## Abstract

We experimentally demonstrate an intensity modulated and direct detection optical OFDM with variable bit rate from 5 Gb/s to 9 Gb/s using BPSK format. A fast processing based on the Hartley transform is performed with low complexity DSP, achieving the same performance as 4QAM FFT-based processing. Using the same bandwidth occupancy as required for 5 Gb/s, the bit rate can be increased up to 80% and transmitted over 25 km SSMF, by reducing the guard band and adopting an optimized transceiver design with additional overhead, including half-length training symbols and cyclic extension.

© 2012 OSA

## 1. Introduction

Optical orthogonal frequency division multiplexing (O-OFDM) is increasingly emerging as enabling technology for future optical networks. Due to its robustness against transmission impairments and its unique flexibility and scalability to high-speed transmission, the range of applications is really huge, spanning different network segments, from long-haul to optical access, and different optical channel types, from standard single mode fiber to optical wireless or optical interconnects [1]. Moreover, it is also arising as suitable solution for elastic networks, where the transponders can be adapted to variable bandwidth and bit rate for optimal spectral resources allocation. Despite the recent advances in electronic digital signal processing (DSP) enabling software-defined optical transmission [1], the reduction of the complexity and cost of the implementation of this technology is still a key issue. A cost-effective implementation of the O-OFDM, often referred in the literature as discrete multitone modulation (DMT), is possible when the OFDM signal is real-valued and can be transmitted with a simplified electronic design and an intensity-modulated direct-detection (IM/DD) optical system using simple commercial components [1]. Nevertheless, this is at the expense of the spectral efficiency, as a double side band spectrum is transmitted and a guard band is required for correct photodetection. Usually, in order to avoid intermodulation products between the OFDM signal and the optical carrier, a guard band equal to the OFDM signal bandwidth is selected. However, it has been demonstrated [2] that if IM is performed with an external Mach Zehnder Modulator (MZM) biased at the quadrature point, the intermodulation products, due to the square law characteristic of the photodetector, are reduced. Therefore, the guard band can be decreased for increasing the system spectral efficiency at the expense of the receiver sensitivity.

Recently, the fast Hartley transform (FHT) has been proposed as an alternative OFDM modulation for optical communications. It deals with real-valued signals without the need of the Hermitian symmetry (HS) constraint and uses single-dimensional (1D) lower-size constellations compared to O-OFDM based on the fast Fourier transform (FFT), where bidimensional (2D) formats are required [3]. Additionally to the streamlining of the OFDM signal generation/processing, the computational resources needed by the FFT for reversing the kernel sign are saved, due to the FHT self-inverse property. Compared to the Cooley and Tuckey FFT algorithm, the FHT requires half computational complexity and the DSP speed can be further increased by applying fast algorithms with minimum arithmetic complexity [3–5]. The fast and power efficient O-OFDM transmission system based on FHT-processing has been theoretically and numerically demonstrated [3, 6]. In [7], an IM/DD optical system based on OFDM modulation with FHT processing has been experimentally demonstrated. In order to comparatively assess the performance of the proposed system, it has been shown that an FHT-based OFDM system using binary phase shift keying (BPSK) modulation gives the same performance at the same spectral efficiency as an FFT-based OFDM using a quadrature amplitude modulation (4QAM) format and the same number of subcarriers [7]. Additionally, we have demonstrated that it is possible to enhance the spectral efficiency, increasing the bit rate by reducing the guard band. This allows designing a bit rate variable IM/DD transmission system, resulting in a suitable cost-effective solution for elastic networks. We have analyzed the back-to-back (B2B) system at different bit rates, varying the guard band, and evaluated the sensitivity penalty after 25 km of standard single mode fiber (SSMF). It has been shown that, using a reduced equalization overhead including only two training symbols and no cyclic prefix (CP), a variable bit rate, from 5 Gb/s to 8 Gb/s, can be transmitted using BPSK format and low complex processing, with up to 75% reduction of the required guard band, over 25 km SSMF for a target bit error rate (BER) of 10^{−3} [7].

In this paper, we propose to use an optimized equalization processing with a cyclic extension to enhance the performance of the bit rate variable FHT-based O-OFDM system at the expense of additional overhead. We demonstrate that up to 9 Gb/s can be transmitted over a 25 km SSMF link thanks to the improved transceiver design, which also includes digital symmetrically clipping to limit the peak to average power ratio (PAPR) of the OFDM signal. Furthermore, in this extended version of our previous work [7], a more detailed analysis of the proposed transmission system in comparison to the standard O-OFDM based on real-valued FFT is provided and an accurate digital signal processing description is presented.

The paper is organized as follows: in Sec. 2 the digital signal processing required in O-OFDM system using the FHT is described. Its suitability for real-valued data transmission is evidenced based on the FHT properties and in comparison to the FFT processing. Sec. 3 compares the two schemes in terms of performance, presenting the experimental set-up and the analysis of the B2B case. The proposed bit rate variable O-OFDM system is analyzed in Sec. 4 for a guard band reduction up to 89% and a bit rate increase up to 80%, when compared to 5 Gb/s. Finally, in Sec. 5 conclusions are drawn.

## 2. Digital signal processing for optical OFDM based on FHT

The FHT processing has been proposed for multicarrier modulation (MCM) techniques and specifically for DMT [3, 8], as it requires only real-valued arithmetic and can be implemented using fast algorithms and hardware architectures similarly to the FFT [4, 5, 9–11] with the advantage of supporting the same routine for the modulation and demodulation thanks to the self-inverse property. In fact, the transform kernel of the *N*-dimensional discrete Hartley transform

*F*(

*N*) =

*e*

^{−j2πnk/N}, only for the imaginary unit; the real and imaginary parts of the Fourier transform respectively equal the even and odd parts of the Hartley transform, which is a symmetric and Hermitian real linear operator. Therefore, the FHT can be easily related to the discrete Fourier transform by a simple post-processing conversion and represents an effective tool for its computation with real data. In [11], a low-complexity fast processor based on the FHT has been proposed for implementing the FFT and the inverse FFT (IFFT) modulation in very high-speed digital subscriber line. Thus, a DMT scheme based on the FHT is an attractive alternative to the FFT-based scheme in order to meet the real-time requirements of an actual implementation of optical OFDM transceivers.

An O-OFDM system transmitting real-valued signals can be based either on the FFT or the FHT to achieve the same performance (as it will be further detailed in Sec. 3) [7, 12]. In order to obtain the same spectral efficiency, the FFT processing requires 2D constellations and half symbols redundancy, due to the Hermitian symmetry constraint, while the FHT modulation only needs 1D constellations and all the *N* transform inputs can be filled with independent data (for the transceivers schemes, please refer to Fig. 1 in Sec. 3) [3]. In fact, thanks to its intrinsic symmetry, the FHT is a suitable orthogonal basis for real-valued data transmission. Taken into account this symmetry, bit and power loading can also be implemented, similarly to FFT-based adaptively modulated O-OFDM.

Based on the FHT properties and according to [8], a cyclic extension can be added to the OFDM frame and frequency domain equalization can be performed. Due to the kernel structure of Eq. (1), each data symbol is transmitted over two mirror-symmetric subcarriers; thus, two correction factors are required for equalizing each vector element at the receiver side to retrieve the transmitted data. However, since the FHT is a real transform and the mapped symbols are real-valued, no complex calculations are needed for the equalization processing [8, 13]. In fact, only two real-valued multiplications and one addition per vector element are required to equalize the *N* received data. Furthermore, it is important to note that, thanks to the FHT symmetry property, if half of the vector elements of the training symbols are set to zero, a simplified channel estimation is possible, as only *N* real-valued divisions are performed to estimate all the equalization matrix factors [13]. Therefore, this low complexity FHT equalization processing has the same computational load as the processing based on a real-valued FFT, which requires a half-length (*N*/2) equalizer (see the receiver scheme of Fig. 1). Taking into account the redundancy of the transmitted symbols, due to the Hermitian symmetry constraint, in the FFT scheme the equalization matrix is *N*/2-dimensional, but complex computations (4 real multiplications and 2 additions each tap) are performed to recover the transmitted data and complex division are required to estimate the response of each subchannel.

## 3. Experimental set-up and performance assessment

In order to experimentally assess the performance of an optical OFDM based on the FHT, we have compared it with a DMT system based on the FFT. The experimental set-up is described in Fig. 1. The DSP at the transmitter/receiver is performed off-line using Matlab software. To implement O-OFDM systems transmitting real-valued signals based on FFT and FHT, the stream of data randomly generated is mapped into either 4QAM or BPSK format and modulated by an N-IFFT or an N-FHT with *N* = 64 subcarriers, respectively (see Fig. 1(a) and 1(b)). In fact, as detailed in Sec. 2, to transmit at the same spectral efficiency, FFT-based systems require higher constellation size than FHT-based OFDM, due to the HS constraint. Due to the self-inverse property of real-transforms, the inverse FHT is calculated with the same routine of the FHT (see the transmitter DSP (b) of Fig. 1). The baseband signal is up-converted to an intermediate frequency to create a guard band (*B _{G}*). In fact, to avoid intermodulation products between the signal and the optical carrier, it is set to equal the bandwidth of the OFDM signal (

*B*). The real-valued OFDM digital signal (only in-phase component), with electrical bandwidth

_{S}*B*=

_{T}*B*+

_{G}*B*, is loaded into an arbitrary waveform generator, which generates an analog signal at 24 GS/s. A maximum electrical bandwidth

_{S}*B*= 10 GHz is considered, given the limitation of the AWG filter. Therefore, for

_{T}*B*=

_{S}*B*= 5 GHz a maximum bit rate of 5 Gb/s is transmitted using either 1D modulation (BPSK) with FHT or 2D modulation (4QAM) with FFT. The analog RF signal modulates an external MZM biased at the quadrature point (0.5

_{G}*V*, with

_{π}*V*the switching voltage) and driven by a tunable laser source at 1550.92 nm. The optical fiber link is a SSMF (G.652). At the receiver side, the transmitted signal is detected by a PIN photodiode and amplified by a transimpedance amplifier (TIA). The data is captured by using a real-time oscilloscope at a sampling rate of 50 GS/s and then down-converted, demodulated, equalized and demapped off-line with Matlab. The total number of transmitted and analyzed OFDM frames is 5120. For the sensitivity performance analysis of the B2B O-OFDM systems, the fiber link is replaced by a variable optical attenuator (VOA). Thus, measuring the optical power at the PIN input, sensitivity curves are obtained. According to the theoretical and numerical results [3, 6], the inset of Fig. 1 shows a good agreement between the experimental BER curves representing the B2B performance of the O-OFDM systems based on the BPSK-FHT and the 4QAM-FFT modulation [7].

_{π}## 4. Bit rate variable low complexity O-OFDM system with reduced guard band

As the MZM is biased at the quadrature point, the spectral efficiency of the proposed low complexity system of Fig. 1(b) can be enhanced by reducing the guard band, as demonstrated in [2] for FFT-based O-OFDM. At fixed total bandwidth and modulation format (BPSK), the transmitted bit rate is increased, decreasing the guard band and increasing the bandwidth of the OFDM signal generated with FHT processing. We have first analyzed the sensitivity performance at 10^{−3} BER, considering a fixed bandwidth *B _{T}* = 10 GHz and variable bit rate from 5 Gb/s to 9 Gb/s, reducing

*B*from 5 GHz to 1 GHz. The experimental results are shown in Fig. 2(a). In the B2B system, the sensitivity penalty at 10

_{G}^{−3}BER for transmitting 9 Gb/s and 8 Gb/s, corresponding to 80% and 60% bit rate increase, is 1.2 dB and 1 dB, respectively. We have then evaluated the performance of the system in Fig. 1(b) after 25 km SSMF. Every 512 frames, 2 training symbols are inserted for synchronization and further equalization and no CP has been added. An enhanced forward error correction (FEC) with 7% overhead is assumed for considering a target BER of 10

^{−3}[14]. The total overhead can be calculated according to [15]; for the reader convenience, here we report the formula for computing it in OFDM systems:

*R*and

_{g}*R*are the gross and net data rate, respectively;

_{n}*δ*represents the overhead due to the training symbols,

_{TS}*δ*is due to the cyclic prefix and

_{CP}*δ*to the FEC. Thus, in this case, a minimum overhead of 7.4% has been considered. The sensitivity penalty measured at 10

_{FEC}^{−3}BER, compared to the B2B system, is 1.6 dB at 5 Gb/s without

*B*reduction. The penalty for 6 Gb/s, 7 Gb/s and 8 Gb/s, compared to the corresponding B2B cases, ranges from 2.1 dB to 2.6 dB, while transmission at 9 Gb/s could not be achieved. The sensitivity penalty for varying the bit rate from 5 Gb/s to 8 Gb/s and reducing the required guard band up to 75% (from 8 GHz to 2 GHz) is 2 dB. The insets of Fig. 2(a) show the B2B transmitted spectra after photodetection of the proposed variable bit rate FHT-based O-OFDM at 5 Gb/s (no

_{G}*B*reduction) and 8 Gb/s (75%

_{G}*B*reduction). Thanks to the optimal MZM biasing, low intermodulation products are evidenced.

_{G}In order to enhance the performance of the proposed bit rate variable system, we optimize the transceiver design and increase the total overhead. We adopt the low complexity channel estimation using half-length training symbols, as described in Sec. 2, and include a digital symmetrical clipping at the transmitter for limiting the peak power of the OFDM signal. In fact, the PAPR is one of the major drawbacks of MCM systems and in optical DMT systems, high peak power severely impacts on the transceivers front-end, due to the limited resolution of DAC and ADC and the nonlinearity of drivers and modulators. Amplitude clipping can be considered as a simple PAPR reduction technique that relaxes the constraint on the linear dynamic range of drivers and MZM. Nevertheless, since clipping is a memoryless nonlinearity, it can introduce signal distortion. Therefore, the clipping value has been selected in order to minimize the clipping noise. According to our theoretical and numerical study [12, 16], it has been set to a value slightly greater than twice the signal standard deviation, considered optimal for a BPSK format; moreover, it has been previously tested in the experimental set-up for the B2B case. The overhead due to the training symbols has been increased from 0.4% to 1.6% and a 10% of cyclic extension has been added to cope with inter-channel interference and inter-symbol interference using the DSP described in Sec. 2. According to Eq. (2), the total overhead considered in this case is 19.6% and the corresponding gross data rate is 10.8 Gb/s. The optimized bit rate variable transceiver has been tested in the experimental set-up of Fig. 1(b). The transmission at 9 Gb/s, corresponding to the maximum bandwidth reduction (1 GHz), over 25 km of SSMF has been achieved. In Fig. 2(b), the measured BER curves versus the received power in the B2B case and after 25 km of SSMF are reported. The sensitivity penalty measured at the target BER of 10^{−3} is 1.6 dB.

## 5. Conclusion

We have experimentally demonstrated an O-OFDM system based on FHT processing suitable for cost-sensitive applications, showing that similar performance to an FFT-based system, in terms of receiver sensitivity and spectral efficiency, can be achieved using simple 1D constellations and without the need of implementing the Hermitian symmetry. Furthermore, we have implemented a cost-effective bit rate variable system with low-complexity DSP by varying the guard band, without changing the modulation format. By using an optimized transceiver at the expense of additional overhead, we have demonstrated that up to 80% bit rate increase, corresponding to 89% reduction of the required guard band, can be achieved with a sensitivity penalty of 1.6 dB after 25 km SSMF compared to the B2B transmission.

For optimal spectral resources allocation, the total bandwidth occupancy can be varied, by reducing the guard band to a minimum value, also for lower bit rate transmission, resulting in a bandwidth and bit rate variable system. Moreover, the system spectral efficiency and flexibility can be further enhanced using higher 1D modulation formats and adopting bit loading schemes.

## Acknowledgments

Work supported by MINECO project TEC2009-07995 (DORADO), FPI scholarship grant BES-2010-031072, grant PTQ-11-04805, and by EC FP7 IP project IDEALIST grant 317999.

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