Coherent optical communication using
polarization multiple-input-multiple-output
Yan Han and Guifang Li
College of Optics and Photonics / CREOL & FPCE, University of Central Florida
4000 Central Florida Blvd., Orlando, FL 32816
yanhan@creol.ucf.edu
带吉的成语Abstract: Polarization-division multiplexed (PDM) optical signals can
potentially be demultiplexed by coherent detection and digital signal
processing without using optical dynamic polarization control at the
receiver. In this paper, we show that optical communications using PDM is
analogous to wireless communications using multiple-input-multiple-output
(MIMO) antennae and thus algorithms for channel estimation in wireless
MIMO can be ready applied to optical polarization MIMO (PMIMO).
Combined with frequency offt and pha estimation algorithms,
simulations show that PDM quadrature pha-shift keying signals can be
coherently detected by the propod scheme using commercial
miconductor lars while no optical pha locking and polarization
control are required. This analogy further suggests the potential application
of space-time coding in wireless communications to optical polarization
MIMO systems and relates the problem of polarization-mode dispersion in
fiber transmission to the multi-path propagation in wireless
怀孕两个月的症状
communications.
©2005 Optical Society of America
OCIS codes: (060.1660) Coherent communications; (060.4510) Optical communications;看透人生
(060.5060) Pha modulation; (260.5430) Polarization; (070.6020) Signal processing
References and links
1.M. G. Taylor, “Coherent detection method using DSP for demodulation of signal and subquent
equalization of propagation impairments,” IEEE Photonics Technol. Lett. 16, 674-676 (2004).
2. A. H. Gnauck, J. Sinsky, P. J. Winzer, and S. Chandrakhar; “Linear microwave-domain dispersion
compensation of 10-Gb/s signals using heterodyne detection,” in Proceedings of Optical Fiber
Communications Conference 2005, paper PDP31.
3.D-S. Ly-Gagnon, K. Katoh, and K. Kikuchi, “Unrepeated 210-km transmission with coherent detection and
digital signal processing of 20-Gb/s QPSK signal,” in Proceedings of Optical Fiber Communications
Conference 2005, paper OTuL4.
4. B. Glance, “Polarization independent coherent optical receiver,” J. Lightwave Technol. 5, 274-276 (1987).
5. D. Gesbert, M. Shafi, D-S Shiu, P. J. Smith, and A. Naguib, “From theory to practice: an overview of MIMO
space-time coded wireless systems,” IEEE J. Sel. Areas Commun. 21, 281-302 (2003).
6. A.H. Sayed, Fundamentals of Adaptive Filtering, (Wiley, NY, 2003).
7. M. Tytlin, O. Ritterbush, and A. Salamon, “Digital, endless polarization control for polarization
multiplexed fiber-optic communications,” in Proceedings of Optical Fiber Communications Conference
2003, vol. 1, pp. 103-103.
8.S. G.Evangelides Jr., L. F.Mollenauer, J. P.Gordon, and N. S.Bergano, “Polarization multiplexing with
solitons,” J. Lightwave Technol. 10, 28-35, 1992.
1. Introduction
Wavelength-division multiplexing (WDM) can significantly increa the capacity of optical communication systems. The transmission cost per bit is reduced with the increa of capacity since the WDM channels share the same fiber and optical amplifiers. To accommodate more channels to further increa capacity, clor channel spacing and/or more wavelengths should
#7830 - $15.00 USD Received 15 June 2005; revid 1 September 2005; accepted 8 September 2005 (C) 2005 OSA19 September 2005 / Vol. 13, No. 19 / OPTICS EXPRESS 7527
be ud. This may not only require the u of broadband optical amplifiers but also increa system
complexity in terms of multiplexing, demultiplexing and dispersion management. Another potentially economical approach to increasing the overall capacity is to u advanced modulation formats with higher spectral efficiency. With the reduced symbol rates, systems using high-spectral efficiency modulation formats could be more tolerant to chromatic and polarization-mode dispersion. Generally, there exists a tradeoff between spectral efficiency and nsitivity of a modulation format. Coherent detection is usually considered necessary to alleviate this tradeoff. For example, quadrature pha-shift keying (QPSK) with coherent detection has the same nsitivity as binary pha-shift keying (BPSK), but doubles the spectral efficiency. Additionally, coherent detection can also facilitate channel demultiplexing and chromatic dispersion compensation in a WDM system [1, 2].
Optical pha locking and polarization control are generally required in coherent detection. Conventional pha locking us costly optical pha-locking loops. With the advance of A/D converter, pha locking (or pha estimation) using digital signal processing (DSP) at 10 GSymbol/s has been recently reported [3]. Polarization dependence of coherent detection can be managed by using optical dynamic polarization control or polarization diversity receiver [4]. In a conventional polarization diversity receiver, two ts of receivers are ud to independently detect signal components in the two orthogonal polarization states and the original signal is recovered after
combining two components, which is rather inefficient in terms of hardware. However, when two PDM channels are simultaneously transmitted at orthogonal polarization states, polarization diversity receiver in principle can receiver both channels, for example, by using optical dynamic polarization control at the receiver. It has been suggested that PDM optical signals can potentially be demultiplexed by combining coherent detection and polarization/pha diversity [1]. In this paper, we show that optical communications using PDM is analogous to wireless communications using multiple-input-multiple-output (MIMO) antennae and thus algorithms for channel estimation in wireless MIMO can be ready applied to optical polarization MIMO (PMIMO). The effectiveness of this scheme when using commercial miconductor lars free of active optical controls is also investigated by simulations.11月份的节日
2. Optical polarization MIMO
Fig. 1. Schematic of an optical polarization MIMO system. PBS: polarization beam splitter;
PBC: polarization beam combiner; LO: local oscillator.
The schematic of an optical polarization MIMO system is shown in Fig. 1. In the transmitter, two synchronous data are modulated in orthogonal polarizations. The modulation format can be amplitude and/or pha modulation. x E and y E are the complex reprentation of the modulated signal in the parallel and perpendicular polarization state. After transmission
#7830 - $15.00 USD Received 15 June 2005; revid 1 September 2005; accepted 8 September 2005 (C) 2005 OSA19 September 2005 / Vol. 13, No. 19 / OPTICS EXPRESS 7528
through fiber, the polarization of lightwave is usually not prerved. For an arbitrary
orientated PBS, the received signal,'x
E or 'y E , contains significant crosstalk between the original signals in the two orthogonal polarization states. The output electrical field can be related to the input electrical field by
单位考核鉴定意见
⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎟⎠⎞⎜⎜⎝⎛y x y x y x E E JL E E J J J J L E E 2221121
1'' (1) where L is a real scalar to describe the optical loss from the input to the output and the
polarization change due to fiber is described by a unitary Jones matrix J . (For simplicity of analysis, polarization-mode dispersion (PMD) and polarization dependent loss (PDL) of fiber and other inline optical components are neglected.) Equation (1) describes a two-input and two-output MIMO system. Since J is a unitary matrix, this MIMO system, in theory, can transmit two synchronous channels without any penalty [5]. Due to environment variations, the polarization of lightwave in fiber generally drifts with the time. The rate of this polarization drift is generally much slower than the transmission data rate. Therefore, the system can be designed to estimate the Jones matrix J for the entire frame using a training quence in the preamble of each frame to remove polarization crosstalk. Various channel estimation algorithms can be ud to estimate J . Considering the high date rate ud in optical communications, the LMS (least-mean-squares) algorithm is chon in this paper becau of its simplicity [6]. The J can be estimated by using the following iterative algorithm. guess initial ,0 ,1'1''1=≥⎟⎟⎠⎞⎜⎜⎝⎛×⎥⎥⎦⎤⎢⎢⎣
⎡⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛×+=−−−J i E E L E E L J E E J J i y x i y x i i y x
i i μ (2) In-Pha Q u a d r a t u r e
In-Pha Q u a d r a t u r e猪怎么画简笔画
Fig. 2. Signal constellations. (a) Received signal; (b) after applying the estimated Jones matrix.
No lar pha noi and frequency offt.
where μ is a positive step-size, i is the label of training quences and L can be obtained
腹泻可以吃什么from the received average power. Since 'x E and 'y E are generally complex, 90o optical
hybrids are ud to simultaneously measure the in-pha 'x I and 'y I and quadrature 'x Q and
'y Q components. If the 90o hybrid is polarization-innsitive, the receiver in Fig. 1 can be further simplified by using only one hybrid followed by PBSs. The state of polarization of LO is chon so that its power is equally split between orthogonal polarizations. In this ction, lar2 is assumed pha-locked to the lar1. The inver of estimated J can then be applied to the received signals to recover the transmitted data x I , y I , x Q and y Q . Becau J is a unitary matrix, the inversion equals the conjugate transpo. In optical polarization MIMO (C) 2005 OSA 19 September 2005 / Vol. 13, No. 19 / OPTICS EXPRESS 7529#7830 - $15.00 USD Received 15 June 2005; revid 1 September 2005; accepted 8 September 2005
systems, the received signal polarization estimation and tracking is performed by DSP algorithm and no optical dynamic polarization control is required at the receiver. A different scheme named digital endless polarization control using nine-hypothes gradient arch algorithm was propod in [7].
1
Fig. 3. Learning curves of the LMS algorithm ud to estimate the Jones matrix.口才的魅力
The performance of the propod polarization MIMO system is evaluated by numerical simulations.
The transmitter and receiver are the same as in Fig. 1. As an example, BPSK modulation format is attempted, which is generated by an ideal pha modulator. The symbol rate is 10 GSymbol/s. The transmission fibers compri 100 km standard single-mode fiber
μ) and (with a dispersion of -16 ps/nm/km, a loss of 0.2 dB/km and a core area of 80 2
m matching 20 km dispersion compensating fiber (with a dispersion of 80 ps/nm/km, a loss of
μ) with randomly varying birefringence simulated by the 0.5 dB/km and a core area of 20 2
m
coar-step method [8]. The PMD coefficient of the fibers is 0.1 ps/km. The fiber nonlinear-index coefficient is 2.6x10-20m2/W. An optical amplifier is ud to amplify the received signal emulating the ASE-dominated scenario. The received power before optical amplifier is -30 dBm, corresponding to a 0 dBm launch power. The noi figure of the optical amplifier is 5 dB. The optical filter before receiver is a Gaussian filter with a 3 dB bandwidth of 25 GHz. The frame length in simulations is t to 1024 symbols. The length of training quence in the preamble is 32 symbols. The constellations of received signals in orthogonal polarizations are shown in Fig. 2(a), where significant crosstalk exis
ts. In this paper, the blue and red symbols reprent the parallel and perpendicular polarization states, respectively. After applying the Jones matrix J that is estimated from the training quence, the crosstalk is removed and BPSK constellations are obtained in Fig. 2(b). The learning curve of LMS algorithm is shown in Fig. 3. The eight lines reprent the real and imaginary components of Jones matrix i J in the iterative algorithm. A unit matrix is ud as the initial guess. The algorithm reaches the steady state after ~20 iterations. There is a tradeoff between the accuracy and convergence speed in LMS algorithm [6].
3. Optical polarization MIMO with pha estimation
In Section 2, the transmitter lar and LO (lar1 and lar 2) have been assumed to be pha-locked. In practice, pha locking can be performed using DSP algorithms without modification to Fig. 1. The algorithm then compris two steps: i) Estimate J using a training quence and remove polarization crosstalk as in Section 2; ii) Pha drift of LO within a frame is estimated using an algorithm similar to [3]. The pha estimation algorithm squares received signals (quadruples the signal for QPSK signals) to remove the intended pha
#7830 - $15.00 USD Received 15 June 2005; revid 1 September 2005; accepted 8 September 2005 (C) 2005 OSA19 September 2005 / Vol. 13, No. 19 / OPTICS EXPRESS 7530
modulation and track the LO pha relative to carrier. Signals in each frame are parated into 16-symbol blocks. The estimated LO pha within each block is averaged. In experiments reported in [3], the frequency offt between lar1 and lar2 are controlled within 10 MHz and the algorithm did not distinguish the pha drift due to pha noi or frequency offt.
In-Pha Q u a d r a t u r e
In-Pha Q u a d r a t u r e
In-Pha Q u a d r a t u r e
Fig. 4. Signal constellations. (a) Received signal; (b) step-1: remove polarization crosstalk; (c)
step-2: pha estimation. 1 MHz lar linewidth and no frequency offt.
In-Pha Q u a d r a t u r e
In-Pha In-Pha
Fig. 5. Signal constellations. (a) Received signal; (b) step-1: remove polarization crosstalk; (c)
step-2: pha estimation. 1 MHz lar linewidth and 10 MHz frequency offt.
The simulation parameters are the same as in Section 2 except that the lar linewidth is assumed to be 1 MHz, which is typical for commercially available miconductor lars. The results are shown in Fig. 4. After removing the crosstalk between orthogonal polarizations (Fig. 4(b)), the resultant constellations contain significant pha nois. Using the pha estimation algorithm described above, BPSK constellations in Fig. 4(c) are obtained. In Fig. 4, lar frequency offt is neglected. If
lar frequency offt is small, it can be treated as lar pha noi. For a 10 MHz frequency offt, the same algorithm is still effective and the results are shown in Fig. 5. The slight asymmetry in the constellations is due to 5.8o of pha rotation in the 16-symbol block corresponding to 10 MHz frequency offt. This pha error increas with the frequency offt and can be reduced by using block length shorter than 16 symbols, but as a tradeoff, the estimated pha error due to lar linewidth increas.
4. Optical polarization MIMO with frequency and pha estimation
In Fig. 4 and 5, the LMS algorithm ud to estimate J is almost not affected by the pha rotation due to small frequency offt becau the adaptive LMS algorithm can track this pha rotation. In the prence of large frequency offt, the expected J becomes periodic, corresponding to the offt frequency. Simulations show that the LMS algorithm is still effective with a frequency offt of 100 MHz (1% symbol rate), but fails when the offt is 1 GHz (10% symbol rate). Therefore, for an offt as large as 1 GHz, additional frequency estimation algorithm should be employed. The overall algorithm then compris three steps: i) frequency estimation, ii) polarization MIMO channel estimation and iii) pha estimation. The MIMO channel estimation and pha estimation are the same as the steps described in Section (C) 2005 OSA 19 September 2005 / Vol. 13, No. 19 / OPTIC
S EXPRESS 7531#7830 - $15.00 USD Received 15 June 2005; revid 1 September 2005; accepted 8 September 2005
