## Abstract

In reflective semiconductor optical amplifier (RSOA)-based wavelength division multiplexed passive optical network (WDM-PON), the bit rate is limited by low modulation bandwidth of RSOAs. To overcome the limitation, we apply QR decomposition in channel equalizer (QR-CE) to achieve successive interference cancellation (SIC) for discrete Fourier transform spreading orthogonal frequency division multiplexing (DFT-S OFDM) signal. Using an RSOA with a 3-dB modulation bandwidth of only ~800 MHz, we experimentally demonstrate a 15.5-Gb/s over 20-km SSMF DFT-S OFDM transmission with QR-CE. The experimental results show that DFTS-OFDM with QR-CE attains much better BER performance than DFTS-OFDM and OFDM with conventional channel equalizers. The impacts of several parameters on QR-CE are investigated. It is found that 2 sub-bands in one OFDM symbol and 1 pilot in each sub-band are sufficient to achieve optimal performance and maintain the high spectral efficiency.

© 2015 Optical Society of America

## 1. Introduction

Reflective semiconductor optical amplifier (RSOA) based wavelength division multiplexed-passive optical network (WDM-PON) has been considered as one of the most promising candidates for next generation optical access networks [1–5]. Being used as an optical transmitter, RSOA has several advantages such as low cost and power dissipation, wide optical spectral width and large-scale monolithic integration capability [1]. Several experiments on RSOA-based WDM-PONs have demonstrated the color-less operation at customer optical network units side, which reduce the operation and maintenance cost [1–5].

However, commercially available RSOAs have a limited electro-optical modulation bandwidth (1~2 GHz), which significantly restricts the bit rate in the system. Several techniques have been proposed to solve the bandwidth limitation problem [4–8]. Among these techniques, baseband OFDM modulation has been widely used in RSOA-based WDM-PONs due to its high spectral efficiency, strong dispersion tolerance and dynamic bandwidth allocation. Variable power loading and bit power loading are commonly used to overcome the bandwidth limitation problem by optimizing the signal-to-noise ratio (SNR) distribution [7, 8] for OFDM subcarriers, where channel frequency response is required before payload signal transmission, which can be used to compensate the amplitude degradation at high frequency. The additional processing at the transmitter not only increases the computational complexity, but also reduces the flexibility of the fiber transmission systems since the frequency responses of different channels are different and may change over the time.

Conventional channel equalizers (CEs) for OFDM signal are based on one-tap channel equalization, where the signals in the subcarriers are recovered independently [7–9]. These CEs cannot work effectively if spectral nulls occur in the channel frequency response. The signals of the specific subcarriers which are located at the spectral nulls are then undermined due to low SNR. Our recent work in [9] has shown that successive interference cancellation (SIC) scheme can be used to combat power fading induced by polarization mode dispersion in direct-detection zero-padding optical OFDM system (ZP-OFDM). This is mainly because the inter-carrier interference (ICI) is introduced by oversampling at ZP-OFDM receiver, where other subcarriers can be used to recover the data in specific subcarriers which are undermined by severe power fading [9, 10]. It is shown in [9] that QR decomposition based channel equalizer (QR-CE) has better SIC performances than other CEs. In this paper, we apply QR-CE in discrete Fourier transform spread OFDM (DFTS-OFDM) to deal with the bandwidth limitation problem in RSOA-based WDM-PON and achieve SIC, where the ICI is introduced by pre-coding the OFDM symbols with DFT matrix. It is noted that the QR decomposition in DFTS-OFDM is achieved on sub-band basis with much smaller size and lower complexity than that in ZP-OFDM. The bit error rate (BER) performances of DFT-S OFDM with QR-CE, DFT-S OFDM and normal OFDM with conventional CE (CCE) in RSOA-based WDM-PONs are investigated and compared by experiment. Our experimental results show that DFT-S OFDM with QR-CE attains a significantly better performance than DFTS-OFDM and OFDM with CCE. Using an RSOA with a 3-dB modulation bandwidth of only ~800 MHz, we experimentally demonstrate that at a 7% forward error correction (FEC) code threshold 3.8 x 10^{-3}, DFTS-OFDM with QR-CE can achieve a net bit rate of ~15.5-Gb/s over 20-km standard single mode fibre (SSMF) transmission, which outperforms DFT-S OFDM and OFDM with CCEs by increasing the bit rate by ~25% and ~40%, respectively.

## 2. QR decomposition based channel equalization for DFTS-OFDM

In an DFT-S OFDM transmitter, the *i-*th signal block, $NV\times 1$ vector ${S}_{NV}(i)$, is partitioned into *V* sub-bands of *N* subcarriers each. Let ${S}_{N}^{V}\left(i\right)$ be the *v*-th signal sub-band, which is an $N\times 1$ vector. The additional spreading of DFT is introduced by pre-coding the $N\times N$ DFT matrix ${F}_{N}$ on each sub-band. Then, another $M\times M$ inverse DFT (IDFT) matrix ${F}_{M}^{H}$ is used to convert the signal from frequency domain to time domain. At the receiver, the DFT matrix ${F}_{M}$ is applied to the received time-domain samples after cyclic prefix (CP) removal. For easy analysis, we only consider the $N$ payload subcarriers in one sub-band in an OFDM symbol and ignore the block index *i*. The received $N\times 1$ signal vector ${X}_{N}^{V}$ in frequency domain in the *v*-th sub-band can then be written as

*v*-th sub-band; ${D}_{N}\left({h}_{N}^{V}\right)$ denotes an $N\times N$ diagonal matrix with ${h}_{N}^{V}$ on its diagonal. We then define matrix ${G}_{N}={D}_{N}\left({h}_{N}^{V}\right){F}_{N}$ and apply QR decomposition based on the modified Gram-Schmidt algorithm [11] to ${G}_{N}$. Thus Eq. (1) can be re-written as

*k*-th element in ${\tilde{X}}_{N}^{V}$ is given by

*k, i*)-th element in matrix ${R}_{N}^{}$ and ${\text{S}}_{N}^{V}\left(i\right)$ is the

*i*-th element in vector ${S}_{N}^{V}$. From Eq. (4), we can see that ${\tilde{X}}_{N}^{V}\text{(}k\text{)}$ is free of interference from data in subcarriers $1,\cdots k-1$. Therefore, the data in the

*k*-th subcarrier of

*v*-th sub-band ${\text{S}}_{N}^{V}\left(k\right)$ can be recovered via the corresponding data in subcarriers $k+1,\cdots ,N$ successively, which is given by

*k*-th subcarrier of

*v*-th sub-band ${\text{S}}_{N}^{V}\left(k\right)$. From Eq. (5), we can see the accuracy of $\u3008{\text{S}}_{N}^{V}\left(k\right)\u3009$ is actually dependent on the accuracy of $\u3008{\text{S}}_{N}^{V}\left(k+1\right)\u3009,\text{}\u3008{\text{S}}_{N}^{V}\left(k+2\right)\u3009,\cdots ,\text{}\u3008{\text{S}}_{N}^{V}\left(N\right)\u3009$ . Therefore, making use of successive signal recovery property of the QR-CE, we can choose several pilot subcarriers in the initial iterations, e.g. ${\text{S}}_{N}^{V}(N)$, ${\text{S}}_{N}^{V}(N-1)$, to prevent the error propagation and increase the accuracy in the decision stage, as shown by experimental results. It is noted that due to the DFT spreading at the transmitter side, the SNR of signal in each subcarrier is similar after transmission. Therefore, the order of signal detection has no or little effect on the performance, which is different from the case of ZP-OFDM [9]. In this paper, the conventional channel equalizer (CCE) reported in [12] for OFDM and DFTS-OFDM is chosen for performance comparison with QR-CE. The digital signal processing (DSP) of the DFT-S OFDM with QR-CE at the receiver is shown in Fig. 1. From Fig. 1, we can see that the steps including re-sampling, time synchronization, CP removal, FFT demodulation and training symbols-based channel estimation are the same for all the three cases. For OFDM signal with CCE, the channel compensation can be applied directly after channel estimation, as shown in branch (I). For DFT-S OFDM signal with CCE, however, due to the DFT pre-coding for each sub-band at the transmitter side, IFFT is required at the receive side to de-modulate the signal for each sub-band before channel compensation, as shown in branch (II). For DFT-S OFDM signal with QR-CE in branch (III), once the values of ${X}_{N}^{V}$, ${D}_{N}\left({h}_{N}^{V}\right)$ and ${F}_{N}^{}$ for each sub-band in Eq. (1) are obtained, then following the derivations of Eqs. (1)-(5), the original signal ${X}_{N}^{V}$ can be recovered sequentially.

## 3. Experimental system setup

Figure 2 shows the experimental setup for the RSOA-based fiber transmission system. The RSOA used in the experiment has a polarization-dependent gain smaller than 3dB, 7-pin butterfly/SMA package with a thermistor, thermo-electric cooler and single mode fiber pigtails, and a small signal gain of 20dB when bias current is 80mA. An arbitrary waveform generator (AWG, Tektronix) is used to produce OFDM signal at 10-GSa/s with 8-bit resolution. The OFDM signal consists of 128 subcarriers of which 48 subcarriers carry data with Hermitian symmetry and 16-QAM format. A cyclic prefix length of 4 is used to avoid inter-symbol interference. 10 training symbols are used for channel estimation followed by 200 OFDM payload symbols. For the training symbols, only the odd subcarriers are mapped with data to avoid the subcarrier-to-subcarrier beating noise. Therefore, the raw bit rate is 10-GSa/s × 48/128 × 4-b/Sa = 15-Gb/s. Counting the overhead, the bit rate is decreased to 13.8-Gb/s before 7% FEC and 12.9-Gb/s after FEC. For DFTS-OFDM, the number of sub-band is 2 and 1 pilot subcarrier is used in each sub-band for initialization in QR-CE.

As shown in Fig. 2, at the transmitter, a continuous-wave (CW) optical signal is generated by a distributed feedback (DFB) laser at 1550 nm. After passing through an optical circulator with 1.0-dB insertion loss, the CW optical power injected into RSOA is fixed at −8-dBm. The generated analog OFDM signal and a 75-mA DC bias current are combined via a bias tee and then the combined signal is used to modulate an RSOA with a modulation bandwidth of ~800 MHz. The modulated optical OFDM signal is transmitted through a 20-km SSMF, followed by a 0.8-nm optical filter to emulate the de-multiplexer in WDM-PONs and filter out the unwanted optical noise. At the receiver, a variable optical attenuator and a 3-dB coupler are used to adjust and monitor the optical power. The optical signal is collected by a standard 40-GHz PIN photo-detector. After optical-to-electrical conversion, the electrical signals are sampled by a Tectronic oscillator scope operating at 50-GS/s, and processed off-line. One million bits are collected for BER calculation.

Figs. 3(a) and 3(b) show the BER performance versus received optical power for the three schemes of OFDM with CCE, DFTS-OFDM with CCE, and DFTS-OFDM with QR-CE under optical back-to-back and 20-km fiber transmission conditions, respectively. The insets show the measured normalized frequency responses for the two cases, where the 3-dB bandwidth of the transmission system is ~800-MHz with the spectral null of more than 26 dB lower at high frequency, which is mainly due to the RSOA used. From Fig. 3, we can see that DFTS-OFDM with QR-CE can always achieve the 7% FEC threshold and attains much better BER performance than both DFTS-OFDM with CCE and OFDM with CCE which cannot achieve error free transmission in the 20-km fiber transmission system.

In Figs. 4(a) and 4(b), we study the effects of number of sub-bands in one OFDM symbol and number of pilots in each sub-band on the BER performance of the QR-CE in DFTS-OFDM after 20-km fiber transmission. It is shown that the BER performance can be improved by increasing the number of sub-bands in one OFDM symbol and the number of pilots in each sub-band. However, the improvement is negligible when the number of sub-bands in one OFDM symbol is more than 2 and the number of pilots in each sub-band is more than 1. It is noted that further increase in the number of pilots in each sub-band and the number of sub-bands will reduce the spectral efficiency and the overall capacity significantly. Therefore, 2 sub-bands with 1 pilot in each sub-band are sufficient to achieve the optimal performance.

Figure 5 shows the BER versus the achieved bit rate excluding OFDM overhead and 7% FEC after 20-km fiber transmission at the received power of −6 dBm. The bit rate is adjusted by changing the number of payload subcarriers in one OFDM symbol. As shown in Fig. 5, DFTS-OFDM with QR-CE can achieve the bit rate ~15.5-Gb/s, which is ~25% and ~40% improvement, compared with DFTS-OFDM with CCE and OFDM with CCE.

The performance improvement of QR-CE mainly comes from the ICI introduced in DFT-S OFDM symbol, which can be used to recover the signal in specific subcarrier that is severely undermined due to channel spectral nulls. Using QR-CE, the signal is recovered in each subcarrier one by one, the accuracy of the current recovered subcarrier signal is dependent on the accuracy of the previously recovered subcarrier signal. Unlike the CCE for DFT-S OFDM and OFDM, where the signal in each subcarrier is recovered independently, the QR-CE can recover the signal in each subcarrier sequentially. The additional computational effort of QR-CE in DFT-S OFDM mainly comes from the QR decomposition. However, in our QR decomposition, the decomposed matrix is a square matrix which can be efficiently decomposed by the modified Gram-Schmidt algorithm. It is noted that the QR decomposition is only performed once in one OFDM block (200 OFDM symbols in our case) after channel estimation. Therefore, QR-CE is a practical and promising solution to combat the limited bandwidth of RSOAs in WDM-PONs.

## 4. Conclusion

We applied a QR-CE in DFTS-OFDM to overcome the bandwidth limitation in RSOA-based WDM-PONs. Using an RSOA with a 3-dB modulation bandwidth of only ~800 MHz, we experimentally demonstrated a 15.5-Gb/s (net data rate) over 20-km SSMF DFT-S OFDM transmission with QR-CE. For a given limited RSOA bandwidth, the experimental results showed that DFTS-OFDM with QR-CE can achieve much better BER performance and higher data rate than DFTS-OFDM and OFDM with CCEs. The performance improvement mainly comes from the ICI introduced by DFT spreading followed by SIC in QR-CE. For DFTS-OFDM with QR-CE, 2 sub-bands with 1 pilot in each sub-band are sufficient to achieve the optimal performance and maintain the spectral efficiency. Considering the simple scheme of QR-CE and significant performance improvement, QR-CE offers a cost effective solution to overcome the limited bandwidth problem in RSOA-based WDM-PONs.

## Acknowledgments

This work was supported in part by MOE AcRF Tier 1 grants RG85/13 and RG2/12.

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