U.S. patent application number 15/067924 was filed with the patent office on 2016-09-01 for design and optimization of partial response pulse shape filter.
This patent application is currently assigned to MagnaCom Ltd.. The applicant listed for this patent is MagnaCom Ltd.. Invention is credited to Amir Eliaz.
Application Number | 20160254933 15/067924 |
Document ID | / |
Family ID | 49034706 |
Filed Date | 2016-09-01 |
United States Patent
Application |
20160254933 |
Kind Code |
A1 |
Eliaz; Amir |
September 1, 2016 |
Design and Optimization of Partial Response Pulse Shape Filter
Abstract
A method and system for configuring one or both of a transmitter
pulse-shaping filter and a receiver pulse-shaping filter to
generate a total partial response that incorporates a predetermined
amount of inter-symbol interference (ISI), based on one or more
defined performance-related variables and one or more set
constraints that are applicable to one or both of the transmitter
pulse-shaping filter and the receiver pulse-shaping filters. The
predetermined amount of ISI is determined based on an estimation
process during extraction of data from an output of the receiver
pulse-shaping filter, such that performance of total partial
response based communication matches or surpasses performance of
communication incorporating filtering based on no or near-zero ISI.
The configuring may comprise determining optimized filtering
configuration, by applying an optimization process which is based
on, at least in part, the one or more constraints and the one or
more performance-related variables.
Inventors: |
Eliaz; Amir; (Moshav Ben
Shemen, IL) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
MagnaCom Ltd. |
Petach Tikva |
|
IL |
|
|
Assignee: |
MagnaCom Ltd.
Petach Tikva
IL
|
Family ID: |
49034706 |
Appl. No.: |
15/067924 |
Filed: |
March 11, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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14551466 |
Nov 24, 2014 |
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15067924 |
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13754998 |
Jan 31, 2013 |
8897387 |
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14551466 |
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61662085 |
Jun 20, 2012 |
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61726099 |
Nov 14, 2012 |
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61729774 |
Nov 26, 2012 |
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61747132 |
Dec 28, 2012 |
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Current U.S.
Class: |
375/296 |
Current CPC
Class: |
H04L 25/03343 20130101;
H04L 25/03834 20130101; H04L 27/2278 20130101; H04L 1/005 20130101;
H04L 7/0087 20130101; H04B 17/0085 20130101; H04L 25/0236 20130101;
H04L 25/03305 20130101; H04B 2001/0416 20130101; H04L 27/04
20130101; H04L 1/0036 20130101; H04L 27/38 20130101; H04B 1/10
20130101; H04L 1/0054 20130101; H04L 25/03038 20130101; H04L 7/02
20130101; H04L 25/0328 20130101; H04L 2025/03369 20130101; H04L
1/0041 20130101; H04L 25/08 20130101; H04L 27/368 20130101; H04L
1/0048 20130101; H04L 27/36 20130101; H04L 1/206 20130101; H04L
1/203 20130101; H04L 23/02 20130101; H04L 7/0058 20130101; H04L
25/03337 20130101; H04L 27/02 20130101; G06F 11/10 20130101; H04L
25/03057 20130101; H04B 17/15 20150115; H04L 27/00 20130101; H04L
25/03267 20130101; H04B 1/709 20130101; H04L 27/366 20130101; H04L
7/042 20130101; H04L 25/03006 20130101; H04L 25/03197 20130101;
H04B 17/29 20150115; H04B 1/0475 20130101; H04L 25/03885 20130101;
H04L 25/03318 20130101; H04L 25/03949 20130101; H04L 27/01
20130101; H04B 1/16 20130101; H04L 25/03178 20130101 |
International
Class: |
H04L 25/03 20060101
H04L025/03; H04B 1/04 20060101 H04B001/04 |
Claims
1. A method, comprising: utilizing pulse-shaping filtering for
communication of data, wherein: the pulse-shaping filtering
provides a total partial response that incorporates a predetermined
amount of inter-symbol interference (ISI); and the predetermined
amount of inter-symbol interference (ISI) is determined based on an
estimation process applied to an output of the pulse-shaping
filtering.
2. The method of claim 1, wherein the pulse-shaping filtering
comprises use of a transmit-side pulse-shaping filter and a
receive-side pulse-shaping filter.
3. The method of claim 1, comprising configuring the pulse-shaping
filtering to optimize an applicable weighted distances for one or
more selected error patterns for a given spectral compression.
4. The method of claim 1, comprising configuring the pulse-shaping
filtering to optimize a symbol error rate (SER) associated with the
communication of data.
5. The method of claim 1, comprising configuring the pulse-shaping
filtering, the configuring comprising: defining a plurality of
performance-related variables; setting a plurality of constraints;
and determining optimized filtering configuration by applying an
optimization process that is based on, at least in part, the
plurality of constraints and the plurality of performance-related
variables.
6. The method of claim 5, comprising configuring the optimization
process to allow for setting different numbers of filter
coefficients for each of a transmit-side pulse-shaping filter and a
receive-side pulse-shaping filter utilized for the pulse-shaping
filtering.
7. The method of claim 5, comprising configuring the optimization
process to determine one or more early filter taps that are
applicable to one or more filters utilized for the pulse-shaping
filtering while ensuring that a resultant pulse shape remain within
an applicable spectral mask.
8. The method of claim 5, comprising configuring the optimization
process to determine late filter taps applicable to one or more
filters utilized for the pulse-shaping filtering while ensuring
that a resultant pulse shape remain within an applicable spectral
mask.
9. The method of claim 5, wherein the optimization process
comprises optimizing at least one of a tap configuration, a number
of taps, and one or more of a plurality of tap coefficients.
10. The method of claim 5, comprising applying as part of the
optimization process one or more cost functions while meeting the
plurality of constraints.
11. The method of claim 10, wherein at least one of the one or more
cost functions cost function is defined over one or more of the
plurality of performance-related variables.
12. The method of claim 5, wherein the plurality of
performance-related variables comprise minimum distance reduction,
symbol error rate (SER) and/or bit error rate (BER), early taps
amplitude, residual non-compensated early response, receive-side
noise enhancement, receive-side out-of-band rejection, amplitude of
tail response, channel response, and/or nonlinear distortion.
13. The method of claim 5, wherein the plurality of constraints
comprise spectrum mask limits, amplitudes early filter taps,
amplitude of tail response, residual non-compensated early
response, receive-side out-of-band rejection, noise mismatch,
and/or nonlinear distortion tolerance.
14. The method of claim 1, wherein the estimation process is
configured such that communications based on the total partial
response provide data rates and error measurements that are at
least equal to the data rates and error measurements associated
with no inter-symbol interference (ISI) or near-zero inter-symbol
interference (ISI) based communications subject to same spectrum
mask limits for said partial response and said no ISI or near-zero
ISI communications.
15. The method of claim 1, wherein the predetermined amount of
inter-symbol interference (ISI) is greater than the maximum
inter-symbol interference (ISI) practically allowed in reference
communication using zero or near-zero ISI filters.
16. A system, comprising: one or more circuits for performing a
pulse-shaping filtering, wherein: the pulse-shaping filtering
provides a total partial response that incorporates a predetermined
amount of inter-symbol interference (ISI); and the predetermined
amount of inter-symbol interference (ISI) is determined based on an
estimation process applied to an output of the pulse-shaping
filtering.
17. The system of claim 16, wherein the pulse-shaping filtering
comprises use of a transmit-side pulse-shaping filter and a
receive-side pulse-shaping filter.
18. The system of claim 16, wherein the one or more circuits are
operable to configure the pulse-shaping filtering to optimize an
applicable weighted distances for one or more selected error
patterns for a given spectral compression.
19. The system of claim 16, wherein the one or more circuits are
operable to configure the pulse-shaping filtering to optimize a
symbol error rate (SER) associated with the communication of
data.
20. The system of claim 16, wherein the one or more circuits are
operable to configure the pulse-shaping filtering, the configuring
comprising: defining a plurality of performance-related variables;
setting a plurality of constraints; and determining optimized
filtering configuration by applying an optimization process that is
based on, at least in part, the plurality of constraints and the
plurality of performance-related variables.
Description
CLAIM OF PRIORITY
[0001] This application is a continuation of U.S. patent
application Ser. No. 14/551,466 filed Nov. 24, 2014, which is a
continuation of U.S. patent application Ser. No. 13/754,998, filed
Jan. 31, 2013 (now patented as U.S. Pat. No. 8,897,387), which
claims the benefit of priority to U.S. Provisional Patent
Application Ser. No. 61/662,085 filed on Jun. 20, 2012, U.S.
Provisional Patent Application Ser. No. 61/726,099 filed on Nov.
14, 2012, U.S. Provisional Patent Application Ser. No. 61/729,774
filed on Nov. 26, 2012, U.S. Provisional Patent Application Ser.
No. 61/747,132 filed on Dec. 28, 2012.
[0002] Each of the above identified applications is hereby
incorporated herein by reference in its entirety.
INCORPORATION BY REFERENCE
[0003] This application makes reference to:
U.S. Pat. No. 8,582,637, titled "Low-Complexity,
Highly-Spectrally-Efficient Communications," and filed on Jan. 31,
2013; U.S. Pat. No. 8,675,769, titled "Constellation Map
Optimization For Highly Spectrally Efficient Communications," and
filed on Jan. 31, 2013; U.S. Pat. No. 8,571,131, titled "Dynamic
Filter Adjustment for Highly-Spectrally-Efficient Communications,"
and filed on Jan. 31, 2013; U.S. Pat. No. 8,559,494, titled "Timing
Synchronization for Reception of Highly-Spectrally-Efficient
Communications," and filed on Jan. 31, 2013; U.S. Pat. No.
8,599,914, titled "Feed Forward Equalization for
Highly-Spectrally-Efficient Communications," and filed on Jan. 31,
2013; U.S. Pat. No. 8,665,941, titled "Decision Feedback Equalizer
for Highly-Spectrally-Efficient Communications," and filed on Jan.
31, 2013; U.S. Pat. No. 8,873,612, titled "Decision Feedback
Equalizer with Multiple Cores for Highly-Spectrally-Efficient
Communications," and filed on Jan. 31, 2013; U.S. Pat. No.
8,559,498, titled "Decision Feedback Equalizer Utilizing Symbol
Error Rate Biased Adaptation Function for
Highly-Spectrally-Efficient Communications," and filed on Jan. 31,
2013; U.S. Pat. No. 8,548,097, titled "Coarse Phase Estimation for
Highly-Spectrally-Efficient Communications," and filed on Jan. 31,
2013; U.S. Pat. No. 8,565,363, titled "Fine Phase Estimation for
Highly Spectrally Efficient Communications," and filed on Jan. 31,
2013; and U.S. Pat. No. 8,605,832, titled "Joint Sequence
Estimation of Symbol and Phase with High Tolerance of
Nonlinearity," and filed on Jan. 31, 2013.
[0004] Each of the above stated applications is hereby incorporated
herein by reference in its entirety.
FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
[0005] [Not Applicable].
MICROFICHE/COPYRIGHT REFERENCE
[0006] [Not Applicable].
TECHNICAL FIELD
[0007] Aspects of the present application relate to electronic
communications. More specifically, certain implementations of the
present disclosure relate to design and optimization of partial
response pulse shape filter.
BACKGROUND
[0008] Existing communications methods and systems are overly power
hungry and/or spectrally inefficient. Further limitations and
disadvantages of conventional and traditional approaches will
become apparent to one of skill in the art, through comparison of
such approaches with some aspects of the present method and
apparatus set forth in the remainder of this disclosure with
reference to the drawings.
BRIEF SUMMARY
[0009] A system and/or method is provided for design and
optimization of partial response pulse shape filter, substantially
as shown in and/or described in connection with at least one of the
figures, as set forth more completely in the claims.
[0010] These and other advantages, aspects and novel features of
the present disclosure, as well as details of illustrated
implementation(s) thereof, will be more fully understood from the
following description and drawings.
BRIEF DESCRIPTION OF SEVERAL VIEWS OF THE DRAWINGS
[0011] FIG. 1 is a block diagram depicting an example system
configured for low-complexity, highly-spectrally-efficient
communications.
[0012] FIG. 2 is a block diagram depicting an example equalization
and sequence estimation circuit for use in a system configured for
low-complexity, highly-spectrally-efficient communications.
[0013] FIG. 3 is a block diagram depicting an example sequence
estimation circuit for use in a system configured for
low-complexity, highly-spectrally-efficient communications.
[0014] FIG. 4 is a block diagram depicting an example partial
response pulse-shaping filtering setup for use in a system
configured for low-complexity, highly-spectrally-efficient
communications.
[0015] FIG. 5 is a block diagram depicting an example finite
impulse response (FIR) implementation of partial response
pulse-shaping filters, in accordance with an embodiment of the
present invention.
[0016] FIG. 6 is a flow chart depicting an example of a process for
joint optimization of transmitter and receiver pulse-shaping
filters, in accordance with an embodiment of the present
invention.
[0017] FIG. 7 is a chart diagram depicting a comparison between the
frequency-domain responses of a legacy transmit filter and an
optimized partial response pulse-shaping transmit filter.
DETAILED DESCRIPTION
[0018] The present disclosure relates to a method and system for
design and optimization of partial response pulse shape filter.
[0019] As utilized herein the terms "circuits" and "circuitry"
refer to physical electronic components (i.e. hardware) and any
software and/or firmware ("code") which may configure the hardware,
be executed by the hardware, and or otherwise be associated with
the hardware. As used herein, for example, a particular processor
and memory may comprise a first "circuit" when executing a first
plurality of lines of code and may comprise a second "circuit" when
executing a second plurality of lines of code. As utilized herein,
"and/or" means any one or more of the items in the list joined by
"and/or". As an example, "x and/or y" means any element of the
three-element set {(x), (y), (x, y)}. As another example, "x, y,
and/or z" means any element of the seven-element set {(x), (y),
(z), (x, y), (x, z), (y, z), (x, y, z)}. As utilized herein, the
terms "block" and "module" refer to functions than can be performed
by one or more circuits. As utilized herein, the term "exemplary"
means serving as a non-limiting example, instance, or illustration.
As utilized herein, the terms "for example" and "e.g.," introduce a
list of one or more non-limiting examples, instances, or
illustrations. As utilized herein, circuitry is "operable" to
perform a function whenever the circuitry comprises the necessary
hardware and code (if any is necessary) to perform the function,
regardless of whether performance of the function is disabled, or
not enabled, by some user-configurable setting.
[0020] FIG. 1 is a block diagram depicting an example system
configured for low-complexity, highly-spectrally-efficient
communications. The system 100 comprises a mapper circuit 102, a
pulse shaping filter circuit 104, a timing pilot insertion circuit
105, a transmitter front-end circuit 106, a channel 107, a receiver
front-end 108, a filter circuit 109, a timing pilot removal circuit
110, an equalization and sequence estimation circuit 112, and a
de-mapping circuit 114. The components 102, 104, 105, and 106 may
be part of a transmitter (e.g., a base station or access point, a
router, a gateway, a mobile device, a server, a computer, a
computer peripheral device, a table, a modem, a set-top box, etc.),
the components 108, 109, 110, 112, and 114 may be part of a
receiver (e.g., a base station or access point, a router, a
gateway, a mobile device, a server, a computer, a computer
peripheral device, a table, a modem, a set-top box, etc.), and the
transmitter and receiver may communicate via the channel 107.
[0021] The mapper 102 may be operable to map bits of the
Tx_bitstream to be transmitted to symbols according to a selected
modulation scheme. The symbols may be output via signal 103. For
example, for an quadrature amplitude modulation scheme having a
symbol alphabet of N (N-QAM), the mapper may map each Log.sub.2(N)
bits of the Tx_bitstream to single symbol represented as a complex
number and/or as in-phase (I) and quadrature-phase (Q) components.
Although N-QAM is used for illustration in this disclosure, aspects
of this disclosure are applicable to any modulation scheme (e.g.,
amplitude shift keying (ASK), phase shift keying (PSK), frequency
shift keying (FSK), etc.). Additionally, points of the N-QAM
constellation may be regularly spaced ("on-grid") or irregularly
spaced ("off-grid"). Furthermore, the symbol constellation used by
the mapper may be optimized for best bit-error rate performance
that is related to log-likelihood ratio (LLR) and to optimizing
mean mutual information bit (MMIB). The Tx_bitstream may, for
example, be the result of bits of data passing through a forward
error correction (FEC) encoder and/or an interleaver. Additionally,
or alternatively, the symbols out of the mapper 102 may pass
through an interleaver.
[0022] The pulse shaper 104 may be operable to adjust the waveform
of the signal 103 such that the waveform of the resulting signal
113 complies with the spectral requirements of the channel over
which the signal 113 is to be transmitted. The spectral
requirements may be referred to as the "spectral mask" and may be
established by a regulatory body (e.g., the Federal Communications
Commission in the United States or the European Telecommunications
Standards Institute) and/or a standards body (e.g., Third
Generation Partnership Project) that governs the communication
channel(s) and/or standard(s) in use. The pulse shaper 104 may
comprise, for example, an infinite impulse response (IIR) and/or a
finite impulse response (FIR) filter. The number of taps, or
"length," of the pulse shaper 104 is denoted herein as LTx, which
is an integer. The impulse response of the pulse shaper 104 is
denoted herein as hTx. The pulse shaper 104 may be configured such
that its output signal 113 intentionally has a substantial amount
of inter-symbol interference (ISI). Accordingly, the pulse shaper
104 may be referred to as a partial response pulse shaping filter,
and the signal 113 may be referred to as a partial response signal
or as residing in the partial response domain, whereas the signal
103 may be referred to as residing in the symbol domain. The number
of taps and/or the values of the tap coefficients of the pulse
shaper 104 may be designed such that the pulse shaper 104 is
intentionally non-optimal for additive white Gaussian noise (AWGN)
in order to improve tolerance of non-linearity in the signal path.
In this regard, the pulse shaper 104 may offer superior performance
in the presence of non-linearity as compared to, for example, a
conventional zero (or near zero) positive ISI pulse shaping filter
(e.g., root raised cosine (RRC) pulse shaping filter). The pulse
shaper 104 may be designed as described in at least some of the
following figures (e.g., FIGS. 4-7), and in one or more of: the
United States patent application titled "Constellation Map
Optimization For Highly Spectrally Efficient Communications," and
the United States patent application titled "Dynamic Filter
Adjustment For Highly-Spectrally-Efficient Communications," each of
which is incorporated herein by reference, as set forth above.
[0023] It should be noted that a partial response signal (or
signals in the "partial response domain") is just one example of a
type of signal for which there is correlation among symbols of the
signal (referred to herein as "inter-symbol-correlated (ISC)
signals"). Such ISC signals are in contrast to zero (or near zero)
ISI signals generated by, for example, raised-cosine (RC) or
root-raised-cosine (RRC) filtering. For simplicity of illustration,
this disclosure focuses on partial response signals generated via
partial response filtering. Nevertheless, aspects of this
disclosure are applicable to other ISC signals such as, for
example, signals generated via matrix multiplication (e.g., lattice
coding), and signals generated via decimation below the Nyquist
frequency such that aliasing creates correlation between
symbols.
[0024] The timing pilot insertion circuit 105 may insert a pilot
signal which may be utilized by the receiver for timing
synchronization. The output signal 115 of the timing pilot
insertion circuit 105 may thus comprise the signal 113 plus an
inserted pilot signal (e.g., a sine wave at 1/4.times.fbaud, where
fbaud is the symbol rate). An example implementation of the pilot
insertion circuit 105 is described in the United States patent
application titled "Timing Synchronization for Reception of
Highly-Spectrally-Efficient Communications," which is incorporated
herein by reference, as set forth above.
[0025] The transmitter front-end 106 may be operable to amplify
and/or upconvert the signal 115 to generate the signal 116. Thus,
the transmitter front-end 106 may comprise, for example, a power
amplifier and/or a mixer. The front-end may introduce non-linear
distortion and/or phase noise (and/or other non-idealities) to the
signal 116. The non-linearity of the circuit 106 may be represented
as FnITx which may be, for example, a polynomial, or an exponential
(e.g., Rapp model). The non-linearity may incorporate memory (e.g.,
Voltera series).
[0026] The channel 107 may comprise a wired, wireless, and/or
optical communication medium. The signal 116 may propagate through
the channel 107 and arrive at the receive front-end 108 as signal
118. Signal 118 may be noisier than signal 116 (e.g., as a result
of thermal noise in the channel) and may have higher or different
ISI than signal 116 (e.g., as a result of multi-path).
[0027] The receiver front-end 108 may be operable to amplify and/or
downconvert the signal 118 to generate the signal 119. Thus, the
receiver front-end may comprise, for example, a low-noise amplifier
and/or a mixer. The receiver front-end may introduce non-linear
distortion and/or phase noise to the signal 119. The non-linearity
of the circuit 108 may be represented as FnIRx which may be, for
example, a polynomial, or an exponential (e.g., Rapp model). The
non-linearity may incorporate memory (e.g., Voltera series).
[0028] The timing pilot recovery and removal circuit 110 may be
operable to lock to the timing pilot signal inserted by the pilot
insertion circuit 105 in order to recover the symbol timing of the
received signal. The output 122 may thus comprise the signal 120
minus (i.e. without) the timing pilot signal. An example
implementation of the timing pilot recovery and removal circuit 110
is described in the United States patent application titled "Timing
Synchronization for Reception of Highly-Spectrally-Efficient
Communications," which is incorporated herein by reference, as set
forth above.
[0029] The input filter 109 may be operable to adjust the waveform
of the partial response signal 119 to generate partial response
signal 120. The input filter 109 may comprise, for example, an
infinite impulse response (IIR) and/or a finite impulse response
(FIR) filter. The number of taps, or "length," of the input filter
109 is denoted herein as LRx, an integer. The impulse response of
the input filter 109 is denoted herein as hRx. The number of taps,
and/or tap coefficients of the input filter 109 may be configured
based on: a non-linearity model, , signal-to-noise ratio (SNR) of
signal 120, the number of taps and/or tap coefficients of the Tx
partial response filter 104, and/or other parameters. The number of
taps and/or the values of the tap coefficients of the input filter
109 may be configured such that noise rejection is intentionally
compromised (relative to a perfect match filter) in order to
improve performance in the presence of non-linearity. As a result,
the input filter 109 may offer superior performance in the presence
of non-linearity as compared to, for example, a conventional zero
(or near zero) positive ISI matching filter (e.g., root raised
cosine (RRC) matched filter). The input filter 109 may be designed
as described in at least some of the following figures (e.g., FIGS.
4-7), and in one or more of: the United States patent application
titled "Constellation Map Optimization For Highly Spectrally
Efficient Communications," and the United States patent application
titled "Dynamic Filter Adjustment For Highly-Spectrally-Efficient
Communications," each of which is incorporated herein by reference,
as set forth above.
[0030] As utilized herein, the "total partial response (h)" may be
equal to the convolution of hTx and hRx, and, thus, the "total
partial response length (L)" may be equal to LTx+LRx-1. L may,
however, be chosen to be less than LTx+LRx-1 where, for example,
one or more taps of the Tx pulse shaper 104 and/or the Rx input
filter 109 are below a determined level. Reducing L may reduce
decoding complexity of the sequence estimation. This tradeoff may
be optimized during the design of the system 100. In various
embodiments, the design and/or configuration of filters and/or
filtering operations of the pulse shaper 104 and the input filter
109 (particularly, to realize the desired total partial response)
may be optimized. The filter(s) used and/or the filtering performed
(e.g., at transmit-side and/or receive-side) during partial
response pulse shaping may be optimized symmetrically (i.e. the
linear phase) and/or asymmetrically (i.e. nonlinear phase). In this
regard, in symmetric implementations the tap coefficients may be
set symmetrically around zero, assuming the filter is centered
around zero (i.e. tap coefficient function, h(k), is an even
function that provides linear phase). Optimizing filters/filtering
design and/or configuration may comprise, for example, optimizing
Symbol Error Rate function of transmitter and receiver partial
response taps; optimizing (weighted) minimal distance reduction
(e.g., over transmit-side filter only or both transmit-side and
receive-side filters); optimizing distance between a spectrum mask
imposed on transmission and the response of the transmit-side
filter incorporating nonlinear distortion model; optimizing
non-compensated (residual) preceding taps of the total response
(i.e. both the transmit-side and receive-side filters); optimizing
noise enhancement of receiver side; reducing noise enhancement of
receiver side in case of frequency selective fading (multipath)
using transmit-side and/or receive-side filters; optimizing
adjacent and/or interferes signals and noise folding caused by
decimation (anti-aliasing) at the receiver; optimizing non-linear
tolerance at the receiver originated at Tx side by the overall time
domain response; and/or optimizing `early` taps. In some instances,
the optimization process may be performed per modulation--i.e.
based on the particular modulation scheme (e.g., PSK, QAM, etc.)
that is to be used. In some instances, real time optimization of
the transmit-side and/or receive-side filters may be performed. In
some instances, filtering optimization may comprise optimizing a
constellation symbol mapping used for modulation, such as for the
smallest minimum distance reduction possible or Symbol Error Rate
(SER). In some instances, filtering operations may comprise use of
adaptive transmit-side and/or receive-side filters--e.g., for
adaptive baud rate vs. minimal distance reduction or Symbol Error
Rate (SER), based on particular parameters or criteria, such as
link condition parameters, SER, metric function of sequence
estimation detection and/or other performance indication
measurements (e.g., any parameters that may pertain to receiver
ability to recover timing needed for information detection). The
adaptive transmit-side and/or receive-side filters may also be
configured to account for dynamic channel (fading) compensation.
Filter/filtering optimization is described in more details with
respect to FIG. 4.
[0031] The equalizer and sequence estimator 112 may be operable to
perform an equalization process and a sequence estimation process.
Details of an example implementation of the equalizer and sequence
estimator 112 are described below with respect to FIG. 2. The
output signal 132 of the equalizer and sequence estimator 112 may
be in the symbol domain and may carry estimated values of
corresponding transmitted symbols (and/or estimated values of the
corresponding transmitted information bits of the Tx_bitstream) of
signal 103. Although not depicted, the signal 132 may pass through
an interleaver en route to the de-mapper 114. The estimated values
may comprise soft-decision estimates, hard-decision estimates, or
both.
[0032] The de-mapper 114 may be operable to map symbols to bit
sequences according to a selected modulation scheme. For example,
for an N-QAM modulation scheme, the mapper may map each symbol to
Log.sub.2(N) bits of the Rx_bitstream. The Rx_bitstream may, for
example, be output to a de-interleaver and/or an FEC decoder.
Alternatively, or additionally, the de-mapper 114 may generate a
soft output for each bit, referred as LLR (Log-Likelihood Ratio).
The soft output bits may be used by a soft-decoding forward error
corrector (e.g. a low-density parity check (LDPC) dedecoder). The
soft output bits may be generated using, for example, a Soft Output
Viterbi Algorithm (SOVA) or similar. Such algorithms may use
additional information of the sequence decoding process including
metrics levels of dropped paths and/or estimated bit probabilities
for generating the LLR, where
LLR ( b ) = log ( P b 1 - P b ) , ##EQU00001##
where P.sub.b is the probability that bit b=1.
[0033] In an example implementation, components of the system
upstream of the pulse shaper 104 in the transmitter and downstream
of the equalizer and sequence estimator 112 in the receiver may be
as found in a conventional N-QAM system. Thus, through modification
of the transmit side physical layer and the receive side physical
layer, aspects of the invention may be implemented in an otherwise
conventional N-QAM system in order to improve performance of the
system in the presence of non-linearity as compared, for example,
to use of RRC filters and an N-QAM slicer.
[0034] FIG. 2 is a block diagram depicting an example equalization
and sequence estimation circuit for use in a system configured for
low-complexity, highly-spectrally-efficient communications. Shown
are an equalizer circuit 202, a signal combiner circuit 204, a
phase adjust circuit 206, a sequence estimation circuit 210, and
non-linearity modeling circuits 236a and 236b.
[0035] The equalizer 202 may be operable to process the signal 122
to reduce ISI caused by the channel 107. The output 222 of the
equalizer 202 is a partial response domain signal. The ISI of the
signal 222 is primarily the result of the pulse shaper 104 and the
input filter 109 (there may be some residual ISI from multipath,
for example, due to use of the least means square (LMS) approach in
the equalizer 202). The error signal, 201, fed back to the
equalizer 202 is also in the partial response domain. The signal
201 is the difference, calculated by combiner 204, between 222 and
a partial response signal 203 that is output by non-linearity
modeling circuit 236a. An example implementation of the equalizer
is described in the United States patent application titled "Feed
Forward Equalization for Highly-Spectrally-Efficient
Communications," which is incorporated herein by reference, as set
forth above.
[0036] The carrier recovery circuit 208 may be operable to generate
a signal 228 based on a phase difference between the signal 222 and
a partial response signal 207 output by the non-linearity modeling
circuit 236b. The carrier recovery circuit 208 may be as described
in the United States patent application titled "Coarse Phase
Estimation for Highly-Spectrally-Efficient Communications," which
is incorporated herein by reference, as set forth above.
[0037] The phase adjust circuit 206 may be operable to adjust the
phase of the signal 222 to generate the signal 226. The amount and
direction of the phase adjustment may be determined by the signal
228 output by the carrier recovery circuit 208. The signal 226 is a
partial response signal that approximates (up to an equalization
error caused by finite length of the equalizer 202, a residual
phase error not corrected by the phase adjust circuit 206,
non-linearities, and/or other non-idealities) the total partial
response signal resulting from corresponding symbols of signal 103
passing through pulse shaper 104 and input filter 109.
[0038] The buffer 212 buffers samples of the signal 226 and outputs
a plurality of samples of the signal 226 via signal 232. The signal
232 is denoted PR1, where the underlining indicates that it is a
vector (in this case each element of the vector corresponds to a
sample of a partial response signal). In an example implementation,
the length of the vector PR1 may be Q samples.
[0039] Input to the sequence estimation circuit 210 are the signal
232, the signal 228, and a response h. Response h is based on h
(the total partial response, discussed above). For example,
response h may represent a compromise between h (described above)
and a filter response that compensates for channel non-idealities
such as multi-path. The response h may be conveyed and/or stored in
the form of LTx+LRx-1 tap coefficients resulting from convolution
of the LTx tap coefficients of the pulse shaper 104 and the LRx tap
coefficients of the input filter 109. Alternatively, response h may
be conveyed and/or stored in the form of fewer than LTx+LRx-1 tap
coefficients--for example, where one or more taps of the LTx and
LRx is ignored due to being below a determined threshold. The
sequence estimation circuit 210 may output partial response
feedback signals 205 and 209, a signal 234 that corresponds to the
finely determined phase error of the signal 120, and signal 132
(which carries hard and/or soft estimates of transmitted symbols
and/or transmitted bits). An example implementation of the sequence
estimation circuit 210 is described below with reference to FIG.
3.
[0040] The non-linear modeling circuit 236a may apply a
non-linearity function (a model of the non-linearity seen by the
received signal en route to the circuit 210) to the signal 205
resulting in the signal 203. Similarly, the non-linear modeling
circuit 236b may apply the non-linearity function to the signal 209
resulting in the signal 207. may be, for example, a third-order or
fifth-order polynomial. Increased accuracy resulting from the use
of a higher-order polynomial for may tradeoff with increased
complexity of implementing a higher-order polynomial. Where FnITx
is the dominant non-linearity of the communication system 100,
modeling only FnITx may be sufficient. Where degradation in
receiver performance is above a threshold due to other
non-linearities in the system (e.g., non-linearity of the receiver
front-end 108) the model may take into account such other
non-linearities
[0041] FIG. 3 is a block diagram depicting an example sequence
estimation circuit for use in a system configured for
low-complexity, highly-spectrally-efficient communications. Shown
are a candidate generation circuit 302, a metrics calculation
circuit 304, a candidate selection circuit 306, a combiner circuit
308, a buffer circuit 310, a buffer circuit 312, a phase adjust
circuit 314, and convolution circuits 316a and 316b. The sequence
estimation process described with respect to FIG. 3 is an example
only. Many variations of the sequence estimation process are also
possible. For example, although the implementation described here
uses one phase survivor per symbol survivor, another implementation
may have PSu (e.g., PSu<Su) phase survivors that will be used
commonly for each symbol survivor.
[0042] For each symbol candidate at time n, the metrics calculation
circuit 304 may be operable to generate a metric vector
D.sub.n.sup.1 . . . D.sub.n.sup.M.times.Su.times.P based on the
partial response signal PR1, the signal 303a conveying the phase
candidate vectors PC.sub.n.sup.1 . . .
PC.sub.n.sup.M.times.Su.times.P and the signal 303b conveying the
symbol candidate vectors SC.sub.n.sup.1 . . .
SC.sub.n.sup.Mn.times.Su.times.P, where underlining indicates a
vector, subscript n indicates that it is the candidate vectors for
time n, M is an integer equal to the size of the symbol alphabet
(e.g., for N-QAM, M is equal to N), Su is an integer equal to the
number of symbol survivor vectors retained for each iteration of
the sequence estimation process, and P is an integer equal to the
size of the phase alphabet. In an example implementation, the size
of phase alphabet is three, with each of the three symbols
corresponding to one of: a positive shift, a negative phase shift,
or zero phase shift, as further described in the United States
patent application titled "Low-Complexity,
Highly-Spectrally-Efficient Communications," and in the United
States patent application titled "Fine Phase Estimation for Highly
Spectrally Efficient Communications," each of which is incorporated
herein by reference, as set forth above. In an example
implementation, each phase candidate vector may comprise Q phase
values and each symbol candidate vector may comprise Q symbols. An
example implementation of the metrics calculation block is
described in the United States patent application titled
"Low-Complexity, Highly-Spectrally-Efficient Communications," which
is incorporated herein by reference, as set forth above.
[0043] The candidate selection circuit 306 may be operable to
select Su of the symbol candidates SC.sub.n.sup.1 . . .
SC.sub.n.sup.Mn.times.Su.times.P and Su of the phase candidates
PC.sub.n.sup.1 . . . PC.sub.n.sup.Mn.times.Su.times.P based on the
metrics D.sub.n.sup.1 . . . D.sub.n.sup.Mn.times.Su.times.P. The
selected phase candidates are referred to as the phase survivors
PS.sub.n.sup.1 . . . PS.sub.n.sup.Su. Each element of each phase
survivors PS.sub.n.sup.1 . . . PS.sub.n.sup.Su may correspond to an
estimate of residual phase error in the signal 232. That is, the
phase error remaining in the signal after coarse phase error
correction via the phase adjust circuit 206. The best phase
survivor PS.sub.n.sup.1 is conveyed via signal 307a. The Su phase
survivors are retained for the next iteration of the sequence
estimation process (at which time they are conveyed via signal
301b). The selected symbol candidates are referred to as the symbol
survivors SS.sub.n.sup.1 . . . SS.sub.n.sup.Su. Each element of
each symbol survivors SS.sub.n.sup.1 . . . SS.sub.n.sup.Su may
comprise a soft-decision estimate and/or a hard-decision estimate
of a symbol of the signal 232. The best symbol survivor
SS.sub.n.sup.1 is conveyed to symbol buffer 310 via the signal
307b. The Su symbol survivors are retained for the next iteration
of the sequence estimation process (at which time they are conveyed
via signal 301a). Although, the example implementation described
selects the same number, Su, of phase survivors and symbol
survivors, such is not necessarily the case. Operation of example
candidate selection circuits 306 are described in the United States
patent application titled "Low-Complexity,
Highly-Spectrally-Efficient Communications," which is incorporated
herein by reference, as set forth above.
[0044] The candidate generation circuit 302 may be operable to
generate phase candidates PC.sub.n.sup.1 . . .
PC.sub.n.sup.M.times.Su.times.P and symbol candidates
SC.sub.n.sup.1 . . . SC.sub.n.sup.Mn.times.Su.times.P from phase
survivors PS.sub.n-1.sup.1 . . . PS.sub.n-1.sup.Su and symbol
survivors SS.sub.n-1.sup.1 . . . SS.sub.n-1.sup.Su, wherein the
index n-1 indicates that they are survivors from time n-1 are used
for generating the candidates for time n. In an example
implementation, generation of the phase and/or symbol candidates
may be as, for example, described in one or more of: the United
States patent application titled "Low-Complexity,
Highly-Spectrally-Efficient Communications," and the United States
patent application titled "Joint Sequence Estimation of Symbol and
Phase with High Tolerance of Nonlinearity," each of which is
incorporated herein by reference, as set forth above.
[0045] The symbol buffer circuit 310 may comprise a plurality of
memory elements operable to store one or more symbol survivor
elements of one or more symbol survivor vectors. The phase buffer
circuit 312 may comprise a plurality of memory elements operable to
store one or more phase survivor vectors. Example implementations
of the buffers 310 and 312 are described in the United States
patent application titled "Low-Complexity,
Highly-Spectrally-Efficient Communications," which is incorporated
herein by reference, as set forth above.
[0046] The combiner circuit 308 may be operable to combine the best
phase survivor, PS.sub.n.sup.1, conveyed via signal 307a, with the
signal 228 generated by the carrier recovery circuit 208 (FIG. 2)
to generate fine phase error vector FPE.sub.n.sup.1, conveyed via
signal 309, which corresponds to the finely estimated phase error
of the signal 222 (FIG. 2). At each time n, fine phase error vector
FPE.sub.n-1.sup.1 stored in phase buffer 312 may be overwritten by
FPE.sub.n.sup.1.
[0047] The phase adjust circuit 314 may be operable to adjust the
phase of the signal 315a by an amount determined by the signal 234
output by phase buffer 312, to generate the signal 205.
[0048] The circuit 316a, which performs a convolution, may comprise
a FIR filter or IIR filter, for example. The circuit 316a may be
operable to convolve the signal 132 with response h, resulting in
the partial response signal 315a. Similarly, the convolution
circuit 316b may be operable to convolve the signal 317 with
response h, resulting in the partial response signal 209. As noted
above, response h may be stored by, and/or conveyed to, the
sequence estimation circuit 210 in the form of one or more tap
coefficients, which may be determined based on the tap coefficients
of the pulse shaper 104 and/or input filter 109 and/or based on an
adaptation algorithm of a decision feedback equalizer (DFE).
Response h may thus represent a compromise between attempting to
perfectly reconstruct the total partial response signal (103 as
modified by pulse shaper 104 and input filter 109) on the one hand,
and compensating for multipath and/or other non-idealities of the
channel 107 on the other hand. In this regard, the system 100 may
comprise one or more DFEs as described in one or more of: the
United States patent application titled "Decision Feedback
Equalizer for Highly-Spectrally-Efficient Communications," the
United States patent application titled "Decision Feedback
Equalizer with Multiple Cores for Highly-Spectrally-Efficient
Communications," and the United States patent application titled
"Decision Feedback Equalizer Utilizing Symbol Error Rate Biased
Adaptation Function for Highly-Spectrally-Efficient
Communications," each of which is incorporated herein by reference,
as set forth above.
[0049] Thus, signal 203 is generated by taking a first estimate of
transmitted symbols, (an element of symbol survivor SS.sub.n.sup.1
SS.sub.n.sup.1), converting the first estimate of transmitted
symbols to the partial response domain via circuit 316a, and then
compensating for non-linearity in the communication system 100 via
circuit 236a (FIG. 2). Similarly, signal 207 is generated from a
second estimate of transmitted symbols (an element of symbol
survivor SS.sub.n.sup.1) that is converted to the partial response
domain by circuit 316b to generate signal 209, and then applying a
non-linear model to the signal 209b to compensate for non-linearity
in the signal path.
[0050] FIG. 4 is a block diagram depicting an example partial
response pulse-shaping filtering setup for use in a system
configured for low-complexity, highly-spectrally-efficient
communications. Referring to FIG. 4, there is shown a filtering
system 400, which may comprise a transmit (Tx) pulse-shaper 410, a
receive (Rx) pulse-shaper 420, and a filtering manager 430.
[0051] Each of the Tx pulse-shaper 410 and the Rx pulse-shaper 420
may comprise suitable circuitry, interfaces, logic, and/or code for
performing pulse shaping, such as during communication of data
between a transmitter and a receiver which may comprise the Tx
pulse-shaper 410 and the Rx pulse-shaper 420, respectively. The Tx
pulse-shaper 410 and the Rx pulse-shaper 420 may correspond to the
pulse shaper 104 and the input filter 109, respectively, of FIG. 1.
In this regard, the Tx pulse-shaper 410 and the Rx pulse-shaper 420
may enable adjusting signal waveforms (e.g., of communicated
signals) such as to comply with particular spectral requirements
(i.e. the "spectral masks") of communication channels that may be
used. The waveform adjustments provided by the Tx pulse-shaper 410
and the Rx pulse-shaper 420 may entail various processing
operations and/or functions, particularly filtering. In this
regard, processing signals by the Tx pulse-shaper 410 and the Rx
pulse-shaper 420 may comprise filtering. For example, filtering may
be performed (at the transmit-side and the receive-side) to ensure
that communicated signals conform to the applicable spectral
mask(s) and/or to ensure successful and/or proper recovery of
signals at the receiver side.
[0052] The Tx pulse-shaper 410 and the Rx pulse-shaper 420 may be
implemented using various types of filters, including, for example,
infinite impulse response (IIR) filters and/or finite impulse
response (FIR) filters. The invention is not necessarily limited,
however, to any particular type of filter. In various embodiments
of the invention, the pulse-shaper 410 and the Rx pulse-shaper 420
may be configured to provide partial response pulse-shaping,
substantially as described with respect to FIG. 1, for example. In
this regard, partial response pulse shaping may comprise generating
(and/or handling) waveforms that intentionally incorporate a
substantial amount of inter-symbol interference (ISI). Allowing
such a substantial amount of ISI may provide enhanced communication
performance. For example, partial response based modulation, as
compared to legacy and/or existing modulation schemes, may allow
for use of less bandwidth for communicating the same amount of data
(and with the similar error rates), for communication of same
amount of data over same bandwidth but with lower power
consumption, and/or for communication more data with similar
bandwidth. Accordingly, while legacy/existing pulse shaping (and
particularly filtering related thereto) may be configured to have
no-ISI (or minimal amount of ISI--e.g., corresponding to applicable
error rates), the PR based modulation applied using the Tx
pulse-shaper 410 and the Rx pulse-shaper 420 may be implemented to
operate with a substantial amount of ISI.
[0053] The filtering manager 430 may comprise suitable circuitry,
interfaces, logic, and/or code that may be operable to manage
filtering related processing, such as filtering processing
performed via one or both of the Tx pulse-shaper 410, the Rx
pulse-shaper 420. In this regard, filtering management may comprise
configuring filters and/or filtering operations to meet spectrum
mask limitations according to an underlying
communication/modulation standard without degrading demodulation
performance. Thus, the filtering manager 430 may be operable to
determine and/or provide filtering configuration related parameters
to one or both of the Tx pulse-shaper 410 and the Rx pulse-shaper
420 (Tx_side configuration data 452 and Rx_side configuration data
454, respectively). In this regard, the configuration data may
comprise, for example, filtering configuration parameters such as
number of filter taps and/or filter coefficients values.
[0054] In various embodiments of the invention, the filtering
manager 430 may be configured to implement and/or execute filtering
optimization processes, which may be used to determine filtering
configurations that optimize filtering operations based on
particular criteria or conditions (e.g., for partial response based
filtering). For example, the filtering manager 430 may be used to
perform filtering optimization processes, which may be based on,
for example, control data 442 that may comprise preconfigured
criteria or user inputs (e.g., definitions, preferences, etc.), to
produce optimized filter coefficient values (e.g., for the Tx
pulse-shaper 410 and the Rx pulse-shaper 420). In some instances,
the optimization processes may also be based on information
pertaining to and/or provided by the transmitter, the receiver,
and/or the communication channels/links. The results 444 of the
optimization process (e.g., optimized filter configuration
parameters) may be used in generating the Tx_side configuration
data 452 and Rx_side configuration data 454 which may be sent
directly to the filters and/or may be outputted to the users (e.g.,
to system designers or operators), such as using log files or
screens.
[0055] The filtering manager 430 may comprise various components
and/or subsystems which may be utilized during filtering
management. For example, in some instances, the filtering manager
430 may comprise an input/output (I/O) component 432, which may
incorporate various I/O mechanisms or devices (e.g., mice,
keyboards, keypads, user interface, displays, touch screens or
touchpads, and the like) to enable interacting with users (e.g.,
system designers and/or operators). In this regard, the I/O
component 432 may be used to allow inputting control data or
commands, such as implementation-specific parameters, variables,
constraints and cost functions that may define the desired
optimization. The I/O component 432 may also be used to allow
outputting data to the system users. For example, the I/O component
432 may comprise suitable graphic user interfaces (GUIs) and/or
interface (e.g., a file transfer interface) for acknowledging (or
repeating--e.g., for confirmation) user inputs, and/or to provide
corresponding output (e.g., optimization results), such as suitable
filter tap coefficients or other configuration parameters, for
example.
[0056] The filtering manager 430 may also comprise a processing
component 434, which may be configured to perform various
processing functions or tasks in support of operations performed by
the filtering manager 430. For example, the processing component
434 may be used to implement and/or execute any filtering
optimization processes that may be supported by the filtering
manager 430 (e.g., PR filtering optimization process). In this
regard, designing and/or configuring filtering operations may
entail analysis of the spectrum response of any filters used (at
the transmit-side and/or the receive-side). The spectrum response
may be calculated using, for example, Fourier transform. In this
regard, the spectrum response of the PR signal (i.e. the total
partial response of the system) may be calculated or estimated
using, for example, a model for nonlinear distortion (e.g., 3rd
order polynomial, or Voltera series).
[0057] The filtering manager 430 may be implemented as a dedicated,
stand-alone system or device (e.g., general-purpose computer,
dedicated controller, or the like), which may be connected (e.g.,
using wireless and/or wired connections, based on any appropriate
interface/standard) to one or both of the transmitter and receiver
comprising the Tx pulse-shaper 410, the Rx pulse-shaper 420,
respectively, to enable interactions therewith during filtering
management. Alternatively, in some instances, at least a portion of
the filtering manager 430 (and/or functions or operations performed
thereby) may be incorporated into the transmitter and/or the
receiver, or component(s) thereof. In some instances, the filtering
manager 430 may be implemented in distributed manner, with
components and/or functions thereof being distributed among the
transmitters, the receiver, and/or a stand-alone device/system. In
some instances, the filter manager 430 may be configured to
optimize filtering processing in the Tx pulse-shaper 410 and/or the
Rx pulse-shaper 420.
[0058] In operation, the Tx pulse shaper 410 and the Rx pulse
shaper 420 may be used to provide pulse shaping--e.g., waveform
adjustments based on particular spectral masks, nonlinearity,
symbol constellation, etc.--which would typically entail performing
filtering. In this regard, the filter manager 430 may be used to
configure, control, and/or manage filtering performed by the Tx
pulse shaper 410 and/or the Rx pulse shaper 420. For example, the
Tx pulse shaper 410 and the Rx pulse shaper 420 may be implemented
using infinite impulse response (IIR) filters and/or finite impulse
response (FIR) filters, and as such configuring, controlling,
and/or managing filtering may comprise, inter alia, determining or
setting the number of taps (or "length") and/or the values of the
tap coefficients of the Tx pulse shaper 410 and the Rx pulse shaper
420. In this regard, the number of taps may comprise the number of
filter taps for each of the Tx pulse shaper 410 and the Rx pulse
shaper 420, and/or the total number of taps (i.e. combined number
of taps of both of the Tx pulse shaper 410 and the Rx pulse shaper
420).
[0059] In some instances, the Tx pulse shaper 410 and/or the Rx
pulse shaper 420 may be configured for use in conjunction with
partial response based communications. In this regard, one
distinction between a partial response (PR) based scheme and
existing/legacy schemes pertains to inter-symbol interference
(ISI). Inter-symbol interference (ISI) is typically undesired, and
existing/legacy schemes are typically tailored to eliminate or
significantly minimize ISI (e.g., either being configured to
achieve zero ISI or near-zero ISI, or when allowing for ISI it
would be minimal amount, typically based on specified acceptable
error rates). Achieving such zero (or near-zero) ISI usually comes
at the expense of the baud rate (or the bandwidth
efficiency)--e.g., being significantly worse than the channel's
Shannon capacity bound.
[0060] For example, most existing filtering implementations,
particularly Root Raised Cosine (RRC) and/or Raised Cosine (RC)
based implementations, are typically configured to have near-zero
ISI, to assure demodulating performance. For example, with
RRC-based implementations, RRC-based filters would typically be
used in both of the transmitter and receiver, serving as pulse
shaping filter and match filter, respectively. The challenge in
RRC-based filter design is to adjust the truncated and quantized
RRC taps to meet spectrum mask limitations without generating
inherent ISI. In this regard, the conventional root raised cosine
(RRC) pulse shaping filter is an even function to assure linear
phase response (i.e. the time domain filter response is symmetric)
and the length of the casual part is equal or similar to the
non-casual. The modulated signal, which is the convolution between
the filter taps and the symbols, may incorporate peaks that are
associated with nonlinear distortion that typically cannot be
compensated in the receiver because the non-casual part may not be
known to the receiver.
[0061] In partial response (PR) based communications as implemented
in accordance with aspects of the present invention, however,
end-to-end system/path (particularly the Tx pulse shaper 410 and
the Rx pulse shaper 420) may be configured such that signals
communicated between the transmitter and the receiver would
intentionally have a substantial amount of inter-symbol
interference (ISI). In this regard, allowing for substantial amount
of ISI may allow for increasing the symbol rate (and/or reducing
required bandwidth), which may allow, when drawbacks of having
substantial ISI are mitigated (e.g., through signal processing
techniques in the receiver) for enhanced performance. In other
words, use of partial response pulse shaping may allow for
generating signals with particular inherent and substantial amount
of ISI such that to enable compressing the signal spectrum to allow
improved spectral efficiency. In this regard, ISI level allowed in
partial response based implementations may be worse than the
threshold signal-to-noise ratio (SNR) whereas in legacy
systems/schemes, which typically have near zero ISI (having similar
spectral efficiency), the ISI level would typically be much better
than threshold SNR. For example, in a legacy system that is
configured (e.g., based on particular standard) to have particular
SNR threshold (e.g., 30 dB), the ISI, which would be treated as an
interference and thus factor into the overall noise, would have to
be negligible (e.g., be 20 to 30 dB down from the SNR threshold).
On the other hand, in a corresponding partial response based
implementation that specifically allows for the presence of ISI
(and account for it in the PR based estimation process), the ISI
may be substantial relative to the same SNR threshold (30 dB) since
it does not be counted as noise (e.g., ISI can be equal to or
greater than the SNR threshold of 30 dB).
[0062] Therefore, to achieve the desired performance enhancements
when using partial response pulse shaping, various aspects of
operations and/or functions that may be required for providing
end-to-end communicability may be configured and/or adjusted to
account for the partial response (and particularly, for the
presence of substantial ISI). With respect to the filtering
operations, in PR-based implementations, the number of taps and/or
the values of the tap coefficients of the Tx pulse shaper 410 and
the Rx pulse shaper 420 (e.g., as determined by the filtering
manager 430) may be designed such that the pulse shaper
intentionally may be non-optimal in terms of noise tolerance in
order to improve tolerance of nonlinearity. In this regard, the PR
pulse shaping providing by the Tx pulse shaper 410 and the Rx pulse
shaper 420 may offer superior performance in the presence of
nonlinearity as compared to, for example, the conventional root
raised cosine (RRC) pulse shaping filters. In this regard, the PR
communication path may be designed and/or configured such that
effects of the substantial ISI may be mitigated and/or accounted
for based on use of a specifically configured estimation process,
as described, for example, in the United States patent application
titled "Low-Complexity, Highly-Spectrally-Efficient
Communications," which is incorporated herein by reference, as set
forth above.
[0063] In various embodiments, the design and configuration of the
pulse shape filtering (i.e. transmit-side and/or receive-side
filters) may be based on optimization processes, which may be
configured to achieve and/or balance between several objectives.
Furthermore, the filtering optimization processes may be subject to
implementation-specific performance-related parameters, variables,
constraints, and/or cost functions, which may be defined for
particular desired optimization. In this regard, the one or more
performance-related parameters may pertain to the filtering itself
and/or other aspects of the communication that may be affected by
it (e.g., error measurements). The constraints may comprise
particular limits or requirements, which may apply to, for example,
the performance-related variables and/or the filters (or their
configuration). For example, spectral mask limits and/or compliance
therewith may be constraint in any filtering configuration or
optimization thereof. The cost functions may be defined over one or
more performance-related parameters or variables--e.g., specifying
the filter configuration (for example, filter tap coefficient
values) is to be optimized based on a function of one or more
variables. The cost functions may, in some instances, specify
different weights to pertinent parameters or variables. The
implementation-specific parameters, variables, constraints and/or
cost functions may be defined by system designers or operators,
such as via user input (which may be provided as part of the
control data 442). Thus, the filter optimization process may
provide optimal filtering configuration that may achieve the
primary objective(s), as applied to the cost functions to meet (as
much as possible) the specified performance-related parameters or
variables, while complying with the specified constraints.
[0064] For example, the primary design objective for filtering
optimization may be spectrum mask compliance, including impact of
nonlinear distortion. In particular, it may be desirable (and thus
be considered in designing and/or optimizing filtering operation)
to comply with applicable spectrum masks as closely as possible to
achieve as close to the Shannon capacity limit as possible. Another
(or alternative) primary design objective for filtering
optimization may be symbol error rate minimization for equalization
processing. In this regard, typical adaptive equalization method
may be based on least means square (LMS) algorithms, which may not
be optimal in certain conditions (e.g., in case of severe
multipath) and may not assure lowest SER and/or BER. Accordingly,
the equalization process used in conjunction with partial response
based communications may be configured as an adaptive process which
may minimize SER (thus possibly providing optimal performance
subject to the finite equalizer length). In some instances, the
adaptive equalization used may incorporate parameters that may be
based on the SER expression of a PR system/path. An example
implementation of such equalization method is described in the
United States patent application titled "Decision Feedback
Equalizer Utilizing Symbol Error Rate Biased Adaptation Function
for Highly-Spectrally-Efficient Communications," which is
incorporated herein by reference, as set forth above.
[0065] The filtering design and/or configuration may account for
nonlinearity, such as by considering nonlinear distortion when
configuring the filters (e.g., filter taps). In this regard,
tolerating nonlinearity (particularly at the receive-side) may
allow for use of an optimal observation model--i.e. not needing to
account for nonlinearity at the transmit-side. Other design
objectives may comprise partial response minimum distance reduction
(e.g., for worst case error patterns), minimization of symbol error
rate (SER) and/or bit error rate (BER), early taps amplitude
maximization, residual non-compensated early response, minimization
of noise enhancement (e.g., at the receive-side), minimization of
amplitude of tail response, nonlinear tolerance, adjacent channel
rejection, and/or decimation filtering to avoid noise folding (i.e.
anti-aliasing).
[0066] The partial response (PR) filtering, and/or the configuring
thereof, may be associated with minimum distance reduction. In this
regard, minimum distance reduction may be caused by the partial
response's inherent ISI and the fact that every sample (at the
transmit-side and/or the receive-side) may correspond to a linear
combination of multiple symbols. In other words, rather than slice
or sample for a single symbol as many legacy/existing systems do,
in PR based implementations, the receive side may be configured to
estimate a sequence of symbols. The degradation associated with PR
pulse shaping may be compared to flat pulse shape (or RRC/RC
shaping) which may typically introduce no (or very little) ISI. The
determined degradation may represent a theoretical bound for the
more optimal (e.g., Maximum Likelihood or ML) estimation, and it
may be perceived as the penalty for spectrum compression--i.e. a
tradeoff for using less bandwidth or being able to send more
symbols. In various instances, partial response detection may be
associated with error bursts that may have typical patterns, which
may be determined based on analysis, simulations and/or based on
tracking/monitoring. In this regard, every symbol mapping may have
a worst case error pattern that may yield the minimum distance
reduction. Error patterns and/or minimum distance are described in
more detail in the United States patent application titled
"Decision Feedback Equalizer for Highly-Spectrally-Efficient
Communications," which is incorporated herein by reference, as set
forth above.
[0067] Typically, high order mapping (e.g., 128-QAM) may associate
with higher reduction of minimum distance than low order mapping
(e.g. QPSK) because high order mapping may have much more
combinations of error patterns than low order mapping would have.
For example worst case pattern error of QPSK mapping may be [1 -1]
and for 16-QAM is [1 -2 2 -1], where a `1` in the error pattern
vector may reflect the distance to an adjacent symbol. The
following table shows examples of partial response pulse shape
performance:
TABLE-US-00001 TABLE 1 Examples of particular partial response
based schemes Error Pattern Gross Minimum Related to PR Base
Capacity Spectral Distance Minimum Scheme Modulation Gain
Efficiency Reduction Distance PR5 QPSK 2.5 5 b/s/Hz -2.5 dB [1 -1 1
-1] PR10 32-QAM 2 10 b/s/Hz -8.0 dB [1 -2 2 1]
[0068] Accordingly, one of the filtering design optimization goals
may be minimizing minimum distance reduction. In some instances,
there may be several error patterns which have similar reduction of
minimum distance, and thus more than one error pattern should be
considered in the optimization. Another optimization goal may be
based on symbol error ration. In this regard, the SER function
applicable in the system may be configured such that it may
consider the contribution of worse error patterns, each associated
with its weight.
[0069] The design method can be based on an analytic or a numerical
approach (or may use both). The optimization may be driven by one
or more design considerations or goals, such as minimum distance
reduction for selected error patterns for a given spectrum
compression gain, or for spectrum compression gain for a given
minimum distance level. In this regard, the selected error patterns
may be the `n` most frequently occurring error patterns (`n` being
a non-zero natural number), such as seen during simulation and/or
operation (i.e. use) of the system. The optimization may be limited
by one or more constraints, such as spectrum mask limitations of
the pulse shape taps (with or without the impact of a nonlinear
model).
[0070] Due to spectrum mask limitations the pulse shape impulse
response is typically smooth. Accordingly, it may be desirable to
select filter tap coefficients that grow gradually from zero. Thus
the first ("early") taps of the pulse shape filter may be chosen
(e.g., by filtering manager 430) to have low values. The partial
response signal (at the transmit-side) may be a convolution between
the partial response filter taps and symbol stream. The new
(current) symbol contributes only to the most new sample and the
contribution level in the newest sample is proportional to the
value of the first (earliest) tap coefficient of the partial
response filter. On the receive side, data (e.g., symbol)
extraction may be based on use of suboptimal search mechanisms
(e.g., based on M-ary algorithm, an implementation of which is
referred to herein as High Probability Sequence Estimation or
`HPSE`). Use of such mechanism (i.e. sub-optimal estimation) may
result in estimates of a symbol with low reliability. In case of
low signal-to-noise ratio (SNR), new symbol estimation might be
faulty, and may cause error bursts. Therefore, to improve error
performance, a consideration (goal) of the filter optimization may
be maximizing "early" taps amplitude while complying with other
constraints. Alternatively, constraints can be applied for some
(i.e. a subset) of the "early" taps amplitude. By optimizing the
level of early taps, the demodulator resources and complexity may
be significantly relaxed. In this regard, demodulating/decoding (at
the receive-side) based on sequence estimation may grow
significantly (e.g., exponentially) with the search dimension. The
HPSE process may use the early taps for exercising the search. The
number of survivors and taps needed for effective search, which
provide high performance in low SNR conditions, may highly depend
on the amplitude of the early taps. Therefore, optimizing early
taps level may be important for reducing the number of survivors
and taps participating in the search process, thus saving
dramatically resources, power, and cost of the demodulator (in
particular resources used for the sequence estimation).
[0071] Minimum distance of the partial response signal may affect
sequence estimation performance, thus it can be considered when
optimizing the minimum distance reduction of the entire path (i.e.
including both of the transmit-side and the receive-side filters).
In this regard, the receive-side filter may be optimized to
minimize minimum distance reduction while also providing a
determined (e.g., based on the control data 442) amount of noise
rejection and out-of-band rejection to reject interferences such as
adjacent channels.
[0072] As discussed above, the total partial response consists of
the convolution of pulse shaping transmit-side and receive-side
filters. The convolution may yield a preceding tail, which may not
be compensated by the demodulator (thus resulting in introduction
of floor to the demodulator). Therefore, an optimization design
goal may be to minimize the preceding tail, such as below the
operating point. In this regard, because the tail of the partial
response may cause error duplication in the sequence estimation,
the optimization process may be tailored to control the value of
tail tap coefficients to improve stability, such as at low SNR
conditions.
[0073] The receive-side filter may be configured, for example, to
reject interference and provide optimal SNR performance in presence
of additive white Gaussian noise (AWGN). Design considerations
(goals) particularly for the receive-side filter may include noise
enhancement (e.g., in comparison to an ideal match filter), partial
response performance, out-of-band rejection and impacts on tap
coefficients of early taps as well as tap coefficients of residual
taps.
[0074] The observation model (referred to as the "WAM" observation)
used in designing/optimizing PR pulse shaping filters as described
herein may not necessarily provides "sufficient statistics" and
consequently may be sub-optimal in comparison to estimation
approaches currently in use (which are typically based on maximum
likelihood or `ML`). The WAM observation model, however, may
perform better in case of reduced complexity sequence estimation
with less degradation around threshold SNR. Additionally the
observation model may incorporate, as an optimization consideration
or goal (e.g., as part of the transmit-side and/or receive-side
pulsing shaping design), nonlinear distortion compensation.
Therefore, the nonlinear model may be applied on the reconstructed
partial response survivors/successors to ensure that the partial
response being used by the time domain sequence estimation would be
close to the transmit-side pulse shape taps (i.e. assure that
nonlinearities generated on the transmit-side, such as by the power
amplifier, may be observed by the sequence estimation in the
receive-side). Accordingly, the observation model used herein may
optimize the distance between transmit-side pulse shape and the
observation response (overall PR) in presence of the nonlinear
distortion.
[0075] The sequence estimation used in the receive-side may be
configured such that its time domain response should be close to
the transmit-side pulse shape response (e.g., to assure nonlinear
tolerance). The transmit-side partial response signal may be
affected by the transmit-side nonlinearities. The sequence
estimation, however, is typically configured to use the total
partial response, which may be different from transmit-side pulse
shape due to the use of filter on the receive side (i.e.
receive-side filter). In this regard, the nonlinear model is
applied over the reconstructed signal in the receiver to satisfy
the receive-side samples. Therefore it may be important that the
time domain response of the total partial response be similar to
(or very close to) the transmit-side partial response, so the
impact of applying the nonlinear model on the receive-side may
provide similar output as the actual nonlinearities (i.e. including
the transmit-side nonlinearities). This may be achieved by using,
as part of the filtering optimization processing, a cost function
or a constraint that may be applied to assure the above requirement
is a least means square (LMS) function between the transmit-side
pulse shape taps and the total PR response taps that is used for
the sequence estimation.
[0076] Another type of factors that may affect partial response
(and thus filtering operations and/or filter configuration
pertaining thereto) is channel conditions. In other words, channel
conditions (and any measures or functions adapted to handle or
compensate for them in one or both of the transmitter and the
receiver) may constitute performance-variables and/or constraints
which may pertinent to (and thus must be accounted for in) the
optimization process. In this regard, channel variations, such as
channel attenuation (fading), which has impact on signal-to-noise
ratio (SNR), multipath (selective fading), and received
interference signals, may be accounted and/or compensated for,
preferably concurrently by both the transmit-side and the
receive-side for best performance. In some implementations, certain
channel conditions (e.g., flat channel attenuation) may be
accounted and/or compensated for, including at the transmit side.
For example, flat channel attenuation may be compensated for, such
as by adapting transmit (Tx) power (in the Tx pulse shaper 410), as
well as supporting receiver (Rx) dynamic range (in the Rx pulse
shaper 420). Multipath can be compensated for by the receive-side
equalization, which may incorporate, for example, a noise
enhancement penalty. In addition, in some instances multipath may
partially be addressed by use of transmit-side equalization, which
advantageously may not suffer from the noise enhancement as in the
case of the receive-side equalization. In this regard, use of
partial response based communications may allow for use of
equalization in the transmitter since introducing (controlled) ISI
is acceptable (and mainly part of the partial response scheme).
Thus, as result of the use of transmit side equalization, noise may
not be enhanced as much in the receive-side equalization. Use of
transmit-side equalization may have its limitations, however. For
example, use of full equalization at the transmit-side may affect
minimum distance, and/or transmit-side equalization may be limited
by the transmit spectrum mask. Accordingly, in one embodiment,
desired total equalization may be achieved based on combining of
transmit-side and receive-side equalization. In this regard, in
some instances, only "partial" equalization may be performed in the
transmit-side (i.e. in the Tx pulse shaper 410), with the remaining
equalization being performed in the receive-side (i.e. in the Rx
pulse shaper 420).
[0077] In case of interference signals, the Rx pulse shaper 420
(particularly filters therein and/or filtering operations performed
thereby) may be adaptively configured to nullify the interference.
Such adaptation may, however, cause degradations such as noise
enhancement. Therefore an optimization may be used to achieve
better performance. In this regard, transmit-side and receive-side
filters adaptation may be associated with impact for partial
response modulation attributes, such as minimum distance reduction,
early taps amplitude, and/or uncompensated preceding response,
which may be considered in the adaptation optimization. For
example, the transmit-side and receive-side filters may adapt
dynamically to optimize BER, SER and/or throughput performance, and
to improve stability under channel variations and interferences
mentioned above. The optimization objectives could be subject to
the constrains that are applied in the filters design/optimization
process--e.g., spectrum mask, minimum distance reduction, receiver
noise enhancement, receiver adjacent rejection, receiver
anti-aliasing, matching the transmitter time domain response with
the total response for non-linear toleration, early taps amplitude
and the uncompensated preceding response (floor). In this regard,
although the SER and BER may be highly coupled, and BER may
typically improve when SER improves, it is possible that BER may
not provide the expected improvement for a given SER improvement
due to possible dependency within symbol errors and/or the
characteristics of the forward error correction (FEC) or channel
coding being used. In this regard, in some instances the best BER
performance for a given SER may result from less dependency within
the symbol errors--i.e. when symbol errors have less bursty nature.
The statistical length of a symbol error burst may depend, for
example, on the time domain profile of the partial response (e.g.,
taps amplitude). In instances where the partial response decays
fast (e.g., within a small number of taps), it may assure shorter
bursts of symbol error, but it may impact other important
attributes of the partial response, such as early taps amplitude
and uncompensated preceding response, which are related to the
overall performance. Therefore the BER may be considered for the
optimization along with the SER.
[0078] In various embodiments, different configurations may be
utilized for achieving a given (i.e. the same) gross spectral
efficiency. The following table describes examples of different
configuration modes for achieving a particular spectral
efficiency--e.g., 10 bit/sec/Hz, which may correspond to PR10:
TABLE-US-00002 TABLE 2 Examples of different configuration modes
for PR10 Bits Spectrum Spectrum Symbol per Compression Compression
Constellation Symbol Rate Efficiency 16-QAM 4 2.50 10 b/s/Hz 32-QAM
5 2.00 10 b/s/Hz 64-QAM 6 1.67 10 b/s/Hz
[0079] As shown in table 2, it is possible to achieve the same
spectrum compression efficiency by use of different configuration
modes, each of which resulting in different spectrum compression
rate, which may be measured in relation to the same reference
(legacy) configuration--e.g., a spectrum compression rate value of
1.00 may correspond to, for all three modes, a legacy RRC based
1024-QAM. Having higher spectrum compression rate may provide
higher dimensions in the Euclidian domain (which may generate a
steeper SER curve). However, due to the limited complexity of
practical sequence estimation performance at low SNR are degraded
(cutoff). The opposite result may be obtained by using low spectrum
compression rate with high order modulation. The amplitude
distribution characteristics (CCDF) of the partial response signals
which may have been deeply compressed may be degraded--i.e. such PR
signals may be more sensitive to nonlinear distortion than PR
signals configured with lower spectrum compression rate and higher
constellation order. In some instances, spectrum compression rate
and constellation order may be optimized according to system
requirements (e.g., performance under nonlinearities, SNR dynamic
range, and complexity). In some instances, when using high spectrum
compression rate it may be possible to exclude FEC in the system as
the SER and BER curve may be steep enough.
[0080] For example, filtering operations performed via the Tx pulse
shaper 410 and the Rx pulse shaper 420, corresponding to the total
partial response, may be configured using, e.g., simulation (which
may be performed during system design). For example, the filtering
of the Tx pulse shaper 410 and the Rx pulse shaper 420 may be
designed in a MATLAB environment, such as using the function
`fmincon( )`. In this regard, the function `fmincon( )` may
minimize a particular object under predefined constraints. In the
present partial response (PR) scheme described herein the
minimization objective may be minimal distance reduction, or a
weighted combination of minimal distance reductions for the worst
case error patterns, or SER.
[0081] The constraints may comprise, for example, spectrum mask
limits, tap coefficients of early taps, preceding power
response(s), receive-side out-of-band rejection, matching the
transmitter time domain response with the total response for
non-linear toleration and/or noise mismatch. In this regard, a
significant constraint in designing and/or configuring filtering
operations may the transmit-side (i.e. at the Tx filters) spectrum
mask limits, with or without the impact of nonlinear distortion. In
other words, the pulse shaping resulting from the filtering
operations (particularly at the transmit-side) must typically
comply with specific spectral masks, such as in accordance with the
applicable governmental regulation. The tap coefficients of the
filters' `early` taps may also be treated as a constraint. In this
regard, the tap coefficients of the filters' `early` taps may be
constrained to assure the performance of the sequence estimation,
particularly the High Probability Sequence Estimation (HPSE) used
herein or any other sub-optimal sequence estimation. The preceding
(i.e. pre cursor) power responses may be included as part of the
optimization constraints. In this regard, the preceding
(pre-cursor) power response of the total partial response may be
limited to a certain level, such as to minimize the impact of
sensitivity degradation and flooring. The total pre-cursor power
may be a summation of all individual pre-cursor taps, but the
sequence estimation (e.g., HPSE) may consist of convolution with
the overall partial response taps that reject out-of-band signal
components, thus the actual pre-cursor floor may be evaluated by
the total taps power of the convolution of pre-cursor taps with
partial response taps. Such approach may allow further flexibility
and consequently better performance of the system. Noise mismatch
may also be treated as an optimization constraint. In this regard,
the receive-side filtering (e.g., filtering by the Rx pulse shaper
420) may be incorporated into the minimization objective, but may
also affect the SNR at its output. For example, the output SNR
degradation (at the receive-side filter) comparing to a perfectly
match filter may be set as a constraint.
[0082] FIG. 5 is a block diagram depicting an example finite
impulse response (FIR) implementation of partial response
pulse-shaping filters, in accordance with an embodiment of the
present invention. Referring to FIG. 5, there is shown a transmit
(Tx) filter 510 and a receive (Rx) filter 520. In this regard, the
Tx filter 510 and the Rx filter 520 may correspond to the Tx pulse
shaper 410 and the pulse shaper 420 (or at least the filtering
components/functions thereof), respectively.
[0083] In the example embodiment shown in FIG. 5, the Tx filter 510
and the Rx filter 520 may be implemented as finite impulse response
(FIR) filters. It is understood, however, that the invention is not
so limited, and that the FIR implementation is provided as
non-limiting example embodiment.
[0084] The Tx filter 510 may be configured as FIR of LTx-1
order--i.e. having LTx taps. In this regard, the Tx filter 510
comprise a plurality of delay (e.g., Z transform, applied as
z.sup.-1 operator) elements 512.sub.1-512.sub.LTx-1, a plurality of
multipliers 514.sub.1-514.sub.LTx (for applying a plurality of
corresponding tap coefficients or weights: T.sub.1-T.sub.LTx), and
an accumulator 516 (which may be implemented using a plurality of
combiners 516.sub.1-516.sub.LTx1, which may connected in
series--such that to allow accumulating the weighted sum of the
current and a finite number of previous values of the Tx filter
input).
[0085] Similarly, the Rx filter 520 may be configured as FIR of
LRx-1 order--i.e. having LRx taps. In this regard, the Rx filter
520 comprise a plurality of delay (e.g., Z transform, applied as
z.sup.-1 operator) elements 522.sub.1-522.sub.LRx-1, a plurality of
multipliers 524.sub.1-524.sub.LRx (for applying a plurality of
corresponding tap coefficients or weights: R.sub.1-R.sub.LRx), and
an accumulator 526 (which may be implemented using a plurality of
combiners 526.sub.1-526.sub.LRx-1, which may connected in
series--such that to allow accumulating the weighted sum of the
current and a finite number of previous values of the Rx filter
input).
[0086] In operation, the Tx filter 510 (operating in the
transmitter) and the Rx filter 520 (operating in the receiver) may
be used to provide the required overall filtering during
communications, particularly to provide pulse shaping and noise
rejection. For example, in some instances the Tx filter 510 and the
Rx filter 520 may be configured provide a total partial response,
as described in FIGS. 1-4 for example. In this regard, the number
and values of the filters taps (i.e. number of taps at the
transmit-side and receive-side: LTx and LRx, and the values of the
transmit-side and receive-side tap coefficients: T.sub.1-T.sub.LTx
and R.sub.1-R.sub.LRx) may be determined based on application of
filtering optimization that may be tailored for partial response
based paths, substantially as described with respect to FIG. 4 for
example.
[0087] FIG. 6 is a flow chart depicting an example of a process for
joint optimization of transmitter and receiver pulse-shaping
filters, in accordance with an embodiment of the present invention.
Referring to FIG. 6, there is shown a flow chart 600 comprising a
plurality of exemplary steps for configuring and/or optimizing
partial-response pulse-shaping based filtering.
[0088] In step 602, filtering related fixed constants and/or
optimization-related parameters may be configured--e.g., determined
and/or set. In this regard, filtering-related fixed constants may
comprise, for example, Tx filter length and/or Rx filter length,
sampling per symbol, nonlinear distortion backoff (which may be a
proxy for Tx power), baud rate, and/or channel spacing. The
optimization-related parameters may be selected based on the
optimization process. For example, in instances where the
optimization is performed using MATLAB function `fmincon( )`, the
optimization parameters may comprise maximum number of iterations,
tolerance, and/or search algorithm. In step 604, optimization
constraints may be defined. In this regard, the optimization
constraints may comprise, for example, spectral mask limit(s), Rx
filter noise mismatch, Rx filter out-of-band rejection, early taps
amplitude, preceding tail power, matching the transmitter time
domain response with the total response for non-linear toleration
and the like. In step 606, optimization variables may be
structured, such as based on the applicable optimization process.
For example, in instances where the optimization is performed by
use of MATLAB function `fmincon( )`, the variables under
optimization may comprise filters tap coefficients, which may be
structured in vectors format according to the fmincon( )
definitions, for example.
[0089] In step 608, the filtering optimization processing may be
performed, such as by initiating running of the MATLAB function
fmincon( ) (or any other constrained nonlinear optimization
technique). The function fmincon( ) may use one or more user
defined scripts. For example, the function fmincon( ) may use two
user defined scripts, including one for the cost function which
holds the minimal distance reduction or SER as function of the
filter tap coefficients, and a second function for holding the
constraints expressions as function of the optimization variables
(i.e. filters taps). In step 610, results of the optimization
process may be monitored, and may be used in configuring the
filtering operations (and/or the results may be stored for
subsequent use).
[0090] FIG. 7 is a chart diagram depicting a comparison between the
frequency-domain responses of a legacy transmit filter and an
optimized partial response pulse-shaping transmit filter. Referring
to FIG. 7, there is shown two charts 710 and 720.
[0091] In this regard, chart 710 shows a frequency-domain response
of a reference transmit filter whereas the chart 720 shows a
frequency-domain response of a corresponding optimized partial
response (PR) pulse-shaping transmit filter. As shown in FIG. 7,
the reference transmit filter may comprise an RRC-based filter
configured for 1024-QAM (with the transmitter RRC filter being
configured to have a roll-off factor of 0.2), whereas the
corresponding partial response (PR) pulse-shaping transmit filter
may comprise an optimized PR transmit filter for processing 32-QAM
symbols. In this regard, the PR pulse-shaping transmit filter
represented in FIG. 7 may be optimized (along with the
corresponding receive filter) using an optimization process as
described in FIG. 6 for example.
[0092] Both of charts 710 and 720 show a spectral mask 730 that may
be defined for the transmitted signal. Spectral masks may be
defined by a particular standards body, such as the European
Telecommunications Standards Institute (ETSI). For example, the
spectral mask 730 may represent a spectral mask defined by the ETSI
EN 302 217-2-2 standard titled "Fixed Radio Systems;
Characteristics and Requirements for Point-to-Point Equipment and
Antennas." This standard is available at www.etsi.org.
[0093] In chart 710, representing the frequency-domain response of
the reference transmit filter (1024-QAM RRC transmit filter with
roll-off factor of 0.2), curve 712 represent the modulated signal
of the reference (RRC-based) transmit filter whereas the curve 714
represent the distorted signal of the reference (RRC-based)
transmit filter. In chart 720, representing the frequency-domain
response of the optimized PR transmit filter (driven by 32-QAM),
curve 722 represent the modulated signal of the optimized PR
transmit filter whereas the curve 724 represent the distorted
signal of the optimized PR transmit filter. Comparing the
corresponding signals (i.e. 712 vs. 722 and/or 714 vs. 724)
demonstrates that the optimized PR transmit filter provides
enhanced performance. For example, the response of the optimized PR
transmit filter shows that it may be able to match the spectral
mask limits as good or even better than reference (RRC-based)
transmit filter (e.g., up to a particular target symbol rate--such
as .about.15 MHz).
[0094] Other implementations may provide a non-transitory computer
readable medium and/or storage medium, and/or a non-transitory
machine readable medium and/or storage medium, having stored
thereon, a machine code and/or a computer program having at least
one code section executable by a machine and/or a computer, thereby
causing the machine and/or computer to perform the steps as
described herein for design and optimization of partial response
pulse shape filter.
[0095] Accordingly, the present method and/or system may be
realized in hardware, software, or a combination of hardware and
software. The present method and/or system may be realized in a
centralized fashion in at least one computer system, or in a
distributed fashion where different elements are spread across
several interconnected computer systems. Any kind of computer
system or other system adapted for carrying out the methods
described herein is suited. A typical combination of hardware and
software may be a general-purpose computer system with a computer
program that, when being loaded and executed, controls the computer
system such that it carries out the methods described herein.
[0096] The present method and/or system may also be embedded in a
computer program product, which comprises all the features enabling
the implementation of the methods described herein, and which when
loaded in a computer system is able to carry out these methods.
Computer program in the present context means any expression, in
any language, code or notation, of a set of instructions intended
to cause a system having an information processing capability to
perform a particular function either directly or after either or
both of the following: a) conversion to another language, code or
notation; b) reproduction in a different material form.
[0097] While the present methods and/or apparatus may have been
described with reference to certain implementations, it will be
understood by those skilled in the art that various changes may be
made and equivalents may be substituted without departing from the
scope of the present method and/or apparatus. In addition, many
modifications may be made to adapt a particular situation or
material to the teachings of the present disclosure without
departing from its scope. Therefore, it is intended that the
present method and/or apparatus not be limited to the particular
implementations disclosed, but that the present method and/or
apparatus will include all implementations falling within the scope
of the appended claims.
* * * * *
References