100-Gb/s ∼ Tb/s or higher, which is much higher than electrical bandwidth (typically, at most 10 ∼ 40 Gb/s). Another advantage is that the system relies on less number of local oscillator (LO) laser sources because a multi-tone LO source is used instead of multiple continuous-wave (CW) LO lasers. It is a known problem that conventional homodyne detection requires numbers of low-phase noise LO laser sources frequency-stabilized at wavelength channels. To apply the multi-tone LO source to conventional homodyne receivers for superchannels detection, however, the multi-tone signal should be separated into CW lights by using optical filters. Even if multi-tone LO is utilized, in our case, it is not necessary to separate frequency components of either received signals or local-oscillator (LO) lasers, achieving color-less operation, contrast to other conventional approaches based on channel-by-channel separation and detection schemes. This multi-tone and filter-less demultiplexing/detection scheme simplifies the receiver structure, reducing complexity of the receivers for superchannels.

In this paper, we investigate multi-tone parallel coherent matched detection for multi-channel demultiplexing of superchannels. Two-channel demultiplexing from even-odd interleaved 23 × 20-Gb/s QPSK super-channel signals is demonstrated as a proof of the concept.

## 2. Principles

Figure 1 shows the basic construction for multi-tone parallel coherent matched detection, which enables demultiplexing and demodulation of multiple tributary channels from received supperchannels. The receiver mainly consists of two sections: (a) *n*-parallel coherent matched detector and (b) *n* × *n* transform matrix section, where *n* is the number of the channels received with this setup.

The first section (a), in Fig. 1, comprises *n* sets of coherent matched detector, where the received superchannels signal is split in *n* and individually led into the coherent matched detector. In each coherent matched detector, the signal is homodyne mixed with a locally generated optical multi-frequency carriers (hereafter, we call it local comb) in a similar way with optical sampling systems sampled with local pulse trains [7–9], instead of mixing with a CW LO light. The multi-frequency carriers led to the detectors have *n* frequency components with the equal amplitude and with the constant frequency spacing of *B* [Hz], which is same as the symbol rate of each tributary channel, *B* [Baud]. Through the multi-frequency homodyne mixing in each detector, the *i*-th channel, *d _{i}* at the wavelength of

*λ*(for

_{i}*i*= 1, ⋯ ,

*n*), is mixed with the corresponding frequency component of the local comb and all channels [

*d*

_{1}, ⋯ ,

*d*] are simultaneously downconverted to the baseband frequencies, while other beating components between the received channels,

_{n}*d*, and the frequency components of local comb at

_{i}*λ*(

_{j}*i*≠

*j*) are filtered out with a low-pass filter (LPF) followed by the homodyne mixer. By this downconversion process, all channels are constructively added and matched detected if the detected waveform matches the condition of [Δ

*θ*

_{1}, ⋯ ,Δ

*θ*] = [

_{n}*θ*

_{s,1}−

*θ*

_{l,1}, ⋯ ,

*θ*

_{s,n}−

*θ*

_{l,n}] = [0, ⋯ ,0], where

*θ*

_{s,i}and

*θ*

_{l,i}are the optical phase offset of the received signal and local comb at the wavelength of

*λ*; Δ

_{i}*θ*is relative phase difference between them.

_{i}To orthogonally detect all the *n* sets of tributary channel, we should choose *n* sets of local comb independent and orthogonal each other, giving appropriate amplitude and phase relationships to them; and they should be individually launched into the coherent matched detector. When this condition is satisfied, the detectors independently match to different patterns of waveform formed by the combinations of the received signal components within the bandwidth between *λ*_{1} and *λ _{n}*. This means that all channels are linearly projected on a

*n*-dimensional space created by the orthogonal comb sets. The

*n*sets of the coherent matched detected signal contain all the amplitude and phase information of the tributary channels even if the channels have any phase offset between them. In other words, the downconverted signal sets [

*r*

_{1}, ⋯ ,

*r*] are related in [

_{n}*r*

_{1}, ⋯ ,

*r*]

_{n}*=*

^{t}*A*[

*d*

_{1}, ⋯ ,

*d*]

_{n}*, where*

^{t}*A*is an

*n*×

*n*orthogonal matrix standing for the transfer function of the coherent matched detection. This orthogonal condition is achieved, for example, when the local comb has the equal-amplitude frequency components and the difference of phase offset (at each comb line) between the local comb sets is given as 2

*π*(

*k*− 1)/

*n*at the

*k*-th homodyne detector, which translate into time domain delays of (

*k*− 1)/(

*nB*) if the comb source is coherent enough. This allows us to use local comb sets which are generated from a common comb source, split in

*n*and correctly given the delay sets. Practically, electro-optic modulator based comb source is suitable for this purpose because it can coherently generate equal-amplitude multiple carriers [10].

The coherent matched detected signals, [*r*_{1}, ⋯ ,*r _{n}*], are mixtures of data channels, [

*d*

_{1}, ⋯ ,

*d*]. To recover the original data sets from [

_{n}*r*

_{1}, ⋯ ,

*r*], we need to apply

_{n}*n*×

*n*transform matrix,

*M*, as shown in section (b) in Fig. 1, which should be the inverse of the transfer matrix of the coherent matched detectors,

*A*.

Here, we identify the matrix, *M*, just focusing on two-tone (*n* = 2) and three-tone (*n* = 3) coherent matched detection cases, for simplified explanation. Figure 2 shows orthogonal sets of local comb for *n* = 2 and *n* = 3. Two coherent matched detectors give *π* phase difference to the phase offset between the two frequency components, in the two-tone detected case. If the local comb in the first coherent matched detector has phase offsets of [*θ*_{l,1} +*π*/4, *θ*_{l,2} − *π*/4], those of local comb in the second detector should be [*θ*_{l,1} − *π*/4, *θ*_{l,2} + *π*/4]. In the three-tone detected case, 2*π*/3 phase difference are given to the phase offset of each frequency component between the three sets of coherent matched detectors. The phase offsets of local comb in the first and third detectors should be [*θ*_{l,1} + 2*π*/3, *θ*_{l,2}, *θ*_{l,3} − 2*π*/3] and [*θ*_{l,1} − 2*π*/3, *θ*_{l,2}, *θ*_{l,3} + 2*π*/3] if those in the second detector are [*θ*_{l,1}, *θ*_{l,2}, *θ*_{l,3}]. These phase offsets can be translated to the temporal delays of (2*B*)^{−1} for *n* = 2 and (3*B*)^{−1} for *n* = 3, respectively. With these orthogonal local comb sets, the transfer matrices of the coherent matched detectors, *A*_{2} for *n* = 2 and *A*_{3} for *n* = 3, are described as

*θ*

_{1}, Δ

*θ*

_{2}and Δ

*θ*

_{3}stand for phase offsets at tributary channels relative to corresponding local comb line (

*i.e.*Δ

*θ*≡

_{i}*θ*

_{s,i}−

*θ*

_{l,i}); Δ

*ϕ*

_{1}, Δ

*ϕ*

_{2}, Δ

*ϕ*

_{3}are phase differences between the received signal and local combs. To derive these transfer matrices, we assumed that influence from the second neighboring channels is negligible, which is satisfied if the LPFs applied in the coherent matched detectors have good suppression around the frequency region. Practically, we can choose root-raised-cosine (RRC) or any other filters with roll-off factors steep enough. (If filters with non-steep slope are chosen, dimension of the matrices need to be enhanced to deal with the influence from the second neighboring channels, increasing the complexity of the system.) The 2 × 2 and 3 × 3 transform matrices

*M*

_{2}and

*M*

_{3}, corresponding to

*A*

_{2}and

*A*

_{3}respectively, yield the inverse of the transfer matrices:

Practically, however, Δ*θ _{i}* and Δ

*ϕ*are always drifting due to carrier phase noise of lasers; thus, the elements of matrices requires real-time update. Multi-input-multi-output (MIMO) updating algorithm [11, 12] is helpful to track and update Δ

_{i}*θ*. On the other hand, Δ

_{i}*ϕ*is recovered and canceled out by using the algorithm for carrier phase estimation used in single-carrier homodyne systems. Through the digital signal processing, slowly varying drift of Δ

_{i}*θ*and Δ

_{i}*ϕ*are always tracked and updated. This practically makes it easier to implement the coherent matched detectors. First, optical carrier phase drift of the received signal against LO combs can be canceled without using optical phase locking technique, similarly with single-carrier digital homodyne detection. The signals and local combs input into coherent matched detectors are also not required to be phase locked each other, which means that typically available optical hybrid couplers can be used for the parallel coherent matched detection without integrating them nor stabilizing optical phase between the local combs. The MIMO equalization implemented in the transform matrix section also helps to cancel the impairments of the system, misalignment of the delay between the local comb, residual chromatic dispersion, and so on. For example, it is numerically confirmed that almost no penalty is observed even if there is 5 % misalignment in the optical delay between the local combs, in the 2 × 2 case.

_{i}Comparing with single-channel homodyne detection scheme, this transform matrix section with MIMO processing requires additional DSP resources; however, complexity of this part is at almost the same level as that of polarization diversity technique for demodulation of polarization multiplexed signals. In addition, as mentioned above, RRC or any other steep filters implemented in the coherent matched detection suppress the influence from the second or higher neighboring channels, which helps reducing the complexity of the matrices. Even if compared with other superchannels detection scheme, we can say that complexity of the DSP is comparable or less; however, it should be noticed that we can reduce the number of the CW LO lasers, which is a great advantage in terms of hardware complexity because it is not so easy to practically develop low-cost low-phase noise CW lasers accurately frequency locked at channel wavelengths.

## 3. Experiments

To prove the concept, we experimentally demonstrate two-tone coherent matched detection, demultiplexing QPSK superchannels. For simplicity, we focus on the case with *n* = 2, where we assume that superchannels interleaved from even and odd channels are received with a two-parallel two-tone coherent matched detector.

Experimental setup is shown in Fig. 3. 23-ch, 20-Gb/s QPSK signals are generated and multiplexed in a frequency spacing of 10 GHz to form supperchannels. On the transmitter side, a bundle of optical comb is generated with a Mach-Zehnder modulator based flat comb generator (MZ-FCG) and shaped into a multicarrier signal having 23 CW components by using an optical bandpass filter. The generated multicarriers are interleaved to even and odd channels with a delay interferometer based optical interleaver that has a free spectral range (FSR) of 20 GHz. The even and odd separated multicarriers are individually QPSK modulated with inphase-quadrature (IQ) modulators which are driven with 2^{15} − 1 pseudo-random binary sequence (PRBS) non-return-to-zero (NRZ) data decorrelated with each other enough. The even and odd channels are combined again with an optical combiner to get superchannels at 23 × 20 = 460 Gb/s.

On the receiver side, the even-odd interleaved superchannels are received with the two-parallel two-tone coherent matched detectors. Each coherent matched detector consists of optical hybrid coupler followed by balanced detectors. As for the local comb, a two-tone (2 × 10-GHz) optical comb is generated from another MZ-FCG and split in two with an optical coupler. The two sets of the local comb are individually input into the hybrid coupler in the coherent matched detectors, where 50-ps optical delay is given to one side. In each coherent matched detector, balanced photodiodes detect the optical signals output from the hybrid coupler and downconvert them to the baseband frequencies; inphase and quadrature components of the downconverted signals are digitized with a 4-ch, 50-GSa/s real-time sampling oscilloscope (Tektronix DPO71254) and filtered with RRC LPFs with a cut off frequency of 5 GHz and roll-off factor of 1.0. The two sets of the coherent matched signal are led to a 2 × 2 transform matrix section, *M*_{2}, after the resampling at 20 GSa/s with a locally recovered clock signal. Each element of the transform matrix consists of a fractional FIR filter with a tap length of 15; co-efficients of the center (7-th) tap are initiated in accordance with Eq. 2; the tap coefficients are always updated using MIMO equalizing technique, watching them not to be diverged. This section has a role to cancel the crosstalk between the channel, compensating for signal distortion due to impairments like residual chromatic dispersion and clock misalignment, and so on. After the processing in the transform matrix section, the carrier phase is recovered with 4-th power algorithm and the QPSK signal in each channel is decoded for bit-error-rate evaluation. All these functions are implemented on offline DSP.

Experimental results are shown in Fig. 4. Figure 4(a) shows the optical spectra for the generated 23 × 20-Gb/s supperchannels, where dotted and broken curves are the modulation spectra for even and odd channels, respectively; the solid one stands for the combined superchannels. The spectral ripple originated from the residual unflatness of the comb source was less than 2.3 dB within the superchannels band.

Figure 4(b) shows the constellations obtained when the superchannels are received with the two-tone coherent matched detector without using the transform matrix, *M*_{2}. The constellations are monitored at the Ch. 0 as pointed in Fig. 4(a). It is clearly seen that two channels are simultaneously downconverted to the baseband frequencies causing large crosstalk, in this situation. If we turn on the *M*_{2} and keep updating the matrix elements, on the other hand, the two signal sources are clearly separated, as shown in Figs. 4(c) and 4(d), where (c) and (d) correspond to the constellations of Ch. 0 and Ch. 1, respectively.

Bit error rate (BER) characteristics measured against OSNR at 0.1 nm are shown in Fig. 5. In the plot, squares are measured BERs of the two channels received with the two-channel, two-tone coherent matched detector. As a reference, single-channel BERs measured for Ch. 0 are plotted as triangles, where the signal (without multiplexing) is detected with conventional single-tone coherent receiver. Theoretical BER for the 20-Gb/s QPSK is also plotted as a solid curve in the plot. The required OSNR penalty for the two-tone detected signal is 0.5 dB from the single-channel detected one; 1.5-dB from theoretical limit.

## 4. Conclusion

We have investigated multi-tone coherent matched detection for simultaneous multi-channel demultiplexing and demodulation of superchannels. Even-and-odd interleaved 23 × 20-Gb/s QPSK superchannels have been demultiplexed with good orthogonality.

## Acknowledgment

This work was partly supported by Grant-in-Aid for Young Scientists (A), 22686039, Japan Society for the Promotion of Science (JSPS).

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