1. Field of the Art
The disclosure relates generally to communication systems, and more specifically, to timing recovery in an optical receiver.
2. Description of the Related Art
The most recent generation of high-speed optical transport network systems has widely adopted receiver technologies with electronic dispersion compensation (EDC). In coherent as well as in intensity modulation direct detection (IM-DD) receivers, EDC mitigates fiber impairments such as chromatic dispersion (CD) and polarization mode dispersion (PMD).
Timing recovery (TR) in the presence of differential group delay (DGD) has been identified as one of the most critical challenges for intradyne coherent receivers. In particular, it has been shown that timing information can be completely lost in optical channels with half-baud (or half-symbol period) DGD. This can result in the receiver failing to recover data received over the fiber channel, thereby decreasing performance of the optical network system.
A receiver processes a signal received over an optical communication channel. The signal includes first and second polarization components and the optical communication channel introduces polarization mode dispersion effects into the signal. In one embodiment, the receiver comprises an analog front end to sample the signal based on a sampling clock to generate digital vector representing the first and second polarization components of the signal. A matrix transformation block applies a transformation matrix (which in one embodiment, comprises a rotation matrix) to the digital vector representing the first and second polarization components to generate a transformed digital vector such that the tone energy of the transformed digital vector is increased relative to the timing tone energy of the received digital vector when the timing tone energy is based on a memoryless nonlinearity of one of the first and second polarization components of the transformed digital vector. A timing recovery block detects a symbol rate of the transformed digital vector and generates the sampling clock based on the detected symbol rate.
In one embodiment, the optical signal comprises a half symbol period differential group delay for at least a portion of the optical signal. The analog front end samples the signal based on a sampling clock to generate a digital vector representing first and second polarization components. A digital signal processor executes instructions for timing recovery. The digital signal process generates a sampling clock based on a detected symbol rate in the digital vector. The sampling clock achieves a non-zero timing tone energy for the portion of the optical signal having the half symbol period differential group delay.
The invention has other advantages and features which will be more readily apparent from the following detailed description of the invention and the appended claims, when taken in conjunction with the accompanying drawings, in which:
A receiver architecture and method for timing recovery is described for transmissions received over an optical fiber channel in the presence of differential group delay (DGD) (caused, for example, by polarization mode dispersion). A matrix-based linear transformation is applied to the vector of polarization components of a signal received over the optical fiber channel that mitigates or eliminates the effects of the differential group delay on timing recovery. Timing recovery can then be performed on the transformed signal to recover a clock signal. Beneficially, the described technique can recover timing information even in half-baud DGD channels. Furthermore, latency and computational load can be minimized with the described timing recovery technique.
High Level System Architecture
The transmitter 110 comprises an encoder 112, a modulator 114, a transmitter (Tx) digital signal processor (DSP) 116, and Tx analog front end (AFE) 118. The encoder 112 receives input data 105 and encodes the data for transmission over the optical network. For example, in one embodiment, the encoder 112 encodes the input data 105 using forward error correction (FEC) codes that will enable the receiver 160 to detect, and in many cases, correct errors in the data received over the channel 130. The modulator 114 modulates the encoded data via one or more carrier signals for transmission over the channel 130. For example, in one embodiment, the modulator 114 applies phase-shift keying (PSK) or different phase-shift keying (DPSK) to the encoded data. The Tx DSP 116 adapts (by filtering, etc.) the modulator's output signal according to the channel characteristics in order to improve the overall performance of the transmitter 110. The Tx AFE 118 further processes and converts the Tx DSP's digital output signal to the analog domain before it is passed to the optical transmitter (Optical Tx) 120 where it is converted to an optical signal and transmitted via the channel 130. One example of the optical transmitter 120 transmits independent modulations on both polarizations of the optical carrier. An example modulation is QPSK, though other modulations can be used, and the choice can be made to transmit on either one or both polarizations.
In addition to the illustrated components, the transmitter 110 may comprise other conventional features of a transmitter 110 which are omitted from
The channel 130 may have a limited frequency bandwidth and may act as a filter on the transmitted data. Transmission over the channel 130 may add noise to the transmitted signal including various types of random disturbances arising from outside or within the communication system 100. Furthermore, the channel 130 may introduce fading and/or attenuation effects to the transmitted data. Additionally, the channel 130 may introduce chromatic dispersion (CD) and polarization mode dispersion (PMD) effects that cause a spreading of pulses in the channel 130. Based on these imperfections in the channel 130, the receiver 160 is designed to process the received data and recover the input data 105.
In general, the optical front end 150 receives the optical signal, converts the optical signal to an electrical signal, and passes the electrical signal to the receiver 160. The receiver 160 receives the encoded and modulated data from the transmitter 110 via the optical transmitter 120, communication channel 130, and optical front end 150, and produces recovered data 175 representative of the input data 105. The receiver 160 includes a receiver (Rx) analog front end (AFE) 168, an RX DSP 166, a demodulator 164, and a decoder 162. The Rx AFE 168 samples the analog signal from the optical front end 150 based on a clock signal 181 to convert the signal to the digital domain. The Rx DSP 166 further processes the digital signal by applying one or more filters to improve signal quality. As will be discussed in further detail below, the Rx DSP 166 includes a timing recovery block 179 that operates to generate the sampling clock 181 and to adjust the sampling frequency and phase of the sampling clock signal 181 to ensure that the sampling clock remains synchronized with the symbol rate and phase of the incoming optical signal. This timing recovery problem becomes challenging due to the imperfections in the channel 130 that may alter the received optical signal. For example, chromatic dispersion (CD) and polarization mode dispersion (PMD) effects may cause a spreading of pulses in the channel 130, thereby increasing the difficulty of timing recovery, as will be explained below.
The demodulator 164 receives the modulated signal from the Rx DSP 166 and demodulates the signal. The decoder 162 decodes the demodulated signal (e.g., using error correction codes) to recover the original input data 105.
Embodiments of the receiver may operate to process data modulated on both polarizations of the optical signal (e.g., using dual polarization modulation), or alternatively, the receiver may operate to process data modulated on only one of the polarizations. Although the operation of the receiver below focuses on a signal transmitted on both polarizations, it will be apparent to one of ordinary skill in the art that the described operation could be similarly adapted to transmitters/receivers that modulate data on only one polarization.
In addition to the illustrated components, the receiver 160 may comprise other conventional features of a receiver 160 which are omitted from
Components of the transmitter 110 and the receiver 160 described herein may be implemented, for example, as an integrated circuit (e.g., an Application-Specific Integrated Circuit (ASIC) or using a field-programmable gate array (FPGA), in software (e.g., loading program instructions to a processor (e.g., a digital signal processor (DSP)) from a computer-readable storage medium and executing the instructions by the processor), or by a combination of hardware and software.
Impact of DGD on Timing Recovery
This section explains how the PMD is expressed mathematically, which provides a basis for an explanation of the effects of particular PMD on the timing information in the received signal. Particular examples are presented which show that the timing information can disappear completely for certain PMD situations. Two different situations are examined: the first is when the timing recovery is based on a single polarization at the receiver, and the second is when timing recovery is based on both polarizations at the receiver. The signal from the optical front end 150 presented to the receiver 160 consists of electrical signals from both polarizations of the optical signal received by the optical front end 150. These two polarizations can be treated mathematically as a two-dimensional complex vector, where each component corresponds to one of the polarizations of the received optical signal. Alternatively, the two polarizations can be treated mathematically as a four-dimensional real vector, where two of the dimensions correspond to the in-phase and quadrature components of one polarization, and the other two components correspond to the in-phase and quadrature components of the other polarization. Without loss of generality, the analysis below treats the signal as a two-dimensional complex vector.
This example demonstrates the embodiment where the two polarizations at the transmitter are each modulated independently. Let {ak} and {bk} respectively represent the symbol sequences transmitted on the horizontal and vertical polarizations of the optical signal, where the symbols are in general complex. For this example, it is assumed that ak and bk are independent and identically distributed complex data symbols with E{aka*m}=E{bkb*m}=δm−k where δk is the discrete time impulse function and E{•} denotes expected value. Let X(ω) be the Fourier transform of the channel input
where δ(t) is the continuous time impulse function (or delta function), and T is the symbol period (also called one baud). Let S(ω) be the Fourier transform of the transmit pulse, s(t). In the presence of CD and PMD, the channel output can be written as H(ω)X(ω), with the channel transfer matrix expressed as
H(ω)=e−jβ(ω)LJ(ω)S(ω), (1)
where ω is the angular frequency, L is the fiber length of the optical channel 130, β(ω) is the CD parameter,
and J(ω) is the Jones matrix. The components of J(ω) are defined by
where * denotes complex conjugate. Matrix J(ω) is special unitary (i.e., J(ω)†J(ω)=I, det(J(ω))=1, where I is the 2×2 identity matrix and † denotes conjugate transpose) and models the effects of the PMD. For example, the Jones matrix for first-order PMD reduces to
where τ is the differential group delay (DGD), ψ0is the polarization phase, and R(•,•) is the rotation matrix given by
where θ is the polarization angle and Φ is a random phase angle. Note that first order DGD may be more generally expressed as:
but the last rotation matrix does not affect the strength of the timing tone, so the simpler form given in (4) is used herein.
Assuming that CD is completely compensated in the receiver Rx DSP 166 of the receiver 160 or prior to the signal reaching the receiver Rx DSP 166, (i.e., H(ω)=J(ω)S(ω)), the noiseless signal entering the timing recovery block 179 can be expressed as:
where 1/T is the symbol rate, while
h11(t)=F−1{U(ω)S(ω)}, h12(t)=F−1{V(ω)S(ω)}, h21(t)=F−1{−V*(ω)S(ω)}, h22(t)=F−1{U*(ω)S(ω)}), (7)
where F−1{•} denotes the inverse Fourier transform.
Although other timing recovery methods may be used, in one example, the timing recovery block 179 applies a “nonlinear spectral line method” for timing recovery, as commonly used in oversampled receivers. In this scheme, the timing recovery block 179 processes the received signal by a memoryless nonlinearity in order to generate a timing tone with frequency 1/T. Furthermore, although other variations are possible, in one example, the timing recovery block 179 uses a “magnitude squared nonlinearity” as the memoryless nonlinearity applied to the received signal. Then, the mean value of the magnitude squared of the received signal is periodic with period T and can be expressed through a Fourier series as
where
The timing information can be extracted either from the periodic signal derived from the received x polarization (E{|rx(t)|2}), or from the periodic signal derived from the received y polarization (E{|ry(t)|2}), or from some combination of these two periodic signals. Additional details regarding the nonlinear spectral line method for timing recovery is described in J. R. Barry, E. A. Lee, and D. G. Messerschmitt, Digital Communication. KAP, third ed. 2004 which is incorporated by reference herein.
Timing Information Using One Polarization
The following description explains the effects of PMD when one polarization is used for timing recovery and gives example conditions where the timing recovery information can disappear. From (8)-(9), it can be seen that the clock signal 181 will be different from zero in |rx(t)|2 (or |ry(t)|2) if the magnitude of the Fourier coefficient |zx,1|>0 (or |zy,1|>0). On the other hand, from (10) and (11) it can be verified that the timing tone in each polarization component will be zero if
where ψ is an arbitrary phase. Since the Jones matrix is unitary (i.e., |U(ω)|2+|V(ω)|2=1), the following expression can be derived from (12)
Let γ(ω)/2 be the phase response of U(ω). Then, from (12) and (13), the clock signal disappears when the Jones matrix representing the PMD at the input of the timing recovery block 179 can be expressed as
For example, the impact of the first-order PMD defined by (4) is analyzed in
The matrix in (15) can be written as (14) (with γ(ω)=Φ0 and ψ=ψ0). It can be inferred from the equations above that the clock signal may disappear with half-baud DGD, as illustrated in
Timing Information Using Two Polarizations
The effects of PMD are now described when both polarizations are used for timing recovery and conditions where the timing recovery information can disappear are presented. In particular, the sum of the squared signals of both polarizations may be used for timing recovery (i.e., |rx(t)|2+|ry(t)|2). Then, the total timing tone coefficient zx+y,1 can be expressed as:
where {•} denotes the real part of the expression.
For example, from (16) it is observed that the clock signal will be zero if
where ψU and ψV are arbitrary angles. As can be seen, the first-order PMD defined by (4) with τ=T/2 satisfies condition (17) for any combination of θ0, Φ0 and ψ0. Therefore, the clock signal contained in |rx(t)|2+|ry(t)|2 is lost in the presence of half-baud DGD. This is illustrated in
General Approach to Timing Recovery in PMD Channels
The operating principles of the Rx DSP 166 are now described in further detail. A general approach to mitigate the timing recovery problem is to equalize the higher-order PMD (represented by a non-constant γ(ω) in (14)) leaving only first order PMD, and de-rotating the received signal so that the fast and slow PMD axes correspond to the polarization axes at the receiver 160. This corresponds to inverting the matrix R (θ0, γ(ω)) in (14).
As shown before, the timing tone in clock signal 181 can be lost if the PMD matrix can be expressed as:
Thus, to mitigate this problem, an equalizer can be used before the timing recovery block 179 of the receiver 160 with transfer matrix HTR(ω)=R−1(θ0, γ(ω)). This way, the Jones matrix at the input of timing recovery block 179 is:
Based on (10) and (18), the timing tone complex coefficient results in
From (19), it can be seen that for a given transmit pulse s(t), the timing tone magnitude |
Reduced Complexity Approach to Timing Recovery
A more efficient approach to timing recovery is now described. Without substantial loss of performance, the equalizing matrix HTR(ω) can be made independent of frequency, so that it is a simple memoryless rotation matrix. It is possible to show that the timing tone coefficients for each polarization (i.e., zx,1 and zy,1) are given by the diagonal elements of the 2×2 matrix
In the following, it is assumed that SOPMD is the dominant component of PMD. In this case, the PMD Jones matrix can be written as (i.e., the Bruyere model)
where pω is the depolarization rate of the principle state of polarization (PSP) (for simplicity, the polarization dependent chromatic dispersion (PCD) component is neglected). Next it is shown that a simple matrix rotator at the input of the timing recovery block 179 is a good approach to provide a good timing tone level at a given polarization (i.e., zx,1 or zy,1) in the presence of DGD and SOPMD channels. Based on this finding, an algorithm is described to compute the proper angles to generate such a matrix rotator.
In the case that the bandwidth excess of the pulse s(t) is low (e.g., ≦50%), then the product
is concentrated around
i.e.,
Note that |Ks| is the magnitude of the timing tone coefficient for each polarization in the absence of channel dispersion.
For Δω sufficiently small and moderate PMD, the following approximation can be made:
Then, it is possible to show that matrix Z reduces to
Z≈KSZ1 (22a)
with
Z1−R(θ0,Φ0)PR−1(θ0,Φ0) (22b)
where P is a special unitary matrix, while θ0 and φ0 are certain angles.
Since matrix Z1 is also special unitary, it can be expressed as
Z1=R(θ1,Φ1)ΛR−1(θ1,Φ1) (22c)
where Λ is a special unitary diagonal matrix.
If the transfer matrix at the timing recovery input is
HTR(ω)=M(θ1,Φ1)=RH(θ1,Φ1) (23a)
and taking into account that
it is possible to show that
Since the diagonal matrix Λ is unitary, it is observed that the magnitudes of the timing tone coefficients for both polarizations are
{tilde over (z)}x,1={tilde over (z)}y,1≈|Ks| (25)
Therefore the impact of the DGD and SOPMD on the timing tone energy is mitigated. From the above, it can be inferred that a simple matrix rotator at the input of the timing recovery block 179 is a good approach to provide a good timing tone level at a given polarization in the presence of DGD and SOPMD channels.
Estimating Parameters of Rotation Matrix
It is shown above that the equalizer for timing recovery can be approximated by a simple time-varying matrix transformation (e.g., a simple memoryless rotation matrix M, as in (23a)). A method is now described to compute the components of the rotation matrix M. By observing the channel response H(ω), the effect on the timing tone can be computed by applying a rotation matrix M. In general, H(ω) is not precisely known, but it can be approximated based on an equalizer response as described below. While matrix M is generally referred to herein as a rotation matrix for consistency with the example mathematical explanation described, this matrix M may comprise a more general transformation matrix in some embodiments. For example, in one embodiment, the matrix M may have the general form of (5a), in which both an angle and phase term are introduced, or its conjugate transpose as in (23a), or a more general rotation as in
in which both an angle and two phase terms are introduced. In other embodiments, a transformation matrix having a different form may be used as matrix M.
In one embodiment described below, matrix M comprises rotation matrix with respective angle and phase parameters θ,Φ. These parameters of the rotation matrix M can be estimated according to the following technique. Let {tilde over (H)}(ω) be the channel transfer matrix at the output of a linear transformation with a generic rotation matrix M({tilde over (θ)},{tilde over (Φ)})=RH({tilde over (θ)},{tilde over (Φ)}), i.e.,
with H(ω) given by (1) and S(ω) given by (2) (again assuming that the CD is completely compensated as described above). Since the timing tone level is maximum at the optimal values of {tilde over (θ)} and {tilde over (Φ)}, their estimation can be achieved by maximizing the clock signal energy, that is,
where {tilde over (z)}x,1({tilde over (θ)},{tilde over (Φ)}) is derived from (10) with U(ω)→Ũ(ω) and V(ω)→{tilde over (V)}(ω). Since S(ω) is a diagonal matrix with elements S(ω) (see (2)), the optimal values of {tilde over (θ)} and {tilde over (Φ)} are independent of the pulse s(t).
The channel transfer matrix H(ω) should be estimated at the receiver in order to evaluate the timing tone amplitude |{tilde over (z)}x,1({tilde over (θ)},{tilde over (Φ)}|2. This task can be carried out by using the response of the equalizer (414, described below) used for PMD compensation. Let
be the frequency response matrix of a PMD equalizer in the receiver. The zero-forcing equalizer response is given by
F(ω)=H−1(ω)=S−1(ω)JH(ω). (29)
A matrix G(ω) is defined as:
where H denotes complex conjugate and transpose. From (29) it is observed that
G(ω)=J(ω)P(ω), (31)
where P(ω)=[S−1(ω)]*. Then, a linear transformation is defined:
From (26) and (31), the following can be derived:
Taking into account that only Ũ(ω) and {tilde over (V)}(ω) depend on {tilde over (θ)} and {tilde over (Φ)} from (26) and (32), it can be shown that criteria (27) is equivalent to
where {circumflex over ({tilde over (z)}x,1({tilde over (θ)},{tilde over (Φ)}) is the timing tone amplitude obtained from (10) with U(ω)→Ũ(ω), V(ω)→{tilde over (V)}(ω) and S(ω)→P(ω)=1/S*(ω).
Note that {circumflex over ({tilde over (z)}x,1({tilde over (θ)},{tilde over (Φ)}) can be derived from the equalizer response through matrix (32) as follows:
(36) can be rewritten as
{circumflex over ({tilde over (z)}x,1({tilde over (θ)},{tilde over (Φ)})=α+β+cos(2{tilde over (θ)})(α−β)+sin(2{tilde over (θ)})(ej{tilde over (Φ)}+δe−j{tilde over (Φ)}), (37)
where α, β, ξ, and δ are complex parameters independent of the phases ({tilde over (θ)},{tilde over (Φ)}) and given as follows:
α=ε11/11+ε12/12
β=ε21/21+ε22/22
=ε11/21+ε12/22
ε=ε21/11+ε22/12
where
The parameters α, β, ξ, and δ are derived directly from the matrix response of the equalizer G(ω)=FH(ω). Furthermore, it can be seen from the (37) that {circumflex over ({tilde over (z)}x,1({tilde over (θ)},{tilde over (Φ)})={circumflex over ({tilde over (z)}x,1({tilde over (θ)}+mπ,{tilde over (Φ)}) with m integer. Therefore the optimal solution {circumflex over (θ)}op is not unique for {circumflex over (θ)}op∈{−π,π}. Furthermore, if {circumflex over (θ)}op=0, the timing tone coefficient is independent of the phase {tilde over (Φ)}.
The maximization in (35) can be carried out iteratively by using a gradient algorithm as follows:
({tilde over (θ)}i+1{tilde over (Φ)}i+1)=({tilde over (θ)}i{tilde over (Φ)}i)+μ∇({tilde over (θ)}
Where μ is the step size, Niter is the total number of iterations, and
Taking into account that, e.g.,
from (37) it is possible to show
where {•} denotes imaginary part.
Implementation in Digital Receivers with FSE
Evaluation of the Timing Tone Amplitude
An example implementation is now described in which a multiple-input multiple-output (MIMO) T/2 fractional-spaced equalizer (FSE) is used for PMD compensation. Similar principles may be applied to embodiments using other types of equalizers.
Let {tilde over (g)}ab(t) be the continuous time pulse given by {tilde over (g)}ab(t)=F−1{{tilde over (G)}ab(jω)}, with a,b∈{1,2}. Let
denote the Fourier transform of the discrete-time pulse {tilde over (g)}ab[k]={tilde over (g)}ab(kT/2). Assuming that the bandwidth excess of the received signal is lower than 100% (i.e., |Gab(jω)|=0 for |ω|>2π/T), it can be verified that
From (36) and (42) the timing tone amplitude {circumflex over ({tilde over (z)}x,1({tilde over (θ)},{tilde over (Φ)}) results in
where Ω=ωT/2 and K0 is a predetermined constant (i.e., it does not depend on ({tilde over (θ)},{tilde over (Φ)})). In order to simplify the evaluation of {circumflex over ({tilde over (z)}x,1({tilde over (θ)},{tilde over (Φ)}), it is assumed that the terms {tilde over (G)}ab(ω){tilde over (G)}*ab
in (36) are concentrated around ω=π/T. Thus,
Furthermore, the integral can be approximated by a sum of discrete values of the Fourier transforms around Ω=π/2, i.e.,
where K1 is a certain factor independent of ({tilde over (θ)},{tilde over (Φ)}),
with N being the number of taps of {tilde over (g)}ab[k].
Based on (45), it is possible to show that
{circumflex over ({tilde over (z)}x,1({tilde over (θ)},{tilde over (Φ)})≈K2{circumflex over ({tilde over (z)}′x,1({tilde over (θ)},{tilde over (Φ)}), (47)
where K2 is a constant factor,
{circumflex over ({tilde over (z)}′x,1({tilde over (θ)},{tilde over (Φ)})={circumflex over (α)}+{circumflex over (β)}+cos(2{tilde over (θ)})({circumflex over (α)}−{tilde over (β)})+sin(2{tilde over (θ)})(ej{tilde over (Φ)}+{circumflex over (δ)}e−{tilde over (Φ)}), (48)
while
{circumflex over (α)}={circumflex over (ε)}11/11+{circumflex over (ε)}12/12, {circumflex over (β)}={circumflex over (ε)}21/21+{circumflex over (ε)}22/22,
{circumflex over (ξ)}={circumflex over (ε)}11/21+{circumflex over (ε)}12/22, {circumflex over (ε)}={circumflex over (ε)}21/11+{circumflex over (ε)}22/12, (49)
with
Let
be the discrete-time impulse response of the MIMO FSE. Then, from (30), {circumflex over (ε)}ab/cd can be derived directly from the impulse response of the FSE:
with
g11[k]=f*11[N−k−1], g12[k]=f*21[N−k−1],
g21[k]=f*12[N−k−1], g22[k]=f*22[N−k−1],
k=0,1, . . . , N−1. (52)
As will be shown below, the set
provides very good accuracy to maximize the timing tone energy.
Gradient Algorithm Based Maximization
Since factor K2 in (47) is independent of ({tilde over (θ)},{tilde over (Φ)}), criteria (35) reduces to
where {circumflex over ({tilde over (z)}′x,1({tilde over (θ)},{tilde over (Φ)}) is given by (48). As described previously, maximization in (53) can be carried out iteratively by using the gradient algorithm as follows:
({tilde over (θ)}i+1,{tilde over (Φ)}i+1)=({tilde over (θ)}i,{tilde over (Φ)}i)+μ∇({tilde over (θ)}
where
with
The technique described above will achieve best performance when there is an initial convergence of the FSE. Towards this end, a proper start-up strategy of the receiver is desired.
Receiver Architecture with PMD Compensation
In an ideal optical fiber transmitting a dual-polarized optical signal, the two polarization components of the optical signal will travel through fiber at the same speed. However, in a real fiber, imperfections can result in the two polarization components traveling at different speeds, which can be modeled as a random time delay between the two polarizations and a different spreading of the two polarizations. A measure of the time delay between the two polarizations is referred to as DGD, which depends on both the length and the quality of the fiber. Channel impairments may result in both first order and second order PMD effects; DGD (or first-order PMD) is a frequency-independent delay between the two polarizations, and second-order PMD is a frequency dependent delay between the two polarizations, resulting in different pulse spreading on the two polarizations. Moreover, the DGD is not necessarily constant over time. Thus, DGD/SOPMD block 402 represents the PMD introduced by the channel and how the PMD changes over time. As shown above, the PMD becomes particularly problematic for timing recovery when the DGD is half the symbol period. It can also be problematic when the DGD exceeds half the symbol period when there is also second order PMD present.
The polarization rotation block 404 models polarization rotation of the optical signal as it propagates through the channel 130 with a rotation frequency frx, where the rotation frequency here means how fast the state of polarization is changing on the Poincare sphere, measured in Hz. As the state of polarization changes at the output of the channel 130, a new matrix M for the matrix rotator 414 is used to track the state of polarization to mitigate problems with timing recovery. Thus, as frx increases, the update rate of the matrix rotator will increase.
As described above, optical front end 150 receives the optical signal and produces an electrical signal representing the polarization components as, for example, a two-dimensional complex vector (or alternatively as four dimensional vector of real components). The Rx AFE 168 samples the analog signal vector produced by the optical front end 150 based on a clock signal 181 to convert the analog electrical signal vector to the digital domain for processing by the Rx DSP 166. The Rx DSP 166 processes the digitized signal (e.g., a vector) to compensate for the channel impairments described above and recover the transmitted data. Furthermore, the Rx DSP 166 processes the digitized signal to generate the clock signal 181 for sampling the received analog signal.
In the illustrated embodiment, operation of the Rx DSP 166 is illustrated in terms of functional blocks representing various functions carried out by the Rx DSP 166. In practice, the illustrated functional blocks may be implemented as instructions stored to a non-transitory computer-readable storage medium that are loaded and executed by the Rx DSP 166. In alternative embodiments, all or portions of the functions described herein may be implemented in hardware, software, firmware, or a combination of hardware, software, and/or firmware.
In one embodiment, the Rx DSP 166 comprises a matrix rotator 414, an equalizer 416 (e.g., a fractionally spaced equalizer (FSE)), a rotation and phase estimator 422, a matrix updater 424, and the timing recovery block 179. The matrix rotator 414 is configured to approximate a transfer function that reduces or eliminates the effect of PMD on the timing tone energy. In general, the matrix rotator 414 orients the received signal vector to minimize problems in the timing recovery loop indicated by the clock feedback from the timing recovery 179. For example, in one embodiment, matrix rotator 414 applies a rotation matrix M to the digital signal from the Rx AFE 168 based on a matrix received from matrix updater 424 in a feedback loop. Operation of the matrix rotator 414 is described in further detail below.
Based on the compensated signal from the matrix rotator 414, timing recovery block 179 performs a timing recovery algorithm to generate clock signal 181 used to sample the analog signal in the Rx AFE 168. For example, in one embodiment, timing recovery is achieved using the nonlinear spectral line method and may be based on either one or two polarizations, as discussed above.
Equalizer 416 (which in one embodiment is a fractionally-spaced equalizer (FSE)) equalizes the compensated signal from the matrix rotator 414 to compensate for various channel impairments such as intersymbol interference effects. For example, in one embodiment, equalizer 416 applies a transfer function to received digital samples to generate equalized samples. Each equalized sample comprises a weighted average of a given digital sample and one or more other samples. The weights may be dynamically updated to adjust to perceived channel impairments. The primary purpose of the equalizer 416 is to remove pulse spreading and intersymbol interference caused by time-varying impairments in the channel 130.
Rotation and phase estimator 422 estimates rotation and phase parameters θ, Φ, of the rotation matrix M applied by the matrix rotator 414. This estimation may be based on the transfer function applied by equalizer 416 as will be described below. Thus, the rotation and phase parameters may be dynamically updated over time.
Matrix updater 424 updates the rotation matrix M applied by matrix rotator 414 based on the rotation and phase parameters, θ, Φ, generated by rotation and phase estimator 422. For example, in one embodiment, matrix updater 424 applies the update periodically with frequency fm.
Note that the embodiment of
As will be apparent, other variations of the disclosed architecture are also possible.
Beginning with
Mn=M′nMn−1.
Matrix updater 424 may optionally apply 612 an interpolator to smooth the update. For example, instead of transitioning directly from matrix Mn−1 to matrix Mn matrix updater 424 may apply incremental updates over time (e.g., in k steps) to ensure a smoother transition. In some embodiments, matrix updater 424 may instead transition directly from matrix Mn−1 to matrix Mn (e.g., k=1). The process of
Matrix updater 424 may optionally apply 662 an interpolator to smooth the update. For example, instead of transitioning directly from matrix Mn−1 to matrix Mn matrix updater 424 may apply incremental updates over time (e.g., in k steps) to ensure a smoother transition. In some embodiments, the matrix updater 424 may transition directly from matrix Mn−1 to matrix Mn (e.g., k=1). The process of
Numerical Results for Example Embodiment
Time Invariant Optical Channels
Example simulations of the timing recovery technique described above is now described for example transmissions over optical channels in the presence of PMD and second-order PMD (SOPMD). Example results are illustrated in
For example,
({tilde over (θ)}i+1,{tilde over (Φ)}i+1)=({tilde over (θ)}i,{tilde over (Φ)}i)+μsign(∇({tilde over (θ)}
where sign(•) is the sign function. The number of iterations and the step size are Niter=20 and μ=2−4, respectively. The number of taps of the FSE is N=16 (see (46)) and the optical signal-to-noise ratio (OSNR) is 10 dB.
From
Time Variant Optical Channels
where fRx is the polarization rotation frequency at the input of the receiver (introduced in block 404 of the channel model) and fM is the update frequency of the rotation matrix (applied by block 424). From
Although the detailed description contains many specifics, these should not be construed as limiting the scope but merely as illustrating different examples and aspects of the described embodiments. It should be appreciated that the scope of the described embodiments includes other embodiments not discussed in detail above. For example, the functionality of the various components and the processes described above can be performed by hardware, firmware, software, and/or combinations thereof.
Various other modifications, changes and variations which will be apparent to those skilled in the art may be made in the arrangement, operation and details of the method and apparatus of the described embodiments disclosed herein without departing from the spirit and scope of the invention as defined in the appended claims. Therefore, the scope of the invention should be determined by the appended claims and their legal equivalents.
This application claims priority under 35 U.S.C. §119(e) to U.S. Provisional Patent Application Ser. No. 61/527,013 entitled “Timing Recovery for Optical Coherent Receiver in the Presence of PMD” filed Aug. 24, 2011 to Mario R. Hueda, et al. and to U.S. Provisional Patent Application Ser. No. 61/676,943 entitled “Timing Recovery for Optical Coherent Receivers in the Presence of Polarization Mode Dispersion (PMD),” filed on Jul. 28, 2012 to Mario R. Hueda, et al., the content of which are each incorporated by reference herein.
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Number | Date | Country | |
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61676943 | Jul 2012 | US | |
61527013 | Aug 2011 | US |