Polarization-interleave-multiplexed discrete multi-tone modulation with direct detection utilizing MIMO equalization

Xian Zhou; Kangping Zhong; Yuliang Gao; Qi Sui; Zhenghua Dong; Jinhui Yuan; Liang Wang; Keping Long; Alan Pak Tao Lau; Chao Lu

doi:10.1364/OE.23.008409

1. Introduction

With the rapid development of broadband mobile communication and cloud computing, the extensive bandwidth growth has generated huge pressure to optical transmission networks, optical access networks are no exception [1,2]. Furthermore, unlike long-haul networks, access networks must be cost-effective and easily reconfigurable to remain attractive and practical. For the client optics application, direct detection is the preferred approach comparing to coherent detection because of its low hardware and operational complexity. To realize high capacity at low cost and using a simple configuration, advanced modulation formats with intensity modulation and direct detection (IM-DD) [3–10], including pulse amplitude modulation (PAM) [4,5], carrier-less amplitude modulation (CAP) [6–8] and discrete multi-tone (DMT) [9,10], have been investigated in short reach optical transmission systems. As one of orthogonal-frequency-division-multiplexing (OFDM) schemes, DMT systems can obtain real-valued time symbols by enforcing Hermitian symmetry (HS) in the input symbols of inverse fast Fourier transformation (IFFT) and independently assemble arbitrary M-QAM modulation transmit data in each subcarrier. Based on the flexible modulation and bandwidth allocation, it is regarded as the most competitive technology for achieving the best use of the available signal channel bandwidth and SNR in client optics.

In order to further increase transmission capacity, research has been carried out to exploit polarization dimension to transmit more information using direct-detection (DD), such as polarization division multiplexed OFDM transmission with DD (PDM-OFDM-DD) proposed by D. Qian, et al. [11], and PDM-PAM4-DD proposed by M. Moray-Osman, et al. [12]. In this paper, we derive a common theoretical channel model for dual-polarization systems with IM-DD, and for the first time to employ DMT modulation on two orthogonal polarizations, and present a novel polarization-interleave-multiplexed (PIM) DMT-DD transmission system. The polarization de-multiplexing of the proposed PIM-DMT-DD system is realized by a simple multiple-input-multiple-output (MIMO) equalization. Moreover, in order to mitigate the influence resulted from the singular receiving problem, 45° polar angle difference receiving method is used in the proposed PIM-DMT-DD system. Based on our theoretical and simulation analyses, the feasibility and effectiveness of the proposed PIM-DMT-DD system are demonstrated.

2. Transmission model for dual polarization with IM-DD

At transmitter side, two real-valued baseband signals s_x_(y)(t) are intensity modulated onto the two orthogonal polarizations. This results in a transmitted signal

{\vec{E}}_{T X} (t) = (\begin{matrix} E_{x} (t) \\ E_{y} (t) \end{matrix}) = (\begin{matrix} \sqrt{C_{x} + s_{x} (t)} \cdot e^{j (2 π f_{x} t + φ_{x})} \\ \sqrt{C_{y} + s_{y} (t)} \cdot e^{j (2 π f_{y} t + φ_{y})} \end{matrix})

where C_x_(y) denotes the direct current (DC) bias, which is equal to the average power of the nonnegative input signal waveform for intensity modulation, f_x(y) and

φ_{x (y)}

are the frequency and the phase of the optical carrier in the X(Y) - polarization.

Additive white Gaussian noise (AWGN) is not considered in our analysis for simplicity purpose and assuming that the major transmission impairments are the random polarization rotation, and chromatic dispersion (CD) (first-order polarization-mode dispersion (PMD) is not considered as it is negligible for short-reach applications), the transfer function of the fiber-optic channel can be represented by

H (ω) = (\begin{matrix} \cos α e^{j ε} & - \sin α e^{- j ε} \\ \sin α e^{j ε} & \cos α e^{- j ε} \end{matrix}) \times e^{- j \frac{1}{2} β_{2} L ω^{2}}

where

L

,

β_{2}

denote fiber length and group velocity dispersion coefficient respectively,

ω

represents the angular frequency,

α

is a random polar angle between the input and output polarization states, and

ε

is the azimuth angle. The corresponding impulse response of the optical channel is then given by

h (t) = (\begin{matrix} h_{11} (t) & h_{12} (t) \\ h_{21} (t) & h_{22} (t) \end{matrix}) .

After propagating through the fiber, the electric field of the multiplexed signal can be written as

{\vec{E}}_{R X} (t) = (\begin{matrix} E_{h} (t) \\ E_{v} (t) \end{matrix}) = (\begin{matrix} h_{11} (t) \otimes E_{x} (t) + h_{12} (t) \otimes E_{y} (t) \\ h_{21} (t) \otimes E_{x} (t) + h_{22} (t) \otimes E_{y} (t) \end{matrix})

where E_h(t), E_v(t) denote the two field components of the horizontal and vertical polarizations in the receiver respectively and

\otimes

represents the convolution operation. Two square-law photo detectors (PD) convert E_h(t) and E_v(t) into photocurrents. Taking one of the polarizations as an example, the unfiltered photocurrent can be expressed as

\begin{array}{l} r_{h} (t) = {| E_{h} (t) |}^{2} = {| h_{11} (t) \otimes E_{x} (t) + h_{12} (t) \otimes E_{y} (t) |}^{2} \\ = {| h_{11} (t) \otimes \sqrt{C_{x} + s_{x} (t)} |}^{2} + {| h_{12} (t) \otimes \sqrt{C_{y} + s_{y} (t)} |}^{2} \\ + 2 Re {[h_{11} (t) \otimes \sqrt{C_{x} + s_{x} (t)} e^{j (2 π f_{x} t + φ_{x})}] \cdot [h_{12}^{*} (t) \otimes {\sqrt{C_{y} + s_{y} (t)}}^{- j (2 π f_{y} t + φ_{y})}]} \end{array}

where Re{} denotes the real part of a complex number. Here, the photodiode responsivity is assumed as 1. The first two terms contain the transmitted signals in the X and Y polarization respectively, and the last term correspond to beating interference between the two polarizations. In order to analyze them in more detail, we Taylor expand

\sqrt{C_{x (y)} + s_{x (y)} (t)}

and discard higher order terms (which can be suppressed by the increasing C_x_(y) in practice anyways). The first two terms in Eq. (5) can be expressed as follows:

\begin{array}{l} r_{h - S i g n a l} ≃ {| h_{11} (t) \otimes (\sqrt{C_{x}} + \frac{s_{x} (t)}{2 \sqrt{C_{x}}}) |}^{2} + {| h_{12} (t) \otimes (\sqrt{C_{y}} + \frac{s_{y} (t)}{2 \sqrt{C_{y}}}) |}^{2} \\ = (\cos α \cdot s_{x} (t) \otimes R e {h_{11} (t) e^{- j ε}} - \sin α \cdot s_{Y} (t) \otimes R e {h_{12} (t) e^{j ε}}) \\ + (\frac{1}{4 C_{x}} {| s_{x} (t) \otimes h_{11} (t) |}^{2} + \frac{1}{4 C_{y}} {| s_{y} (t) \otimes h_{12} (t) |}^{2}) \\ + (C_{x} \cos^{2} α + C_{y} \sin^{2} α) \end{array}

Here, Eq. (6) contains three parts: 1) the fundamental term consisting of polarization multiplexed signal that is located in baseband after PD without the influences of laser frequency and phase, 2) the second-order nonlinear term that can be suppressed by DC bias, and 3) a DC component that can be easily removed.

Then, the beat interference term from Eq. (5) can be addressed as follows:

\begin{array}{l} r_{h - I n t e r f e r e n c e} ≃ 2 Re {[h_{11} (t) \otimes (\sqrt{C_{x}} + \frac{s_{x} (t)}{2 \sqrt{C_{x}}}) e^{j (2 π f_{x} t + φ_{x})}] \cdot [h_{12}^{*} (t) \otimes (\sqrt{C_{y}} + \frac{s_{y} (t)}{2 \sqrt{C_{y}}}) e^{- j (2 π f_{y} t + φ_{y})}]} \\ ≃ \underset{I1}{\underset{︸}{- 2 \sqrt{C_{x} C_{y}} \cos α \sin α \cos (2 π Δ f t + Δ φ + 2 ε + ϕ_{D})}} \\ + \underset{I2}{\underset{︸}{2 Re {\frac{[h_{11}^{*} (t) \otimes s_{x} (t)] [h_{12} (t) \otimes s_{y} (t)]}{4 \sqrt{C_{x} C_{y}}} \cdot e^{j (2 π Δ f t + Δ φ)}}}} \\ - \underset{I3}{\underset{︸}{2 Re {(h_{11} (t) \otimes s_{x} (t) \frac{\sin α \sqrt{C_{y}}}{2 \sqrt{C_{x}}} + h_{12}^{*} (t) \otimes s_{y} (t) \frac{\cos α \sqrt{C_{x}}}{2 \sqrt{C_{y}}}) \cdot e^{j (2 π Δ f t + Δ φ + 2 ε + ϕ_{D})}}}} \end{array}

where

Δ f

and

Δ φ

denote the frequency and phase difference between the two orthogonal polarization components,

ϕ_{D}

is the phase delay due to the fiber dispersion effect for

Δ f

. It can be seen form Eq. (7) that the frequency spectra of all interference products depend on △f. Assuming that the baseband transmitted signal occupies a bandwidth from -B/2 to + B/2 as depicted in Fig. 1, I2 and I3 in Eq. (7) have bandwidth of B and 2B respectively. It is worth noting that I1 is a single frequency component at ± △f, and I2 should be small since it is suppressed by DC bias. Thus, if △f is equal or larger than B, the dominating interference component I3 can be avoided in theory.

Fig. 1 Power spectral distribution of the detected signal in one of polarization tributaries.

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Similarly, we can get another detected signal r_v(t) on the quadrature polarization tributary. Assuming that △f≥B (it is called the polarization-interleave-multiplexed (PIM)), after an low-pass filter and ignoring the interference noises suppressed by DC-bias (i.e., the 2nd order nonlinear interference term in Eq. (6) and I3 in Eq. (7)), the received signal can be simplified as

[\begin{array}{l} {r^{'}}_{h} (t) \\ {r^{'}}_{v} (t) \end{array}] = h^{'} (t) \otimes [\begin{array}{l} s_{x} (t) \\ s_{y} (t) \end{array}]

where h'(t) represents the effective channel response given by

h' (t) = (\begin{matrix} \cos α \cdot R e {h_{11} (t) e^{- j ε}} & - \sin α \cdot R e {h_{12} (t) e^{j ε}} \\ \sin α \cdot R e {h_{21} (t) e^{- j ε}} & \cos α \cdot R e {h_{22} (t) e^{j ε}} \end{matrix})

Combining Eq. (2) and Eq. (9), the corresponding transfer function H' ( $ω$ ) is then given by

H^{'} (ω) = (\begin{matrix} \cos^{2} α & \sin^{2} α \\ \sin^{2} α & \cos^{2} α \end{matrix}) R e {e^{- j \frac{1}{2} β_{2} L ω^{2}}} = (\begin{matrix} \cos^{2} α & \sin^{2} α \\ \sin^{2} α & \cos^{2} α \end{matrix}) \cos (\frac{β_{2} L ω^{2}}{2})

3. PIM-DMT-DD transmission with MIMO equalization

Based on above transmission model, we employ DMT modulation on two orthogonal polarization dimensions. Therefore, s_x₍_y₎(t) of Eq. (1) should be the baseband DMT signal in the X (Y) - polarization, which is given by

s_{x (y)} (t) = \sum_{i = - \infty}^{+ \infty} \sum_{k = 0}^{N - 1} c_{x (y), k, i} g (t - i T_{s}) e^{j 2 π f_{k} (t - i T_{s})}

where N is the size of FFT/IFFT, f_k is the frequency for k^th subcarrier, T_s is the symbol period, g is the rectangular pulse waveform of the DMT symbol, and c_x₍_y₎_,k,i is the i^th information symbol at the k^th subcarrier in the X(Y) - polarization, which must satisfy a conjugate symmetry over subcarriers as

c_{x (y),}_{N - j, i} = c^{*} {_{x (y),}}_{j, i}, j = 1 ~ N - 1

where the asterisk denotes complex conjugation. The optical spectral diagram of the PIM-DMT signal is illustrated in Fig. 2.

Fig. 2 Optical spectral spectrum diagram of the PIM-DMT signal.

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At the receiver, the detected electrical signal can be written as

[\begin{array}{l} {r^{'}}_{h} (t) \\ {r^{'}}_{v} (t) \end{array}] = h^{'} (t) \otimes [\begin{array}{l} s_{x} (t) \\ s_{y} (t) \end{array}] + [\begin{array}{l} n_{h} (t) \\ n_{v} (t) \end{array}]

where n_h(t) and n_v(t) denote AWGN noise. Then, taking the appropriate sampling and assuming perfect frame synchronization, the detected signals

{r^{'}}_{h} (t)

and

{r^{'}}_{v} (t)

after FFT operation for the k^th subcarrier and the i^th symbol can be expressed as

[\begin{array}{l} {R^{'}}_{_{h, i, k}} \\ {R^{'}}_{v, i, k} \end{array}] = H^{'} (k) [\begin{array}{l} c_{x, i, k} \\ c_{y, i, k} \end{array}] + [\begin{array}{l} N_{h, i, k} \\ N_{v, i, k} \end{array}]

where

H^{'} (k)

denotes the discretized version of

H^{'} (ω)

H^{'} (k) = H^{'} (ω) |_{ω = 2 π k f_{s c}} = [\begin{array}{l} {H^{'}}_{11} (k) {H^{'}}_{12} (k) \\ {H^{'}}_{21} (k) {H^{'}}_{22} (k) \end{array}]

and f_sc is the subcarrier frequency spacing.

According to Eq. (10), we note that the PIM-IM-DD channel transfer function inherits the frequency selective fading feature that occurs in traditional IM-DD systems [13]. In order to maximize the bit rate in DMT systems, many adaptive loading algorithms [14,15] have been proposed, which can also be applied to the PIM-DMT-DD system. Hence, we mainly focus on the polarization crosstalk effect induced by random polar angle rotation. Based on the modulation characteristic of the DMT signal, a simple 2 × 2 MIMO equalizer is employed to de-multiplex polarization after FFT operation.

In the 2 × 2 MIMO equalization, the time-interleaved training symbols are used to estimate the channel transfer matrix as shown in Fig. 3. In the odd time slots, ${H^{'}}_{11} (k)$ and ${H^{'}}_{21} (k)$ can be estimated as

[\begin{array}{l} {R^{'}}_{h, i, k} \\ {R^{'}}_{v, i, k} \end{array}] = [\begin{array}{l} {H^{'}}_{11} (k) {H^{'}}_{12} (k) \\ {H^{'}}_{21} (k) {H^{'}}_{22} (k) \end{array}] [\begin{array}{l} c_{x, i, k} \\ 0 \end{array}] \to {\begin{cases} {\tilde{H^{'}}}_{11} (k) = \frac{1}{L} \sum_{i = 1}^{L} \frac{{R^{'}}_{h, i, k}}{c_{x, i, k}} \\ {\tilde{H^{'}}}_{21} (k) = \frac{1}{L} \sum_{i = 1}^{L} \frac{{R^{'}}_{v, i, k}}{c_{x, i, k}} \end{cases}

and using the training symbol in even time slots,

{H^{'}}_{12} (k)

and

{H^{'}}_{22} (k)

can be estimated as

[\begin{array}{l} {R^{'}}_{h, i, k} \\ {R^{'}}_{v, i, k} \end{array}] = [\begin{array}{l} {H^{'}}_{11} (k) {H^{'}}_{12} (k) \\ {H^{'}}_{21} (k) {H^{'}}_{22} (k) \end{array}] [\begin{array}{l} 0 \\ c_{y, i, k} \end{array}] \to {\begin{cases} {\tilde{H^{'}}}_{12} (k) = \frac{1}{L} \sum_{i = 1}^{L} \frac{{R^{'}}_{h, i, k}}{c_{y, i, k}} \\ {\tilde{H^{'}}}_{22} (k) = \frac{1}{L} \sum_{i = 1}^{L} \frac{{R^{'}}_{v, i, k}}{c_{y, i, k}} \end{cases}

where L is the number of training symbols,

{\tilde{H^{'}}}_{i j} (k)

is the channel estimation for the k^th subcarrier. Note that an average operation is implemented here to mitigate AWGN effect on the estimated channel matrix. Then depending on the inverse of the estimated channel matrix and the received data samples, the transmitted data in two polarizations can be recovered:

\begin{array}{l} c_{x, i, k} = \frac{{\tilde{H^{'}}}_{22} (k) {R^{'}}_{h, i, k} - {\tilde{H^{'}}}_{12} (k) {R^{'}}_{v, i, k}}{{\tilde{H^{'}}}_{11} (k) {\tilde{H^{'}}}_{22} (k) - {\tilde{H^{'}}}_{12} (k) {\tilde{H^{'}}}_{21} (k)} + \frac{{N^{'}}_{i, k}}{{\tilde{H^{'}}}_{11} (k) {\tilde{H^{'}}}_{22} (k) - {\tilde{H^{'}}}_{12} (k) {\tilde{H^{'}}}_{21} (k)} \\ c_{y, i, k} = \frac{{\tilde{H^{'}}}_{21} (k) {R^{'}}_{h, i, k} - {\tilde{H^{'}}}_{11} (k) {R^{'}}_{v, i, k}}{{\tilde{H^{'}}}_{11} (k) {\tilde{H^{'}}}_{22} (k) - {\tilde{H^{'}}}_{12} (k) {\tilde{H^{'}}}_{21} (k)} + \frac{{N^{″}}_{i, k}}{{\tilde{H^{'}}}_{11} (k) {\tilde{H^{'}}}_{22} (k) - {\tilde{H^{'}}}_{12} (k) {\tilde{H^{'}}}_{21} (k)} \end{array}

where

Fig. 3 The structure of straining symbols for MIMO channel estimation.

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{N^{'}}_{i, k} = {\tilde{H^{'}}}_{12} (k) N_{v, i, k} - {\tilde{H^{'}}}_{22} (k) N_{h, i, k}, {N^{″}}_{i, k} = {\tilde{H^{'}}}_{21} (k) N_{v, i, k} - {\tilde{H^{'}}}_{11} (k) N_{h, i, k} .

Figure 4(a) shows |H_ij| ₍_i _{= 1,2}_;j _{= 1,2)} as a function of polarization rotation angle $α$ over [0, $π$ ], which are obtained by Eq. (10). To validate the correctness of the theoretical results, a simulation is also conducted on the PIM-DMT-DD system (the main parameters setting can be found in Table 1). The results are shown in Fig. 4(b).

Fig. 4 Chanel function vector as a function of polarization rotation angle $α$ .

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Table 1. General Simulation Parameters

View Table

It can be observed that there is a singular receiving problem in the PIM-DD system. The two values of |H_ij|₍_i ₌ _j₎ and |H_ij|₍_i≠j₎ get close together gradually when $α$ is changing to $\pm \frac{π}{4} (2 k + 1)$ , where $k = 0, 1, ...$ . At $α = \pm \frac{π}{4} (2 k + 1)$ , the same information will be received from two polarization tributaries, i.e. ${r^{'}}_{h} = {r^{'}}_{v}$ . In order to confirm the change, the correlation ratios between ${r^{'}}_{h}$ and ${r^{'}}_{v}$ are also measured in the simulation, as shown in Fig. 5. Here, since four symmetrical and repeated changing processes for |H_ij| occur in one period of $α$ , we only have to focus on one of the ranges, namely from 0° to 45 ^o, for the sake of simplicity.

Fig. 5 Normalized correlation ratio as a function of polarization rotation angle.

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Furthermore, we know that the signal deep fading will occur when $α$ is close to 45°, 135°, etc. based on Eq. (18). Effectively, the noise impact will be greatly amplified, leading to a lower signal-to-noise ratio. We further measure the receiver sensitivity penalty (RSP) as a function of polarization rotation angle in the back-to-back (BTB) scenario (see Fig. 6). Here, the received optical power at BER = 3.8 × 10⁻³ is used as the measurement criteria. It can be seen that the impact due to the singular receiving cannot be neglected. As expected, more RSP is required when $α$ getting close to 45°. In Fig. 6, if $α$ is greater than 35°, optical power penalty will be more than 10dB. Furthermore, different from the singularity problem induced by adaptive equalization in coherent polarization multiplexing systems [16, 17], here the singularity problem will be inevitably created at some certain polarization rotation angle, which is hard to be compensated by improving DSP algorithm. Nevertheless, in Fig. 6, the power penalty will be limited if $α$ is confined within certain range. Only about 1dB of power penalty will resulted for increasing $α$ from 0° to 22.5°. Therefore, in order to limit this influence and avoid the irreversible damage occurred in practice, the transmitted signal will be received in two polarization coordinates respectively, which are with 45° relative polarization angle difference, and one of branches that has a smaller correlation ratio between ${r^{'}}_{h}$ and ${r^{'}}_{v}$ will be kept and used for subsequent digital signal processing processes. The detailed operation description and performance analysis will be discussed in the next section.

Fig. 6 Receiver sensitivity penalty as a function of polarization rotation angle.

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3. Simulations and discussion

3.1 Simulation system model

The simulation configuration of the proposed PIM-DMT-DD system is depicted in Fig. 7(a), which is built by VPI transmission Maker 8.7 and MATLAB software. In the transmitter, DSP modules are used to generate the DMT baseband signals. Figure 7(b) shows the different signal processing steps for one polarization. The pseudo-random bit sequence (PRBS) with a length of 2¹⁷-1 as the transmitted data stream is mapped into 16QAM and used to fill 56 subcarriers in the positive frequency. The time domain DMT signal is generated by an inverse fast Fourier transform (IFFT) size of 128, where the 56 subcarriers in the negative frequency are filled with corresponding Hermitian symmetric data and other subcarriers are null for dc-bias and oversampling. Here, the length of cyclic prefix (CP) is set to be 10. At the beginning of each data frame, 41 training symbols are inserted, which consists of 1 symbol for symbol frame synchronization, 40 time-interleaved training symbols for channel estimation (including 20 null symbols that are located in odd/even time slots in X/Y-pol respectively). Afterwards, the digital DMT signals are uploaded into a DAC operated at 64GSam/s, and filtered by a 4th order Bessel low pass filter (LPF) in order to simulate the bandwidth limitation of transmitter. Here, the center frequencies of electric absorption modulated lasers (EMLs) for X-pol and Y-pol are 229.01e12 Hz and (229.01e12 + △f) Hz respectively, where △f is a tunable frequency spacing between the two polarizations. In general, △f is set to be 70 GHz during our simulation. After PBC, the optical PIM-DMT signal is obtained with 207.8Gbit/s data rate and 28 GHz signal bandwidth in the positive frequency bins.

Fig. 7 (a) Simulation setup of the 207.8Gbit/s PIM-DMT-DD system, the schematics of the DSP (b) in the transmitter and (c) the receiver, SSMF: standard single mode fiber, VOA: variable optical attenuator, PBC/S: polarization beam combiner/splitter.

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Fiber link compose of standard single mode fiber (SSMF), a variable optical attenuator (VOA) that is used to adjust the received optical power, and a polarization rotator that is used to change $α$ in BTB scenario. At the receiver, the optical signal is divided into two parts, and one of which goes through a fixed 45° polarization rotator. The two PIM-DMT signals with different polarization coordinates are further divided into two arbitrary orthogonal polarization tributaries via a polarization beam splitter (PBS) respectively. Then, the split signals are mapped into electrical signals by utilizing four photo-detectors (PDs). After PD, electric 4th order Bessel LPF is also used to simulate the bandwidth limitation of the receiver. Next, the filtered electrical signals are digitized by ADCs at 64Gsam/s and stored for DSP using MATLAB, as shown in Fig. 7(c). Firstly, the correlation ratios between every two digital signals which are in a same polarization coordinate are computed and compared, where the pair of orthogonal signals with smaller correlation ratio will be retained for further signal processing, including FFT window synchronization, FFT operation, MIMO channel estimation, and data recovery. Table 1 summarizes the general settings of the simulation parameters, some of which are possible to be adjusted in certain simulations.

3.2 Simulation results and analysis

In order to assess the effectiveness and performance of the 45° polarization angle difference receiving scheme, the correlation ratio (CR) and the BER performance of the two branches are measured with different polarization rotation angles in BTB, as shown in Fig. 8(a) and 8(b) respectively. Here, 150 samples are used to calculate CR and the received power before PD is set to be −6.5dBm. For the sake of simplicity as mentioned before, only the range of $α$ from 0° to 45 ^o is taken into account.

Fig. 8 (a) Normalized correlation ratio and (b) measured BER as a function of polarization rotation angle (Received power before PD = −6.5dBm).

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Figure 8(a) and 8(b) show the variation of CR and BER with $α$ . In this case, smaller BER can be achieved using data obtained from the branch with relatively low correlation, and the deterioration in BER is limited to a small range, as expected. As shown in the simulation, the BER increases from 1.8 × 10⁻³ at $α = 0^{o}$ to 3.8 × 10⁻³ at the worst case, i.e., $α = {22.5}^{o}$ . In Fig. 9, the BER performances as a function of 3dB receiver bandwidth are investigated in the cases of $α = 0^{o}$ and $α = {22.5}^{o}$ . According to above theoretical analysis, the main beat interference I3 will be shifted from baseband based on △f (as shown Fig. 1), and the receiver with an appropriate bandwidth is very important to filter out this interference component and ASE noise effectively. From Fig. 9, it can be seen that the BER will increase significantly if the receiver bandwidth is too narrow, since there will be significant attenuation to high frequency subcarriers. However, too large receiver bandwidth is also not suitable for optimal performance, due to the influence induced from ASE noise and the beat interference. In Fig. 9, the optimal 3dB bandwidth is around 16GHz in both two extreme polarization rotation cases, which is about 58 percent of whole signal bandwidth.

Fig. 9 BER performance as a function of 3dB bandwidth of receiver (Received power before PD = −6.5 dBm).

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From Fig. 9, it can be noted that the BER performance is more sensitive to the increase of receiver bandwidth when $α = {22.5}^{o}$ . This phenomenon can easily be interpreted in frequency domain. Figure 10(a) depicts the whole optical spectrum of the transmitted PIM-DMT signal. At the receiver, the PIM-DMT signal is split into two orthogonal polarizations using a PBS. In the case of $α = 0^{o}$ , one split signal only contains a single polarization information (see Fig. 10(b)), so there is no polarization beat interference after PD (see Fig. 10(d)), and only the ASE noise will increase by increasing the receiver bandwidth. Figure 10(c) and 10(e) display the corresponding optical and electrical spectrum for the case of $α = {22.5}^{o}$ . Agreeing well with theoretical analyses, the dominated beat interference (shown in Fig. 10(e)) can be found at the centre frequency of △f, i.e.70 GHz, and its bandwidth is twice that of the baseband bandwidth of the DMT signal. Therefore, additional beat interference will be induced in the case of $α = {22.5}^{o}$ when taking a large receiver bandwidth.

Fig. 10 Representative spectra of PIM-DD-DMT transmission (Received power before PD = −6.5dBm), (a) optical spectrum after PBC in transmitter, optical spectrum of V-pol. after PBS in receiver (b) for a = 0°, (c) for a = 22.5°, electrical spectrum of V-pol. after PD for (d) for a = 0°, (f) for a = 22.5°.

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Next, the influence of frequency space △f between the two polarizations is studied for 16GHz receiver bandwidth. As shown in Fig. 11(a), there is no △f related influence in the case of $α = 0^{o}$ , since there is no beat interference. However, it is difficult to avoid polarization crosstalk and neglect the beat interference effect because of the random polarization rotation in practice. Taking the worst case of $α = {22.5}^{o}$ for example, it can be seen from Fig. 11(a), the evident BER degradation is caused when △f <70GHz, but the system performance will not degrade further if △f > = 70GHz. These results demonstrate that the dominant beat interference can be removed from signal frequency band effectively by controlling △f. Figure 11(b) shows the measured BER performance for each data subcarrier, where the influence of the beat interference can be observed more clearly. The impairments are proportional to the frequency difference between the subcarriers and the beat interference component.

Fig. 11 (a) BER performance as a function of frequency space, (b) BER per data subcarrier (Received power before PD = −6.5dBm).

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In order to consider the random polarization rotation, the BER performance of the proposed PIM-DD-DMT system is analyzed considering a SSMF link of 10km (see Fig. 12). The results for BTB simulation at $α = 0^{o}$ and $α = {22.5}^{o}$ are also measured as references. At 1310nm wavelength region, CD is negligible. There is no CD-induced frequency selective fading. Depending on sufficient CP to eliminate PMD-induced inter-symbol interference (ISI), the BER performances for 10km transmission are between the curve for the two BTB cases, i.e. $α = 0^{o}$ and $α = {22.5}^{o}$ . It is demonstrated that the singular receiving induced impairment can be limited effectively. The receiver sensitivities at 7% FEC overhead of 3.8 × 10⁻³ are around −6.9 dBm, −7.3 dBm and −6.5 dBm for after 10km SSMF transmission and at BTB in $α = 0^{o}$ and $α = {22.5}^{o}$ respectively.

Fig. 12 BER performance as a function of receiver optical power.

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4. Conclusions

To exploit two orthogonal polarizations for transmission using IM-DD, a general theoretical channel model for two polarizations and IM-DD was derived in this paper. Based on the theoretical model, we proposed a novel PIM-DMT-DD transmission system, studied polarization de-multiplexing scheme for such a system. The extensive theoretical analyses and simulation results demonstrate that by controlling the frequency difference between the two polarizations, the dominant beat interference can be removed from signal frequency band effectively, and polarization de-multiplexing can be achieved by using a simple MIMO equalizer. Besides, the influence induced by the inherent singular receiving problem of the PIM-DD system can be eliminated by using a pair of receivers with 45° polarization angle difference. The new PIM-DMT-DD transceiver is highly promising for future short reach and optical access systems.

Acknowledgment

The authors would like to acknowledge the support of National Natural Science Foundation of China (61401020), Beijing Natural Science and Foundation (4154080), Hong Kong Government General Research Fund (GRF) under project number PolyU 152079/14E and G-YJ84, Hong Kong Scholars Program (XJ2013026), and Fundamental Research Funds for the Central Universities (FRF-TP-14-027A1).

References and links

1. C. Cole, I. Lyubomirsky, A. Ghiasi, and V. Telang, “Higher-order modulation for client optics,” Communications Magazine IEEE 51(3), 50–57 (2013). [CrossRef]

2. L. Tao, Y. Ji, J. Liu, A. P. T. Lau, N. Chi, and C. Lu, “Advanced modulation formats for short reach optical communication systems,” IEEE Netw. 27(6), 6–13 (2013). [CrossRef]

3. K. P. Zhong, X. Zhou, T. Gui, L. Tao, Y. Gao, W. Chen, J. Man, L. Zeng, A. P. T. Lau, and C. Lu, “Experimental study of PAM-4, CAP-16, and DMT for 100 Gb/s Short Reach Optical Transmission Systems,” Opt. Express 23(2), 1176–1189 (2015). [CrossRef]

4. M. Chagnon, M. Osman, M. Poulin, C. Latrasse, J. F. Gagné, Y. Painchaud, C. Paquet, S. Lessard, and D. Plant, “Experimental study of 112 Gb/s short reach transmission employing PAM formats and SiP intensity modulator at 1.3 μm,” Opt. Express 22(17), 21018–21036 (2014). [CrossRef] [PubMed]

5. K. P. Zhong, W. Chen, Q. Sui, M. J. Wei, A. P. T. Lau, C. Lu, and L. Zeng, “Low cost 400GE transceiver for 2km optical interconnect using PAM4 and direct detection, ” in Asia Communications and Photonics Conference (ACP) (2014), paper, ATh4D.2. [CrossRef]

6. L. Tao, Y. Wang, Y. Gao, A. P. T. Lau, N. Chi, and C. Lu, “Experimental demonstration of 10 Gb/s multi-level carrier-less amplitude and phase modulation for short range optical communication systems,” Opt. Express 21(5), 6459–6465 (2013). [CrossRef] [PubMed]

7. M. I. Olmedo, T. Zuo, J. B. Jensen, Q. Zhong, X. Xu, S. Popov, and I. T. Monroy, “Multiband carrierless amplitude phase modulation for high capacity optical data links,” J. Lightwave Technol. 32(4), 798–804 (2014). [CrossRef]

8. L. Tao, Y. Wang, J. Xiao, and N. Chi, “Enhanced performance of 400 Gb/s DML-based CAP systems using optical filtering technique for short reach communication,” Opt. Express 22(24), 29331–29339 (2014). [CrossRef] [PubMed]

9. T. Takahara, T. Tanaka, M. Nishihara, Y. Kai, L. Li, Z. Tao, and J. Rasmussen, “Discrete-multi-tone for 100 Gb/s optical access network,” in Proc. Conf. Optical Fiber Commun. Conf. (OFC) (2014), Page M2I.1.

10. F. Li, X. Li, J. Yu, and L. Chen, “Optimization of training sequence for DFT-spread DMT signal in optical access network with direct detection utilizing DML,” Opt. Express 22(19), 22962–22967 (2014). [CrossRef] [PubMed]

11. D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON with polarization multiplexing and direct detection,” J. Lightwave Technol. 28(4), 484–493 (2010). [CrossRef]

12. M. Morsy-Osman, M. Chagnon, M. Poulin, S. Lessard, and D. V. Plant, “1λ × 224 Gb/s 10 km transmission of polarization division multiplexed PAM-signals Using 1.3 μm SiP intensity modulator and a direct-detection MIMO-based Receiver,” in Proc. ECOC (2014), Post-deadline paper PD. 4.4.

13. D. J. F. Barros and J. M. Kahn, “Comparison of orthogonal frequency-division multiplexing and on-off keying in amplified direct-detection single-mode fiber systems,” J. Lightwave Technol. 28(12), 1811–1820 (2010). [CrossRef]

14. C. Chen, M. Zamani, Z. Zhang, and C. Li, “Rate-adaptive coding for direct-detection of discrete multi-tones,” in Proc. Conf. Optical Fiber Commun. Conf. (OFC) (2014), paper M2C.2. [CrossRef]

15. L. Nadal, M. S. Moreolo, J. M. Fàbrega, A. L. Nadal, M. S. Moreolo, J. M. Fàbrega, A. Dochhan, H. Grießer, M. Eiselt, and J. P. Elbers, “DMT modulation with adaptive loading for high bit rate transmission over directly detected optical channels,” J. Lightwave Technol. 32(21), 3541–3551 (2014). [CrossRef]

16. L. Liu, Z. Tao, W. Yan, S. Oda, T. Hoshida, and J. C. Rasmussen, “Initial tap setup of constant modulus algorithm for polarization de-multiplexing in optical coherent receivers,” in Proc. Conf. Optical Fiber Commun. Conf. (OFC) (2009), paper OMT2. [CrossRef]

17. A. Vgenis, C. S. Petrou, C. B. Papadias, I. Roudas, and L. Raptis, “Nonsingular constant modulus equalizer for PDM-QPSK coherent optical receivers,” IEEE Photon. Technol. Lett. 22(1), 45–47 (2010). [CrossRef]

Parameter	Values	Parameter	Values
Modulation format (w/o variable bit loading)	16QAM	EML output power	3.5dBm
IFFT/FFT size	128	EML RIN	-160dB/Hz
Number of Data Subcarriers	56	EML line-width	5MHz
cyclic prefix length	10	Rx bandwidth	16GHz
DAC/ADC rate	64GSam/s	PD responsibility	0.65W/A
TX bandwidth	20GHz	PD thermal noise	20pA/Hz0.5
Frequency space (△f)	70GHz	PD dark current	10nA

Polarization-interleave-multiplexed discrete multi-tone modulation with direct detection utilizing MIMO equalization

Abstract

1. Introduction

2. Transmission model for dual polarization with IM-DD

3. PIM-DMT-DD transmission with MIMO equalization

3. Simulations and discussion

3.1 Simulation system model

3.2 Simulation results and analysis

4. Conclusions

Acknowledgment

References and links

Cited By

Figures (12)

Tables (1)

Equations (19)

Optics Express