## Abstract

Fast channel estimation is crucial to increase the payload efficiency which is of particular importance for optical packet networks. In this paper, we propose a novel least-square based dispersion estimation method in coherent optical fast OFDM (F-OFDM) systems. Additionally, we experimentally demonstrate for the first time a 37.5 Gb/s 16QAM coherent F-OFDM system with 480 km transmission using the proposed scheme. The results show that this method outperforms the conventional channel estimation methods in minimizing the overhead load. A single training symbol can achieve near-optimum channel estimation without any prior information of the transmission distance. This makes optical F-OFDM a very promising scheme for the future burst-mode applications.

©2013 Optical Society of America

## 1. Introduction

Optical orthogonal frequency division multiplexing (OFDM) [1–8] has drawn much interest recently due to its enhanced spectral efficiency and high dispersion tolerance. It also allows adaptive modulation of each subcarrier according to the traffic demands, which enables dynamic bandwidth allocation with low granularity and provides great system flexibility [1]. One of major concerns in the implementation of optical OFDM is the channel estimation and compensation which are commonly achieved by using training symbols (TSs). For spectrally efficient applications, the requirement of keeping the overhead at the minimum is a crucial issue. This is of particular importance to burst-mode transceivers for optical packet networks where the signal is detected on a packet-by-packet basis [9]. Therefore, it is desirable to estimate the channel response rapidly even without any prior information of the transmission distance. The conventional method uses a time-domain averaging algorithm that averages over multiple TSs [2]. An intra-symbol frequency-domain averaging (ISFA) [4] was proposed which averaged over multiple subcarriers in the same TS to increase the payload efficiency. Differential amplitude phase shift keying OFDM can potentially eliminate the needs for TSs [5], however, this format has fundamental back-to-back performance penalty.

Optical fast OFDM (F-OFDM) [10–13] is a promising OFDM scheme, where the subcarrier spacing is reduced to the half of that in the conventional OFDM. This scheme exhibits greatly improved performance in frequency offset compensation [10] when compared to conventional OFDM, so is more suitable for fast tunable transceivers. The subcarrier multiplexing/demultiplexing can be implemented by using a discrete cosine transform (DCT) pair. The design of guard interval (GI) specific to optical F-OFDM was proposed [11]. It was shown that by using a symmetric extension (SE) rather than cyclic extension based GI, the F-OFDM subcarriers could be demultiplexed by DCT without intercarrier interference (ICI) and the chromatic dispersion (CD) could be compensated using one-tap equalizers.

However, the coefficients of the one-tap equalizers in previous works were obtained using the conventional time-domain averaging that reduced the overall data rate. In this paper, we propose a novel least-square based dispersion estimation. We experimentally demonstrate for the first time a 37.5 Gb/s 16QAM optical F-OFDM system with 480 km transmission using the proposed scheme. It is shown that this method outperforms the previous methods, and single TS can achieve near-optimum performance without prior transmission information. The principle of the proposed method can also be applied in conventional OFDM.

## 2. Principle

The overall channel response, *H*(*ω*), at frequency *ω _{i}* can be written as:

*H*(

_{s}*ω*) represents the static response at

_{i}*ω*regardless of the transmission paths of the packets, including the transfer functions of the modulator, drive amplifier, and receiver.

_{i}*A*and

*D*are the channel gain/loss and the accumulated CD value respectively. These parameters are unknown and may vary packet by packet.

_{a}*H*(

*ω*) may be obtained using TSs. Because

*H*(

_{s}*ω*) is fixed for all received packets and can be readily obtained beforehand, we define the estimated normalized frequency response,

_{i}*H*

_{m}(

*ω*), at frequency

*ω*by using

_{i}*m*TSs as:

*d*(

_{j}*ω*) and

_{i}*a*

_{j}(

*ω*) are the received and transmitted data at frequency

_{i}*ω*for the

_{i}*j*

^{th}F-OFDM symbol. In Eq. (2), the number,

*m*, should be sufficient to mitigate the noise effect on

*H*(

_{m}*ω*), which however increases the overhead or reduces the payload efficiency.

_{i}It can be seen from Eq. (1) that there are only two unknown parameters, *A* and *D _{a}*, that require rapid estimation for each packet. The proposed method finds the parameter values for the model Eq. (1) that best fit

*H*(

_{m}*ω*) with the minimal overhead. We define the sum of the squares of the errors between

_{i}*H*(

_{m}*ω*) and the fitted values provided by Eq. (1),

_{i}*S*(

*A*,

*D*), as:

_{a}*N*represents the number of subcarriers in the TS used for the parameter estimation.

*A*and

*D*are estimated by minimizing

_{a}*S*(

*A*,

*D*) and setting the gradient to zero:Equations (3)-(4) result in a nonlinear least-square problem, which can be solved by choosing initial values for

_{a}*A*and

*D*and then refining the parameters iteratively. Assuming the initial values are

_{a}*A*and

_{1}*D*, we linearize the model by using the first-order Taylor series expansion:

_{a,1}*A*and

*D*:

_{a}*k*is the iteration number. Typically, near-optimal parameter values can be obtained after only several iterations. The initial values of

*A*and

*D*depend on the amount of prior information. In this paper, we assume that no prior information is available, and set

_{a}*A*as |

_{1}*H*(

_{m}*ω*)|. The initial value,

_{1}*D*, is set as:

_{a,1}*D*, it does not require extensive search with fine resolutions. The principle of this method can be extended to polarization multiplexed systems where the channel gain/loss should be replaced by a 2 × 2 matrix.

_{a}## 3. Experimental setup

Figure 1 shows the experimental setup of 16QAM coherent optical F-OFDM. Two bi-polar four-amplitude-shift-keying (4-ASK) data were encoded with Gray code in Matlab. The inverse-DCT (IDCT) and DCT used 128 points, of which 100 and 6 subcarriers were used for data transmission and phase estimation, respectively. The first two subcarriers were not modulated, allowing for AC-coupled drive amplifiers and receivers. The last 20 subcarriers were zero-padded to avoid aliasing. After IDCT and parallel-to-serial (P/S) conversion, 6 samples were added to each symbol as a SE-based GI. The generated F-OFDM signal was downloaded to a 12-GS/s arbitrary waveform generator (AWG). The signal line rate including the GI and forward error correction overhead was 37.5 Gb/s (4 × 12 × 100/128).

A laser with 100-kHz linewidth was used to generate the optical carrier. Two 4-ASK electrical F-OFDM signals were fed into the in-phase and quadrature arms of an optical I/Q modulator to generate an optical 16QAM F-OFDM signal. The input signals to the optical modulator had a peak-to-peak driving swing of 0.5*V*_{π} to avoid nonlinear distortion. The generated optical signal was amplified by an erbium doped fiber amplifier (EDFA), filtered by a 0.8-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 5 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 −5.5 dBm.

At the receiver, the optical signal was detected with a pre-amplified coherent receiver and 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 OBPF with a 3-dB bandwidth of 0.64 nm, a second EDFA, and another optical filter with a 3-dB bandwidth of 1 nm. A polarization controller (PC) was used to align the polarization of the filtered F-OFDM signal before entering the signal path of a 90° optical hybrid. A tap of the transmitter laser signal was used as the local oscillator at the receiver. 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 decoding algorithms included interpolation of the 50-GS/s data, down-sampling to 12 GS/s with precise symbol synchronization, DCT, phase estimation, and one-tap equalizers to compensate CD. The coefficients of one-tap equalizers were estimated using different methods: 1) the conventional time-domain averaging over multiple TSs; 2) ISFA where *H _{m}*(

*ω*) was further averaged over multiple adjacent subcarriers. The subcarrier number for averaging was 5, which was verified by additional results to obtain the near-optimum performance; 3) the proposed method where

_{i}*H*(

_{m}*ω*) was employed to estimate

_{i}*A*and

*D*that were then used to reconstruct the channel response based on Eq. (1). 2400 F-OFDM symbols were measured, giving a total number of measured 16QAM symbols of 240,000.

_{a}## 4. Experimental results

We demonstrated for the first time 16QAM F-OFDM with 480 km transmission as shown in Fig. 2(a)
, which depicts the measured BER versus the received OSNR at back-to-back (circles), after 360 km (triangles) and 480 km (squares) using 20 TSs. The required OSNR at BER of 10^{−3} was ~16 dB, and the penalties after 360 km and 480 km were around 1 dB and 2 dB respectively. This penalty may have been caused by the de-polarization during transmission. When the number of TSs was reduced to one, the estimated channel response was highly distorted by the noise, resulting in significantly degraded performance when the conventional method (pluses) was applied. ISFA improved the performance but still exhibited large performance penalties. On the other hand, the proposed method with *m* = 1 could achieve similar performance as that with *m* = 20. Insets of Fig. 2(a) illustrate the constellation diagrams of the 16QAM F-OFDM at 19.6 dB OSNR and confirm the performance advantage of the proposed method. Figure 2(b) shows the BER versus the transmission distance for three aforementioned methods when single TS was used. The OSNR values for 0, 120, 240, 360 and 480 km were 18.4, 19, 19, 19.2, and 19.6 dB respectively. It can be seen that the conventional method resulted in the poorest performance, with BER of ~10^{−2} for all distances. ISFA mitigated the noise effect by averaging *H _{m}*(

*ω*) over multiple subcarriers. When the proposed method was applied, the performance was the best with more than one order of magnitude BER improvement when compared to the conventional method.

_{i}The performance benefit induced by the proposed method can be interpreted by the estimated channel response as shown in Fig. 3
. Conventionally, the channel response of subcarriers is obtained based on Eq. (2) and is sensitive to the noise for *m* = 1. The curve for the ISFA method is smoother due to the reduced noise effect. In the proposed method, *A* and *D _{a}* can be well estimated from an over-determined system, in which the subcarrier number of the TSs is more than the unknowns. The solid curves in Fig. 3 are actually the fitting curves of

*H*(

_{1}*ω*) based on the model of Eq. (1) that greatly reduce the noise effect.

_{i}Figure 4(a)
shows the performance versus the number of TSs. The figure clearly shows that more than 10 TSs were required to achieve the near-optimum performance by using the conventional time-domain averaging. ISFA mitigated the noise effect and consequently reduced the required TS number to 5. By using the proposed method, the performance was insensitive to the number of TSs and single TS could achieve near-optimal channel estimation. Additional results show that similar curves could be obtained except a fixed penalty when the phase noise was not well mitigated (the number of pilot tones for phase estimation was reduced from six in Fig. 4(a) to one). The parameters in the proposed method were estimated iteratively after the initial selection of *A*_{1} and *D*_{a,1}. Figure 4(b) shows the BER versus the iteration number. The OSNR values for 360 and 480 km were 19.2 and 19.6 dB, respectively. It can be seen that one iteration could obtain the optimal BER for both distances.

## 5. Conclusions

We have proposed a novel least-square based dispersion estimation method in coherent optical F-OFDM. With this method, we have experimentally demonstrated for the first time a 37.5 Gb/s 16QAM coherent optical F-OFDM system over 480-km fiber transmission. The proposed method can achieve near-optimum performance by using only single training symbol and without prior knowledge of the transmission distance. This makes the optical F-OFDM scheme very promising for the future burst mode applications.

## Acknowledgments:

This work was supported by Science Foundation Ireland under grant number 11/SIRG/I2124 and 06/IN/I969, and the EU 7th Framework Program under grant agreement 318415 (FOX-C).

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