A Feedforward Partial Phase Noise Mitigation in the TimeDomain using Cyclic Prefix for COOFDM Systems
 Author: Ha Youngsun, Chung Wonzoo
 Organization: Ha Youngsun; Chung Wonzoo
 Publish: Journal of the Optical Society of Korea Volume 17, Issue6, p467~470, 25 Dec 2013

ABSTRACT
We propose a blind feedforward phase noise mitigation method in the timedomain for a coherent optical orthogonal frequency division multiplexing (COOFDM) systems. By exploiting the redundancy of the cyclic prefix (CP), the proposed scheme acquires the overall phase noise difference information during an OFDM block and attempts to mitigate the phase noise in the time domain using a linear approximation. The proposed algorithm mitigates common phase error (CPE) and intercarrierinterference (ICI) due to phase noise simultaneously, improving the system performance, especially when decisiondirected equalizers are used. The simulation results demonstrate the effectiveness of the proposed feedforward phase noise mitigation approach in time domain.

KEYWORD
Coherent optical orthogonal frequency division multiplexing , Phase noise , Optical communication systems

I. INTRODUCTION
Coherent optical orthogonal frequency division multiplexing (COOFDM) is a highly effective technique to achieve highspeed optical communication systems for its high chromatic dispersion (CD) and polarizationmode dispersion (PMD) tolerance [1, 2]. However, COOFDM is vulnerable to the laser phase noise which destroys the orthogonality of the subcarriers. This loss of orthogonality results in intercarrierinterference (ICI) and common phase error (CPE) in all subcarriers [3]. Since this distortion significantly degrades the system performance, various phase noise compensation techniques have been proposed.
These have mostly focused on frequencydomain phase noise mitigation, i.e., after removing the cyclic prefix (CP) and applying a fast Fourier transform (FFT), where pilot signals or decision direction (DD) methods are available. As mitigation of ICI requires sophisticated methods that incur considerable (indeed, prohibitive) computational expense [4], practical phase compensation studies have mainly considered only CPE mitigation based on either DD methods or highorderstatistics (HOS) blindadaptive algorithms [5, 6].
In [7] a simple partial ICI mitigation approach has been considered. Using the CPE estimations from the postdiscrete Fourier transform (DFT) signals, the algorithm linearly approximates the phase noise in an OFDM block and compensates for it in the frequency domain by convolving of the DFT version of the linear phase model [7]. Although this algorithm is, as far as we know, the simplest algorithm for reducing ICI distortion, it requires accurate CPE estimation from the corrupted data by the phase noise and post convolution processing cost due to its structure. Since the phase noise is a scalar multiplication in the time domain, a direct timedomain correction would be preferable.
In this paper, we propose a nondataaided feedforward time domain phase noise mitigation scheme that reduces both CPE and ICI by exploiting the redundancy of the cyclic prefix (CP) structure. The CP is a copy of the last few samples of an OFDM block, which are inserted at the beginning of the block to sustain subcarrier orthogonality over multipath channels. At the receiver, the CP structure guarantees that certain received samples match in the absence of phase noise. Based on this property, the phase difference between the beginning and the end of an OFDM block can be roughly estimated. We utilize this phase difference to compensate for ICI and CPE. Especially for systems with a DD equalizer, the proposed feedforward method alleviates the adverse effects of phase noise distortion on the DD equalizer and improves the overall performance.
The remainder of this paper is organized as follows. In Section 2, we describe the discrete time baseband OFDM system and the properties of the CP. In Section 3, we describe the proposed phase noise mitigation algorithm. The numerical results are shown in Section 4, and a conclusion is given in Section 5.
II. SYSTEM MODEL
Let us consider a discrete time baseband COOFDM system model, where the
m th OFDM symbol consists ofN QAM symbolss_{m} (0),⋯,s_{m} (N −1), and is processed by an inverse DFT (IDFT). At the beginning of the IDFT processed signal block, denoted byx (0),⋯,x (N −1), the lastP samples are inserted and these insertedP samples are called the cyclic prefix (CP). Letz_{m} (k ) fork =−P ,⋯, −1, 0,⋯,N −1 denote the baseband signal after the insertion of the CP. We then haveThe purpose of CP is to maintain the orthogonality of the subcarriers after multipath channel transmission and the length of the CP,
P , should be greater than the channel length. After passing through the optical channel, assuming proper synchronization, the received signal corresponding to them th OFDM symbol in the presence of laser phase noise is modeled as follows [8]:for
k =−P ,··· − 1, 0, 1 ···N − 1, whereZ_{m} ⊗h_{m} denotes convolution of the transmitted OFDM symbolz_{m} (k ) and the baseband optical channel transfer functionh_{m} (k ), andn_{m} (k ) denotes the zeromean additive white Gaussian noise (AWGN) with varianceσ ^{2}. The optical fiber nonlinearity is not considered here in order to focus on the impact of the phase noise, which is consistent with the analysis described in other previous studies [3, 9]. The phase noiseϕ_{m} (k ) fork =−P , ···,N −1 is modeled as an Wiener process with variance 2πβT , whereβ is the laser linewidth andT is the sample period [10]. In the absence of phase noise and AWGN, we haveas far as the CP length is set to meet the fundamental requirement of an OFDM system [11]. Note that in the presence of phase noise we can extract the phase difference between
r_{m} (−1) andr_{m} (N −1) using this property,We will exploit this to estimate and compensate for the phase noise in the OFDM blocks.
At the receiver, assuming perfect synchronization under proper distortion monitoring such as in [12, 13], the first
P samples,r_{m} (−P ),···,r_{m} (−1), i.e., those corresponding to the CP, are removed and processed using a DFT. The outputy_{m} (k ), which corresponds to the source QAM symbols_{m} (k ), is given aswhere
H_{m} andI_{m,n} are the channel frequency response and the distortion due to the phase noise, respectively, andw_{m} (k ) is the noise in the frequency domain. The phase noise distortion term,I_{m,n} , is given byThe principal phase distortion
I _{m,0} is the CPE and applies for all subcarriers, and the remaining terms contribute to the ICI. Note that the relative deviation ofϕ_{m} (k ) is the main factor that results in ICI, as a constant phase offsetφ does not affect the ICI (but does affect the CPE) as shown by the following equation:III. PHASE NOISE MITIGATION SCHEME
Figure 1 shows a block diagram illustrating the proposed phase mitigation scheme. First, let us define an estimator for the phase noise difference between
ϕ_{m} (−1) andϕ_{m} (N −1) asAssuming that the first OFDM block (
m = 0) is a pilot block for channel equalization, we setThe phase noise sequence
ϕ_{m} (0),···,ϕ_{m} (N −1) is a one dimensional random walk and compensation with a linear line model fromϕ_{m} (0) toϕ_{m} (N −1) has been shown to be effective for ICI mitigation [7]. Since we only have the relative phase difference betweenϕ_{m} (−1) andϕ_{m} (N −1), we approximate the phase noise sequenceϕ_{m} (0),⋯,ϕ_{m} (N −1) with the following linear model denoted by with respect to a phase offsetφ_{m} (ifϕ_{m} (−1) is available,φ_{m} is set toϕ_{m} (−1)), i.e.,as shown in Fig. 2. This is the optimum mean square error (MSE) interpolation for the phase noise [10]. The phasecompensated signal, denoted by (
k ), is given byRegardless of the value of
φ_{m} (as observed in (9)), this compensation reduces the relative deviation of the phase noise and mitigates the ICI distortion. However, the choice ofφ_{m} becomes important for CPE. The CPE for the compensated OFDM symbol is given byAssuming mild phase noise, the CPE is can be approximated in the following manner [3]
Note that if
φ_{m} =ϕ_{m} (−1)holds, this approximation reduces the CPE as well (refer to Fig. 2), for we haveGiven that
ϕ_{m} (−1) is not available, we use the following approximationwhere
N_{f} denotes the size of the OFDM frame. We then have,As
m increases the accumulated cyclic prefix phase noise becomes significant and the CPE may increase. This problem can be resolved with the help of a DD equalizer. Since the phase offset grows for eachm , an adaptive DD equalizer can track this increasing phase offset, treating it as a timevarying channel. An estimate of CPE denoted by , is given byBy updating the DD equalizer to compensate this CPE at every
m , we can setφ_{m} = 0. Since this approach is simpler and less computationally expensive, it is used for performance evaluation in the following simulation sections. Note that the proposed algorithm does not require past CPE values in the time domain or recomputation of the output symbols as was used in [7].IV. NUMERICAL RESULTS
We consider a 21.4Gb/s COOFDM system based on 16QAM signals using 1024 subcarriers (
N = 1024) with a cyclic prefix ofP = 256 and 32 symbols (N_{f} = 32) per OFDM frame. The pilot symbols were used at the beginning of the frame for channel frequency response estimation. The optical channel response function was assumed to be timeinvariant within one OFDM frame. The transmission length was 500 km over standard singlemode fiber (SSMF). Fig. 3 shows a comparison of the bit error rate (BER) of the proposed schemes and conventional DD equalizer to compensate for CPE (this is described in (17)) with laser linewidths of 100 kHz and 125 kHz. As seen in Fig. 3(a), the proposed scheme provided a 2.7dB improvement with a BER of 10^{−1.5}. Fig. 3(b) shows the BER performance of the proposed scheme with a laser linewidth of 125 kHz. The conventional DD equalizer encounters the error floor; however, the performance of our algorithm is only slightly degraded in comparison with that of the laser linewidth of 100 kHz.V. CONCLUSION
We have described a blind feedforward phase noise mitigation scheme. The proposed technique reduced both the CPE and ICI by using a linear approximation in the time domain The simulation results demonstrated that the proposed approach effectively improved system performance, especially when DD equalizers were used. In comparision with the conventional phase noise mitigation schemes, the precompensation approach of the proposed algorithm significantly improved the system performance with maginal computation load addition.

[FIG. 1.] Detailed block diagram of the proposed algorithm.

[FIG. 2.] Phase noise and linearly estimated phase noise.

[FIG. 3.] The BER performance of the proposed scheme for laser linewidth of (a) 100 and (b) 125 kHz.