This disclosure relates to the use of non-linear equalizers in a physical layer transceiver. More particularly, this disclosure relates to the use of non-linear neural-network equalizers in the transmit and receive paths of a physical layer transceiver such as an Ethernet physical layer transceiver, as well as for cancellation echo, near-end crosstalk, and far-end crosstalk.
The background description provided herein is for the purpose of generally presenting the context of the disclosure. Work of the inventors hereof, to the extent the work is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted to be prior art against the subject matter of the present disclosure.
Many integrated circuit devices, particularly “systems-on-chip” (SoCs), include high-speed serial links between various device components (such as the individual silicon dice in an SoC). Typical high-speed serial links of that type, commonly known as “SERDES” (serializer/deserializer), may suffer from significant non-linearity or channel impairment in the signal path, as a result of, e.g., insertion loss, inter-symbol-interference (ISI), and, in an optical system, non-linearities such as dispersion loss, or, in a copper (i.e., wired) system, cross-talk, jitter, etc. Various forms of linear equalization typically are used, at the receiver end of such links, to attempt to mitigate such channel impairments. However, linear equalization may not be sufficient to compensate for such non-linearities, particularly when the signal levels (e.g., voltage levels) to be distinguished in a data signal are close together and there is a low signal-to-noise ratio (SNR).
In accordance with implementations of the subject matter of this disclosure, a physical layer transceiver for connecting a host device to a wireline channel medium includes a host interface for coupling to the host device, a line interface for coupling to the wireline channel medium, a transmit path operatively coupled to the host interface and the line interface, including circuitry for encoding host data and driving encoded host data onto the wireline channel medium, a receive path operatively coupled to the line interface and the host interface, including circuitry for decoding data received from the wireline channel medium and passing the decoded data to the host interface, and adaptive filter circuitry operatively coupled to at least one of the transmit path and the receive path for filtering signals on the at least one of the transmit path and the receive path, the adaptive filter circuitry comprising a non-linear equalizer.
In a first implementation of such a physical layer transceiver, the adaptive filter circuitry may include a non-linear equalizer inline in the transmit path and configured to equalize transmit signals.
In a second implementation of such a physical layer transceiver, the adaptive filter circuitry may include a non-linear equalizer inline in the receive path and configured to equalize received signals.
In a third implementation of the subject matter of this disclosure, the adaptive filter circuitry may include non-linear echo cancellation circuitry coupled to both the transmit path and the receive path and configured to cancel echo between the transmit path and the receive path.
According to a first aspect of that third implementation, the adaptive filter circuitry may include non-linear echo cancellation circuitry operating in an analog domain of the physical layer transceiver.
According to a second aspect of that third implementation, the adaptive filter circuitry may include non-linear echo cancellation circuitry operating in a digital domain of the physical layer transceiver.
According to a fourth aspect of that third implementation, the adaptive filter circuitry may include non-linear crosstalk cancellation circuitry coupled to both the transmit path and the receive path for cancelling at least one of (a) near-end crosstalk, and (b) far-end crosstalk, between the transmit path and the receive path.
A fourth implementation of such a physical layer transceiver may further include adaptation circuitry configured to compare output of the adaptive filter circuitry to known data and to adapt the adaptive filter circuitry based on a cost function to reduce error in the output on a subsequent iteration.
In a fifth implementation of such a physical layer transceiver, the adaptation circuitry may be configured to adapt the adaptive filter circuitry based on cross-entropy between a respective bit and a log-likelihood ratio corresponding to the respective bit.
In a sixth implementation of such a physical layer transceiver, the non-linear equalizer may include a neural network equalizer.
According to a first aspect of that sixth implementation, the neural network equalizer may include a multi-layer perceptron neural network equalizer.
According to a second aspect of that sixth implementation, the neural network equalizer may include a radial-basis function neural network equalizer.
According to a third aspect of that sixth implementation, the neural network equalizer may be a reduced complexity neural network equalizer including a front-end filter having a first number of inputs and a second number of outputs, the second number being smaller than the first number, and a neural network filter having as inputs the outputs of the front-end filter.
In a first instance of that third aspect of the sixth implementation, the front-end filter of the reduced complexity neural network equalizer may include a finite-impulse-response filter to reduce the first number of inputs to the second number of inputs.
In a seventh implementation of such physical layer transceiver, the non-linear equalizer may include a linear filter and a non-linear activation function.
According to a first aspect of that seventh implementation, the non-linear activation function may be a hyperbolic tangent function.
According to a first aspect of that seventh implementation, the non-linear activation function may be a sigmoid function.
In accordance with implementations of the subject matter of this disclosure, a method of filtering interference in a physical layer transceiver for connecting a host device to a wireline channel medium includes performing non-linear equalization on at least one of the transmit path and the receive path for filtering signals on the at least one of the transmit path and the receive path, and adapting the non-linear equalizer based on cross-entropy between equalizer output and data signals on the wireline channel medium.
In a first implementation of such a method, performing non-linear equalization on at least one of the transmit path and the receive path may include performing non-linear equalization inline in the transmit path to equalize transmit signals.
In a second implementation of such a method, performing non-linear equalization on at least one of the transmit path and the receive path may include performing non-linear equalization inline in the receive path to equalize received signals.
In a third implementation of such a method, performing non-linear equalization may include performing non-linear echo cancellation between the transmit path and the receive path.
In a fourth implementation of such a method, performing non-linear equalization may include performing non-linear crosstalk cancellation for cancelling at least one of (a) near-end crosstalk, and (b) far-end crosstalk, between the transmit path and the receive path.
In a fifth implementation of such a method, performing non-linear equalization may include applying a non-linear activation function and performing linear filtering.
According to a first aspect of that fifth implementation, applying a non-linear activation function may include applying a hyperbolic tangent function.
According to a second aspect of that fifth implementation, applying a non-linear activation function may include applying a sigmoid function.
A sixth implementation of such a method may further include applying initial filtering of equalization inputs prior to performing the non-linear equalization, to reduce complexity by reducing number of inputs to the non-linear equalization.
According to a first aspect of that sixth implementation, applying initial filtering may include applying finite-impulse-response filtering.
Further features of the disclosure, its nature and various advantages, will be apparent upon consideration of the following detailed description, taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout, and in which:
As noted above, integrated circuit devices may include high-speed SERDES links between various device components. Typical SERDES links may suffer from significant non-linearity or channel impairment in the signal path, as a result of, e.g., insertion loss, inter-symbol-interference (ISI), and, in an optical system, non-linearities such as dispersion loss or, in a copper (i.e., wireline) system, cross-talk, jitter, etc. Various forms of linear equalization typically are used, at the receiver end of such links, to attempt to deal with such channel impairments.
However, particularly in an Ethernet physical layer transceiver (PHY), linear equalization may not be sufficient to compensate for such non-linearities, because the signal levels (e.g., voltage levels) to be distinguished in a data signal may be close together. For example, as opposed to typical non-return-to-zero (NRZ) signaling, which uses two levels to represent ‘0’ and ‘1’, a SERDES in an SoC device may use 4-level pulse-amplitude modulation (PAM4) signaling having four voltage levels, but with the same maximum voltage swing as NRZ signaling, to represent four possible two-bit symbols (‘00’, ‘01’, ‘10’, ‘11’). Moreover, Ethernet signaling may use an even higher modulation, such as 8-level pulse-amplitude modulation (PAM8) or 16-level pulse-amplitude modulation (PAM16) or higher. Thus, rather than one threshold within that voltage range dividing between two signal levels, there could be fifteen (or more) thresholds within the voltage range, dividing among as many as sixteen (or more) signal levels. Linear equalization may not be sufficient to correctly assign received samples near the thresholds between levels to the correct transmitted bit or symbol when the thresholds are close together and the signal-to-noise ratio is low.
Moreover, in Ethernet-type signaling, there may be many signal sources on the channel contributing to various forms different of interference—particularly echoes, near-end crosstalk and far-end crosstalk.
In accordance with implementations of the subject matter of this disclosure, non-linear equalization is used to compensate for non-linearities in the PHY channel, as well as to cancel echoes, to cancel near-end crosstalk, and to cancel far-end crosstalk, thereby reducing the bit-error rate (BER). In different implementations, different types of non-linear equalizers may be used.
Conceptually, a linear equalizer performs the separation of samples for assignment to one level or another by effectively drawing a straight line between groups of samples plotted in a two-dimensional (e.g., (x, y)) space. In channels that are insufficiently linear, or where the levels are too close together, there may not be a straight line that can be drawn between samples from different levels on such a plot. A non-linear equalizer effectively re-maps the samples into a different, non-linear (e.g., radial or polar) space in which the samples from different levels may be separated by a straight line or other smooth curve.
A non-linear equalizer in accordance with implementations of the subject matter of this disclosure may be more or less complex. For example, a non-linear equalizer may have more or fewer variables, or taps, with complexity being proportional to the number of variables. In addition, a non-linear equalizer that operates at the bit level—i.e., operates separately on the bits of each symbol (e.g., two bits/symbol for PAM4 signaling) rather than on the symbol as a whole—may be less complex than a non-linear equalizer that operates at the symbol level. Either way, greater complexity yields greater performance when all other considerations are equal. However, greater complexity also may require greater device area and/or power consumption.
Types of non-linear equalizers that may be used in accordance with the subject matter of this disclosure may include multi-layer perceptron neural network (MLPNN) equalizers, and reduced-complexity multi-layer perceptron neural network (RC-MLPNN) equalizers, as well as radial-basis function neural network (RBFNN) equalizers, and reduced-complexity radial-basis function neural network (RC-RBFNN) equalizers, as described in more detail below.
Performance of the non-linear equalizer may be affected by the cost function used for adaptation of the equalizer. For example, according to implementations of the subject matter of this disclosure, the non-linear equalizer may use one of various different cost functions for adaptation, including either a minimum mean-square error (MMSE or MSE) cost function, or a cross-entropy (CE)-based cost function. A CE-based cost function may yield a better result than an MMSE cost function, but a CE-based cost function is more complex than an MMSE cost function.
Therefore, according to implementations of the subject matter of this disclosure, the choice of which form of non-linear equalizer to use, and of which cost function to use, may be a tradeoff of complexity (and therefore expense) versus performance.
The subject matter of this disclosure may be better understood by reference to
In the receiver path/channel 102 of transceiver 190, data may be received from the channel medium 180 at the hybrid coupler and transformer 145, and sent to an analog front end 151 of receiver 102, and then to an analog-to-digital converter (ADC) 152. An equalizer 153 can include one or more equalizers to remove interference. The output of the equalizer block 153 is sliced at slicer 154 and provided to a decoder 155—e.g., a forward-error correction (FEC) decoder—which outputs received data bits 156.
An analog echo canceller 161 may be provided between transmit path 101 and the analog domain of receive path 102 at 112. A digital echo canceller 162 may be provided between transmit path 101 and the digital domain of receive path 102 at 122. Crosstalk cancellers 163, which may filter near-end crosstalk, far-end crosstalk or both, also may be provided between transmit path 101 and the digital domain of receive path 102 at 122.
In accordance with implementations of the subject matter of this disclosure, any one or more of transmit equalizer 142, receiver equalizer 153, analog echo canceller 161, digital echo canceller 162, and crosstalk cancellers 163, may be based on non-linear filters, and particularly on non-linear neural network filters. Suitable non-linear neural network filters are described in copending, commonly-assigned U.S. patent application Ser. No. 17/248,658, filed Feb. 2, 2021 and copending, commonly-assigned U.S. patent application Ser. No. 17/648,831, filed Patent Application No. concurrently herewith, each of which is hereby incorporated herein by reference in its respective entirely.
An adaptation function 164 may compare log-likelihood ratios 165 output by equalizer 153 to output data bits 156 or, during a training mode, to training bits 166, to adapt the various non-linear equalizers 142, 153, 161, 162, 163.
The purpose of implementing equalization on the channel is to correct for various sources of interference referred to above and thereby effectively move samples that are on the wrong side of the threshold to the correct side of the threshold. Linear equalization effectively takes a plot of the samples in a two-dimensional (x, y) space and draws a straight line between the samples to indicate where the threshold ought to be. However, in a channel with non-linearities, there may be no straight line that can be drawn on that two-dimensional plot that would correctly separate the samples. In such a case, non-linear equalization can be used. Non-linear equalization may effectively remap the samples into a different space (e.g., having a different scale or coordinate system) in which there does exist a straight line that correctly separates the samples.
Alternatively, the non-linear equalization function may remap the samples into a space in which there exists some smooth curve other than a straight line that correctly separates the samples. For example, the non-linear equalization function may remap the samples into a polar-coordinate or radial space in which the samples are grouped into circular or annular bands that can be separated by circles or ellipses.
The advantage of non-linear equalization over linear equalization in a non-linear channel may be seen in a simplified illustration as shown in
However, a radial basis function
can be used to transform the XOR function from the linear Cartesian (x1, x2) space to a non-linear radial (φ(r1), φ(r2)) space as follows:
As discussed below, various types of non-linear equalizers are available. Whatever type of non-linear equalizer is used may be adaptive to account for changing channel conditions. Various forms of cost function may be used for adaptation, to reduce errors on subsequent iterations.
One type of adaptation function that may be used is minimum mean-squared error (MMSE), where the mean-squared error (MSE) is defined as the square of the norm of the difference between the equalized signal (Y) and the ideal signal (Ŷ). The equalizer may initially be adapted in a training mode in which the ideal signal values are available. Later, during run-time operation, the detected output values of the equalized channel should be close enough to the ideal values to be used for adaptation.
Another type of adaptation function that may be used is the cross-entropy (CE) between a training bit and its log-likelihood ratio (LLR). In particular, cost function circuitry may be configured to compute a cross-entropy value indicative of a difference between a probability distribution of the detected bit value (which is a function of the LLR signal) and a probability distribution of the training bit value. The cost function circuitry then adapts the equalizer by setting an equalizer parameter (e.g., one or more coefficients of filter taps of the equalizer) to a value that corresponds to a minimum cross-entropy value from among the computed cross-entropy values and one or more previously computed cross-entropy values, to decrease a bit-error rate for the channel. As in the case of MSE equalization, the equalizer may initially be adapted in a training mode in which the ideal signal values are available. Later, during run-time operation, the detected output values of the equalized channel should be close enough to the ideal values to be used for adaptation. Specifically, if any forward error correction code (FEC) decoder (e.g., a Reed Solomon (RS) decoder or Low-Density Parity Check (LDPC) decoder) is available after the equalizer, then successfully decoded frames from the FEC decoder output may be used for adaptation.
LLR may be defined as the relationship between the probability (P0) of a bit being ‘0’ and the probability (P1) of a bit being ‘1’:
The cross-entropy between a training bit and its LLR may be computed as follows:
When the true bit is a logic ‘0’ but the probability of the detected bit represented by the LLR indicates that P0=0, or the true bit is a logic ‘1’ but the probability of the detected bit represented by the LLR indicates that P1=0, then the true value is the complete opposite of the expected value, meaning that cost (cross-entropy) approaches infinity. On the other hand, when the probability of a detected bit value as indicated by the LLR agrees with the true bit value, then cross-entropy equals zero. Insofar as in most cases both probabilities P0 and P1 are higher than 0 and lower than 1, cross-entropy will be a finite non-zero value. Thus, this cost function can be used for adaptation and reflects the quality of the detected bits, with the goal being to minimize cross-entropy.
The gradient of cross-entropy with respect to the LLR may be computed by substituting for P0 and P1 in the cross-entropy equation:
The LLR may be adapted to minimize cross-entropy (i.e.,
as follows:
LLRt+i=LLRt−α·P1 if bit=0
LLRt+i=LLRt+α·P0 if bit=1
A negative LLR means bit=0 has a higher probability than bit=1, while a positive LLR means bit=1 has a higher probability than bit=0. In these equations, P0 and P1 are probabilities and therefore are positive values, and α is an adaptation bandwidth which also is positive. Therefore, when the true bit=0 then adaptation using cross-entropy will make a negative LLR more negative, and when the true bit=1 then adaptation using cross-entropy will make a positive LLR more positive. Therefore, cross-entropy-based adaptation maximizes the magnitude of the LLR and hence is a maximum-likelihood adaptation which reduces BER. Thus, adaptation of the equalizer to minimize cross-entropy also minimizes BER.
If one assumes that there is a general computation graph from parameter X→Y→LLR→CE such that parameter X affects the value of output Y which affects the LLR, from which the cross-entropy may be computed, then the cross-entropy gradient can be expressed in terms of other parameters:
Therefore, any parameter can be adapted to minimize the cross-entropy.
One suitable implementation of a non-linear filter that may be used in accordance with the subject matter of this disclosure is non-linear equalizer 401, seen in
As seen in
Each hidden node 451 multiplies delayed samples 421 (to avoid crowding the drawing, only one of delays 431 is shown as being coupled to nodes 451; however, each delay 431 is coupled to nodes 451) by parameters (filter tap coefficients; not shown) and then sums (Σ) the filter taps. Each hidden node 451 then applies to its computed sum a non-linear activation function (e.g., a hyperbolic tangent activation function, tanh (ƒ), although other non-linear activation functions may be used), to generate a node output, which is then passed to the next layer, and so on. The final layer 452 does not include a non-linear activation function but simply sums its inputs.
Hidden nodes 451 may receive inputs not only from feed-forward delays 431, but also from feed-back delays 461, representing samples 460 of a fed-back prior symbol decision 412 of slicer 402, which may be helpful in mitigating inter-symbol interference.
The aforementioned parameters of non-linear equalizer 401 are adapted based on the output Y. One approach for adapting the parameters of non-linear equalizer 401 is to compute at 472 the error (e) with respect to an ideal sample Ŷ derived from training symbols 469. Minimization of the mean square error at 473 may then be used as the cost function to adapt the filter tap coefficients at nodes 451 as indicated at 471.
As an alternative to multi-layer perceptron neural network 401, an implementation 500 (
Similarly to the case of non-linear equalizer 401, the parameters of non-linear equalizer 501 are adapted based on the output Y. One approach for adapting the parameters of non-linear equalizer 501 is to compute the error (e) with respect to an ideal sample Ŷ derived from training symbols 569. Minimization of the mean square error at 573 is then used as the cost function to adapt the filter tap coefficients of FIR filters 542, 543 as indicated at 571.
However, as described above, cross-entropy may serve as a more effective cost function for adapting the parameters of a non-linear equalizer to minimize BER.
implemented in circuitry 602 provides an output decision (sym) 612, which is fed back (after conversion at 648 to a voltage—e.g., −1 for ‘00’, −⅓ for ‘01’, +⅓ for ‘10’ and +1 for ‘11’, in the case of a 4-level signaling system such as PAM4) to multi-layer perceptron neural network 641 to mitigate inter-symbol interference from a previous symbol, and an output log-likelihood ratio (LLRsym) 622.
As in the case of
Each hidden node 651 multiplies delayed samples (to avoid crowding the drawing, only one of delays 631 is shown as being coupled to nodes 651; however, each delay 631 is coupled to nodes 651) by parameters (filter tap coefficients; not shown) and then sums (Σ) the filter taps. Each hidden node 651 then applies to its computed sum a non-linear activation function (e.g., a hyperbolic tangent activation function, tanh (ƒ), although other non-linear activation functions may be used), to generate a node output, which is then passed to the next layer, and so on. The final layer 652 does not have non-linear activation function but simply sums its inputs separately for each of the four symbols.
Hidden nodes 651 receive inputs not only from feed-forward delays 631, but also from feed-back delays 661, representing samples of a fed-back prior symbol decision 660, for mitigating inter-symbol interference.
Because equalizer 601 provides soft output in the form of an LLR, the output may be used with a further outer decoder (not shown), which may be a forward error-correcting (FEC) decoder such as a low-density parity check (LDPC) decoder or a Reed-Solomon decoder.
The aforementioned parameters of non-linear equalizer 601 may be adapted to minimize cross-entropy, using cross-entropy adaptation circuitry 670, between a training symbol () that is obtained by grouping training bits 671, and output log-likelihood ratio (LLRssym) 622. Cross-entropy adaptation circuitry 670 is able to adjust parameters of non-linear equalizer 601, at 680, to minimize the cross-entropy between the training symbol () and the probability of the detected symbol which is represented by LLRsym 622. During run-time, output bits 690 of an outer decoder (such as a Forward Error Correcting, or FEC, decoder; not shown), but only from successfully decoded frames, may be used in place of training bits 671.
Reduced-complexity multi-layer perceptron neural network 741 includes two feed-forward filters 746, 747, which may, e.g., be finite impulse response (FIR) filters. A non-linear activation function 748 (e.g., a hyperbolic tangent activation function, tanh (ƒ)), although other non-linear activation functions may be used) is applied to the output of feed-forward filter 746 which is then input to feed-forward filter 747. Symbol decision 744 is converted at 749 to a voltage for input to decision-feedback equalizer 742, the output of which is combined at 750 with the output of feed-forward filter 747 to mitigate inter-symbol interference from a previous symbol, to yield equalized signal (Y) 711.
The parameters of feed-forward filters 746, 747 may be adapted to minimize cross-entropy between output log-likelihood ratio (LLRsym) 745 and “true” symbols obtained from true bits which may be training bits or, during run-time, the output of a further outer decoder (not shown). Cross-entropy adaptation circuitry 760 has, as an input, the output log-likelihood ratio (LLRsym) 745. In a training mode, cross-entropy adaptation circuitry 760 also has as inputs known training bits 761, which serve as “true” bits which are then grouped to obtain true symbols. Cross-entropy adaptation circuitry 760 is able to adjust parameters of feed-forward filters 746, 747, at 770, by minimizing the cross-entropy between the training symbol obtained by grouping training bits () and the probability of the detected symbol which is represented by output log-likelihood ratio (LLRsym) 745. At run-time, output bits 790 of an outer decoder (such as an FEC decoder; not shown), but only from successfully decoded frames, may be used in place of training bits 761.
Because a neural network equalizer is capable of decorrelating the bits of a multi-bit symbol, such as the two bits in a PAM4 symbol, a further implementation 800 according to the subject matter of this disclosure may be provided (
MLPNN 841 differs from MLPNN 541 in that the final layer 852 includes two nodes 853, 854, in which the inputs are not merely summed as in layer 552 of MLPNN 541, but also have applied after summation a non-linear activation function, different from the non-linear activation function of nodes 851, that decorrelate the two bits of each symbol, with each node 853, 854 providing one of the two bits. The non-linear activation function of each node 853, 854 may be, instead of a hyperbolic tangent activation function, a sigmoid function having a profile similar to that of tanh (ƒ), but ranging from 0 to +1 rather than from −1 to +1.
Node 853 provides a probability estimate 863 (p(bitmsb)) for the most significant bit of the two bits in a symbol, and node 854 provides a probability estimate 864 (p(bitlsb)) for the least significant bit of the two bits of the symbol. The two probability estimates 863, 864 are then compared in slicers 855 to a threshold value of 0.5 to a obtain bit estimate (e.g., bit=0 if p<0.5 and bit=1 if p≥0.5) for each bit in the symbol.
In an implementation in which the signaling includes more than four levels (e.g., PAM8 or PAM16), there would be more bits per symbol (e.g., 3 or 4 bits, respectively). In such a case, there would be a corresponding number of nodes rather than just two nodes 853, 854.
At 856, the separate bits are grouped back into a symbol, then fed back at 857 and converted to a corresponding voltage at 858 (e.g., −1 for ‘00’, −⅓ for ‘01’, +⅓ for ‘10’ and +1 for ‘11’, in a 4-level signaling system such as PAM4) for input to feed-back delays 861, representing samples of a fed-back prior symbol decision relative to the next inputs from feed-forward delays 831, for mitigating inter-symbol interference.
Because implementation 800 operates at the bit level rather than at the symbol level, cross-entropy adaptation circuitry 870 also operates at the bit level, determining the cross-entropy based on the separate bit-level probabilities 863, 864 and the training bits 871, or at run-time, the output 890 of an outer decoder (such as an FEC decoder; not shown).
At the bit level, cross-entropy may be determined by first determining the log-likelihood ratios from the probability estimates as described above. Starting with the most significant bit, where P0 is p(bitmsb=0) and P1 is p(bitmsb=1), LLR(bitmsb) can be computed. CE(bitmsb) can then be computed from LLR(bitmsb) and the most significant bit of the training bits or the outer decoder bits. Then using p(bitlsb=0) as P0 and p(bitlsb=1) as P1, LLR(bitlsb) can be computed. CE(bitlsb) can then be computed from LLR(bitlsb) and the least significant bit of the training bits or the outer decoder bits. The bit level cross-entropy is the sum of CE(bitmsb)+CE(bitlsb).
Reduced-complexity multi-layer perceptron neural network 941 includes a first feed-forward filter 946, which may, e.g., be a finite impulse response (FIR) filter. A non-linear activation function 945 (e.g., a hyperbolic tangent activation function, tanh (ƒ), although other non-linear activation functions may be used) is applied to the output of feed-forward filter 946 which is then input to a second feed-forward filter 947, and in parallel to third feed-forward filter 957. Each of feed-forward filters 947, 957 produces a respective equalized bit output Ymsb 944, and Ylsb 954.
A respective non-linear activation function 961, 962, different from non-linear activation function 945, is applied to each respective equalized bit output Ymsb 944, and Ylsb 954. Non-linear activation functions 961, 962 may be, instead of a hyperbolic tangent activation function, a sigmoid function having a profile similar to that of tanh (ƒ), but ranging from 0 to +1 rather than from −1 to +1.
Non-linear activation function 961 provides a probability estimate p(bitmsb) for the most significant bit of the two bits in a symbol, and non-linear activation function 962 provides a probability estimate p(bitlsb) for the least significant bit of the two bits of the symbol. Each of the two probability estimates is then compared in a respective slicers 955, 956 to a threshold value of 0.5 to a obtain bit estimate (e.g., bit=0 if p<0.5 and bit=1 if p≥0.5) for each bit in the symbol.
At 970, the two bits are grouped into a symbol 971, and then converted to a corresponding voltage at 972 (e.g., −1 for ‘00’, −⅓ for ‘01’, +⅓ for ‘9’ and +1 for ‘11’) for input to decision feed-back equalizer 942 in the most-significant-bit path, and to decision feed-back equalizer 952 in the least-significant-bit path. The output of each respective decision feed-back equalizer 942, 952 is combined at 943, 953, respectively, with the output of respective feed-forward filter 947, 957 to mitigate inter-symbol interference from a previous symbol, to yield the respective equalized bit outputs Ymsb 944, and Ylsb 954 that are, as described above, input to non-linear activation functions 961, 962 to yield.
Cross-entropy may be determined, from p(bitmsb), p(bitmsb), and training bits 981 or outer decoder output 990, in cross-entropy adaptation circuitry 980 by, as in the case of implementation 800, first determining the log-likelihood ratios from the probability estimates as described above. Starting with the most significant bit, where P0 is p(bitmsb=0) and P1 is p(bitmsb=1), LLR(bitmsb) can be computed. CE(bitmsb) can then be computed from LLR(bitmsb) and the most significant bit of the training bits or the outer decoder bits. Then using p(bitlsb=0) as P0 and p(bitlsb=1) and P1, LLR(bitlsb) can be computed. CE(bitlsb) can then be computed from LLR(bitlsb) and the least significant bit of the training bits or the outer decoder bits. The bit level cross-entropy is the sum of CE(bitmsb)+CE(bitlsb).
A number of additional reduced-complexity implementations of non-linear neural network filters which may be used in accordance with the subject matter of this disclosure are illustrated in
A first implementation of a reduced-complexity non-linear neural network filter 1100, shown in
In radial-basis function non-linear neural network filter 1101, digital samples from two inputs 1111, 1121 are delayed by delay line 1131 and combined in radial-basis function non-linear neural network 1141. As seen in
Each sample input at 1111, 1121 adds a parameter or dimension to radial-basis function non-linear neural network filter 1101, increasing filter complexity. In order to reduce the complexity of radial-basis function non-linear neural network filter 1101, reduced-complexity non-linear neural network filter 1100 includes front-end filter 1102, which combines some of the inputs from ADC outputs 111, 121 to provide a reduced number of inputs 1111, 1121 to radial-basis function non-linear neural network filter 1101. As can be seen in
In the implementation of
A second implementation 1200 of a reduced-complexity non-linear neural network filter, shown in
However, in this implementation, rather than being summed, the taps of delay line 1212 are input directly to the hidden nodes 1250 of radial-basis function non-linear neural network filter stage 1201, which in this implementation are upstream of delay line 1231.
Once again, with inputs 111, 121 from two sources, half 1213 of delay line 1212 of front-end filter 1202 is devoted to input 111, while half 1214 of delay line 1212 of front-end filter 1202 is devoted to input 121, with one respective hidden node 1250 of radial-basis function non-linear neural network filter stage 1201 for each input source 111, 121. The same is true of delay line 1231 within radial-basis function non-linear neural network filter stage 1201, with separate halves 1232, 1233 of delay line 1231 devoted to inputs deriving separately from inputs 111, 121. Here too, the delays 1231 form individual taps of a final FIR filter, which are combined at summation node 1241 to yield the output Y.
A third implementation of a reduced-complexity non-linear neural network filter 1300, shown in
Typically, an MLP filter includes a delay line for input samples, followed by at least one hidden layer in which the samples are summed and then passed through a non-linear activation function such as, e.g., a hyperbolic tangent function tanh (ƒ), followed by a layer including one or more summations.
In finite-impulse-response-(FIR)-based front-end filter 1301, delay line 1331 is divided into a first portion 1332 receiving inputs 111 and a second portion 1333 receiving inputs 121. Each line connecting a delay 1312 to sum 1322 represents a multiplication of a sample by a coefficient (not shown; see discussion above in connection with
In this implementation, the boundary between the front-end filter 1301 and the MLP non-linear neural network filter 1302 runs through the hidden layer of hidden nodes 1350, but that is not necessarily the case in all implementations.
MLP non-linear neural network filter 1302 in this implementation includes a respective tanh (ƒ) non-linear activation function as part of each respective one of hidden nodes 1350 and a FIR filter formed by a delay line 1312 and a summation node 1322. A portion 1351 of delay line 1312 receives output samples 1311 from front-end filter 1302, while a portion 1352 of delay line 1312 receives output samples 1321 from front-end filter 1301. Each line connecting a delay 1312 to sum 1322 represents a multiplication of a sample by a coefficient (not shown; see discussion above in connection with
Reduced-complexity non-linear neural network filter 1300 may be represented as an equivalent filter arrangement 1400, shown in
FIR filters 1401, 1402 form finite-impulse-response-(FIR)-based front-end filter 1410, with FIR filter 1401 receiving inputs 111 while FIR filter 1402 receives inputs 121. FIR filters 1403, 1404 and non-linear activation functions 1405, 1406 form reduced-complexity non-linear neural network 1420. In reduced-complexity non-linear neural network 1420, activation function 1405 receives the outputs of FIR filter 1401 and passes those outputs, after non-linear activation, to FIR filter 1403, while activation function 1406 receives the outputs of FIR filter 1402 and passes those outputs, after non-linear activation, to FIR filter 1404. The outputs of FIR filter 1403 and FIR filter 1404 are combined at summation node 1408 to yield the output Y.
Another implementation of a reduced-complexity non-linear neural network filter 1500, shown in
The outputs 1541 of finite-impulse-response-(FIR)-based front-end filter 1501 are then filtered by multilayer perceptron (MLP) non-linear neural network filter 1502, which includes a non-linear activation function 1512 (which may be a tanh (ƒ) non-linear activation function), followed by FIR filter 1522.
In a variation 1600 of reduced-complexity non-linear neural network filter 1500, shown in
In addition, a non-linear function 1700 (particularly one that is close to a linear function 1701) can be approximated as a series of linear functions 1702 of different slopes, as shown in
A similar variation 1800, based on reduced-complexity non-linear neural network filter 1400, is shown in
In each of the implementations shown, additional filter layers or stages may be added (not shown). For example, when nonlinearity in the channel is severe or interference length in the time domain is longer, then more than one nonlinear transformation may be needed to separate signals. Each nonlinear stage would transform its input to a different space at the output. After multiple transformations, a final space would result where signals can be then linearly separated. In the implementations of
It can be shown that the various implementations of a reduced-complexity non-linear neural network filter shown above provide nearly as good performance as a non-reduced-complexity non-linear neural network filter, particularly when adapted using cross-entropy. However, the reduced complexity provides substantial savings in device area and power consumption.
A method 1900 according to implementations of the subject matter of this disclosure is diagrammed in
Method 1900 begins at 1901 where non-linear equalization is performed on at least one of the transmit path and the receive path in a physical layer transceiver for connecting a host device to a wireline channel medium, for filtering signals on the at least one of the transmit path and the receive path. At 1902, the non-linear equalization is adapted based on cross-entropy between equalizer output and data signals on the wireline channel medium, and method 1900 ends. However, as seen at 1903, optionally (indicated by dashed lines), initial filtering—e.g., finite-impulse-response (FIR) filtering—may be applied prior to the non-linear equalization to reduce complexity of the non-linear equalization.
As seen in
Thus it is seen that a physical layer transceiver using non-linear neural-network equalizers in the transmit and/or receive paths, and/or for cancellation echo, near-end crosstalk, and far-end crosstalk, has been provided.
As used herein and in the claims which follow, the construction “one of A and B” shall mean “A or B.”
It is noted that the foregoing is only illustrative of the principles of the invention, and that the invention can be practiced by other than the described embodiments, which are presented for purposes of illustration and not of limitation, and the present invention is limited only by the claims which follow.
This disclosure claims the benefit of, commonly-assigned U.S. Provisional Patent Application No. 63/141,460, filed Jan. 25, 2021, which is hereby incorporated by reference herein in its entirety.
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