OFDM subcarrier monitoring using high resolution optical spectrum analysis

Abstract In this paper, we demonstrate in-band OSNR monitoring of individual subcarriers in optical OFDM using a high-resolution optical spectrum analyzer. The relationships between OSNR, electrical SNR and BER at the receiver are experimentally analyzed and compared to theoretical results. A linear dependency in dB is found between electrical SNR and subcarrier OSNR for total OSNR values below 26 dB. Above this limit, the correlation degree decreases due to the electrical SNR degradation at the edge subcarriers. The BER analysis per subcarrier also shows a clear correlation with the proposed in-band optical measurements.


Introduction
Optical performance monitoring of signal quality is one of the key enablers of intelligent optical networks [1]. Precisely, transmission impairments monitoring is needed at the nodes of the network, where add/drop, routing and grooming functionalities are performed. Reconfigurable optical add-drop multiplexers 5 and optical cross-connects are usually configured and managed by a control plane, which requires also in-band knowledge of the transmission impairments (e.g. noise, cross-talks, filtering effects, non-linearities, attenuation, dispersion, and component faults). The monitoring information is used by the control layer for configuring and optimizing optical paths, determining the causes of potential problems, setting up signal degradation alarms, preventing failures, and activating the corresponding resiliency mechanisms [2]. For example, the monitoring information can be disseminated by the control layer in order to compute spatial and spectral routes by means of impairment aware algorithms [3]. Then, a suitable network resources allocation and management can be performed. The 15 optical signal to noise ratio (OSNR) is the most common parameter used to measure the degradation of signal the quality, because it is transparent to bit rate and modulation format, and can be easily related to the bit error ratio (BER), which is the main performance indicator [1].
The advent of new and advanced optical modulation formats is attractive for 20 improving the transmission performance; even they pose new challenges and/or opportunities from the optical performance monitoring point of view. Precisely, optical orthogonal frequency division multiplexing (O-OFDM) has gained attention in optical communications as it represents a promising candidate for high data rate optical systems and enables software-defined optical transmission [4]. 25 In fact, this modulation format is able to provide high spectral efficiency, robustness to chromatic dispersion and scalability to higher bit rates. Furthermore, this multicarrier-modulation is suitable for future elastic and adaptive optical networks [4,5]. In these networks, the bandwidth and bit rate of the OFDMbased transponders can be configured by the control layer, varying the electronic 30 digital signal processing (DSP) of the transponder and, thus, properly selecting the number of subcarriers and the modulation format.
Additionally to the robustness against transmission impairments, O-OFDM can provide electronic dispersion compensation. The overhead of information (e.g. pilot tones, training symbols, cyclic prefix), which must be allocated for 35 correctly recovering the signal, allows monitoring system parameters for channel estimation and performance optimization [4,6]. However, this self-performance monitoring technique is performed in the electrical domain, requiring an optical receiver front-end. For an appropriate network management, a more simple and non-intrusive signal quality monitoring per subcarrier would be desirable The remainder of the paper is organized as follows. Section 2 deals with 60 the method for estimating the OSNR per subcarrier (SC-OSNR). Afterwards, in section 3, an experimental setup is detailed. Next, section 4 reports and discusses the results of the experiments. Finally, the main conclusions are drawn in section 5.

OSNR Estimation Method
Alternatively, when the fast Hartley transform (FHT) is used for OFDM modulation, the spectral symmetry is obtained with no additional process-85 ing [10]. In the following lines, we will go through some concepts of the FHT, in order to detail how digital data are finally mapped onto the electrical and optical spectra following the transmission scheme depicted in Figure 2. At the transmitter DSP, input data are first parallelized and mapped onto a real constellation (e.g. binary phase shift keying -BPSK). Next, the training symbols 90 (TS) are added and the transform is performed. It is worth noting that the FHT is a real transform with kernel [10] cos ( 2πkn being N the total number of subcarriers, n the number of sample, and k = 1, 2, 3, · · · , N the subcarrier number. An interesting property of the Hartley transform is that it is self-inverse [10] and, thus, the same implementation can 95 be used at the transmitter and receiver signal processing. After performing the transform, a cyclic prefix (CP) is added. Next, the resulting signal is serialized and upconverted to an intermediate frequency f c .
So, the upconverted OFDM signal after the digital to analog converter (DAC) can be described as where V DAC corresponds to the voltage swing present at the output of the DAC and s(t) is the OFDM signal itself with X k indicating the data symbol carried by the k-th subcarrier, and T k (t) being t = nT and f k the k-th subcarrier frequency where T is the symbol period.
So, the optical field at the output of the Mach-Zehnder modulator can be expressed as where P s is the optical power at the output of the modulator, V b is the bias voltage, V π is the switching voltage of the modulator, and f o is the optical 110 carrier frequency.
In case the bias point of the Mach-Zehnder modulator is set to and assuming low voltage swing of m(t), a pure intensity modulation is achieved and |E s (t)| 2 can be approximated as Figure 1(c) shows the double sideband optical spectrum after optical modulation. As expected, the electrical spectrum is symmetrically repeated at both sides of the optical frequency f o .
At the receiver, a standard photodiode with responsivity R is used, giving as output current being n(t) a noise process, mainly contributed by optical noise.

120
After photodetection, the signal I(t) is converted into the digital domain by an analog to digital converter (ADC). The resulting digital signal is processed in the DSP following the equivalent steps made in transmission, but in reverse order.
As expected, the digital OFDM signal is linearly mapped into the optical 125 power, and can be recovered after photodetection with no distortion. Thus, if a direct spectrum analysis is made in the optical domain (prior to detection), the status of the OFDM signal carriers can be conveniently monitored.
The digitization, downconversion and FHT processing can be considered as a correlator bank plus sampling. Thus, after some algebra, the demodulated 130 signal can be written as S k is the undistorted signal and N k is the noise term. Similarly to [11], S k can be found as and its power can be written as Now, some assumptions on the noise should be considered. When the signal a certain SNR degradation is obtained after photodetection. According to the noise beating theory [12], the beating between signal and noise can be considered dominant for high OSNR, and it can be approximated as Gaussian noise. Thus, the power spectrum of n(t) is approximately flat and with density where B o is the optical reference bandwidth for measuring the OSNR, and According to (4) and (9), N k can be expressed as two Fourier coefficients of [11]. After making the necessary calculations, the variance of N k can be expressed as The output of the k-th correlator is thus comprised of a signal component S k and an additive Gaussian noise component N k , leaving an SNR of being B e = 1/T the equivalent bandwidth occupied by each OFDM subcarrier.

150
So the probability of error can be found as that of BPSK modulated data with additive Gaussian noise [13] P e = 1 2 erfc Since a high resolution optical spectrum analysis is to be performed, an OSNR figure per subcarrier is defined. For convenience, this subcarrier OSNR (SC-OSNR) is defined as the quotient between the optical power measured per 155 subcarrier P sc , and the power of the optical noise P no . Using (2), (3), and (7), P sc can be written as consequently, the OSNR per subcarrier is Thus, a linear relationship between SNR osc and SNR e can be found as In other words, as SNR e is proportional to the SNR osc , one can estimate the 160 performance of the OFDM modulation by a simple inspection of SNR osc , and even extrapolate a limit for the symbol error probability.
Up to this point we have seen the relationship of the OFDM signal before and after optical modulation, and how the OSNR is related to the electrical SNR at the receiver side. However, an additional consideration should be made, when 165 monitoring the proposed transmission system. According to Equation (3), the

Fourier transform of s(t)
is where * is the convolution operator and F {·} is the Fourier transform. The spectral behavior of the Hartley transform is related only to the term associated to the kernel Taken into account the Fourier transform of the kernel, each data symbol X k is mapped onto two mirror symmetric subcarriers (f k and −f k ). For example, X 1 contributes to subcarriers 1 and N of Figure 1 by Figure 1(b), the symmetry is with respect to f c . Therefore, the FHT is an Hermitian linear operator, similarly to the real-valued FFT.
In order to assess the impact of the optical signal degradation at a subcarrier level, the optical spectrum of Figure 1(c) has to be mapped with the corresponding digital subcarriers, which are related to the electrical spectrum of Figure 1(a) and Figure 1(b). The procedure to employ is the following 1. A SC-OSNR is measured in the spectral interval occupied by each subcarrier. In contrast with the total OSNR defined for 0.1 nm and accounting for an average performance of the whole system, this value allows specific characterization and performance degradation monitoring for each

Experimental Setup
In order to perform a first test of the OSNR monitoring at subcarrier level, the experimental set-up described in Figure 3 is used for a back-to-back con-  Figure 2. At the transmitter, data are pseudo-randomly generated using the Mersenne-Twister generator [14]. Next, these data are mapped optical filter [16]. Compared with other filtering techniques the main advantage of SBS is the high optical rejection ratio that it can achieve. Due to its non-

Results and Discussion
Several OSNR values are analysed, ranging from 18 dB up to 32 dB, within a bandwidth of 0.1 nm. These values are further referred to as total OSNR, in 260 order to distinguish them from SC-OSNR. Sample optical spectra are depicted in Figure 4 using a resolution bandwidth of 10 MHz at -3 dB. Please note that for the case of 28 dB all the useful signal within the OFDM bands is above the optical noise, as shown in Figure 4  Similarly, the signal at the receiver is recovered just after the FHT block, where the electrical SNR is calculated as the quotient between the mean power and the variance per subcarrier, for the proposed range of total OSNR values.

295
The distribution of this electrical SNR over the FHT subcarriers is depicted in Figure 6 the sampling frequency offset depends on the number of subcarrier, degrading 305 more the edges of the OFDM band than the central subcarriers [18].
A direct relationship is found between the SC-OSNR calculated from the high-resolution OSA spectrum and the electrical SNR calculated at the receiver. This is shown in Figure 7, where the SC-OSNR is plotted as a function of the electrical SNR before equalization (a) and after equalization (b). As expected, the electrical SNR before equalization is highly correlated with the SC-OSNR.
In fact, their dependency is almost linear in dB, meaning that increasing one dB of electrical SNR is directly translated to a 1 dB increase of SC-OSNR. Also, for electrical SNR in the neighborhood of 15 dB and higher, the theoretical model based on (18) is a lower limit, following the curve trend. For values of electrical 315 SNR above 13 dB, there is a high dispersion of points, due to the fact observed in Figure 6(b). For total OSNR values beyond 26 dB, the electrical SNR of the subcarriers at the edges is limited to ∼ 13 dB. In order to overcome this effect, the electrical SNR is calculated after equalization, as shown in Figure 7(b).
For this case, the points corresponding to higher electrical SNR have lower 320 dispersion. However, the other parts of the plot show less correlation between SC-OSNR and electrical SNR.
Finally, BER measurements are obtained by statistical bit error counting up to obtain 10 3 errors. Results are shown in Figs. 8, 9, and 10. Figure 8 shows the total BER as a function of the total OSNR. There it can be observed that 325 10 −3 BER is attained at 23.7 dB of OSNR. Also a direct relationship is found between SC-OSNR measured with BOSA and BER. This is shown in Figure 10. As expected, the BER is correlated with the SC-OSNR, in a similar way to the total OSNR, see Figure 6 This is because the theoretical model describes the limit performance, when SC-OSNR is above 15 dB and assuming a Gaussian distribution of the electrical noise, according to the discussion presented in section 2.

340
In this work we have proposed a methodology to estimate the sub-carrier OSNR and we have demonstrated the direct correlation between the BER performance of individual sub-carriers and the measured sub-carrier OSNR. Live