## Abstract

We theoretically and experimentally evaluate a beat interference cancellation receiver (BICR) for direct detection optical orthogonal frequency-division multiplexing (DD-OFDM) systems that improves the spectral efficiency (SE) by reducing the guard band between the optical carrier and the optical OFDM signal while mitigating the impact of signal-signal mixing interference (SSMI). Experimental results show that the bit-error-rate (BER) is improved by about three orders of magnitude compared to the conventional receiver after 320 km single-mode fiber (SMF) transmission for 10 Gb/s data with a 4-QAM modulation using reduced guard band single-sideband OFDM (RSSB-OFDM) signal with 1.67 bits/s/Hz SE.

© 2013 optical society of america

## 1. Introduction

The fast growth of Internet applications such as voice, video, and gaming has lead to a huge demand on the bandwidth of optical networks. To satisfy this increasing demand, extensive research has been conducted to increase the spectral efficiency (SE) both in access [1] and core fiber optic networks [2]. Optical orthogonal frequency division multiplexing (OOFDM) has gained much attention as one of the attractive candidates for future optical communication systems [3]. Moreover, it has been shown that chromatic dispersion (CD) and polarization mode dispersion (PMD) in single-mode fiber (SMF) systems could be compensated electrically using digital signal processor (DSP) at the receiver [4,5]. OOFDM systems can be classified into two categories according to their underlying techniques and applications: Coherent OFDM (CO-OFDM) [6], and Direct Detection OFDM (DD-OFDM) [4].

CO-OFDM represents the ultimate performance in receiver sensitivity, SE, and robustness against PMD [5], [7], [8] compared to DD-OFDM. Therefore, CO-OFDM has been seen as a potential candidate for future long-haul optical transmission systems. However, CO-OFDM requires high complexity in the transceiver design and because of the sensitivity of OFDM to frequency offset and phase noise [9], lasers with very narrow linewidth are required at the transmitter and receiver sides [10]. To solve these complexities, DD-OFDM systems have been proposed for low cost systems. The DD-OFDM receiver structure is simple and generally requires only a photodetector (PD) for detection [3]. There is no need to estimate the frequency and phase offset due to the elimination of the local oscillators and optical hybrids. Moreover, the channel estimation and CD compensation can be done at the receiver side without any link information.

In DD-OFDM, the optical single-sideband OFDM (SSB-OFDM) has been proposed since it can overcome the inherent CD-induced fading problem associated with double-sideband (DSB) transmission [4]. Generally, the transmitted OFDM signal is recovered by detecting the carrier and signal mixing products [12] in a square-law PD. However, this desired mixing product is affected by the signal-signal mixing interference (SSMI). Several methods have been proposed to minimize the penalty due to SSMI. In offset SSB-OFDM (OSSB-OFDM) [12], a sufficient guard band (GB) is allocated between the optical carrier and the OOFDM signal such that the SSMI and desired RF spectra are nonoverlapping. The minimum GB should be equal to the bandwidth of OOFDM signal; therefore, the SE is half of that in the CO-OFDM system. In order to increase the SE, the GB should be reduced or even eliminated. However, in this case the system performance is degraded due to SSMI. Several methods have been proposed to address this issue [13–15]. It is worth mentioning that improving the SE in DD-OFDM systems results in the electronic components’ bandwidth requirements relaxation at both the transmitter and receiver. This leads to reduce required PD bandwidth, ADC and DAC sampling rates. In addition, for wavelength-division multiplexing SSB-OFDM (WDM-SSB-OFDM) systems [16] where several SSB-OFDM signals are transmitted over different wavelengths, the aggregate per-fiber capacity can be increased.

In [17], a beat interference cancellation receiver (BICR) that mitigates SSMI in Reduced GB SSB-OFDM (RSSB-OFDM) systems where the GB is less than the bandwidth of the OOFDM signal was proposed. This BICR is relatively simple since it requires only one optical filter and one balanced receiver in the front end without the need for careful polarization management. The impact of filter parameters (e.g., order, bandwidth) on the system performance was assessed using numerical simulations. Furthermore, system tolerance to both phase noise and PMD can be improved using the BICR. In this paper, the working principle of the BICR is analyzed in detail taking into account all the linear impairments from the transmitter to the receiver. Moreover, the BICR is experimentally verified by transmitting 10 Gb/s data with 4-quadrature amplitude modulation (4-QAM) using RSSB-OFDM signals over 320 km SMF. The experimental results reveal that the bit-error-rate (BER) is improved by three orders of magnitude compared to the conventional receiver when a fourth-order super-Gaussian filter is used.

## 2. System model

Figure 1 shows a schematic and principle of conventional DD-OFDM. The real and imaginary parts of the complex baseband electrical OFDM signal are fed into an optical I/Q modulator. Assume that the total OFDM bandwidth is *B* and the number of data subcarriers is *N*. As depicted in Fig. 1(a), the optical spectrum of the optical signal at the transmitter side is a linear version of the electrical OFDM spectrum plus an optical carrier. Therefore, the transmitted optical OFDM signal can be represented as

*s*(

*t*) is the optical OFDM signal,

*f*

_{0}is the main optical carrier frequency, Δ

*f*is the GB between the main optical carrier and the OFDM signal,

*β*is the scaling coefficient that describes the OFDM signal strength related to the main carrier,

*H*(

_{T}*f*) is the frequency response of the transmitter,

*ϕ*(

*t*) is the phase noise,

*a*is the OFDM information symbol for the

_{k}*k*th subcarrier, and ${f}_{k}=k\frac{B}{N}$ is the frequency for the

*k*th subcarrier. It is worth mentioning that the GB (Δ

*f*) is an integer multiple of $\frac{B}{N}$ since the RF tone-assisted OFDM method [18] is used to generate the optical carrier. Therefore, the GB can be shown as $\mathrm{\Delta}f=m\frac{B}{N}$ where

*m*is an integer number. In Eq. (1), for the sake of mathematical simplicity, only one OFDM symbol is assumed.

If the fiber nonlinearity remains sufficiently low, the optical fiber can be modeled as a linear system (*H _{CD}*(

*f*)). Hence, the signal, and the added amplified spontaneous emission (ASE) noise by erbium-doped-fiber-amplifiers (EDFAs) can be assumed independent. Therefore, the received signal at the PD can be represented as [11]

*H*(

_{TF}*f*) =

*H*(

_{O}*f*)

*H*(

_{T}*f*)

*H*(

_{CD}*f*) denotes the overall transfer function from the transmitter to the receiver, and

*n*(

_{ASE}*t*) represents the ASE noise as complex circular AWGN. We denote the frequency responses of the optical fiber, and optical filters as

*H*(

_{CD}*f*), and

*H*(

_{O}*f*), respectively. At the receiver, the PD is modeled as an ideal square-law device [20] with quantum efficiency equal to one. Therefore, the resultant photocurrent after the PD can be expressed as follows

*Re*{x} denotes the real value of

*x*. In the rest of the paper, for simplicity,

*Ĥ*(

_{x}*n*,

*m*) is defined as ${H}_{x}\left({f}_{0}+n\frac{B}{N}\right){H}_{x}^{*}\left({f}_{0}+m\frac{B}{N}\right)$. The first term of Eq. (3) is a dc component, the second term shows the fundamental term consisting of linear OFDM subcarriers that are to be retrieved, and the third term is the SSMI which degrades the desired OFDM signal.

*n*(

_{SABN}*t*),

*n*(

_{AABN}*t*), and

*n*(

_{CABN}*t*) are the signal-ASE beat noise (SABN), the ASE-ASE beat noise (AABN), and the carrier-ASE beat noise (CABN), respectively. The power spectral density (PSD) of these noises has been studied in [19]. From Eq. (3), we can see that the SSMI is distributed from $-\frac{N-1}{N}B$ to $\frac{N-1}{N}B$ in the frequency domain. The non-negative frequency components of the SSMI are shown in Fig. 1(c). The SSMI at the

*n*th subcarrier (0 ≤

*n*) can be expressed as follows

*N*− 1)th subcarrier. Moreover, the desired term at the

*n*th subcarrier (0 ≤

*n*) can be shown as

From Eq. (5) it is obvious that the desired signal is located from
$m\frac{B}{N}$ to
$m\frac{B}{N}+\frac{N-1}{N}B$ in the frequency domain as shown in Fig. 1(b). Considering Eqs. (4) and (5) reveals that the SSMI (*I _{n}*) will fully overlap with the desired signal (

*D*) when the GB (

_{n}*m*) is zero. There are several approaches to address this issue. In the baseband optical SSB-OFDM (BSSB-OFDM) method [13], the authors proposed to decrease

*β*as much as possible such that the distortion caused by SSMI is reduced to an acceptable level. Additionally, Cao

*et al.*[15] proposed the use of subcarrier modulation and turbo coding to compensate SSMI. Moreover in [14], the authors proposed an iterative detection method to reduce SSMI. On the other hand in OSSB-OFDM [4], sufficient GB is allocated such that the desired term and SSMI are nonoverlapping in the frequency domain. From Eqs. (4) and (5), we can see that the by choosing

*m*greater than

*N*,

*B*≤ Δ

*f*, the desired signal is nonoverlapping with SSMI. There are advantages and disadvantages to all these approaches. For instance, OSSB-OFDM has better sensitivity compared to the BSSB-OFDM but with the half of SE. The turbo coding and iterative approaches have good SE, but with a burden of computational complexity.

## 3. Theoretical model of BICR

In order to improve the SE in OSSB-OFDM, the GB should be reduced. However, SSMI would interfere with the OFDM subcarriers which degrades the system performance. To mitigate the SSMI when the GB is smaller than *B*, the BICR was proposed in [17] which is depicted in Fig. 2. In this receiver, an optical coupler splits the received optical signal into two parallel branches. The optical signal in the upper branch is sent to the PD directly. But, the optical signal in the lower branch passes through an optical filter to remove the optical carrier. Consequently, in the upper branch, the optical carrier and OOFDM signal are present, while in the lower branch only the OOFDM signal exists, i.e., the output of the PD in the upper branch consists of the dc, desired, and SSMI terms while the output of the PD in the lower branch consists of only the SSMI term. Thus, by simply subtracting the output of the upper branch from that of the lower branch, the SSMI term will be removed. The optical signal prior to a PD in the upper branch (*r _{U}*) and the photocurrent in the upper branch (

*q*) are given by Eqs. (2) and (3), respectively. The optical signal prior to a PD in the lower branch (

_{U}*r*) can be written as

_{L}*H*(

_{OF}*f*) represents the transfer function of the optical filter in the lower branch. Therefore, the photocurrent in the lower (

*q*) branch can be noted as follows

_{L}*q*(

_{U}*t*) from

*q*(

_{L}*t*), we have

*n*th subcarrier (0 ≤

*n*) can be expressed as

*n*th subcarrier (0 ≤

*n*) can be shown as

*H*(

_{OF}*f*), is

*Ĥ*(

_{OF}*n*, 0) as shown in (12). Second, the band-edge OOFDM subcarriers are attenuated by the non-ideal optical filter. As such, the SSBI term in the upper and lower branches would not be identical; hence the SSBI cannot be removed completely. It is worth noting that the mitigation of SSMI relies heavily on the common mode rejection ratio of a balanced PD. Moreover, in practical systems, the insertion loss and delay caused by the optical filter in the lower branch should be compensated before the photocurrent from the upper and lower branches are subtracted. In general, two approaches can be applied to address these issues: (1) using a balanced PD and then these impairments are compensated in the optical domain; and (2) using two PDs instead of a balanced PD, where these impairments are compensated in the digital domain. With the former approach it is not easy to estimate and compensate the impairments whereas the latter approach is more practical and adaptive. However, two analog-to-digital converters are needed in the second approach while only one analog-to-digital converter is required in the first approach. We have chosen the second approach for the experiment because it is more practical.

## 4. Results and discussion

#### 4.1. Simulation results

We investigate the system performance of the BICR numerically using OptiSystem 10.0 and MATLAB. In the simulations, the system parameters used are the same as those for the experimental setup described in Section 4.2. The data rate is 10 Gb/s and we use 4-QAM to map bit stream data onto the OFDM subcarriers. The FFT size, and the cyclic prefix length are 512, and 32, respectively. The OOFDM bandwidth is 5 GHz and the GB is varied from 4.5GHz to 0.5GHz in 0.5GHz decrements. The transmission link consists of four 80km spans of SMF-28e+ fiber. The fiber loss, dispersion, and the nonlinearity coefficient are 0.18 dB/km, 17 ps/(nm.km), and 1.2*W*^{−1}*km*^{−1}, respectively. The noise figure of the EDFAs used to compensate the loss of each span is 6 dB. The optical filter is modeled with a super-Gaussian response,
${H}_{OF}\left(f\right)=\mathit{exp}\left(-\mathit{ln}\sqrt{2}{\left(\frac{f-{f}_{c}}{B/2}\right)}^{2M}\right)$, where *f _{c}*,

*B*, and

*M*are the center frequency, 3dB bandwidth, and filter order, respectively. In the simulations, the center frequency and 3dB bandwidth are fixed at ${f}_{c}=m\frac{B}{N}+\frac{B}{2}$ and 6GHz, respectively, to focus on the filter order.

In Fig. 3, we compare the *Q*-factor for both the BICR with different optical filter orders *M* and the conventional receiver by varying the GB. As depicted in the figure, as GB decreases, the number of OFDM subcarriers that suffer from SSMI increases and therefore the *Q*-factor gets worse. It can be seen that the BICR outperforms the conventional receiver in terms of *Q*-factor. This is because most SSMI is eliminated using the BICR and a better signal quality is achieved. Moreover, the *Q*-factor improves by increasing the optical filter order at a fixed GB (i.e., the optical filter becomes more ideal thereby reducing the impairments associated with a non-ideal filter response). Additionally, for the fixed system performance, a higher-order optical filter is required to remove the optical carrier without affecting the OOFDM signal as the GB decreases. In other words, to further improve the SE for a given *Q*-factor, a higher-order optical filter should be used. For instance, at a *Q*-factor of 16 dB, the GB can be reduced to 3.7, 3, 2.3, 1.8, and 1.3 GHz using optical filters with orders of 2, 4, 6, 8, and 10, respectively.

Figure 4 illustrates the *Q*-factor as a function of launch power with different optical filter orders and for GBs of 2 GHz and 3 GHz. As depicted in these figures, at a fixed optical filter order, the *Q*-factor is maximized at the same optical launch power for the two different GBs. Also, at lower input powers, the *Q*-factor is limited by ASE noise while for high launch powers, the *Q*-factor is limited by fiber nonlinearity. Furthermore, the optimum *Q*-factor increases by increasing either the optical filter order or the GB.

#### 4.2. Experimental setup

Figure 5 depicts the experimental setup for RF tone-assisted OFDM transmission system with the BICR. In this experiment, the original binary pseudo-random bit sequence (PRBS) data is first divided and mapped onto 97 frequency subcarriers with 4-QAM modulation format and then transferred to the time-domain by an IFFT of size 512 while zeros occupy the remainder of subcarriers. A cyclic prefix of 32 samples is used, resulting in 19.42 ns OFDM symbol duration. We use 27 training symbols preceding the 227 OFDM symbols for frame synchronization and channel estimation. The OFDM signal is generated offline using MATLAB. Then the inphase (I) and quadrature (Q) components of the OFDM signal are loaded separately on two field-programmable gate arrays (FPGAs) to generate the electrical I and Q signals via two digital-to-analogue convertors (DACs) operating at 28 GSamples/s. Therefore, the data rate of each subcarrier is 51.47 MSymbol/s and the total data rate is 10 Gb/s. The analogue electrical I and Q signals are then fed into an IQ Mach-Zehnder Modulator (IQ-MZM) to generate the OOFDM signal. The carrier to signal power ratio is 0 dB. The optical source for the IQ-MZM is a commercial external cavity laser (ECL) with a linewidth of 100kHz. The modulated optical signal is transmitted through the four 80 km spans of Corning SMF-28e+ fiber. After each span, the signal is amplified by an in-line EDFA with a noise figure of approximately 6 dB to compensate fiber losses. Two optical filters with bandwidths of 0.4nm and 0.8nm are placed before and after the preamplifier, respectively, to remove the out-of-band ASE noise. The received signal is fed into the BICR where the signal is divided into two branches by a 50/50 coupler. The signal in the upper branch is sent to a PD directly, while in the lower branch the signal passes through an optical filter prior to photodetection. We consider two different optical filter orders. First, we use an optical filter (Finisar Waveshaper 1000S) with a second-order Gaussian response. We then cascade a second filter (Yenista WSM-160), also with a second-order Gaussian response, to obtain a fourth-order Gaussian filter response. The center frequency and 3dB bandwidth should be carefully tuned to optimize system performance. Moreover, a optical filter with tunable center frequency is required to compensate for wavelength drift of the carrier. The converted photocurrents at each branch are electrically sampled and then recorded at 80 GSamples/s using an Agilent X96204Q real-time oscilloscope (RTO). The related signal processing is performed offline in MATLAB. The insertion loss and delay caused by the optical filter(s) in the lower branch are calculated and compensated in the digital domain. Then the digital signals from upper and lower branches are subtracted. This is followed by other signal processing functions such as synchronization, CP removal, FFT, and decision. The channel estimation is implemented by comparing the received OFDM symbols with the known transmitted OFDM symbols to find a series of channel responses. The final channel estimation is then obtained by averaging over the responses to reduce the noise effect. The one tap zero forcing channel equalization is used to compensate the channel.

The BER performance is depicted in Fig. 6 versus the GB for both simulation and experiment. The curves in the figure correspond to different receiver structures: conventional receiver, and the BICR using second- and fourth-order optical filters. The dashed and solid lines correspond to the simulation and experimental results, respectively. Due to the limitation on the number of transmitted bits, a BER below 10^{−5} cannot be measured. As depicted in this figure, the experimental results are in good agreement with the numerical simulations. Moreover, since the SSMI is reduced using the BICR, the BICR outperforms the conventional receiver. The results show that using the second-order optical filter, the measured BER improvement varies from one to two orders of magnitude depending on the GB compared to the conventional receiver. An even greater improvement in BER can be obtained using a higher-order optical filter: the fourth-order optical filter improves the BER by about three orders of magnitude compared to the conventional receiver. In other words, for a given BER, a better SE can be achieved using a higher-order optical filter.

## 5. Conclusion

In this paper, we evaluated the BICR which improves the SE in DD-OFDM systems. The increased SE results in relaxing electronic components’ bandwidth requirements in DD-OFDM systems. Additionally, the system capacity in WDM-SSB-OFDM systems can be increased. Moreover, the computational complexity is the same as that of the conventional receiver. We studied theoretically in detail how this receiver can mitigate SSMI in RSSB-OFDM systems and recover the transmitted data. Furthermore, we investigated the system performance both with simulation and experiment. To address some practical issues, in the experimental setup, we used two PDs followed by two analog-to-digital convertors instead of a balanced PD followed by one analog-to-digital convertor. The experimental results show that the receiver is efficient to improve the SE of DD-OFDM systems. For a 10Gb/s data with a 4-QAM modulation, using RSSB-OFDM signal with 1.67 bits/s/Hz SE, the BER is improved approximately by one and a half orders of magnitude compared to the conventional receiver when a second-order optical filter is used at the receiver; also with a fourth-order optical filter, the BER performance improves by three orders of magnitude. The center frequency and 3dB bandwidth should be carefully tuned to optimize system performance. Therefore, a sharp optical filter with tunable center frequency is required to compensate for wavelength drift of the carrier.

## Acknowledgments

This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) Canada via the CREATE program on Next-Generation Optical Networks, as well as the Ministry of higher education and the Iran Telecom Research Center (ITRC).

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