Phase noise tolerance study in coherent optical circular QAM transmissions with ViterbiViterbi carrier phase estimation Sebastian Ortega Zafra,1, 2 Xiaodan Pang,1 Gunnar Jacobsen,1* Sergei Popov,2 and Sergey Sergeyev3 2
1 Network and Transmission Laboratory, Acreo Swedish ICT AB, SE-164 25 Kista, Sweden Optics and Photonics division, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista, Sweden 3 Aston University, Birmingham, B4 7ET, UK *
[email protected] Abstract: We present a performance evaluation of a non-conventional approach to implement phase noise tolerant optical systems with multilevel modulation formats. The performance of normalized Viterbi-Viterbi carrier phase estimation (V-V CPE) is investigated in detail for circular m-level quadrature amplitude modulation (C-mQAM) signals. The intrinsic property of C-mQAM constellation points with a uniform phase separation allows a straightforward employment of V-V CPE without the need to adapt constellation. Compared with conventional feed-forward CPE for square QAM signals, the simulated results show an enhanced tolerance of linewidth symbol duration product (ΔνTs) at a low sensitivity penalty by using feed-forward CPE structure with C-mQAM. This scheme can be easily upgraded to higher order modulations without inducing considerable complexity. ©2014 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.1660) Coherent communications; (060.4080) Modulation.
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#224702 - $15.00 USD Received 10 Oct 2014; revised 21 Nov 2014; accepted 21 Nov 2014; published 1 Dec 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.030579 | OPTICS EXPRESS 30579
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1. Introduction The fast growing bandwidth demand has been driving recent research efforts on high-capacity and high-speed optical communication systems [1]. To increase capacity, the use of optical multi-level quadrature amplitude modulation (mQAM) – rather than the conventional binary modulation schemes [2,3] – has emerged as a promising solution. By using both phase and amplitude of optical fields, mQAM enhances the system spectral efficiency at no cost of optoelectronic bandwidth. The key technology which enables the demodulation of advanced modulation formats at high data rates is coherent detection with powerful digital signal processing (DSP) [4,5] instead of optical phase locking [6]. An important constraint in coherent systems is the phase noise induced by the signal laser and the free running local oscillator (LO) laser, which limits the laser linewidth tolerance and a cost-effective implementation. Nevertheless, phase noise can be compensated using digital carrier phase estimation (CPE) [7,8]. Several CPE algorithms have been proposed for conventional square QAM signals with both decision-directed feedback [9–12] and blind feed-forward structures [13–21]. In practice, it is desired to implement the digital CPE in a blind feed-forward manner for hardware efficiency and better phase noise tolerance [8,15]. For this reason, ViterbiViterbi (V-V) algorithm is widely adopted for CPE of phase shift keying (PSK) signals with uniform phase distribution [22]. However, adapting the V-V algorithm for CPE of square 16QAM signals is more complex due to intrinsic characteristics of square constellations i.e. non-uniform phase distribution. Different approaches have been proposed to address this problem, such as QPSK partitioning [13,14] and blind phase search (BPS) [15]. Due to the complexity of such techniques, which greatly increases with the modulation level, recent efforts have been focused on trying to reduce its complexity and improving accuracy using two stage [16–19] and/or pilot-aided carrier recovery [20,21]. Although some of these methods achieve a linewidth tolerance which allows implementation with some available
#224702 - $15.00 USD Received 10 Oct 2014; revised 21 Nov 2014; accepted 21 Nov 2014; published 1 Dec 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.030579 | OPTICS EXPRESS 30580
distributed feedback (DFB) lasers, there is still a significant sensitivity penalty and a considerably reduced linewidth tolerance at higher modulation levels. On the other hand, circular constellations, as opposed to square QAM, provide a more flexible constellation design which can improve performance and enhance phase noise tolerance [23,24]. The uniform phase distribution in circular mQAM (C-mQAM) enables a direct implementation of V-V CPE in an efficient, simple, feed-forward receiver without additional stages or complex hardware implementation. Additionally, due to the geometry of C-mQAM, this CPE scheme can be easily extended for high order modulation levels. Available multi-format transmitter structures can generate arbitrary modulations by only adapting the electrical driving signals of the optical modulators [25]. In this sense, C-mQAM transmission only increases the complexity in the electrical domain by adjusting the driving signals generated by the digital-to-analog converter (DAC), without introducing additional complexity in the optical domain. However, by using transmitter configurations with reduced optical complexity, like serial intensity and phase modulator (IM/PM), C-mQAM would require considerably less signal levels in the DAC than the equivalent mQAM format (4-/8ary for C-16QAM and 3-/12-ary for 16QAM, 8-/16-ary for C-64QAM and 9-/52-ary for 64QAM) [25]. The power of V-V CPE combined with circular constellations inherent characteristics is an area of opportunity which has not been addressed previously. This unique approach would enable a cost-effective implementation of multi-level coherent systems by relaxing the strict laser linewidth requirements. In this article, we study the phase noise tolerance for C-mQAM transmissions along with normalized V-V CPE scheme, which includes an amplitude normalization stage on the received signal. Sensitivity penalties are used to estimate the phase noise tolerance, which are defined as the additional optical signal to noise ratio (OSNR) required to achieve symbol error rate (SER) of 10−3 compared to ideal (ΔνTs = 0) square 16QAM performance. For C-16QAM, a combined linewidth symbol duration product (ΔνTs) of 1x10−4 is tolerable at a minimum sensitivity penalty (~0.37 dB). Normalized V-V CPE was also tested for C-64QAM achieving a ΔνTs of 3.6x10−5 for a ~1 dB penalty and proving its simple extension for high order modulation formats. These results show that C-mQAM systems implemented with V-V CPE are a viable and potential alternative for phase noise tolerant high-speed optical transmissions. 2. Methodology 2.1 Construction of circular 16QAM signal Circular QAM constellations can be constructed with arbitrary phase distribution, number of amplitude circles, and number of symbols per circle. These parameters can be optimized and designed to increase robustness against phase noise or overall system performance [23,24]. The C-16QAM constellation considered in this work has 16 (4/4/4/4) symbols distributed in 4 amplitude circles (as opposed to conventional 16QAM which has 4/8/4 symbols distributed in 3 amplitude circles). Within each circle there is a constant phase separation of π/2 between symbols. In this way, C-16QAM has 16 symbols distributed along 8 possible phase positions and 4 amplitude levels. In this study, we construct a C-16QAM constellation in a way considering the influence of both additive and phase noise. The radii of the amplitude circles are defined so that the distance between neighboring symbols is close to the minimum distance between symbols in the inner circle. Following this rule, the radii for the 4 amplitude circles are chosen to be 1,
2+ 3 , 1+ 2 ,
2+ 3 + 2 , respectively, as illustrated in Fig.
1(a), resulting a minimum distance of 2 . High order circular constellations can be constructed in a similar way, e.g. C-64QAM with 64 symbols distributed along 8 amplitude levels and 16 phase positions.
#224702 - $15.00 USD Received 10 Oct 2014; revised 21 Nov 2014; accepted 21 Nov 2014; published 1 Dec 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.030579 | OPTICS EXPRESS 30581
Fig. 1. (a) C-16QAM constellation and (b) comparison of C-16QAM and 16QAM without CPE.
To set as a reference, we firstly compare the performance of square 16QAM and C16QAM at 28 GBaud in a back-to-back (B2B) implementation by simulations with VPItransmissionMakerTM [26], where no or very low phase noise are applied to the signal in the form of setting the combined 3-dB linewidth of the transmitter and local oscillator (LO) lasers. It is noted that in this work the phase noise is modeled as Wiener process [26]. A total number of 216 symbols (218 bits) are transmitted for performance evaluation. Figure 1(b) shows the simulational comparison results of both cases without any phase recovery scheme. Under ideal (no phase noise) conditions, C-16QAM shows a slight penalty (< 0.3 dB) at SER = 10−3 compared to 16QAM. However, in the presence of low phase noise with laser 3-dB linewidth of 10 kHz (ΔνTs = 3.6 × 10−7), C-16QAM outperforms 16QAM due to its inherent phase noise tolerant property. Since for C-16QAM the number of neighboring symbols for a given symbol is not equal or less than the number of bits per symbol, Gray mapping scheme is not possible. For this reason, a different mapping scheme is used and SER measurements are considered as they provide a general performance assessment of the constellation [23]. As indicated in Fig. 1(a), for C-16QAM the first symbol is assigned to the point in first circle with the lowest phase equal to 0. Subsequent mapping is assigned by increasing symbol number counterclockwise, from the lowest amplitude circle to the largest. 2.2 Principle of normalized V-V carrier phase recovery The V-V algorithm, which has been described and studied in detail [27], raises a received complex signal to the M-th power, taking advantage of the geometric properties of a constellation in order to remove modulation. A received symbol can be represented as a complex signal xk = rk e jϕk by its amplitude and phase components. The phase offset for symbol xk is estimated by averaging a total block size N block = 2 N + 1 considering the preceding and following N symbols of xk . After raising the signal to the M-th power, summation, argument calculation and phase unwrapping are performed, and an average phase offset for the block is estimated and applied to xk . It is noted that we perform amplitude normalization prior to V-V CPE, which aims to reduce the ambiguity in phase estimation due to additive noise and different amplitude levels in the QAM signal. Thus, the overall estimator can be defined by [13]:
#224702 - $15.00 USD Received 10 Oct 2014; revised 21 Nov 2014; accepted 21 Nov 2014; published 1 Dec 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.030579 | OPTICS EXPRESS 30582
+ N x 1 θˆk = angle k − n M n =− N xk − n
M
(1)
where θˆk is the estimated phase deviation which is then used to correct the phase deviation of the received symbol: x = x exp{−θˆ } . k
k
k
For the described C-16QAM constellation, the optimum M value is 8, since there are 8 different phase positions in this constellation. Implementation for C-64QAM is possible using exactly the same procedure and only changing M to 16 to consider additional phase positions. 3. Simulation results and discussion A C-16QAM coherent system with B2B implementation transmitting 216 symbols at 28 GBaud rate was simulated with VPItransmissionMakerTM. Normalized V-V CPE was implemented using MATLAB / VPI cosimulation [28]. SER was measured using MonteCarlo approach with direct error counting. The V-V block size range for a successful phase recovery is limited by the signal OSNR and laser linewidth. Figure 2 shows an overview of relationship between block size, signal linewidth and OSNR. A maximum linewidth tolerance was determined if the constellation was recovered for an OSNR penalty lower than 1 dB when compared to ideal (ΔνTs = 0) performance at a target SER of 10−3. It is observed that increasing the block size is necessary at low OSNR to cancel the effects of additive noise in phase estimation (i.e. the minimum block size is determined by the OSNR). On the other hand, using a too large block size leads to wrong phase estimation and a decrease of linewidth tolerance (i.e. the maximum block size is eventually determined by the linewidth). For all OSNR cases the optimum block size is near the minimum block size. As expected, the maximum linewidth tolerance increases with signal OSNR. At high OSNR of 32 dB, the linewidth tolerance is even close to 1x10−3 and can achieve an error-free transmission.
Fig. 2. Maximum linewidth tolerance at different OSNR and block size.
#224702 - $15.00 USD Received 10 Oct 2014; revised 21 Nov 2014; accepted 21 Nov 2014; published 1 Dec 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.030579 | OPTICS EXPRESS 30583
Fig. 3. SER performance of C-16QAM with V-V CPE for different linewidth values.
Fig. 4. (a) Linewidth tolerance and associated penalties for C-16QAM with V-V CPE, (b) Constellation before and after carrier recovery (ΔνTs = 1.8x10−4, OSNR = 18.7 dB).
Based on the block size analysis done to consider an optimum block size, SER performance of C-16QAM with normalized V-V CPE was analyzed for different values of ΔνTs, as shown in Fig. 3. OSNR penalties are obtained by comparing the performance of C16QAM to the ideal (ΔνTs = 0) curve of square 16QAM at a target SER of 10−3. Most of the sensitivity penalty (~0.28 dB) is related to the use of the circular constellation which can be seen by comparing the ideal curves. Despite a decrease in linewidth tolerance at low OSNR, the penalties are almost negligible for ΔνTs < 1.4x10−4 when compared to the performance of ideal C-16QAM. Furthermore, a linewidth of ΔνTs = 1.8x10−4 is still tolerable at a penalty lower than 1 dB, which slightly outperforms the widely adopted BPS scheme with max tolerance of ΔνTs of 1.4x10−4 for square 16-QAM [15]. This can be seen more clearly in Fig. 4(a) which summarizes the linewidth tolerance for the simulated system. Examples of C16QAM constellation before and after CPE are also shown in Fig. 4(b) to visualize its performance.
#224702 - $15.00 USD Received 10 Oct 2014; revised 21 Nov 2014; accepted 21 Nov 2014; published 1 Dec 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.030579 | OPTICS EXPRESS 30584
C-64QAM transmissions were also tested considering an optimum block size and the same simulation parameters previously described. The linewidth tolerance for C-64QAM with V-V CPE and the penalties compared to square 64QAM performance were estimated at a SER of 10−3. As with C-16QAM, most of the penalty (~0.8 dB) comes from use of the circular constellation which is illustrated in Fig. 5. A linewidth of ΔνTs = 3.6x10−5, which corresponds to 1 MHz 3-dB linewidth in a 28 GBaud system, is tolerable at a penalty close to 1 dB. The same normalized V-V CPE is implemented by only changing the M-th power to 16 due to phase positions of constellation. These results confirm the straightforward adaptation when upgrading to higher modulation orders in a C-QAM system with this phase recovery scheme.
Fig. 5. (a) Linewidth tolerance and associated penalties for C-64QAM with V-V CPE, (b) Constellation before and after carrier recovery (ΔνTs = 3.6x10-4, OSNR = 26.7 dB).
4. Conclusions In this paper we investigated the performance of a non-conventional approach of combining circular QAM constellations with a normalized V-V CPE scheme for high capacity coherent transmissions. The geometrical characteristics of the circular constellation are exploited to implement the described method in a feed-forward blind receiver with low complexity. Results show that, at a target SER of 10−3, a linewidth symbol duration product (ΔνTs) of 1x10−4 is tolerable at a minimum sensitivity penalty (~0.37 dB). For a ~1 dB penalty, ΔνTs of 1.8x10−4 and 3.6x10−5 are tolerable for C-16QAM and C-64QAM, respectively. The achieved linewidth tolerance enables implementation with available cost-effective DFB lasers with the same baud rates. The low sensitivity penalty and simple extension to high order modulation formats represents an enhanced performance over CPE proposed for square mQAM systems. Results show that C-mQAM transmissions with normalized V-V CPE is a viable alternative to be applied in high-capacity, low complexity, phase noise tolerant optical systems. Further investigation on this scheme should include the consideration of long-distant fiber transmission induced impairments. Acknowledgments Support from FP7-PEOPLE-2012-IAPP (project GRIFFON, No. 324391) is acknowledged.
#224702 - $15.00 USD Received 10 Oct 2014; revised 21 Nov 2014; accepted 21 Nov 2014; published 1 Dec 2014 (C) 2014 OSA 15 December 2014 | Vol. 22, No. 25 | DOI:10.1364/OE.22.030579 | OPTICS EXPRESS 30585