Joint adaptive optimization of soft decision device and feedback equalizer

Joint adaptive optimization of soft decision device and feedback equalizer
RE42558

The present invention uses a novel adaptive soft decision device in order to jointly optimize decision device and DFE operation. The soft decision device receives the input and output samples of the slicer and generates a feedback sample by non-linearly combining them with respect to a single decision reference parameter. Moreover, the soft decision device provides novel error terms used to adapt equalizer coefficients in order to jointly optimize decision device and equalizer coefficients.

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Patent RE42558
Priority Dec 18 2001
Filed Feb 20 2009
Issued Jul 19 2011
Expiry Dec 17 2022
Inventors Chung, Won…
Assg.orig Omereen Wi…
Assg.curr CALLAHAN C…
Entity Large
Referenced by 1
References 165
Maint.: all paid

Soft Decision Device
Error Signal Generat…
Passband/Passband Eq…
Passband/Baseband Eq…

1. A method for operating forward and feedback filters in a communications receiver having a decision feedback equalizer, said communications receiver having a decision feedback equalizer, said communications receiver responsive to a received signal to form slicer input samples and hard decision samples corresponding to said slicer output samples, said method comprising:

non-linearly combining said slicer input samples and said hard decision samples to form a soft decision samples in a soft decision device; and

the said soft decision device being adaptively adjusted to control contributions of said slicer input samples and said hard decision samples to form said soft decision samples; and

said soft decision device generating error signals to adjust said forward and feedback filters; and

operating said forward and feedback filters by coupling a composite decision samples to said feedback filter and by adapting said forward and feedback filters with said error signals.

0. 4. A receiver having a decision feedback equalizer, said receiver responsive to a received signal to form slicer input samples and hard decision samples corresponding to said slicer output samples, said receiver comprising:

a forward filter;

a feedback filter;

a slicer that is capable of generating the slicer output samples; and

a soft decision device that is capable of non-linearly combining said slicer input samples and said hard decision samples to form soft decision samples, said soft decision device further being adaptively adjusted to control contributions of said slicer input samples and said hard decision samples to form said soft decision samples, further wherein said soft decision device is capable of generating error signals to adjust said forward and feedback filters;

wherein said forward and feedback filters are capable of coupling a composite decision samples to said feedback filter and by adapting said forward and feedback filters with said error signals.

2. The method of claim 1, wherein said decision feedback equalizer operates in passband.

3. The method of claim 1, wherein said feedback filter operates in baseband.

0. 5. The receiver of claim 4, wherein said decision feedback equalizer operates in passband.

0. 6. The receiver of claim 4, wherein said feedback filter operates in baseband.

0. 7. The receiver of claim 5, wherein said forward filter and said feedback filter operate in the passband.

0. 8. The receiver of claim 6, wherein said forward filter operates in passband.

0. 9. The receiver of claim 4 wherein said forward filter has a plurality of coefficients that are updated using a stochastic gradient descent rule.

where r(n) is the sample sequence input to forward filter 210, x(n) is the output sample sequence of forward filter 210, f_iare the forward filter coefficients (or parameters,) and L_fis the number of forward filter coefficients. Note that the forward filter coefficients are also shown with time index n to indicate that the forward filter 210 is adaptive.

The feedback filter 220 is not multi-channel, and is a FIR filter that calculates its output according to the convolution sum
y(n)=g₀(n)v(n)+g₁(n)v(n−1)+g₂(n)v(n−2)+. . . +g_L_g^−I
where v(n) is the sample sequence input to feedback filter 220, y(n) is the output sample sequence of feedback filter 220, g_iare the feedback filter coefficients (or parameters,) and L_gis the number of feedback filter coefficients. Note that the feedback filter coefficients are also shown with time index n to indicate that the feedback filter 220 is adaptive. Though the feedback filter 220 is a FIR filter, it is embedded in a feedback loop, so that the equalizer has an overall impulse response that is infinite.

Adder 275 combines the outputs of forward filter 210 and feedback filter 220, x(n) and y(n), respectively, to form sample sequence w(n). Sample sequence w(n) is referred to as slicer inputs. The slicer inputs, w(n), are input to slicer 240. Slicer 240 is a nearest-element decision device that outputs a hard decision, ŵ(n), corresponding to the source alphabet member with closest Euclidean distance to its input sample. The slicer input w(n) and the hard decisions, ŵ(n), from slicer 240 are input to the Soft Decision Device 230.

Soft Decision Device

FIG. 3 describes the Soft Decision Device in accordance with the present invention. The slicer input w(n) is splitted into real and imaginary components. For the real and imaginary parts of w(n), w_re(n) and w_im(n) respectively, the Boundary Value Generator 320 produces the nearest decision boundary values {hacek over (w)}_re(n) and {hacek over (w)}_im(n) by treating w_re(n) and w_im(n) as a Pulse Amplitude Modulated (PAM) signals, which belong to a alphabet set
{−(2M−1)Γ, . . . , −3Γ,−Γ,3Γ, . . . (2M−1)Γ}
where the constellation unit Γ and PAM level M are determined from the QAM level.

$\overset{⋓}{w} = \underset{2 k Γ}{\arg \min} \langle w - 2 k Γ \rangle,$
for k=−M+1, . . . , M−1.
with |·| denoting absolute value, or magnitude. Remind that the hard decision of a PAM signal is defined by

$\hat{w} = \underset{(2 k - 1) Γ}{\arg \min} \langle w - (2 k - I) Γ \rangle,$
for k=−M+1, . . . ,M−1.

FIG. 4 illustrates the relation among w(n) (420), ŵ(n) (430), {hacek over (w)}_re(n) (440), and {hacek over (w)}_im(n) (440) for a 16-QAM constellation.

In FIG. 3 the Soft Decision Generator 330 generates the soft decision based on the comparison between the distance between the nearest boundary values from the slicer input, |w_re(n)−{hacek over (w)}_re(n)| and |w_im(n)−{hacek over (w)}_im(n)|, and a decision reference parameter λ(n), according to

$v (n) = {\begin{matrix} \frac{w (n) - \overset{⋓}{w} (n)}{λ (n)} & if \langle w_{re} (n) - {\overset{⋓}{w}}_{re} (n) \rangle < λ (n) or \langle w_{im} (n) - {\overset{⋓}{w}}_{im} (n) \rangle < λ (n) \\ \hat{w} (n) & else \end{matrix}$
where {hacek over (w)}(n)={hacek over (w)}_re+j{hacek over (w)}_im.

The soft decision device is made adaptive by adaptation of the decision reference parameter λ(n). The decision reference parameter λ(n) is initialized by λ(0)=1 and adjusted from 0 to 1 depending on the signal quality. The Soft Decision Optimizer 350 optimizes the decision reference parameter λ(n). The decision reference parameter λ(n) can be approximately optimized by setting λ(n)=E|w(n)−ŵ(n)|²/E|w(n)|²with E{·} denoting statistical expectation) and can be adjusted each symbol instance using the leakage integrator
λ(n)=(1−ρ_λ)·λ(n−1)+ρ_λ·|w(n)−ŵ|²/Δ
where Δ is chosen to normalize |w(n)−ŵ|²(for example average signal power, Δ=E|w(n)|²) and ρ_λis the leakage term and is chosen less than or equal to one and greater than or equal to zero.

Alternatively, λ(n) can be updated on a block by block base based on the block estimation of E|w(n)−ŵ(n)|²/E|w(n)|², or using training signals instead of ŵ(n) for the training periods. Furthermore, the combining weight λ(n) may be compared to two thresholds, T_Uand T_L. If λ(n)>T_U, then λ(n) is set to one; if λ(n)<T_L, then λ(n) is set to zero

Error Signal Generation and Coefficient Adaptation

Adaptation of the forward filter 210 coefficients and feedback filter 220 coefficients uses a stochastic gradient descent update rule:
f_i(n+1)=f_i(n)−μ_fΦ*(n)e(n)
g_i(n+1)=g_i(n)−μ_gφ*(n)e(n)
where (·)* represents complex conjugation, and μ_fand μ_gare small, positive stepsizes governing algorithm convergence rate, tracking capabilities and stochastic jitter. Using simplified updates, the data used in the adaptation equations are set to Φ(n)=r(n) and φ(n)=v(n). The baseband error term e(n) that updates the forward filter 210 and feedback filter 220 at each baud instance is selected by Error Signal Generator 340 in Soft Decision Device 300 and is calculated according to

$e (n) = {\begin{matrix} e_{1} (n) & if \langle w_{re} (n) - {\overset{⋓}{w}}_{re} (n) \rangle < λ (n) or \langle w_{im} (n) - {\overset{⋓}{w}}_{im} (n) \rangle < λ (n) \\ e_{2} (n) & else \end{matrix} .$

The preferred embodiment of the present invention uses a Constant Modulus Algorithm (CMA) error term of order p=2 (as described by Godard in “Self recovering equalization and carrier tracking in two-dimensional data communication systems”) for e₁(n) and a Decision-Directed LMS (DD-LMS) error term for e₂(n). For example, CMA ad DD-LMS error terms may be calculated according to

$e_{cma} = (\frac{w (n) - \overset{⋓}{w} (n)}{λ (n)} + \overset{⋓}{w} (n)) \cdot ({\langle \frac{w (n) - \overset{⋓}{w} (n)}{λ (n)} + \overset{⋓}{w} (n) \rangle}^{2} - γ)$
e_did-lms=w(n)−ŵ(n)
where γ is a real scalar referred to as the CM dispersion constant or Godard radius, and is usually calculated as γ=E{|s(n)|⁴}/E{|s(n)|²} for source sequence s(n), (These error terms are said to be baseband, since they are derived from samples at precise baseband.)

The intuition behind this error term generation is that the slicer inputs near hard decision boundaries are treated less reliable signals than the slicer inputs near hard decision samples. The Error Signal Generator 340 separates the unreliable signals and reliable signals, and apply IIR adaptation for the unreliable signals after proper resealing. For the reliable signals the conventional DD-LMS is applied.

Other choices of error terms may include CMA error terms of order other than p=2; those derived from the Bussgang class of cost functions, as described in chapter 2 of “Blind Deconvolution,” Prentice Hall, written by S. Bellini, edited by S. Haykin, 1994; single-axis error terms which use real-part extraction, as described in a paper by A. Shah et al, entitled “Global convergence of a single-axis constant modulus algorithm,” Proceedings of the IEEE statistical signal and array processing workshop, Pocono Manor, Pa., August, 2000; or error terms derived from other blind or non-blind criteria.

Setting Φ(n)=r(n) and φ(n)=v(n) in the above equations used to adapt forward filter 210 and feedback filter 220 coefficients is referred to as “simplified updates,” since the step known as regressor filtering is omitted. True cost function minimization requires an extra stage of filtering for the regressor data of the forward filter 210 and the feedback filter 220 in the adaptation process, using the current equalizer coefficients. Such regressor filtering is typically omitted in practice due to implementation burden. Regressor filtering is described in Chapter 5 of “Theory and design of adaptive filters” by J. R. Treichler, C. R. Johnson, Jr., and M. G. Larimore, Prentice Hall, 2001. One skilled in the art would recognize how to modify the regressor data used in the adaptation equations above to incorporate the extra stage of regressor filtering.

FIGS. 5a and 5b illustrate the equalizer output and soft decision reference parameter λ(n) in operation from a computer simulation of the preferred embodiment of the present invention. The source signal is 4-QAM (QPSK) data passed through a closed-eye channel that has rapid time variation at the 5,000^thbaud sample. There are 10,000 baud samples, with adaptation of equalizer coefficients and decision reference parameter at the start of the simulation. The leakage value for Soft Decision Device optimization is ρ_λ=0.01. Thresholds for the combining weight are set to T_U=1 and T_L=0.

FIG. 5a shows the real part of slicer inputs converging to correct decisions as adaptation is processed. Sudden dispersion at the 5,000^thbaud sample is due to sudden change of the multipath channel.

FIG. 5b shows the trajectory of decision reference parameter λ(n), initialized to unity, and converging towards zero when channel is static, and optimizing the adaptation and soft decision device when channel is varying.

FIG. 5c draws the soft decision device as a function of slicer input for various choice of decision reference parameter λ(n) in this simulation. For λ(n)=0 the soft decision device agrees with hard limiter and DFE is operating with DD-LMS algorithm. As λ(n) increases the region of unreliable signals are increased too and DFE is operating with the conventional CMA in that region.

Passband/Passband Equalization

An alternative embodiment of the present invention is shown in FIG. 5, in which the equalizer 500 operates in the passband; that is, not at precise baseband. Equalizer 500 is similar to equalizer 200 in FIG. 2, so only the differences in equalizer 500 of FIG. 5 are described.

Forward filter 510 and feedback filter 520 produce data by convolution sums in an analogous manner to that described for the exemplary embodiment in FIG. 2, yielding passband signals x(n) and y(n), respectively. The outputs of forward filter 510 and feedback filter 520 are combined in adder 590, yielding the passband sample {tilde over (w)}(n). This sample is translated to precise baseband (or de-rotated) slicer input w(n) in multiplier 555 by multiplication with the conjugate of the carrier offset, e^−jθ(n), provided by carrier recovery loop 585. The slicer 540 is a nearest-element decision device that outputs a hard decision, ŵ(n), corresponding to the source alphabet member with closest Euclidean distance to its input sample. The slicer input and hard decision samples are input to the Soft Decision Device and the soft decision v(n) is translated back to the passband in multiplier 560 by multiplication with the carrier offset e^jθ(n), provided by the carrier recovery loop 585.

Though soft decision is made actually in baseband, equalizer adaptation must use an error term that is in the passband. The translation rules between passband and baseband error terms are given by:

$e_{dd - lms}^{passband} = e_{dd - lms} \cdot ⅇ^{𝕛θ (n)}$ $e_{CMA}^{passband} = e_{CMA} \cdot ⅇ^{𝕛 θ (n)}$

Since both forward filter 510 and feedback filter 520 operate in the passband, they are updated with passband error terms.

Passband/Baseband Equalization

FIG. 6 shows equalizer 600, an alternative embodiment of the present invention, in which the forward filter 610 operates on passband data, while the feedback filter 650, and all processing after multiplier 645, operate at precise baseband. Forward filter 610 operates on received passband data r(n) and calculates output x_pb(n) via the convolution sum discussed for the filtering process of equalizer 200 in FIG. 2.

Multiplier 645 translates the output of forward filter 610 to precise baseband by multiplication with the conjugate of the carrier offset estimate, e^−jθ(n), provided by carrier recovery loop 685. The remainder of the equalizer 600 operates analogously to the equalizer 200 in FIG. 2, except that the equalizer control module 630 receives also the carrier offset estimate from carrier recovery loop 685 to produce a passband error term, e_pb(n), as well as a baseband error term, e(n). Feedback filter 620 operates on baseband data, and thus is adapted with the baseband error terms described for operation of equalizer 200 in FIG. 2. However, since forward filter 610 in FIG. 6 processes passband data, it is adapted by passband error terms that are generated by rotating the baseband error term with the current offset of the carrier recovery estimate, e^jθ(n).

One skilled in the art would understand that the equations described herein may include scaling, change of sign, or similar constant modifications that are not shown for simplicity. One skilled in the art would realize that such modifications can be readily determined or derived for the particular implementation. Thus, the described equations may be subject to such modifications, and are not limited to the exact forms presented herein.

The present invention has been described using Quadrature Amplitude Modulation (QAM) signals with complex signal processing, unless specifically noted. However, one skilled in the art would realize that the techniques described herein may be applied to a receiver processing Phase-Shift Keyed (PSK), Pulse Amplitude Modulation (PAM), or other signals.

As would be apparent to one skilled in the art, the various functions of equalization, signal combining, and automatic gain control may be implemented with circuit elements or may also be implemented in the digital domain as processing steps in a software program. Such software may be employed in, for example, a digital signal processor, microcontroller, or general-purpose computer.

The present invention can be embodied in the form of methods and apparatuses for practicing those methods. The present invention can also be embodied in the form of program code embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium, wherein, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the invention. The present invention can also be embodied in the form of program code, for example, whether stored in a storage medium, loaded into and/or executed by a machine, or transmitted over some transmission medium, such as over electrical wiring or cabling, through fiber optics, or via electromagnetic radiation, wherein, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the invention. When implemented on a general-purpose processor, the program code segments combine with the processor to provide a unique device that operates analogously to specific logic circuits.

It will be further understood that various changes in the details, materials, and arrangements of the parts which have been described and illustrated in order to explain the nature of this invention may be made by those skilled in the art without departing from the principle and scope of the invention as expressed in the following claims.

INVENTORS:

Chung, Wonzoo, Endres, Thomas J., Long, Christopher D.

THIS PATENT IS REFERENCED BY THESE PATENTS:

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ASSIGNMENT RECORDS Assignment records on the USPTO

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Executed on	Assignor	Assignee	Conveyance	Frame	Reel	Doc
Oct 27 2008	DOTCAST, INC	Omereen Wireless, LLC	ASSIGNMENT OF ASSIGNORS INTEREST SEE DOCUMENT FOR DETAILS	026044	0273	pdf
Feb 20 2009		Omereen Wireless, LLC	(assignment on the face of the patent)
Aug 27 2015	Omereen Wireless, LLC	CALLAHAN CELLULAR L L C	MERGER SEE DOCUMENT FOR DETAILS	037085	0938	pdf

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