Patent Description:
A signal that is transmitted on a channel in a communication system is typically subject to distortion. There are numerous possible sources of distortion in the channel, which may include optical and electrical components. For example, distortion may result from bandwidth-limited components in the channel (e.g., a wavelength selective switch (WSS)), which have passbands that cannot accommodate the entire bandwidth of the signal. The frequency spectrum of the signal may be cut-off or filtered due to these bandwidth-limited components. Another possible source of distortion is due to signaling at a rate that violates Nyquist criterion for interference-free reception, or what is known as Faster than Nyquist (FTN) signaling. In contrast to channel distortion, intentional FTN distortion can be known a-priori at the receiver side. <CIT> describes methods and an apparatuses for whitening colored noise in a communication system. <CIT> describes co-channel separation of communication signals. <CIT> describes iterative joint minimum mean square error decision feedback equalizer and turbo decoder. <CIT> describes systems for high speed, low-cost process for the demodulation and detection in EDGE wireless cellular systems.

Dispersive optical and electrical components are another potential source of distortion. Components in which the phase velocity of the signal is dependent on frequency exhibit chromatic dispersion (CD), and components in which the phase velocity of the signal is dependent on polarization exhibit polarization mode dispersion (PMD). CD and PMD may spread a signal as it propagates, leading to distortion.

Regardless of the source of distortion to the signal, the result may include spreading of the signal in the time-domain. This spreading leads to symbols in the signal overlapping in time with adjacent symbols, which is referred to as inter-symbol interference (ISI). Similar to other sources of interference, ISI typically degrades the performance of a communication system.

Equalization may be implemented on the receiver side to reverse the effects of distortion, and therefore reduce the ISI introduced by the channel. Equalization may be achieved using linear equalizers, such as time-domain (TD) or frequency domain (FD) multiple-input multiple output (MIMO) equalizers. Linear equalizers are generally simple to implement and their outputs can be efficiently used to estimate the channel impairments and equalize the ISI introduced by the channel. On the other hand, linear equalizers will also affect the noise associated with the signal. In some cases, the noise in the signal is amplified. A linear equalizer will affect noise at certain frequencies differently than noise at other frequencies. For example, noise amplification in the signal may be frequency-dependent. This is often referred to as noise coloring, as the noise can no longer be considered white noise. Noise coloring is detrimental to the performance of the receiver, and may lead to an increase in bit-error-rate (BER). This is why it is desirable to implement a second equalization stage or post-compensation stage to deal with the problem of noise correlation.

According to one aspect of the present disclosure, there is provided an apparatus for noise-whitening post-compensation, the apparatus comprising: a first whitening filter configured to filter a received signal comprising symbols to generate a first filtered signal; and a first decision feedback equalizer having an input coupled to an output of the first whitening filter to receive the first filtered signal, the first decision feedback equalizer configured to apply decision feedback equalization (DFE) to the first filtered signal to generate estimates for the symbols of the received signal, wherein the first decision feedback equalizer comprises: a feed-forward filter (FFF) having an input and an output; a first combiner having a first input, a second input, and an output; a first decision device having an input and an output; and a feed-back filter (FBF) having an input and an output, wherein: the input of the FFF is coupled to the output of the first whitening filter to receive the first filtered signal generated by the first whitening filter; the first input of the first combiner is coupled to the output of the FFF to receive a second filtered signal generated by the FFF; the second input of the first combiner is coupled to the output of the FBF to receive a third filtered signal generated by the FBF; the input of the first decision device is coupled to the output of the first combiner to receive a first symbols estimate generated by the first combiner; the input of the FBF is coupled to the output of the first decision device to receive a second symbols estimate generated by the first decision device; the FFF is configured to feed-forward filter the first filtered signal to generate the second filtered signal; the first combiner is configured to combine the second filtered signal generated by the FFF and the third filtered signal generated by the FBF to generate the first symbols estimate; the first decision device is configured to generate the second symbols estimate based on the first symbols estimate; and the FBF is configured to filter the second symbols estimate to generate the third filtered signal.

In some embodiments, the first decision device is a soft decision device configured to generate at least one log likelihood ratio.

In some embodiments, the apparatus further comprises: a first reverser configured to reverse an order of the symbols of the received signal to generate a reversed signal; a second whitening filter having an input coupled to an output of the first reverser to receive the reversed signal, the second whitening filter configured to filter the reversed signal to generate a filtered reversed signal; a second decision feedback equalizer having an input coupled to an output of the second whitening filter to receive the filtered reversed signal, the second decision feedback equalizer configured to apply DFE to the filtered reversed signal to generate a reversed symbols estimate for the symbols of the reversed signal; a second reverser having an input coupled to an output of the second decision feedback equalizer to receive the reversed symbols estimate, the second reverser configured to reverse an order of the symbols of the reversed symbols estimate to generate a third symbols estimate; a second combiner having a first input coupled to an output of the second reverser to receive the third symbols estimate and having a second input coupled to the output of the FFF to receive the second symbols estimate, the second combiner configured to combine the third symbols estimate and the second symbols estimate to generate a fourth symbols estimate; and a second decision device having an input coupled to an output of the second combiner, the second decision device configured to generate a symbols decision based on the fourth symbols estimate.

In some embodiments, the apparatus further comprises: a noise predictor having an input coupled to the output of the second decision device to receive the symbols decision, the noise predictor configured to predict noise in the received signal; and a first subtractor having a input coupled to an output of the noise predictor to receive the predicted noise, the first subtractor configured to subtract the predicted noise from the received signal to generate a fifth symbols estimate.

In some embodiments, the noise predictor comprises: a second subtractor having an input coupled to the input of the noise predictor to receive the symbols decision, the second subtractor configured to subtract the symbols decision from the received signal to generate noise estimates; and a linear predictive coder having an input coupled to an output of the second subtractor to receive the noise estimates, the linear predictive coder having an output coupled to the output of the noise predictor and configured to apply linear predictive coding (LPC) to the noise estimates to generate the predicted noise.

In some embodiments, the linear predictive coder is further configured to calculate: z̃[n] = -q<NUM>z[n - <NUM>] - q<NUM>z[n - <NUM>]. - qMz[n - M] + e[n], wherein z̃ denotes the predicted noise, z denotes the noise estimates, n denotes a symbol index for the symbols of the received signal, q = q<NUM>, q<NUM>. qM denotes a prediction filter, and e denotes a prediction error.

In some embodiments, the first whitening filter and the prediction filter are based on same filter taps.

In some embodiments, the apparatus further comprises a soft-demapper having an input coupled to an output of the first subtractor to receive the fifth symbols estimate, the soft-demapper configured to soft-demap the fifth symbols estimate to generate a first set of log likelihood ratios (LLRs) for the fifth symbols estimate.

In some embodiments, the apparatus further comprises a forward error correction (FEC) decoder having an input coupled to an output soft-demapper to receive the first set of LLRs, the FEC decoder configured to FEC decode the first set of LLRs to generate a second set of LLRs.

In some embodiments, the apparatus further comprises a regenerator having an input coupled to an output of the FEC decoder to receive the second set of LLRs, the regenerator configured to regenerate the symbols of the received signal using the second set of LLRs.

In some embodiments, the apparatus further comprises a decoding loop having an input coupled to the output of the FEC decoder to receive the second set of LLRs, the decoding loop being configured to perform one or more iterations of decoding.

In some embodiments, the decoding loop comprises an output coupled to an input of the first decision feedback equalizer, the first decision feedback equalizer being configured to receive the second set of LLRs.

According to yet another aspect of the present disclosure, there is provided a method for noise whitening post-compensation in a receiver, the method comprising: applying a whitening filter to a received signal comprising symbols to generate a first filtered signal; applying decision feedback equalization (DFE) to the first filtered signal to generate estimates for the symbols of the received signal; wherein applying DFE to the first filtered signal comprises: feed-forward filtering the first filtered signal to generate a second filtered signal; combining the second filtered signal and a third filtered signal to generate a first symbols estimate; generating a second symbols estimate based on the first symbols estimate; and feed-back filtering the second symbols estimate to generate the third filtered signal.

Embodiments will now be described in detail with reference to the accompanying diagrams, in which:.

A solution to the aforementioned problem of noise coloring involves post-compensation through the use of a whitening filter followed by a post-compensation (non-linear) equalizer. Post-compensation is shown in <FIG>, which is a block diagram illustrating an example of a receiver implementing a post-compensation equalization process at the output of a linear (TD or FD MIMO) equalizer.

<FIG> illustrates a received signal input into a linear equalizer <NUM>. At the output of the linear equalizer <NUM>, an X polarization component and a Y polarization component are produced and input into a post-compensation block <NUM>. The outputs of the post-compensation block <NUM> are then input into a forward error correction (FEC) decoder <NUM>. Optionally, the output of the FEC decoder <NUM> may be fed back into the post-compensation block <NUM>, forming an FEC decoding loop as indicated at <NUM> in <FIG>. The linear equalizer <NUM>, post-compensation block <NUM> and the FEC decoder <NUM> may be implemented in whole or in part in hardware, firmware, one or more components that execute software, or some combination thereof. The equalizer of <FIG> may be part of a receiver unit.

The received signal in <FIG> includes a series of transmitted symbols, possibly filtered by the channel, and subjected to noise. In some embodiments, the received signal may be produced by the coherent detection of an optical signal at a receiver. In other embodiments, the received signal may be produced by the detection of a microwave signal at a receiver. Although the X polarization component and the Y polarization component are shown separately in <FIG>, these components may be instead treated together.

The linear equalizer <NUM> equalizes the received signal, which may reduce the associated ISI due to distortion. In some embodiments, the linear equalizer <NUM> is a 2x2 MIMO (or Butterfly) equalizer. However, other embodiments may use other types of linear equalizers. In some implementations of <FIG>, the received signal may be formatted as two orthogonal polarization components (X and Y polarizations), wherein each component may comprise two orthogonal phase components (an in-phase component I and a quadrature-phase component Q). The linear equalizer <NUM> separates the received signal into the X polarization component and the Y polarization component. Separating the X polarization component and Y polarization component may reduce ISI caused by PMD introduced by the channel. Other embodiments where the received signal is treated as a single component (i.e., not formatted as two orthogonal polarization components) are also contemplated.

As discussed above, the linear equalizer <NUM> causes amplification and coloring of the noise in the X polarization component and the Y polarization component. Unless appropriate correction is applied, this amplified and colored noise may significantly degrade the BER performance of the system, requiring a higher SNR (signal-to-noise ratio) to achieve error-free post-FEC decoding.

The signal at the output of the linear equalizer <NUM> may be denoted by rp[n], where p refers to the polarization of the signal (X or Y), and n is the symbol index of the received signal. The variable rp[n] may be expressed as: <MAT>.

Here, sp[n] is the transmitted symbol and z[n] is the colored additive noise. The colored additive noise may also be referred to as correlated additive noise.

To address the issue of noise coloring, the post-compensation block <NUM> is implemented, which includes a filter followed by a post-compensation equalizer. In some embodiments, the filter in the post-compensation block <NUM> is a whitening filter. The filter in the post-compensation block <NUM> reduces the coloring of noise in the X polarization component and the Y polarization component.

Following the filtering stage in the post-compensation block <NUM>, the colored noise is whitened. However, the symbols in the signal are now correlated as a result of the filtering. This correlation results in distortion of the X polarization component and the Y polarization component of the signal, leading to ISI. The purpose of the post-compensation non-linear equalizer in the post-compensation block <NUM> is to equalize the ISI due to this correlation, without amplifying or coloring the whitened noise as a result of filtering. As a result, the overall detection and decoding of the received signal is improved.

In some embodiments, the equalization in the post-compensation block <NUM> results in no noise enhancement or minimal noise enhancement.

Following the equalization in the post-compensation block <NUM>, the X polarization component and the Y polarization component are forwarded to the FEC decoder <NUM> for decoding. The FEC decoder decodes the X polarization component and the Y polarization component to produce decoded bits. In some embodiments, both the X and Y polarizations can be jointly encoded at the transmitter and decoded at the receiver. The FEC decoding may correct for detection errors of the received signal.

When using the optional FEC decoding loop <NUM>, the output of the post-compensation block <NUM> is sent to the FEC decoder <NUM> as a-priori information. Following an iteration of decoding, the FEC decoder <NUM> provides output or extrinsic information in terms of log-likelihood ratios (LLRs) to the post-compensation equalizer of the post-compensation block <NUM> as a-priori information for the next iteration of equalization. This process is known as turbo-equalization.

Post-compensation, such as that performed in the post-compensation block <NUM>, will now be discussed in greater detail.

Referring to <FIG>, shown is a block diagram illustrating an example of a post-compensator. <FIG> includes received symbols, a filter tap calculation block <NUM>, a filter <NUM> and an equalizer <NUM>. The received symbols are sent to the filter tap calculation block <NUM> and the filter <NUM>. The output from the filter tap calculation block <NUM> is also sent to the filter <NUM>. The outputs of the filter tap calculation block <NUM> and the filter <NUM> are sent to the equalizer <NUM>. The output of the equalizer <NUM> is then sent to an FEC decoder. The filter tap calculation block <NUM>, filter <NUM> and equalizer <NUM> may be implemented in whole or in part in hardware, firmware, one or more components that execute software, or some combination thereof. The post-compensator of <FIG> may be part of an equalizer. In some embodiments, the post-compensation block <NUM> of <FIG> includes the post-compensator illustrated in <FIG>.

The received symbols in <FIG> include colored noise, and may include one polarization or two polarizations. These received symbols may be received from a linear equalizer, such as linear equalizer <NUM> illustrated in <FIG>. In some embodiments, the received symbols relate to narrowband-filtered signals.

The filter tap calculation block <NUM> calculates filter taps, which characterize the quality of the channel and at least one of the transmitter and receiver, that the signal carrying the received symbols has traversed. This channel, and the at least one of the transmitter and receiver may be considered an effective channel that the signal carrying the received symbols has traversed. As noted above, this effective channel may include a linear equalizer. The filter taps also represent the noise coloring associated with the received symbols. The filter taps are denoted as g = g<NUM>, g<NUM>. gM, where M denotes the filter length. The filter taps may also be considered filter coefficients.

In some embodiments, the computation of these filter taps is based on pilot signals, which are signals that are known on the receiver side as well as on the transmitter side. The filter tap calculation may be performed using a variety of methods, including autoregressive spectrum estimation and adaptive methods such as least mean square.

In some implementations of <FIG>, the number of taps may be chosen to improve efficiency according to an estimated pattern, such that any tap value greater than a predefined percentage of the main tap is persevered. The filter taps may be real-valued or complex-valued.

In some implementations of <FIG>, the filter taps are calculated only once. However, in other implementations, the filter taps are re-calculated periodically.

Once the filter taps are calculated, they are sent to the filter <NUM>. In some embodiments, the filter <NUM> is a whitening filter used to whiten the colored noise associated with the received symbols. However, as discussed above, filtering the received symbols may lead to the filtered symbols becoming correlated.

The filtered signal output from the filter <NUM> is denoted as ap[n], which may be expressed as: <MAT>.

Here, ẑ[n] is the white additive noise produced by filtering the colored noise z[n] with the filter <NUM>.

The equalizer <NUM> may be considered a post-compensation equalizer, a non-linear equalizer, a post-compensation non-linear equalizer, or a second stage equalizer. Several different equalization methods may be used by the equalizer <NUM>. In one example, the equalizer <NUM> uses a BCJR (Bahl, Cocke, Jelinek and Raviv) method, which is the optimal symbol by symbol detector. In another example, the equalizer <NUM> uses a maximum likelihood sequence estimation (MLSE) method, such as a Viterbi algorithm or a soft output Viterbi algorithm (SOVA). The MLSE method is the optimal sequence detector. However, both the BCJR and MLSE methods may suffer from a large computation complexity.

The BCJR and MLSE methods, as well as the modified versions of the BCJR and MLSE methods including reduced-state and bi-directional methods, consist of a trellis structure. The computation complexity of the trellis increases exponentially as the symbol constellation size (e.g., QPSK (quadrature phase shift keying), <NUM>-QAM (quadrature amplitude modulation)) and the filter length increases. In addition, the trellis may introduce significant delays. These issues make the BCJR and MLSE methods difficult to implement in hardware when resources are limited, even with parallelization of the trellis structures. Resources that are limited in hardware equalizer implementations may include power, cooling capacity and number of gates.

The computational complexity and delays associated with the BCJR and MLSE methods are compounded when the post-compensation equalizer is implemented inside of a decoding loop, such as the FEC decoding loop <NUM> illustrated in <FIG>. In these implementations, the computational complexity and delay caused by the post-compensation equalizer can significantly limit the number of global decoding iterations, as well as the number of internal FEC decoding iterations.

Aspects of the present disclosure relate to post-compensation methods and post-compensators that can perform noise-whitening and post-compensation equalization with comparable BER performance to the optimal method using fewer resources. According to some of these aspects, the computational complexity and delay of the post-compensation methods increases linearly with symbol constellation size and whitening filter length. In addition, the post-compensation methods may be implemented in combination when better equalizer performance is required, or separately when a low computational complexity is required.

In some embodiments of the present disclosure, decision feedback equalization (DFE) is used as a method for post-compensation equalization. DFE is a non-linear equalization method that may exhibit improved BER performance compared to linear equalizers. DFE may be especially useful with severely distorted channels, for example, when the roots of the Z-transform of the channel impulse response are close to the unit circle. The computational complexity of the DFE method is also relatively low compared to the BCJR and MLSE methods. For example, the computational complexity of the DFE method increases linearly with symbol constellation size and whitening filter length.

Referring to <FIG>, shown is a block diagram illustrating an example of a post-compensator using a DFE method. <FIG> includes transmitted symbols s, whitening filter <NUM>, white additive noise ẑ, filtered signal a, feed-forward filter (FFF) <NUM>, estimated symbols s and decided symbols ŝ, decision device <NUM> and feed-backward filter (FBF) <NUM>. The transfer functions of the whitening filter <NUM>, the FFF <NUM> and FBF <NUM> are denoted as G(z), F(z), and B(z) - <NUM>, respectively. Here, z denotes a complex frequency-domain variable. Similar to the post-compensator of <FIG>, the post-compensator of <FIG> may be part of an equalizer. In some embodiments, the post-compensation block <NUM> of <FIG> includes the post-compensator illustrated in <FIG>.

In <FIG>, the transmitted symbols s are input to the whitening filter <NUM>. The output of the whitening filter <NUM> is combined with the white additive noise ẑ to form the filtered signal a. The filtered signal a is then input into the FFF <NUM>. The output of the FFF <NUM> is combined with the output of the FBF <NUM> to form the estimated symbols s. The estimated symbols s are input into the decision device <NUM>, which performs a soft or hard decision on the estimated symbols s and outputs the decided symbols ŝ. The decided symbols ŝ are then input into the FBF <NUM>.

The transmitted symbols s may be received from a linear equalizer, such as linear equalizer <NUM>, and are input into the whitening filter <NUM>. Although not shown in <FIG>, the whitening filter <NUM> reduces the noise coloring associated with the transmitted symbols s, producing white additive noise ẑ. As discussed above, the whitening filter <NUM> may also result in correlation of the transmitted symbols s. The filtered signal a is a combination of these correlated symbols and the white additive noise ẑ. It should be noted that although the transmitted symbols s and the white additive noise ẑ are shown as separate inputs in <FIG>, in practical applications the transmitted symbols and white additive noise would be received as one signal.

Similar to equation (<NUM>) discussed above, the filtered signal a illustrated in <FIG> may be expressed as: <MAT>.

The DFE method processes the filtered signal a and provides the decided symbols ŝ. The DFE method includes two main filters: FFF <NUM> and FBF <NUM>. Both filters may be optimized based on the minimum mean squared error (MMSE) criterion. The FFF <NUM> processes filtered signal a, and the FBF <NUM> forms a weighted linear combination of the previous symbol decisions by decision device <NUM>. The FBF <NUM> then cancels the ISI caused by the previous symbols from the output of the FFF <NUM> to produce the estimated symbols s. The estimated symbols s may be expressed as: <MAT>.

Here, f[k] and b[k] are the time-domain representations of F(z) = ∑kf[k]z-k, and B(z) = Σkb[k]z-k, respectively. LF and LB denote the number of taps for the FFF and FBF, respectively. Solving equation (<NUM>) for f and b, the following equations are produced: <MAT> <MAT>.

Here, D is the convolution matrix of the filter g, Φgg is the autocorrelation matrix of the filter taps g, σ<NUM> is the noise variance per real dimension and I is the identity matrix. In some implementations of <FIG>, the variables f and b are fixed after equations (<NUM>) and (<NUM>) are solved. However, in other implementations, the filter taps g are updated periodically, and therefore the variables f and b may be updated accordingly.

A problem associated with the implementation of the DFE method is the inverse matrix computation required in equation (<NUM>). However, this computation may be simplified by noting that the matrix, Λ = (Φgg - D DH) + σ<NUM>I, is a positive definite matrix. Therefore, Λ may be factorized into Λ = L * L', using Cholesky decomposition, where L is a lower triangular matrix. Therefore, Λ-<NUM> = (L * L')-<NUM> = L-<NUM>L'-<NUM>. Since L is a lower triangular matrix, the computation of the inverse of L can be implemented efficiently using row transformation operations.

The decision device may be implemented in whole or in part in hardware, firmware, one or more components that execute software, or some combination thereof. According to some embodiments of <FIG>, the decision device <NUM> is a hard decision device, such as a hard decision slicer, which makes one decision regarding each of the estimated symbols s. In these embodiments, decided symbols ŝ are hard decision symbols. The DFE method then operates under the assumption that the previous decisions are correct.

According to other embodiments, the decision device <NUM> is a soft decision device. A soft decision device requires knowledge of the noise variance in a signal and provides a better estimate of the decided symbols. A soft decision device may reduce the effect of error propagation in DFE compared to a hard decision device. In these embodiments, decided symbols ŝ are soft decision symbols. The soft decision device generates the soft decision symbols ŝ based on two steps. In the first step, the soft decision device computes the log likelihood ratio (LLR) λb of the bits constituting the estimated symbols s. This is also known as soft-demapping. In the second step, the soft decision device uses the computed LLRs to generate the soft decided symbols ŝ. By way of example, for a symbol with a QPSK constellation and separate processing per dimension of the constellation, these two steps may be performed as follows: <MAT> <MAT>.

In some embodiments, the implementation of the tanh function is performed using a look-up table consisting of relatively few elements by exploiting the following properties of the tanh function:.

When larger constellations are used, such as higher order QAM constellations, the computation of LLRs may become more computationally complex. However, some aspects of the present disclosure use simplified formulas for the computation of LLRs to reduce complexity, as described below.

<FIG> is a plot illustrating an example of a 16QAM constellation. <FIG> includes a real dimension on the x-axis, and an imaginary dimension on the y-axis. The locations of <NUM> symbols in the constellation are also illustrated.

For each dimension of the 16QAM constellation illustrated in <FIG>, the LLRs may calculated by: <MAT> <MAT>.

Here, d denotes the real or imaginary component of estimated symbols s. Using equations (<NUM>) and (<NUM>), the soft symbol estimate may be calculated by: <MAT> <MAT> <MAT>.

Although equations (<NUM>) to (<NUM>) do not represent an exact computation of LLRs, these equations may be less computationally complex than the exact calculation. The approximation of the tanh function described above may also be implemented in equations (<NUM>) and (<NUM>) to improve the speed and efficiency of the soft symbol decision device.

In further embodiments of the present disclosure, linear predictive coding (LPC) is used as a method for post-compensation equalization. LPC is the process of predicting the value of a sample based on a linear combination of past samples. The noise associated with the symbols received from a linear equalizer is correlated, and exploiting this noise correlation may lead to additional improvements in the operation of a post-compensation equalizer. In other words, the LPC method may be implemented to predict noise sample associated with a current received symbol based on the noise samples associated with past symbols.

Mathematically, predicted noise samples z̃ that are provided using the LPC method may be expressed as: <MAT>.

Here, q = q<NUM>, q<NUM>. qM represents a prediction filter, and e represents a prediction error. In some embodiments, the prediction filter that minimizes the mean square error (MSE) corresponds to the filter taps g discussed above, with the first tap set to zero, i.e., g(<NUM>)=<NUM>. In these embodiments, equation (<NUM>) may be expressed as: <MAT>.

The computational complexity associated with the implementation of the LPC method may be relatively low. For example, the LPC method is independent of constellation size and is linearly dependent on the length of the prediction filter. In some implementations, the length of the prediction filter may be <NUM>~<NUM>. One disadvantage of the LPC method is that it adds prediction error to the predicted noise samples. However, in some implementations of the LPC method the noise reduction due to subtracting the predicted noise samples is greater than the added prediction error, and therefore the LPC method is beneficial.

Referring to <FIG>, shown is a block diagram illustrating an example of a post-compensator using an LPC method. <FIG> includes received signal r, decision device <NUM>, decided symbols ŝ, subtractor <NUM>, colored additive noise z, filter taps g, LPC block <NUM>, predicted noise samples z̃, subtractor <NUM> and estimated symbols s̃. The received signal r is input into the decision device <NUM>, the subtractor <NUM> and the subtractor <NUM>. The decided symbols ŝ are output from the decision device <NUM> and also input into the subtractor <NUM>. The colored additive noise z is input into the LPC block <NUM>. The filter taps g are also input into the LPC block <NUM>. The predicted noise samples z̃ are output from the LPC block <NUM> and input into the subtractor <NUM>. The estimated symbols s̃ are output from the subtractor <NUM>.

In <FIG>, the received signal r is de-mapped using soft decisions or hard decisions. Therefore, the decision device <NUM> may be a soft decision device or a hard decision device. Similarly, the decided symbols ŝ may be soft decision symbols or hard decision symbols. In some embodiments, the decision device <NUM> is similar to the decision device <NUM>.

The decided symbols ŝ are subtracted from the received signal by subtractor <NUM> to give an estimate of the noise associated with the received symbols r. The estimate of the noise associated with the received symbols r is the colored additive noise z. The colored additive noise z is further processed using LPC to generate the predicted noise samples z̃. The LPC block <NUM> performs the LPC method on the colored additive noise z. The LPC block <NUM> may use equation <NUM> or equation <NUM> defined above to implement the LPC method. Predicted noise samples z̃ are subtracted from the received signal r using the subtractor <NUM> to produce the estimated symbols s̃. The subtractors <NUM> and <NUM> may be implemented in whole or in part in hardware, firmware, one or more components that execute software, or some combination thereof.

In some embodiments of the present disclosure, a combination of the DFE and LPE methods are used for post-compensation equalization. For example, the DFE method followed by the LPC method may be used for post-compensation equalization.

Referring to <FIG>, shown is a block diagram illustrating an example of a post-compensator using a bi-direction DFE method followed by an LPC method. <FIG> includes a received signal r, reverse symbol order blocks <NUM> and <NUM>, whitening filters <NUM> and <NUM>, DFE blocks <NUM> and <NUM>, estimated symbols s, s<NUM>, s<NUM> and s̃, noise estimate block <NUM>, filter taps g and LPC block <NUM>. The post-compensator of <FIG> may be part of an equalizer. In some embodiments, the post-compensation block <NUM> of <FIG> includes the post-compensator illustrated in <FIG>.

The received signal r is sent to the whitening filter <NUM>, which sends its output to the DFE block <NUM>, producing the estimated symbols s<NUM>. The received signal r is also sent to the reverse symbol order block <NUM>, which sends its output to the whitening filter <NUM> followed by the DFE block <NUM>, producing the estimated symbols s<NUM>. The output of the DFE block <NUM> is then sent to the reverse symbol order block <NUM>. The outputs of the DFE block <NUM> and the reverse symbol order block <NUM> are combined to form the estimated symbols s. The noise estimate block <NUM> computes noise estimates associated with the received signal r, which is sent to the LPC block <NUM>. The LPC block <NUM> then computes predicted noise associated with the received signal r, using the filter taps g as an input. The predicted noise associated with received signal r is then subtracted from the received signal r by subtractor <NUM> to produce the estimated symbols s̃.

The received signal r is an equalized signal with colored noise, and is a combination of the transmitted symbols s and the colored additive noise z. In some embodiments, the equalized signal r is an output of a linear equalizer, such as the linear equalizer <NUM>.

The combination of the whitening filter <NUM> and the DFE block <NUM> operates in a similar manner to the post-compensator illustrated in <FIG>. The combination of the whitening filter <NUM> and the DFE block <NUM> also operates in a similar manner to the post-compensator illustrated in <FIG>. However, the order of the transmitted symbols s in the received signal r has been reversed using the reverse symbol order block <NUM>. The reverse symbol order block <NUM> flips the sequence of symbols in the received signal r such that the first symbol becomes the last symbol. For example, reverse symbol order operation may be expressed as, r(end: -<NUM>: <NUM>). After the estimated symbols s<NUM> are produced, the order is reversed again using the reverse symbol order block <NUM> to match the symbol order in the estimated symbols s<NUM>. This concept of flipping the sequence order of a received signal is known as backward DFE, which may lead to different symbol estimates when compared with forward DFE.

In <FIG>, it is assumed that the filter g is a real-valued whitening filter. However, this may not be the case in all implementations of the bi-directional DFE method. In the case that g is a complex-valued whitening filter for the forward direction, in the reverse direction the whitening filter would be the conjugate of g.

The estimated symbols s<NUM> and s<NUM> are averaged to form the estimated symbols s. These estimated symbols s may have closer Euclidean distances to the transmitted symbols s when compared to the received signal r. This method of using forward DFE and backward DFE together is known as bi-directional DFE, which may lead to ~<NUM> dB gain in SNR compared with forward DFE alone. However, it should be appreciated that post-compensation using a DFE method followed by an LPC method may be performed without bi-directional DFE. According to some embodiments, only one of forward DFE and backward DFE is used in combination with the LPC method.

Following the generation of the estimated symbols s, a noise estimate associated with the received signal r is calculated by the noise estimate block <NUM>. In some implementations, the noise estimate block <NUM> performs this calculation using the equation, noise = r -f(s), where f(s) represents a decision device such as a hard or soft decision device. The decision device f(s) produces decisions for the estimated symbols s. In some embodiments, the decision device f(s) may operate in a manner similar to the decision device <NUM>. The calculation of noise may be performed, for example, by a subtractor. The noise estimates are then sent to LPC block <NUM>. The noise estimate produced by noise estimate block <NUM> may be considered a coarse noise estimate.

The LPC block <NUM> performs the LPC method on the noise estimates. The LPC block <NUM> may operate in a similar manner to the post-compensator illustrated in <FIG>. However, there is no decision device in the LPC block <NUM>. In <FIG>, the prediction filter used by the LPC block <NUM> is based on the filter taps g, which are also used by the whitening filters <NUM> and <NUM>. The LPC block <NUM> may perform the calculation shown in equation (<NUM>), where the noise calculated in the noise estimate block <NUM> is used as the values of z in equation (<NUM>). Since the noise associated with the received signal r is correlated, the LPC method may be used to predict the value of a current noise sample based on past noise samples. The LPC block <NUM> therefore produces a predicted noise associated with the received signal r. The combination of noise estimation block <NUM> and LPC block <NUM> may be considered a noise predictor. The predicted noise associated with the received signal r is then subtracted from the received signal r by subtractor <NUM> to form the estimated symbols s̃.

The post-compensator of <FIG> may exhibit improved BER performance compared with the DFE and LPC methods implemented separately. For example, using the LPC method in combination with the DFE method may result in ~<NUM>-<NUM> dB gain in SNR compared to the DFE method alone. In some implementations, the post-compensator of <FIG> exhibits comparable BER performance to the BCJR method while using fewer resources.

In some embodiments of the present disclosure, the post-compensators illustrated in <FIG>, <FIG> and <FIG> are implemented, at least in part, inside of a turbo-equalization loop, such as the turbo-equalization loop <NUM> illustrated in <FIG>. For example, a post-compensation equalizer may exchange a-priori information with an FEC decoder in order to improve at least one of detection and decoding performance. During each iteration of the turbo-equalization loop, the post-compensation equalizer equalizes a filtered signal. The post-compensation equalizer then outputs LLR values, which are scaled and sent to an FEC decoder as a-priori information for use during decoding. The output of the FEC decoder also includes LLR values, and is scaled and sent back to the post-compensation equalizer as a-priori information for use during post-compensation equalization in the following iteration.

In a turbo-equalization loop, the computational complexity and delay associated with the post-compensation equalizers may form a bottle-neck issue from an implementation point of view. According to some embodiments of the present disclosure, a low complexity implementation of a post-compensation equalizer that is suitable for turbo-equalization loops is provided, which produces a BER performance comparable to the BCJR and MLSE methods.

Referring to <FIG>, shown is a block diagram illustrating an example of a post-compensator with a turbo-equalization loop. <FIG> includes a received signal, a filter tap calculation block <NUM>, a filter <NUM>, a DFE/LPC block <NUM>, LLR calculation blocks <NUM> and <NUM>, an LPC block <NUM>, scaling blocks <NUM> and <NUM>, and an FEC decoder <NUM>.

In <FIG>, the received signal is sent to filter tap calculation block <NUM>. The received signal is also sent to the filter <NUM> and the LPC equalization block <NUM>. The output of the LPC equalization block <NUM> is sent to the LLR calculation block <NUM>. The output of the filter <NUM> is sent to the DFE/LPC block <NUM>. The output of the DFE/LPC block <NUM> is sent to the LLR calculation block <NUM>. The outputs of both the LLR calculation block <NUM> and the LLR calculation block <NUM> are sent to the scaling block <NUM>. The output of the scaling block <NUM> is sent to the FEC decoder <NUM>. The output of the FEC decoder <NUM> is sent to the scaling block <NUM>, and the output of scaling block <NUM> is sent to the LPC block <NUM>.

The received signal in <FIG> includes a series of transmitted symbols, as well as colored noise. The received signal may include one polarization or multiple polarizations. The received signal may be received from a linear equalizer, such as linear equalizer <NUM> illustrated in <FIG>.

The filter tap calculation block <NUM> of <FIG> is similar to the filter tap calculation block <NUM> of <FIG>. The filter tap calculation block <NUM> calculates filter taps for use in filter <NUM>. In some implementations, the filter taps are also used in the LPC prediction filter of the DFE/LPC block <NUM> and the LPC block <NUM>. The filter taps may be calculated once, or they may be calculated periodically.

After the filter taps are calculated, the post-compensator of <FIG> carries out multiple iterations of a turbo-equalization loop for each symbol in the received signal. In the first iteration of the turbo-equalization loop for a specific symbol, filtering using the filter <NUM> is performed to reduce the colored noise associated with the specific symbol. This filter is similar to the filter <NUM> illustrated in <FIG>. In some implementations, the filter <NUM> is a whitening filter.

Following the filter <NUM> in the first iteration, post-compensation equalization is performed in the DFE/LPC block <NUM>, which may use the DFE method, the LPC method, or a combination of the DFE method and the LPC method. In some implementations, post-compensation equalization is performed in the DFE/LPC block <NUM> using a method similar to the method illustrated in <FIG>. In other implementations, the DFE/LPC block <NUM> does not use the LPC method at all. In these implementations, post-compensation equalization may be performed in the DFE/LPC block <NUM> using the post-compensation equalization method illustrated in <FIG>. In further implementations, the DFE/LPC block <NUM> does not use the DFE method. In these implementations, post-compensation equalization may be performed in the DFE/LPC block <NUM> using the post-compensation equalization method illustrated in <FIG>.

The DFE/LPC block <NUM> produces an estimate of the specific symbol that is then sent to the LLR calculation block <NUM>. The calculation block <NUM> then computes an LLR value (or LLR values) for the estimate of the specific symbol. This LLR value is then sent to the scaling block <NUM>, which multiplies the LLR value by a scaling factor. Following the scaling block <NUM>, the LLR value is then sent to the FEC decoder <NUM>, which recovers the transmitted codeword. The scaling block <NUM> may be implemented, for example, if the FEC decoder <NUM> has a limited fixed point precision. It should be noted that the LPC block <NUM> is bypassed in the first iteration of the turbo-equalization loop.

In the second iteration of the turbo-equalization loop of <FIG>, output or extrinsic information from the FEC decoder <NUM> is scaled by the scaling block <NUM> and sent to the LPC block <NUM>. The LPC block <NUM> uses the scaled output or extrinsic information of the FEC decoder <NUM> as a-priori information to generate soft estimates of the transmitted symbols and uses these estimates to calculate an estimate of the noise by subtracting them from the received signal. Then a predicted noise associated with the received signal is computed by the LPC method. The predicted noise is subtracted from the received signal, which is followed by soft-demapping. LLR calculation block <NUM> performs the soft-demapping to produce an updated LLR value for the second iteration of the turbo-equalization loop. The updated LLR value is scaled and fed to the FEC decoder <NUM>. In some implementations, post-compensation equalization is performed in the LPC block <NUM> using a method similar to the method illustrated in <FIG>.

The updated LLRs of the soft symbol estimates that are sent to the FEC decoder <NUM> in the second iteration may be more accurate than the LLRs of the soft symbol estimate sent to the FEC decoder <NUM> in the first iteration. The post-equalization method of <FIG> may end after the second iteration. Alternatively, any number of additional iterations may also be performed to further improve the soft symbol estimates using the LPC block <NUM>. For example, a total of <NUM> or <NUM> iterations may be performed. It should be noted that the filter <NUM> and the DFE/LPC block <NUM> are bypassed in all iterations of the turbo-equalization loop after the first iteration. After all of the iterations of the turbo-equalization loop have been performed, the final LLRs at the output of the FEC decoder <NUM> may be used to regenerate the symbols in the received signal.

Although the LLR calculation blocks <NUM> and <NUM> are described as producing LLR values, in general, the LLR calculation blocks <NUM> and <NUM> may produce any appropriate reliability measure for the estimated symbols.

<FIG> is a flow diagram of example operations <NUM> for noise whitening post-compensation according to example embodiments described herein. In block <NUM>, a whitening filter is applied to a received signal comprising symbols to generate a first filtered signal. In block <NUM>, DFE is then applied to the first filtered signal to generate estimates for the symbols of the received signal. Optionally, in block <NUM>, noise in the received signal is predicted. Optionally, in block <NUM>, the predicted noise is then subtracted from the received signal to generate a symbols estimate. Optionally, in block <NUM>, soft-demapping is performed on the symbols estimate to generate a first set of LLRs for the symbols estimate. Optionally, in block <NUM>, FEC decoding is applied to the first set of LLRs to generate a second set of LLRs. Optionally, as indicated at <NUM>, example operations <NUM> may return to block <NUM> from block <NUM> as a part of performing one or more iterations of a decoding loop that sends the second set of LLRs as a-priori information for a subsequent iteration of the DFE applied to the first filtered signal.

The example operations <NUM> are illustrative of an example embodiment. Various ways to perform the illustrated operations, as well as examples of other operations that may be performed, are described herein. Further variations may be or become apparent.

For example, in some embodiments, applying DFE in block <NUM> may include feed-forward filtering the first filtered signal to generate a second filtered signal; combining the second filtered signal and a third filtered signal to generate a first symbols estimate; generating a second symbols estimate or decision based on the first symbols estimate; and feed-back filtering the second symbols estimate or decision to generate the third filtered signal. In further embodiments, generating the second symbols estimate or decision based on the first symbols estimate includes generating a soft symbols decision based on the first symbols estimate. In some embodiments, generating the soft symbols decision based on the first symbols estimate includes generating at least one log likelihood ratio.

In some embodiments, the example operations <NUM> also include reversing an order of the symbols of the received signal to generate a reversed signal; applying a whitening filter to the reversed signal to generate a filtered reversed signal; applying DFE to the filtered reversed signal to generate a reversed symbols estimate for the symbols of the reversed signal; reversing an order of the symbols of the reversed symbols estimate to generate a third symbols estimate; combining the second symbols estimate and the third symbols estimate to generate a fourth symbols estimate; and generating a symbols decision based on the fourth symbols estimate.

In some embodiments, block <NUM> includes subtracting the symbols decision from the received signal to generate noise estimates; and applying LPC to the noise estimates to generate the predicted noise. In further embodiments, applying LPC includes calculating: <MAT> where z̃ denotes the predicted noise, z denotes the noise estimates, n denotes a symbol index for the symbols of the received signal, q = q<NUM>, q<NUM>. qM denotes a prediction filter, and e denotes a prediction error. In other embodiments, applying a whitening filter to the received signal comprises generating filter taps, and applying LPC to the noise estimates comprises generating the prediction filter based on the filter taps.

In some embodiments, the example operations <NUM> also include regenerating the symbols of the received symbol using the second set of LLRs.

In some embodiments, the decoding loop indicated at <NUM> includes one or more iterations of a decoding loop that sends the second set of LLRs as a-priori information for a subsequent iteration of equalization different from the DFE applied to the first filtered signal.

<FIG> is a flow diagram of example operations <NUM> for noise whitening post-compensation according to example embodiments described herein. In block <NUM>, a symbols decision is generated based on a received signal. In block <NUM>, noise in the received signal is predicted based on the symbols decision. In block <NUM>, the predicted noise is then subtracted from the received signal to generate a symbols estimate. Optionally, in block <NUM>, soft-demapping is performed on the symbols estimate to generate a first set of LLRs for a symbols estimate. Optionally, in block <NUM>, FEC decoding is applied to the first set of LLRs to generate a second set of LLRs. Optionally, as indicated at <NUM>, example operations <NUM> may return to block <NUM> from block <NUM> as a part of performing one or more iterations of a decoding loop that sends the second set of LLRs as a-priori information for a subsequent iteration of predicting noise in the received signal.

For example, in some embodiments, the block <NUM> includes generating a soft symbol decision based on the received symbol. In other embodiments, the block <NUM> includes generating a hard symbol decision based on the received symbol.

In some embodiments, block <NUM> includes subtracting the symbols decision from the received signal to generate noise estimates and applying LPC to the noise estimates to generate the predicted noise. In further embodiments, applying LPC includes calculating: <MAT> where z̃ denotes the predicted noise, z denotes the noise estimates, n denotes a symbol index for the symbols of the received signal, q = q<NUM>, q<NUM>. qM denotes a prediction filter, and e denotes a prediction error. In other embodiments, applying a whitening filter to the received signal comprises generating filter taps, and applying LPC to the noise estimates comprises generating the prediction filter based on the filter taps.

In some embodiments, the decoding loop indicated at <NUM> includes one or more iterations of a decoding loop that sends the second set of LLRs as a-priori information for a subsequent iteration of equalization different from LPC.

What has been described is merely illustrative of the application of the principles of the disclosure. Other arrangements and methods can be implemented by those skilled in the art without departing from the scope of the present disclosure.

Hardware implementations of any block, module, component, or device exemplified herein may include electrical or optical circuitry, such as integrated circuits, printed circuit boards, discrete circuits, analog circuits, digital circuits and any combination thereof.

Claim 1:
An apparatus for noise-whitening post-compensation, the apparatus comprising:
a first whitening filter (<NUM>) configured to filter a received signal comprising symbols to generate a first filtered signal; and
a first decision feedback equalizer (<NUM>) having an input coupled to an output of the first whitening filter to receive the first filtered signal, the first decision feedback equalizer configured to apply decision feedback equalization to the first filtered signal to generate estimates for the symbols of the received signal, wherein the first decision feedback equalizer comprises:
a feed-forward filter FFF having an input and an output;
a first combiner having a first input, a second input, and an output;
a first decision device having an input and an output; and
a feed-back filter FBF having an input and an output,
wherein:
the input of the FFF is coupled to the output of the first whitening filter to receive the first filtered signal generated by the first whitening filter;
the first input of the first combiner is coupled to the output of the FFF to receive a second filtered signal generated by the FFF;
the second input of the first combiner is coupled to the output of the FBF to receive a third filtered signal generated by the FBF;
the input of the first decision device is coupled to the output of the first combiner to receive a first symbols estimate generated by the first combiner;
the input of the FBF is coupled to the output of the first decision device to receive a second symbols estimate generated by the first decision device;
the FFF is configured to feed-forward filter the first filtered signal to generate the second filtered signal;
the first combiner is configured to combine the second filtered signal generated by the FFF and the third filtered signal generated by the FBF to generate the first symbols estimate;
the first decision device is configured to generate the second symbols estimate based on the first symbols estimate; and
the FBF is configured to filter the second symbols estimate to generate the third filtered signal.