## Abstract

Real-time optical orthogonal frequency division multiplexing (OOFDM) transceivers are experimentally demonstrated with advanced pilot subcarrier-assisted channel estimation being implemented. The channel estimation technique is, for the first time, proposed and experimentally verified rigorously, which offers a number of unique features including high accuracy, low complexity, small pilot bandwidth usage, excellent stability and buffer-free data flow. The fastest ever real-time end-to-end transmission of 3Gb/s 16-QAM-encoded OOFDM signals over 75km MetroCor single-mode fibres is achieved with negative power penalties of −2dB at BERs of 1.0×10^{−4} in directly modulated DFB laser-based, intensity-modulation and direct-detection systems without in-line optical amplification and chromatic dispersion compensation.

©2009 Optical Society of America

## 1. Introduction

The concept of optical orthogonal frequency division multiplexing (OOFDM) was first proposed in 2005 [1], soon after, opportunities of employing OOFDM signals converted by directly modulated DFB lasers (DMLs) were theoretically explored over multi-mode fiber (MMF)- and single-mode fiber (SMF)-based optical access networks [2,3]. Since then, world-wide extensive experimental investigations of the transmission performance of OOFDM of various variants have been reported for all the application scenarios including long-haul systems [4–6], metropolitan and access networks [7,8], as well as local area networks [9,10]. However, all those experimental works published so far have been undertaken using off-line digital signal processing (DSP) approaches, which do not consider the limitations imposed by the precision and speed of practical DSP hardware required for realizing real-time transmission. The experimental demonstration of real-time OOFDM transmission is vital for not only rigorously validating the OOFDM technique but also establishing a strong platform for evaluating the feasibility of the OOFDM technique for practical implementation in future high capacity optical networks of various architectures.

Recently, we have made a significant breakthrough in experimentally demonstrating the world-first real-time OOFDM transceivers using off-the-shelf components [11]. The transceivers support real-time end-to-end transmission of a 1.5Gb/s differential quadrature phase shift keying (DQPSK)-encoded OOFDM signal over a DML-based 500m MMF system incorporating intensity-modulation and direct-detection (IMDD) [11]. More recently, a double real-time OOFDM transmission capacity has also been achieved, and transmission of a 3Gb/s DQPSK-encoded OOFDM signal has been successfully demonstrated experimentally over a 500m MMF with a bit error rate (BER) as low as 3.3x10^{−9} in the above-mentioned transmission system [12]. These research works have demonstrated the great potential of OOFDM as a promising solution for next generation high capacity optical networks.

Given the fact that the commercially available key components involved in the real-time OOFDM transceivers have limited operating speeds, to further improve the transmission capacity of the real-time OOFDM transceivers, one of the most effective approaches is to employ high signal modulation formats such as M-ary quadrature amplitude modulation (QAM). In M-ary QAM systems, both amplitudes and phases of transmission system-distorted OOFDM symbols received in the receiver are used to recover the transmitted data. This implies that channel estimation with sufficiently high accuracy is vital, as it influences the system performance to a great extent.

It is well known [13] that, in conventional wireless communications systems, two categories of channel estimation are being widely adopted, which include frequency domain channel estimation and time domain channel estimation. In frequency domain channel estimation, the frequency domain channel transfer function (CTF) of a transmission system is estimated by using known frequency domain pilot subcarriers interspersed with the information-bearing subcarriers in the OFDM signal spectrum in the transmitter, and use is also made of their corresponding OFDM subcarriers received at the output of the fast Fourier transform (FFT) in the receiver. Clearly, such a technique is not capable of obtaining directly the frequency domain CTF corresponding to the information-bearing subcarriers located between two neighboring pilot subcarriers. Thus, linear or low-pass interpolation has to be used to derive the wanted CTF from those estimated by the pilot subcarriers. According to the Nyquist sampling theorem, the accuracy of frequency domain channel estimation depends strongly upon the number of pilot subcarriers utilized in the OFDM spectrum. For typical wireless asynchronous transfer mode systems, to yield a CTF indistinguishable from the perfect function curve, the minimum number of pilot subcarriers required should be approximately 30% of the total number of OFDM subcarriers within a symbol [13]. The above discussions indicate that the frequency domain channel estimation technique suffers a strong trade-off between accuracy and pilot bandwidth usage. In particular, the pilot bandwidth usage may be increased even further when channel oversampling is applied.

On the other hand, in time domain channel estimation, a training sequence embedded in the transmitted data stream is employed to perform a correlation-based channel impulse response estimation, based on which the corresponding frequency domain CTF can be computed by applying the FFT operation. Although time domain channel estimation usually gives a better performance than frequency domain channel estimation, time domain estimation has, however, higher complexity and relatively larger pilot bandwidth usage.

The time-variant and frequency-selective nature of the wireless communications channels are mainly responsible for the above-mentioned challenges associated with the conventional channel estimation techniques. In addition, these techniques are just capable of supporting low signal bit rates of the order of several tens of Mb/s [13]. Owing to the fact that optical communications systems of interest of the present paper is relatively stable and operates at very high signal bit rates, the conventional approaches used in wireless communications systems are, therefore, not suitable for optical communications systems, thus advanced channel estimation techniques are required.

In this paper, an advanced pilot subcarrier-assisted channel estimation technique is, for the first time, proposed, experimentally verified and successfully implemented in the real-time OOFDM transceivers. The proposed technique has the following unique advantages:

- • High accuracy. The entire frequency domain CTF corresponding to all the subcarriers across the whole OOFDM signal spectrum is estimated directly without utilizing interpolation. In addition, pilot subcarrier averaging over a specific time period is also adopted to enable a significant reduction in the noise effect induced by both electrical and optical components. Experimental measurements show that the proposed technique supports no error floor transmission at a BER as low as 1.0×10
^{−10}. - • Low complexity
Use is made of simple multiplication calculations instead of sophisticated convolution operations. The technique is also made free from data buffering. These two features are extremely valuable for high speed real-time optical communications systems.

- • Low pilot bandwidth usage
The transmission bandwidth occupied by pilot subcarriers can be very low, as it is proportional to the inverse of the total number of information-bearing subcarriers within a symbol. In particular, the pilot bandwidth usage can be further reduced to an extremely small value, as this technique allows the pilot subcarriers to be switched off periodically during data transmission, but without affecting the system BER performance considerably.

It is worth mentioning that, the proposed channel estimation technique is applicable for all OOFDM-related application scenarios. In this paper, detailed explorations are made of its applications in IMDD OOFDM transmission systems. It is shown that the successful implementation of the proposed channel estimation technique in improved real-time OOFDM transceivers [12], enables real-time end-to-end transmission of 3Gb/s 16-QAM-encoded OOFDM signals over 75km MetroCor SMFs with negative power penalties of −2.0dB in DML-based IMDD systems without in-line optical amplification and chromatic dispersion compensation. This experimental work demonstrates the great potential of OOFDM as a promising solution for next generation optical access networks.

## 2. Pilot subcarrier assisted- channel estimation

In the transmitter, pilot subcarriers are diagonally embedded in the time-frequency OOFDM symbol space, as illustrated in Fig. 1 . Mathematically, the pilot and information-bearing subcarrier allocation can be expressed as

Having appropriately arranged the pilot and information-bearing subcarriers, the inverse FFT (IFFT) is then performed to these subcarriers to generate real-valued OOFDM symbols in the transmitter. In the receiver, at the output of the FFT, the identification of the received pilot subcarriers is first made by conducting the following two operations to subcarrier 1 of different symbols:

_{s})-th] symbol. C is the preset integer number determining the total number of ${N}_{s}$symbol-spaced D values used for averaging. Complex values encoded using a random data sequence are taken onto the information-bearing subcarriers, giving rise to minimized Q values. Whilst each of the pilot subcarriers has a fixed complex number with a maximal amplitude, causing the occurrence of a Q peak corresponding to a symbol with its subcarrier 1 being the pilot subcarrier, as shown in Fig. 2 . Clearly, a large C makes the Q peak more distinguishable, but requires relatively long time to conduct the averaging operation. Our experimental measurements show that C=16 is sufficiently adequate for all the systems of interest of the present paper. Therefore, C=16 is taken throughout this paper. By making use of one of the generated ${N}_{s}$symbol-spaced Q peaks, subcarrier 1 of the corresponding symbol can be regarded as a pilot subcarrier reference, based on which all other pilot subcarriers in subsequent symbols can be identified easily. After having identified the reference pilot subcarriers by using the Q peaks, the Q averaging process can be terminated. In addition, as discussed in Section 4.1, the pilot subcarriers can also be switched off periodically to considerably reduce the pilot bandwidth usage. The switching speed can be as low as 10Hz without deteriorating the system performance.

Making use of the assigned and received pilot subcarriers, the frequency domain CTF, ${H}_{k}$ (k= 1, 2, …N_{s}), can be computed by

*Ρ*is the fixed value taken on the pilot subcarriers in the transmitter. Given the fact that the impact of noise associated with both electrical and optical components affects considerably the accuracy of channel estimation, to effectively reduce the noise effect, pilot subcarrier averaging is performed over M received pilot subcarriers of the same frequency, as described in Eq. (4). The optimum choice of M is discussed in Section 4. Having obtained the frequency domain CTF, channel equalization is finally conducted following well-known procedures described in [13]. It should be noted that, the proposed channel estimation technique differs completely from traditional time-domain symbol synchronization techniques in two major aspects listed as followings: 1) The proposed technique operates only in the frequency domain for OOFDM transmission systems that have already been symbol-synchronized, and 2) both fixed value-based pilot subcarriers and encoded known random data-based pilot subcarriers can be adopted in the proposed technique.

## 3. Experimental system setup and real-time OOFDM transceiver architecture with channel estimation

The experimental system setup and the real-time OOFDM transceiver architecture with channel estimation are illustrated in Fig. 3(a) and Fig. 3(b), respectively. As detailed discussions of the real-time OOFDM transceiver architecture using DQPSK have already been made in [11], here, along with a description of the experimental system setup, an outline of the real-time transceiver is provided with an emphasis being given to the implementation of the proposed channel estimation technique in the real-time transceiver.

The real-time OOFDM transmitter consists of an Altera Stratix II GX field-programmable gate array (FPGA). 14 parallel pseudo random bit sequences of lengths of 354000 are employed as information data. One extra sequence of a fixed 4-bit pattern (corresponding to one of the four diagonal end points of the 16-QAM constellation) is used for pilot data. Prior to feeding the 15 16-QAM encoders, the pilot data is embedded in the information data in such a way that the encoded data pattern illustrated in Fig. 1 is produced. Here, 32 (2N_{s}+2) 16-QAM-encoded OOFDM subcarriers are considered, of which 16 subcarriers (15 information-carrying subcarriers and one subcarrier with zero power) are arranged to satisfy the Hermitian symmetry with respect to their complex conjugate counterparts to generate real-valued OOFDM symbols. A self-developed 32-point IFFT/FFT logic function, which has been experimentally verified successfully at 10Gb/s [11], is employed to perform the IFFT to the above-mentioned subcarriers. The IFFT/FFT logic function employs a radix-2 decimation-in-time structure comprising of 2-point butterfly elements as the core computational building blocks, and is based on a highly pipelined architecture using a number of extensively paralleled processing stages.

At the output of the IFFT, 13.8dB clipping and 8-bit quantization are applied to the signed, real-valued OOFDM symbols. A cyclic prefix of 8 samples is then added to each symbol, resulting in 40 samples per symbol. The internal system clock is set to 50MHz, which is equal to the symbol rate. The signed samples are converted to unsigned values by adding an appropriate DC offset, as the digital-to-analogue converter (DAC) requires positive values only. After performing sample ordering and bit arrangement, the unsigned 40 samples are streamed to the DAC interface at 2GS/s. An entire symbol is fed in parallel to 32 high speed 10:1 dedicated hardware serialisers, the interface thus consists of 4 samples transferred in parallel at a rate of 0.5GHz. The DAC generates an analogue electrical OOFDM signal having a maximum peak-to-peak voltage of 636mV. The signal is attenuated as necessary and subsequently, together with an appropriate DC bias current, injected into a 1550nm DML with a 3-dB modulation bandwidth of approximately 10GHz.

The OOFDM signal emerging from the DML is coupled into an erbium-doped fibre amplifier (EDFA) with a 15dB optical gain and a 5dB noise figure. After passing through a 0.8nm optical filter, the amplified optical signal is coupled into MetroCor SMFs of different lengths. It should be noted that the use of the EDFA is to increase the optical launch power range in order to explore the fibre nonlinear effects, as discussed in Section 4.

In the receiver, after passing through an optical attenuator, the transmitted OOFDM signal is converted into the electrical domain using a 12GHz PIN with TIA. The PIN has a receiver sensitivity of −17dBm (corresponding to 10 Gb/s non-return-to-zero data at a BER of $1.0\times {10}^{-9}$). The electrical signal is first amplified with a 2.5GHz, 20dB RF amplifier, then attenuated as needed to optimise the signal amplitude to suit the input range of the analogue-to-digital converter (ADC). After passing through an electrical low-pass filter, the signal is converted via a balun to a differential signal and then digitized by a 2GS/s, 8-bit ADC in the receiver. Finally, the digital samples are fed, via a digital interface identical to that corresponding to the DAC, to a second Altera Stratix II GX FPGA, which performs, in a reverse order, the real-time DSP on the received symbols and recovers data. It is worth mentioning that pilot subcarrier detection, pilot subcarrier averaging, frequency domain CTF estimation and channel equalization are performed after the FFT, according to the procedures detailed in Section 2.

Symbol synchronization is performed by continuous transmission of symbols of a fixed pattern over the transmission system. By using the FPGA embedded logic analyser (SignalTap II) with JTAG connection to a PC, the captured samples of the fixed symbols can be viewed, thus the sample offset is determined and subsequently compensated by adjusting the inserted sample offset accordingly. It should be pointed out, in particular, that such a symbol synchronization process is performed only once at the establishment of the transmission connection.

The bit error count over 100 million symbols is continuously updated and displayed with the embedded logic analyser for each subcarrier within a symbol. This enables fine adjustment of the system parameters to maximize the transmission performance. In addition, the logic analyser also displays and continuously updates the total number of bit errors and the corresponding symbols accumulated since the start of a transmission session. This enables the measurements of BERs of each subcarrier and the entire transmission channel at unlimited low values, provided that a sufficiently long operation time is allowed. It is worth mentioning that, clock synthesizers based on a common reference clock are used to generate the system clocks for both the transmitter and the receiver.

## 4. Experimental results

As already discussed in Section 3, with the 50MHz FPGA operating speeds and the 2GS/s sample rates of the DAC/ADC, 3Gb/s OOFDM signals are produced when 16-QAM is taken on all the 15 non-zero subcarriers. In this section, extensive use is made of the 3Gb/s 16-QAM-encoded OOFDM signals to explore: 1) the operating characteristics of the proposed channel estimation technique and the stability of the real-time OOFDM transceivers, and 2) the transmission performance of the real-time OOFDM transceivers over the systems illustrated in Fig. 3(a). For all the experimental measurements presented in this section, the DFB laser operates at a bias current of 35mA, under which the output optical power is −3.7dBm. After appropriately adjusting the optical gain of the EDFA followed by an optical filter, the optical powers injected into the MetroCor SMFs are fixed at 7dBm.

#### 4.1 Evaluation of the channel estimation technique

The effectiveness of pilot subcarrier averaging adopted in the channel estimation technique is shown in Fig. 4
, where the BER versus number of averaged pilot subcarriers of the same frequency, M, is plotted for different received optical powers in a 50km MetroCor SMF system. As already analyzed in Section 2, it can be seen in Fig. 4 that, the BER decreases with increasing M, and such a developing trend is more pronounced for low BERs corresponding to high received optical powers. It is also very important to note that, for M≥32, very flat BER curves are observed for broad ranges of BERs and received optical powers. Moreover, similar characteristics also exist for SMFs of different lengths. The above results indicate that it is sufficiently accurate to adopt M=32 in our experimental measurements presented in this paper. In addition, Fig. 4 also shows that BERs lower than 1.0×10^{−7} is obtainable, which can be further lowered to 1.0×10^{−10} for higher received optical powers, as seen in Fig. 7
. This verifies the accuracy of the proposed channel estimation technique.

Without deteriorating considerably the system performance, a slow CTF updating rate is preferred in practice, as it can reduce greatly the number of pilot subcarriers utilized and thus reduce significantly pilot bandwidth usage. To demonstrate the impact of CTF updating rate on the system performance and, more importantly, the stability of the implemented real-time OOFDM transceivers, Fig. 5 is plotted for a 50km SMF under typical laboratory environments. It can be found in Fig. 5 that, for all the different received optical powers, the CTF updating rate can be reduced to a value as small as 10Hz, implying that the pilot bandwidth usage can be reduced to a value as small as 0.001%, and that the stability of the real-time OOFDM transceivers are truly excellent. Of course, full explorations of system stability require the transmission system to be exposed to extreme environmental conditions. Clearly, this is far beyond the topic of the present paper.

The normalized amplitude CTF estimated using the proposed channel estimationtechnique is plotted in Fig. 6 for various transmission systems including optical back-to-back and different distances of 50km and 75km. For all these cases, identical amplitude transfer functions corresponding to low frequency subcarriers are observed, which decay rapidly with increasing subcarrier frequency. The strong amplitude roll-off effect is mainly due to the analogue electrical components involved in the real-time transceiver. Similar behavior has also been observed in a DQPSK-based 500m MMF transmission system [11].

It is very interesting to note in Fig. 6 that, in comparison with the optical back-to-back case, CTFs corresponding to high frequency subcarriers are slightly lifted up after passing through the SMFs. This contrasts sharply with the long transmission distance-induced CTF narrowing effect for IMDD SMF systems [3]. The physical origin of the observed phenomenon is the compensation between the positive transient frequency chirp associated with the DML and the negative chromatic dispersion parameter associated with the MetroCor fibre [15,16]. As the influence of the DML frequency chirp effect on high frequency subcarriers is much more severer than that on low frequency subcarriers, the long transmission distance-enhanced CTF occurs for high frequency subcarriers only. As a direct result of the aforementioned effects, after transmitting through the SMFs, negative power penalties are expected, as discussed in Section 4.2.

#### 4.2 Transmission performance

Having explored the salient features of the proposed channel estimation technique in Section 4.1, here special attention is given to the real-time end-to-end transmission of 3Gb/s 16-QAM-encoded OOFDM signals over various DML-based IMDD MetroCor SMFs without in-line optical amplification and chromatic dispersion compensation.

The measured BER as a function of received optical power is presented in Fig. 7 for four different scenarios including optical back-to-back and SMF transmissions of 25km, 50km and 75km. For the first three cases, record low BERs of approximately 1.0×10^{−10} are obtained at received optical powers of −10.3dBm for optical back-to-back, −10.75dBm for 25km and −11.4dBm for 50km. Whilst for the 75km case, a BER of 3.98×10^{−7} is measured at −12.26dBm, which is the highest received optical power for the 75km system under the current operating conditions. No error floors are observed for all these four cases, indicating, once again, the excellent accuracy of the developed channel estimation technique. The constellations of the 1^{st}, 9^{th} and 15^{th} subcarriers of the OOFDM signal after transmitting through the 75km SMF are given in Fig. 8
for two representative BERs of 3.98×10^{−7} and 5.65×10^{−4}. To demonstrate the subcarrier amplitude roll-off effect, these constellations recorded prior to channel estimation and channel equalization are shown in Fig. 8. The decrease in subcarrier amplitude for subcarriers locating at high frequencies, as seen in Fig. 8, can be easily understood by considering the frequency-dependent CTF characteristics shown in Fig. 6.

It is very interesting to note that, as expected from the discussions in Fig. 6, negative power penalties are, indeed, observed in Fig. 7(a) for 25km, 50km and 75km SMFs. To highlight the transmission distance dependent-negative power penalty, the negative power penalty corresponding to a BER 1.0×10^{−4} against transmission distance is given in Fig. 7(b), where an almost linear reduction in negative power penalty is shown with increasing transmission distance, and a −2dB power penalty is observed for the 75km SMF. According to Fig. 7(b), it is envisaged that longer distances may be achievable if use is made of in-line optical amplifiers to compensate the linear fibre loss.

The BER of each subcarrier of an OOFDM symbol is given in Fig. 9
, in obtaining which the received optical power and the total channel BER are −16.35dBm (−14.38dBm) and 5.65×10^{−4} (6.18×10^{−4}) for the 75km SMF (optical back-to-back) case. Such BER distribution results directly from the CTF characteristics shown in Fig. 6. In addition, subcarrier 1 has the lowest BER, indicating that the subcarrier×subcarrier intermixing effect taking place upon PIN detection is negligible. Furthermore, it is also experimentally shown that, for the 75km transmission case, the total channel BER does not alter significantly when the optical launch power varies in a wide range from −1dBm to 9.7dBm. This suggests that the impairments of the fibre nonlinear effects are trivial.

## 5. Conclusions

An advanced pilot subcarrier-assisted channel estimation technique has been, for the first time, proposed and experimentally verified rigorously for real-time OOFDM transceivers. The technique offers a number of unique features including, for example, high accuracy, low complexity, small pilot bandwidth usage, excellent stability and buffer-free data flow. Real-time optical OOFDM transceivers have been experimentally demonstrated with the proposed channel estimation technique being implemented. The fastest ever real-time end-to-end transmission of 3Gb/s 16-QAM-encoded OOFDM signals over 75km MetroCor single-mode fibres has been achieved with negative power penalties of −2dB at BERs of 1.0×10^{−4} in DML-based IMDD systems without in-line optical amplification and chromatic dispersion compensation.

## Acknowledgement

This work was partly supported by the European Community's Seventh Framework Programme (FP7/2007-2013) within the project ICT ALPHA under grant agreement n° 212 352, in part by the U.K. Engineering and Physics Sciences Research Council under Grant EP/D036976, and in part by The Royal Society Brian mercer Feasibility Award. The work of X.Q. Jin was also supported by the School of Electronic Engineering and the Bangor University.

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