U.S. patent number 7,116,963 [Application Number 10/649,305] was granted by the patent office on 2006-10-03 for simplified high frequency tuner and tuning method.
This patent grant is currently assigned to University of Washington. Invention is credited to Edwin A. Suominen.
United States Patent |
7,116,963 |
Suominen |
October 3, 2006 |
**Please see images for:
( Certificate of Correction ) ** |
Simplified high frequency tuner and tuning method
Abstract
A disclosed method tunes a signal from a channelized spectrum
having a predetermined channel spacing. A signal of interest having
a predetermined maximum bandwidth is mixed with a local oscillator
signal, which has a frequency that is an integer multiple of the
channel spacing or one-half of a channel spacing displaced from an
integer multiple of the channel spacing. The local oscillator
signal is selected to frequency translate the signal of interest to
within a near-baseband passband whose lower edge is spaced from DC
by at least about the maximum bandwidth of the signal of interest.
Problems associated with 1/f noise, DC offsets, and self-mixing
products are avoided or substantially diminished. Other methods and
systems are also disclosed.
Inventors: |
Suominen; Edwin A. (Valley,
WA) |
Assignee: |
University of Washington
(Seattle, WA)
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Family
ID: |
24867434 |
Appl.
No.: |
10/649,305 |
Filed: |
August 25, 2003 |
Prior Publication Data
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Document
Identifier |
Publication Date |
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US 20040038655 A1 |
Feb 26, 2004 |
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Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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10032526 |
Oct 27, 2001 |
6631256 |
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09317781 |
May 24, 1999 |
6427068 |
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08713761 |
Sep 13, 1996 |
5937341 |
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Current U.S.
Class: |
455/302; 455/316;
375/322 |
Current CPC
Class: |
H03D
3/007 (20130101); H03D 3/009 (20130101); H03D
7/165 (20130101); H04B 1/30 (20130101); H04B
1/06 (20130101); H04B 1/10 (20130101); H04B
1/16 (20130101); H04L 25/067 (20130101); H04B
1/26 (20130101) |
Current International
Class: |
H04B
1/10 (20060101) |
Field of
Search: |
;455/142,143,207,302,303,305,306,316,324,338,214,213,286,299,150.1,182.1,182.3,183.1,339
;375/322,324 |
References Cited
[Referenced By]
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Mar 1990 |
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EP |
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0 508 401 |
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Apr 1992 |
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EP |
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0 595 277 |
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Oct 1993 |
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EP |
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0 602 394 |
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Nov 1993 |
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EP |
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0 651 522 |
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May 1995 |
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EP |
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585907 |
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Feb 1947 |
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GB |
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7-283810 |
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Oct 1995 |
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JP |
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WO 94/10756 |
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May 1994 |
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WO |
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WO 94/29948 |
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Dec 1994 |
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WO |
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Primary Examiner: Eng; George
Assistant Examiner: Bhattacharya; Sam
Attorney, Agent or Firm: Suominen; Edward A.
Parent Case Text
CROSS-REFERENCE TO RELATED APPLICATIONS
This application is a continuation of U.S. patent application Ser.
No. 10/032,526 filed Oct. 27, 2001, now U.S. Pat. No. 6,631,256,
which is a continuation of U.S. patent application Ser. No.
09/317,781 filed May 24, 1999, now U.S. Pat. No. 6,427,068, which
is a divisional of U.S. patent application Ser. No. 08/713,761
filed Sep. 13, 1996, now U.S. Pat. No. 5,937,341.
Claims
What is claimed is:
1. A tuning method comprising: (a) mixing a channel of interest
from a channelized spectrum having a predetermined channel spacing
with a first local oscillator signal; (b) mixing the channel of
interest with a second local oscillator signal having the first
frequency and being approximately in quadrature with the first
local oscillator signal; (c) wherein the first local oscillator
signal has a first frequency that is (1) one-half of a channel
spacing displaced from an integer multiple of the channel spacing,
and (2) selected to frequency translate the channel of interest to
within a passband whose lower edge is spaced from DC by about the
channel spacing and whose width is about the channel spacing; (d)
the channel of interest has a predetermined maximum bandwidth less
than the channel spacing; (e) the channel of interest lies within
one of an upper high frequency spectrum of interest and a lower
high frequency spectrum of interest; and (f) the method further
comprises providing spectrum coverage within one of the high
frequency spectra of interest and not the other.
2. The method of claim 1 further comprising coarse-tuning the local
oscillator signal by one local oscillator step from the first
frequency to a second frequency an integral number of channel
spacings from the first frequency.
3. A tuning method of claim 1 further comprising (a) mixing a
channel of interest from a channelized spectrum having a
predetermined channel spacing with a first local oscillator signal:
(b) mixing the channel of interest with a second local oscillator
signal having the first frequency and being approximately in
quadrature with the first local oscillator signal; (c) wherein the
first local oscillator signal has a first frequency that is (1)
one-half of a channel spacing displaced from an integer multiple of
the channel spacing, and (2) selected to frequency translate the
channel of interest to within a passband whose lower edge is spaced
from DC by about the channel spacing and whose width is about the
channel spacing.
4. A tuning method comprising: (a) mixing a channel of interest
from a channelized spectrum having a predetermined channel spacing
with a first local oscillator signal; (b) wherein the first local
oscillator signal has a first frequency that is (1) one-half of a
channel spacing displaced from an integer multiple of the channel
spacing, and (2) selected to frequency translate the channel of
interest to within a passband whose lower edge is spaced from DC by
about the channel spacing and whose width is about the channel
spacing; (c) the channel of interest lies within one of an upper
high frequency spectrum of interest and a lower high frequency
spectrum of interest; and (d) the method further comprises
providing spectrum coverage within one of the high frequency
spectra of interest and not the other.
5. The method of claim 4 further comprising switching between: (a)
providing spectrum coverage within the lower high frequency
spectrum of interest and not the upper high frequency spectrum of
interest; and (b) providing spectrum coverage within the upper high
frequency spectrum of interest and not the lower high frequency
spectrum of interest.
6. Apparatus turning, from a channelized spectrum having a
predetermined channel spacing, a channel of interest, the apparatus
comprising: (a) a local oscillator configured to generate a local
oscillator signal at a first frequency that is one-half of the
channel spacing displaced from an integer multiple of the channel
spacing; and (b) a mixer responsive to the local oscillator signal
and the channel of interest, wherein the mixer frequency translates
the channel of interest; (c) a second local oscillator configured
to generate a second local oscillator signal having the first
frequency and being approximately in quadrature with the first
local oscillator signal; and (d) a second mixer responsive to the
second local oscillator signal and the channel of interest, wherein
(1) the channel of interest lies within one of an upper high
frequency spectrum of interest and a lower high frequency spectrum
of interest, and (2) the apparatus provides spectrum coverage
within one of the high frequency spectra of interest and not the
other; (e) the frequency-translated channel of interest falls
within a passband that is about a channel spacing wide and that is
spaced from DC by a frequency offset of about the channel spacing;
and (f) the channel of interest has a predetermined maximum
bandwidth less than the channel spacing.
7. Apparatus for tuning, from a channelized spectrum having a
predetermined channel spacing, a channel of interest, the apparatus
comprising: (a) a local oscillator configured to generate a local
oscillator signal at a first frequency that is one-half of the
channel spacing displaced from an integer multiple of the channel
spacing; (b) a mixer responsive to the local oscillator signal and
the channel of interest, wherein the mixer frequency translates the
channel of interest; and (c) a second local oscillator configured
to generate a second local oscillator signal having the first
frequency and being approximately in quadrature with the first
local oscillator signal; (d) wherein the frequency-translated
channel of interest falls within a passband that is about a channel
spacing wide and that is spaced from DC by a frequency offset of
about the channel spacing.
8. The apparatus of claim 7 further comprising a second mixer
responsive to the second local oscillator signal and the channel of
interest, wherein: (a) the channel of interest lies within one of
an upper high frequency spectrum of interest and a lower high
frequency spectrum of interest; and (b) the apparatus provides
spectrum coverage within one of the high frequency spectra of
interest and not the other.
9. Apparatus for tuning, from a channelized spectrum having a
predetermined channel spacing, a channel of interest, the apparatus
comprising: (a) a local oscillator configured to generate a first
local oscillator signal at a first frequency that is an integer
multiple of the channel spacing and a second local oscillator
signal having the first frequency and being approximately in
quadrature with the first local oscillator signal; and (b) a pair
of mixers, each responsive to (1) a respective one of the local
oscillator signals and (2) the channel of interest, wherein the
mixers frequency translate the channel of interest; (c) wherein the
frequency-translated channel of interest falls within a
near-baseband passband spaced from DC by a frequency offset of at
least about the channel spacing.
10. The apparatus of claim 9 wherein the spacing of the lower edge
of the near-baseband passband from DC is greater than the channel
spacing.
11. The apparatus of claim 10 wherein the spacing of the lower edge
of the near-baseband passband from DC is about twice the channel
spacing.
12. The apparatus of claim 9 wherein: (a) the channel of interest
lies within one of an upper high frequency spectrum of interest and
a lower high frequency spectrum of interest; and (b) the apparatus
provides spectrum coverage within one of the high frequency spectra
of interest and not the other.
13. A method for tuning a channelized signal of interest from
within a channelized spectrum, the method comprising: (a) splitting
an incoming signal into two signal paths; (b) generating an
approximately quadrature local oscillator signal from a local
oscillator that is coarse-tunable across the channelized spectrum
with a step size that is an integer multiple of the channel
spacing; (c) quadrature mixing the split incoming signal with the
local oscillator signal, thereby: (1) frequency translating to a
near-baseband passband an upper high frequency spectrum of interest
from above the frequency of the local oscillator signal and a lower
high frequency spectrum of interest from below the frequency of the
local oscillator signal, the near-baseband passband being spaced
from DC by at least about the channel spacing; and (2) producing I
and Q signals in approximate quadrature relation; (d) limiting the
frequency spectrum of the I and Q signals, wherein spectrum
coverage is provided of a selected one of the high frequency
spectra of interest and analog processing of signals at or close to
DC is avoided; and (e) repeating (a) through (d) in turn for a
plurality of local oscillator frequencies, wherein high frequency
spectra of interest tunable with the local oscillator frequencies
of the plurality are interspersed among local oscillator
frequencies of the plurality within the channelized spectrum.
14. The method of claim 13 wherein the near-baseband passband is
sized to fit one channel spacing.
15. The method of claim 13 further comprising providing spectrum
coverage within one of the high frequency spectra of interest and
not the other.
16. The method of claim 13 wherein the spacing of the lower edge of
the near-baseband passband from DC is greater than the channel
spacing.
17. The method of claim 16 wherein the spacing of the lower edge of
the near-baseband passband from DC is about twice the channel
spacing.
18. The method of claim 13 wherein limiting the frequency spectrum
of the I and Q signals comprises filtering the signals in
continuous-time using switched-capacitor circuitry.
19. The method of claim 13 wherein the near-baseband passband is
defined with reference to a lower frequency F1 and an upper
frequency F2, wherein F1=F2-F1 and F2-F1 is about an integer
multiple of channel spacings.
20. The method of claim 13 wherein limiting the frequency spectrum
of the I and Q signals comprises highpass and lowpass filtering the
signals in continuous-time.
21. The method of claim 20 wherein limiting the frequency spectrum
of the I and Q signals comprises filtering the signals in
continuous-time using switched-capacitor circuitry.
22. The method of claim 20 wherein limiting the frequency spectrum
of the I and Q signals further comprises filtering the signals in
discrete-time.
23. The method of claim 13 further comprising providing spectrum
coverage within one of the high frequency spectra of interest and
not the other.
24. The method of claim 23 further comprising: (a) converting the I
and Q signals to digital I and Q signals; and (b) combining the
digital I and Q signals to reject an undesired mixing image.
25. The method of claim 24 further comprising correcting amplitude
and phase errors between the digital I and Q signals.
26. Apparatus for tuning a channelized signal of interest from
within a channelized spectrum having a predetermined channel
spacing, the apparatus comprising: (a) an RF amplifier responsive
to an incoming signal; (b) a local oscillator that is
coarse-tunable across the channelized spectrum with a step size
that is an integer multiple of the channel spacing to a plurality
of local oscillator frequencies; (c) first and second filters
defining a near-baseband passband spaced from DC by about an
integer multiple of the channel spacing; (d) first and second
mixers, responsive to an amplified signal from the RF amplifier and
an approximately quadrature local oscillator signal from the local
oscillator, frequency translating to the near-baseband passband (1)
an upper high frequency spectrum of interest from above the
frequency of the local oscillator signal, and (2) a lower high
frequency spectrum of interest from below the frequency of the
local oscillator signal; and (e) a selector structured to select
one of the high frequency spectra of interest.
27. The apparatus of claim 26 wherein the near-baseband passband is
sized to fit one channel spacing.
28. The apparatus of claim 26 wherein the spacing of the lower edge
of the near-baseband passband from DC is about twice the channel
spacing.
29. The apparatus of claim 26 wherein the filters include
continuous time switched-capacitor circuitry.
30. The apparatus of claim 26 wherein the near-baseband passband is
spaced from DC by about the channel spacing and is about an integer
multiple of the channel spacing wide.
31. The apparatus of claim 30 wherein the spacing of the lower edge
of the near-baseband passband from DC is about twice the channel
spacing.
32. The apparatus of claim 26 wherein the filters include
continuous-time highpass and lowpass filters.
33. The apparatus of claim 32 wherein the filters further include
continuous-time switched-capacitor circuitry.
34. The apparatus of claim 26 further comprising discrete-time
filters.
35. The method of claim 15 further comprising providing spectrum
coverage within the upper high frequency spectrum of interest at
one time and providing spectrum coverage within the lower high
frequency spectrum of interest at a different time.
36. A tuning method comprising: (a) mixing a channel of interest
from a channelized spectrum with a first local oscillator signal;
(b) filtering the mixed signal to define a near-baseband passband
that is (1) sized to fit one channel spacing, and (2) has a lower
edge spaced from DC by about an integer multiple of the channel
spacing or a half-channel-spacing displaced from about an integer
multiple of the channel spacing; (c) splitting the incoming signal
into two signal paths; and (d) quadrature mixing the split incoming
signal with the first local oscillator signal and a second local
oscillator signal approximately in quadrature with the first local
oscillator signal.
37. The method of claim 36 further comprising performing digital
image rejection.
38. The method of claim 36 further comprising performing the image
rejection after the quadrature mixing.
39. The method of claim 38 wherein the lower edge of the
near-baseband passband is spaced from DC by about twice the channel
spacing.
40. A method for tuning a channel of interest, comprising: (a)
receiving a channel of interest from a channelized spectrum having
a predetermined channel spacing, wherein the channel of interest
has a predetermined maximum bandwidth less than the channel
spacing; (b) producing I and Q signals in approximate quadrature
relation by mixing the channel with an approximately quadrature
local oscillator signal having a first frequency that is an integer
multiple of the channel spacing; and (c) defining a near-baseband
passband whose lower edge is spaced from DC by at least about the
channel spacing, by passband filtering the I and Q signals.
41. The method of claim 40 further comprising coarse-tuning the
local oscillator signal by one local oscillator step from the first
frequency to a second frequency an integral number of channel
spacings from the first frequency.
42. The method of claim 41 wherein the second frequency is two
channel spacings from the first frequency.
43. The method of claim 40 wherein passband filtering the I and Q
signals comprises filtering the signals in continuous-time using
switched-capacitor circuitry.
44. A method for tuning a channel of interest, comprising: (a)
receiving a channel of interest from a channelized spectrum having
a predetermined channel spacing, wherein the channel of interest
has a predetermined maximum bandwidth less than the channel
spacing; (b) producing I and Q signals in approximate quadrature
relation by mixing the channel of interest with an approximately
quadrature local oscillator signal having a first frequency that is
one-half of a channel spacing displaced from an integer multiple of
the channel spacing; and (c) defining a near-baseband passband
whose lower edge is spaced from DC by an integer multiple of the
channel spacing, by passband filtering the I and Q signals.
45. The method of claim 44 further comprising coarse-tuning the
local oscillator signal by one local oscillator step from the first
frequency to a second frequency an integral number of channel
spacings from the first frequency.
46. The method of claim 45 wherein the second frequency is two
channel spacings from the first frequency.
47. The method of claim 44 wherein passband filtering the I and Q
signals comprises filtering the signals in continuous-time using
switched-capacitor circuitry.
48. The apparatus of claim 9 further comprising a digital circuit
that substantially rejects the image.
49. A method for tuning a channel from a channelized spectrum
having predetermined channel spacing, the method comprising: (a)
mixing a channel of interest with a first local oscillator signal;
(b) wherein the first local oscillator signal has a first frequency
that (1) is an integer multiple of the channel spacing and (2) is
selected to frequency translate the channel of interest to within a
near-baseband passband whose lower edge is spaced from DC by at
least about the channel spacing; and (c) the method further
comprises mixing the channel of interest with a second local
oscillator signal having the first frequency and being
approximately in quadrature with the first local oscillator
signal.
50. A method for tuning a channel from a channelized spectrum
having predetermined channel spacing, the method comprising: (a)
mixing a channel of interest with a first local oscillator signal;
(b) wherein the first local oscillator signal has a first frequency
that (1) is an integer multiple of the channel spacing and (2) is
selected to frequency translate the channel of interest to within a
near-baseband passband whose lower edge is spaced from DC by at
least about the channel spacing; (c) the channel of interest lies
within one of an upper high frequency spectrum of interest and a
lower high frequency spectrum of interest; and (d) the method
further comprises providing spectrum coverage within one of the
high frequency spectra of interest and not the other.
51. The method of claim 50 further comprising switching between:
(a) providing spectrum coverage within the lower high frequency
spectrum of interest and not the upper high frequency spectrum of
interest; and (b) providing spectrum coverage within the upper high
frequency spectrum of interest and not the lower high frequency
spectrum of interest.
52. A tuning method comprising: (a) receiving a channel of interest
from a channelized spectrum having a predetermined channel spacing;
(b) producing I and Q signals in approximate quadrature relation by
mixing the channel of interest with an approximately quadrature
local oscillator signal having a frequency that is one of a set of
local oscillator frequencies; and (c) passband filtering the I and
Q signals to define a passband whose lower edge is situated near
baseband but spaced from DC by at least about the channel
spacing.
53. The method of claim 52 wherein the channel of interest has a
predetermined maximum bandwidth less than the channel spacing.
54. The method of claim 52 wherein filtering to define the passband
comprises defining a passband whose center frequency has a spacing
from DC that differs from an integer multiple of channel spacing or
a half-channel displaced from an integer multiple of channel
spacing by a frequency adjustment.
55. The method of claim 54 wherein the frequency adjustment is
about half of the channel spacing.
56. The method of claim 54 wherein filtering to define the passband
comprises defining a passband that is approximately a channel
spacing wide.
57. The method of claim 56 wherein defining a passband comprises
defining a passband that is wider than a channel spacing by a
frequency adjustment.
58. The method of claim 54 wherein the frequency adjustment is
predetermined.
59. The method of claim 54 wherein the frequency adjustment is
static.
60. The method of claim 54 wherein defining a passband comprises
defining a passband by extending the upper and lower edges of the
passband by frequency adjustments.
61. The method of claim 60 wherein the frequency adjustments are
not equal.
62. The method of claim 52 wherein filtering to define the passband
comprises determining the edges of the passband by the center
frequency of the channel of interest contained in the I and Q
signals.
63. The method of claim 62 wherein determining the edges of the
passband comprises making the passband wider than the width of the
channel of interest by a predetermined frequency adjustment.
64. The method of claim 63 wherein making the passband wider than
the width of the channel of interest is done by adjusting both the
upper and lower edges of the passband by predetermined frequency
adjustments.
65. The method of claim 61 wherein the predetermined frequency
adjustments are not equal.
66. The method of claim 61 wherein determining the edges of the
passband further comprises separating the edges of the passband by
approximately the maximum bandwidth of the channel of interest.
67. The method of claim 66 wherein separating the edges of the
passband comprises making the passband wider than the spacing of
the channel of interest by a predetermined frequency
adjustment.
68. The method of claim 52 wherein the lower edge of the
near-baseband passband is spaced from DC by about the channel
spacing.
69. The method of claim 52 wherein the lower edge of the passband
is spaced from DC by about 1.5 times the channel spacing.
70. The method of claim 52 wherein the lower edge of the passband
is spaced from DC by about twice the channel spacing.
71. The method of claim 52 wherein the lower edge of the passband
is spaced from DC by about 2.5 times the channel spacing.
Description
FIELD OF THE INVENTION
This invention relates generally to devices and methods for
receiving and transmitting RF signals. More particularly, this
invention relates to an especially useful device and method for
receiving and tuning RF signals, with quadrature mixing to a near
baseband passband performed in continuous-time and image rejection
and translation to baseband performed in discrete-time. The device
may also be adapted to transmit RF signals if desired.
BACKGROUND OF THE INVENTION
Standard RF receiver design incorporates conversion of incoming
high frequency signals to one or more intermediate frequencies, the
last of which is then converted to baseband. A mixer and image
rejection filter are required at each stage, resulting in
complexity proportional to the number of stages. Such complexity is
undesirable, particularly for mobile communications applications
where size, power consumption, and cost per unit must be
minimized.
Various approaches have been taken to reduce the size, power
consumption, and cost of receivers. One approach is to perform
nearly all of the receiver functions in the discrete-time domain in
a DSP (digital signal processor) device. This results in high DSP
performance requirements and cost. Other approaches employ
discrete-time processing for baseband and for some intermediate
frequency operations, reducing the DSP performance requirements,
but still requiring at least one high performance continuous-time
image rejection filter.
Direct conversion receivers offer a potential alternative for
avoiding some of the limitations of other approaches. Receivers of
this type employ quadrature mixing directly to baseband.
Discrete-time processing can be efficiently utilized at baseband
frequencies to demodulate the signal of interest, employing the
quadrature baseband signals to utilize the entire signal spectrum
centered at baseband. The complex-valued signal comprised of the I,
Q samples allows the faithful representation of the signal of
interest on both sides of baseband without distortion from images
from opposite sides of baseband. Thus only a single continuous-time
frequency conversion stage need be employed. No preselecting
bandpass filter is required to eliminate an undesired mixing image,
so that a broad tuning range is possible.
Despite the above potential advantages, direct conversion receivers
also present problems including: (1) 1/f noise, which dominates
active devices at low frequencies, particularly below 100 Hz, (2)
time-varying DC offsets which can saturate the later stages of the
baseband signal chain, (3) products of self-mixing of strong
signals which can be present at baseband, (4) relatively small
phase and amplitude errors between channels considerably reduce
image rejection, and (5) fairly sharp anti-aliasing filters are
required and can distort the desired signal if not carefully
designed and precisely matched.
These problems are not unique to direct conversion receivers. An
example of a receiver that converts to a non-zero intermediate
frequency but remains vulnerable to the low-frequency problems
listed above is illustrated in FIG. 13 of U.S. Pat. No. 5,875,212
to Fleek et al.
Attempts have been made to provide the advantages of direct
conversion without the disadvantages by "notching out" DC from the
baseband signal. This method performs well only if the signal type
contains little or no information at or near DC. If the notch at DC
is sufficiently narrow to minimize loss of information, the
problems listed above related to amplification at or near DC are
not eliminated.
Attempts have been made to avoid losing the information at and near
DC and avoid the need for image rejection by translating a desired
channel frequency from a channelized frequency spectrum to a
frequency offset a small fixed amount from baseband, with the
offset large enough to move the DC portion of the channelized
signal into a passband which excludes DC, but small enough to
prevent the next adjacent channel from appearing in the passband.
This technique may preserve the DC portion of the signal, but
requires sharp cut-off highpass and anti-aliasing filters and,
because of the proximity of the passband to DC, still suffers
somewhat from the other problems listed above.
Another known approach has been to perform image-rejection
downconversion of an RF tuning range to a relatively wide
intermediate frequency range with a local oscillator having no
specified relationship to frequencies of RF channels within the
tuning range. For example, W. Baumberger in "A Single-Chip Image
Rejecting Receiver for the 2.44 GHz Band Using Commercial
GaAs-MESFET-Technology" discloses the use of a 150-MHz intermediate
frequency range (from 130 to 280 MHz) in a receiver having a tuning
range on the order of 500 MHz. Another example is found in
Published EPO Application 0 651 522 by M. Pesola, in which FIG. 3
illustrates the use of two radio frequency bands on opposite side
of a local oscillator frequency, selected using either one of the
outputs of a mixer attenuating the image frequency. Pesola also
discloses the use of intermediate frequencies having widths of 100
kHz and 1 MHz, and a relatively high frequency of 100 MHz, with
image-rejection downconversion using a channel-dependent local
oscillator. This disclosed arrangement suffers from the inefficient
use of a relatively high intermediate frequency (on the order of
100 1000 times the bandwidth).
SUMMARY OF THE INVENTION
In accordance with the present invention, a high frequency spectrum
of interest is translated in continuous-time to a near-baseband
passband by quadrature mixing, preferably with a coarse-tuned local
oscillator, producing I and Q signals in approximate quadrature
relation. The I and Q signals are then filtered in continuous-time
to remove DC and to prevent unwanted aliasing upon digital
conversion, and are then converted to digital I and Q signals.
In digital processing, various steps are performed including (1)
phase correction (optionally including group delay correction) and
amplitude correction between the I and Q signals, (2) rejection of
an image signal by means of complex filtering or a Hilbert
transform pair and adder, (3) further bandlimiting, and, (4)
translation of the desired signal from the near-baseband passband
to baseband, which step may include digital fine-tuning over the
near-baseband passband. If the desired signal is part of a
channelized spectrum, the digital fine-tuning capability may be
omitted or reduced to a coarse step-wise digital tuning capability
with steps equal to the channel spacing, but a translation from
near-baseband to baseband is still performed. These steps may be
performed in combination and in various orders to achieve the
desired effect.
The inventive tuning method provides certain advantages of direct
conversion receivers, including preferably a single continuous-time
down-conversion stage, lack of image rejection filters with
resulting wide possible tuning range, and relatively low frequency
at conversion to discrete-time, allowing lower discrete-time
processing rates and simplified decimation filter architecture. The
inventive method also avoids the problems of 1/f noise and DC
offset and self-mixing by avoiding the need for analog
amplification of signal frequencies at baseband or only slightly
offset from baseband.
The inventive tuning method further provides certain unique
advantages.
For example, some significant advantages result from the inventive
method's optimal division of tasks between continuous-time and
discrete-time components.
In the inventive method, continuous-time components perform those
tasks for which they are well suited, particularly the initial
downconversion of a high frequency signal, while discrete-time
components perform the tasks for which they are well suited, such
as signal processing only at baseband and near baseband
frequencies, yielding both relaxed continuous-time component
tolerances and relatively reduced discrete-time processing speed
and power requirements.
Further, the size and location of the near-baseband passband
utilized in the invention and of the associated digital fine-tuning
range or channelized spectrum channel spacing, if any, are so
organized that the step size of the coarse-tuned local oscillator
may be set to about twice the digital tuning range without any loss
of spectrum coverage. The doubled step size relaxes the local
oscillator requirements and reduces phase noise generated by the
local oscillator. This relaxation of local oscillator (typically a
PLL) requirements allows the local oscillator to cover a wider
frequency range, so that the invention can take better advantage of
the wide tuning range afforded by the lack of an image-rejection
filter.
In the preferred embodiments, the invention also includes a type
III Hilbert transform, i.e., a case III FIR phase-inverting allpass
filter, for image rejection processing. The near-baseband passband
utilized in the invention is then optimally sized and located for
use with a type III Hilbert transform such that substantial
computational and memory resource savings are realized while
maintaining excellent performance.
A fuller appreciation of the above advantages and features and of
additional advantages and features of the invention will be gained
by those of skill in the art from the detailed description of the
preferred embodiments which follows, and from practice of the
invention itself.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram of a device according to the present
invention.
FIG. 2 is a diagram of the near-baseband passband utilized by
present invention.
FIGS. 3 and 4 are diagrams illustrating the use of the
near-baseband passband of the present invention with channelized
frequency spectra.
FIGS. 5 and 6 are diagrams illustrating the doubled local
oscillator step size achievable according to the present
invention.
FIG. 7 is a diagram showing the preferred size and location of the
near-baseband passband of the present invention in relation to
various characteristics of various preferred elements of the
present invention.
FIG. 8 is a diagram of presently preferred embodiments of the
present invention.
FIG. 9 is a diagram showing certain aliasing regions of the
near-baseband passband together with highpass frequency response
curves for filters for use in the present invention.
FIG. 10 is a diagram showing additional aliasing regions of the
near-baseband passband according to an embodiment of the present
invention.
FIG. 11 is a diagram of a preferred embodiment of a decimating
filter for use in an embodiment of the present invention.
FIG. 12 is a simulated frequency response curve of the filter of
FIG. 11.
FIG. 13 is the simulated frequency response curve of FIG. 12 shown
on a smaller scale.
FIG. 14 is a simulation plot of quantization noise both with and
without aliased quantization noise.
FIG. 15 is a diagram illustrating the operation of a Hilbert
transform modified according to the present invention.
FIG. 16 is a diagram illustrating the presently preferred method of
correcting phase errors used in the present invention.
FIG. 17 is a diagram illustrating the generation of coefficients
for a variable group-delay allpass filter usable in an embodiment
of the present invention.
FIGS. 18 and 19 are simulated frequency response curves of certain
elements of an embodiment of the present invention.
FIG. 20 is a simulated frequency response curve of an embodiment of
the present invention.
FIG. 21 is a simulated envelope detector output of an embodiment of
the present invention.
FIGS. 22 and 23 are simulated frequency response curves of certain
elements of an embodiment of the present invention.
FIGS. 24 and 25 are simulated frequency response curves of an
embodiment of the present invention.
FIG. 26 is an additional diagram illustrating the use of the
near-baseband passband with channelized frequency spectra.
DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT
A significant aspect of the present invention is the basic division
of functions between discrete-time (digital) and continuous-time
(analog) components characteristic of the invention, which is
described with reference to FIG. 1.
In FIG. 1, analog portion 12 of a device 10 according to the
present invention receives an incoming signal from a preferably
removable/exchangeable antenna 16. A suitable broad-band or tunable
RF amplifier 18 then amplifies the signal. Alternatively, the
invention could also be used to tune an intermediate frequency from
previous analog processing, rather than an incoming signal directly
from antenna 16 and amplifier 18.
The signal is then split into two signal paths and fed to first and
second mixers 20, 22. The first and second mixers 20, 22 are
supplied with a quadrature local oscillator signal from a
preferably coarse-stepped local oscillator 24. The mixing operation
translates to a near-baseband passband an upper high frequency
spectrum of interest from above the frequency F.sub.LO of the local
oscillator 24 and a lower high frequency spectrum of interest from
below the frequency F.sub.LO of the local oscillator 24, producing
I and Q signals in approximate quadrature relation.
The near-baseband passband is sufficiently low to provide
substantial efficiency gains in the subsequent digital processing,
but does not include baseband. The near-baseband passband is also
sufficiently high to allow a fairly relaxed transition from a
cutoff at or near DC to the lower edge of the passband. Problems
such as self-mixing products and DC offsets and 1/f noise are
avoided by high-pass filtering with a relaxed transition band in
filters 26 and 28. Unwanted aliasing is prevented by low-pass
filtering in filters 26 and 28. The I and Q outputs from the analog
portion 16 of the device 10 are then passed to the digital portion
14 of the device 10.
At least three operations are performed within the digital portion
14 of the device 10. First is analog to digital conversion. The I
and Q signals are converted individually into digital signals.
Second, phase errors (optionally including group delay errors) and
amplitude errors between the I and Q channels are corrected,
particularly to maximize image rejection at and/or near the
frequency of the desired signal, and the channels are combined by a
Hilbert transform pair and summing, or filtering with complex
coefficients is employed, in order to reject the undesired mixing
image, particularly at the frequency of the desired signal. Third,
a portion of the now image-rejected signal containing the desired
signal is translated to baseband. The second two operations may be
performed in various orders or to some extent simultaneously
according to the particular design and programming of the digital
portion 14 of the inventive device 10.
The above-described division of functions into analog and digital
domains, together with the use of the properly located
near-baseband passband, provides important advantages. The number
of analog components is minimized, and the analog components are
employed for those tasks to which they are most suited: the
conversion of high frequencies to low frequencies. The digital
processing is used only at lower frequencies, allowing lower
sampling rates and quantization resolutions to be employed without
substantial loss of signal characteristics, resulting in decreased
memory, processing power, and electrical power requirements. The
near-baseband passband avoids analog processing of signals at or
close to DC, thereby avoiding or substantially diminishing problems
associated with 1/f noise and DC offsets and self-mixing products.
Use of quadrature mixing with subsequent image rejection avoids the
need for relatively high-performance image rejection filters in the
analog portion. Correction in digital processing of phase and
amplitude deviations from the desired quadrature relation allows
relaxation of otherwise relatively strict matching and performance
requirements for the analog filters. Fine-tuning, if employed, is
preferably performed in the digital domain, leaving only
coarse-tuning by a coarse-stepped local oscillator to be performed
in analog processing, thereby reducing the complexity of the local
oscillator and the generation of phase noise.
Another significant aspect of the present invention is that the
local oscillator can be a coarse-tunable local oscillator having a
step size S that is twice as large as would typically be permitted,
given the range of the digital fine-tuning employed, or given the
channel spacing of the channelized spectrum and the digital channel
tuning employed. This is achieved by proper positioning and sizing
of the near-baseband passband and the tuning range or channelized
tuning/translation range of the digital tuning process, and takes
advantage of the fact that complex I, Q signals contain twice the
spectral information of a real signal.
As illustrated in FIG. 2, the near-baseband passband P may be
defined with reference to a lower frequency F.sub.1 and an upper
frequency F.sub.2. To achieve the preferred effective doubling of
the local oscillator step size S, F.sub.1 and F.sub.2 are chosen
such that F.sub.1=k(F.sub.2-F.sub.1), where k is a positive
integer, and S is set to 2(F.sub.2-F.sub.1). This insures that the
center frequency of any desired incoming signal can be translated
to within the positive frequency range of F.sub.1 to F.sub.2
inclusive or the negative frequency range of -F.sub.1 to -F.sub.2
inclusive by mixing with the appropriate local oscillator
frequency. The use of complex I, Q signals allows the positive
frequency range to be distinguished from the negative frequency
range.
For embodiments of the invention designed to tune essentially any
desired frequency from within a given RF range, the digital tuning
process employed preferably has a range extending from
F.sub.1-F.sub.H to F.sub.2+F.sub.H, where F.sub.H is an appropriate
hysteresis amount greater than or equal to zero, the effects and
usefulness of which will be explained hereafter. The near-baseband
passband P is then defined so as to extend from F.sub.1-F.sub.A to
F.sub.2+F.sub.A as shown in FIG. 2, where F.sub.A is a frequency
adjustment equal to at least about W/2+F.sub.H, where W is the
maximum bandwidth of the desired signals to be received. This
ensures that all of the bandwidth of any signal having a center
frequency tunable by the digital tuning process will fall within
the near-baseband passband.
A device of the present invention designed to tune essentially any
frequency can of course be utilized to receive channelized signals.
If decreased digital processing is desired in an embodiment
designed for channelized signal reception, the full digital tuning
capability over the entire near-baseband passband can be restricted
to discrete digital tuning in the form of either (1) a translation
to baseband from a chosen frequency within the near-baseband
passband (preferably the midpoint between F.sub.1 and F.sub.2), or
(2) a step-wise tuning of selected channelized frequencies from the
near-baseband passband to baseband. A small amount of fine-tuning
may be retained if desired for fine-tuning around the discrete
channelized frequency(ies) within the near-baseband passband.
In embodiments of the present invention employing discrete digital
tuning, the center frequency of each channel of any given
channelized spectrum will be translated to within the frequency
range from F.sub.1 to F.sub.2 inclusive or from -F.sub.1 to
-F.sub.2 inclusive by mixing with one of the various possible local
oscillator frequencies.
One possibility for selecting F.sub.1 and F.sub.2, with reference
to which the near-baseband passband may be defined, is choosing
F.sub.1 and F.sub.2 such that F.sub.2-F.sub.1=NC where C is the
channel spacing and N is the number of channels to be contained
within the near-baseband passband. F.sub.1 and F.sub.2 may be
further chosen, along with the local oscillator frequency, such
that F.sub.1 and F.sub.2 each fall at the midpoint between adjacent
channels after translation of the channel frequencies by mixing
with the local oscillator signal. This is possible where the
permissible local oscillator frequencies are at frequencies
one-half of a channel spacing C displaced from integer multiples of
the channel spacing, and is illustrated for the case N=1 in FIG.
3.
In FIG. 3, adjacent channels of bandwidth W have been
down-converted by mixing with the local oscillator signal. F.sub.1
and F.sub.2 fall between adjacent down-converted channels. The
near-baseband passband P extends from F.sub.1-F.sub.A to
F.sub.2+F.sub.A, where F.sub.A is a frequency adjustment equal to
1/2(W-C+W.sub.ft), where W.sub.ft is the width of the digital
fine-tuning, if any, provided for fine-tuning around each
channel.
FIG. 4 shows the near-baseband passband P in a channelized
embodiment using with N=3, W=C, W.sub.ft=0, and F.sub.H=0. The
local oscillator frequency is in this case an integer multiple of
the channel spacing. The near-baseband passband P is defined with
reference to F.sub.1 and F.sub.2 and the full-range digital tuning
frequency adjustment F.sub.A, which is equal to (1/2)(W+W.sub.ft).
F.sub.2-F.sub.1 in this case equals (N-1)C.
The decreased digital processing realized with channelized
operation may be obtained even with irregular intervals between
channels or with local oscillator step sizes not evenly divisible
by the channel spacing or with channels not located at integer
multiples of the channel spacing. A generalized case is illustrated
in FIG. 26. For a given channelized spectrum and a given set of
possible local oscillator frequencies, the center frequency of
every channel is translatable by one of the local oscillator
frequencies to within the range F.sub.1 to F.sub.2 inclusive or the
range -F.sub.1 to -F.sub.2 inclusive. The channel having a center
frequency after such translation the absolute value of which is
closest to (but not greater than) F.sub.2 is used to determine the
upper edge of the near-baseband passband P. The center frequency of
such channel after translation may be either negative or positive,
but is illustrated in FIG. 26 as positive channel C.sub.2. The
upper edge of the near-baseband passband P (the edge with the
greatest absolute value) is then located at the edge of the
bandwidth of channel C.sub.2 furthest from DC, plus another
W.sub.ft/2 from DC, which is half the width of any digital fine
tuning range. Similarly, the channel having a center frequency
after translation the absolute value of which is closest to (but
not less than) F.sub.1 is used to determine the lower edge of the
passband. The center frequency of such channel after translation
may be either negative or positive, but is illustrated in FIG. 26
as negative channel C.sub.1. The lower edge of the near-baseband
passband P (the edge with the least absolute value) is then located
at the edge of the bandwidth of channel C.sub.1 closest to DC, plus
another W.sub.ft/2 toward DC. The resulting frequency adjustments
F.sub.A1 and F.sub.A2 are shown in FIG. 26.
Note that in the above examples and throughout the specification
and claims, it should be understood that the near-baseband passband
refers to that portion of the frequency spectrum to which signals
of interest are to be translated in continuous time for further
processing in discrete time. The actual physical passband created
by the frequency response of the filters 26 and 28 of FIG. 1 may,
of course, be larger than the near-baseband passband itself, and
indeed it is preferred that the actual passband be somewhat larger,
so that the corners of filters 26 and 28 do not appear within the
near-baseband passband. Preventing the corners from appearing in
the near-baseband passband reduces group delay variation that can
cause degradation in image rejection and can worsen intersymbol
interference.
Whether in an embodiment with essentially continuous digital
fine-tuning or with channelized digital tuning, the frequencies
F.sub.1 and F.sub.2 are selected such that
F.sub.1=k(F.sub.2-F.sub.1), where k is a positive integer. Most
preferred is k=1 as in FIG. 2, but other values can be used, such
as k=2 as shown in FIG. 4. The effective doubling of the
permissible step size S of the local oscillator results in part
from utilization of this equation as illustrated below with respect
to FIGS. 5 and 6.
For a given local oscillator frequency F.sub.LO, both an upper high
frequency spectrum of interest and a lower high frequency spectrum
of interest are translated to the near-baseband passband. By means
of image-rejection processing employed in the digital domain,
either the near-baseband image of the upper high frequency spectrum
of interest or the near-baseband image of the lower high frequency
spectrum of interest may be rejected, allowing selection of either
the upper high frequency spectrum of interest or the lower high
frequency spectrum of interest for further processing. Because of
the positioning and size of the near-baseband passband and
associated digital tuning, whether continuous fine-tuning or
stepwise tuning, alternate selection of the upper and lower high
frequency spectra of interest can be used to provide non-redundant
coverage of the broadband frequency spectrum from which the desired
signal is to be received. Any desired frequency may then be
translated to the near-baseband passband with the local oscillator
step size S set to twice the digital tuning range, i.e., S set
equal to 2(F.sub.2-F.sub.1).
FIG. 5 shows a portion of the positive frequency spectrum graphed
on a linear scale. Each possible value of F.sub.LO is indicated
with an arrow and labeled with a letter or letters and a backslash.
The letters are also used to label a number of frequency regions
with a channelized signal in each. This represents an embodiment
for a channelized spectrum with a near-baseband passband sized to
fit one channel, as in FIG. 3. The letters labeling each possible
value of F.sub.LO correspond to the letters labeling the regions
translated to the near-baseband passband by that value of F.sub.LO.
If F.sub.LO is at A\D, for example, regions A and D are translated
to the near-baseband passband. The letter to the left of the
backslash corresponds to the letter labeling the lower high
frequency spectrum of interest for a given F.sub.LO, while the
letter to the right corresponds to the letter labeling the upper
high frequency spectrum of interest for that given F.sub.LO.
To translate to the near base-band passband the channelized signal
frequency within region F, for example, the local oscillator
frequency F.sub.LO would be set to the C\F position. The desired
signal frequency would then fall within the upper high frequency
spectrum of interest of the local oscillator frequency. The image
of region C, the lower high frequency spectrum of interest, would
be rejected by the digital image rejection processing, leaving F as
the selected region.
Similarly, to tune the channelized signal frequency within region G
shown in FIG. 5, the local oscillator frequency F.sub.LO would be
set to the G\J position. The desired signal frequency would then
fall within the lower high frequency spectrum of interest of the
local oscillator frequency, and the image of region J would be
rejected by the digital image rejection processing, leaving G
selected.
While k=1 is preferred as noted above, other values are possible
such as k=2, illustrated in FIG. 6 for an embodiment with
essentially continuous digital fine-tuning. The upper and lower
high frequency spectra of interest are now each about two tuning
ranges separated from the applicable local oscillator frequency
F.sub.LO, but the same complete coverage, with a step size
S=2(F.sub.2-F.sub.1), is provided. To tune a signal frequency
within region C, for example, the local oscillator frequency would
be set to the C\H position, and the lower high frequency spectrum
of interest would be selected.
The proper F.sub.LO to receive a given desired signal frequency
F.sub.t may be found by any appropriate method. For example, the
proper F.sub.LO may be found generally by setting
NLO=floor(F.sub.t/S+1/2), which is the factor NLO such that NLOS is
the nearest F.sub.LO to the desired signal frequency F.sub.t. If
NLOS.gtoreq.F.sub.t, the proper F.sub.LO to employ to translate
F.sub.t to the near-baseband passband is then given generally by
(NLO+(-1).sup.kfloor(k/2+1/2))S, with F.sub.t found in the upper
high frequency spectrum of interest if (-1).sup.k<0, and in the
lower high frequency spectrum of interest otherwise. Similarly, if
NLOS.ltoreq.F.sub.t, the proper F.sub.LO is given by
(NLO-(-1).sup.kfloor(k/2+1/2))S, with F.sub.t in the upper high
frequency spectrum of interest if (-1).sup.k>0, and in the lower
high frequency spectrum of interest otherwise. (The ambiguity in
F.sub.LO selection at NLOS=F.sub.t is caused by the overlap of
adjacent high frequency spectra of interest as seen in FIG. 6,
which allows a desired signal of frequency .sub.F.sub.t equal to
NLOS to be translated to the near-baseband passband by either of
two possible values of F.sub.LO.)
To avoid having to repeatedly change the value of NLO when
fine-tuning around a signal frequency F.sub.t about equal to NLOS,
the hysteresis amount F.sub.H for essentially continuous
fine-tuning embodiments may be set to a value greater than zero.
This allows fine tuning on both sides of a signal frequency F.sub.t
equal to about NLOS with only one local oscillator frequency
F.sub.LO, and widens each high frequency spectrum of interest by
2F.sub.H. If a desired frequency F.sub.t moves out of a first
widened high frequency spectrum of interest associated with a first
F.sub.LO, a second F.sub.LO is selected. If F.sub.t then moves back
into the first widened high frequency spectrum of interest, the
second F.sub.LO is maintained until F.sub.t is within the first
widened high frequency spectrum of interest by the distance
F.sub.H. Thus excessive switching from one F.sub.LO to another is
prevented.
If the invention is used to tune an intermediate frequency from
previous analog processing, either a local oscillator in the
previous analog processing or the quadrature local oscillator 24
may be varied and the other local oscillator set to a fixed
frequency. The effective doubling of the permissible step size S of
the varied local oscillator is preferably retained in either case
through the alternate selection of the upper and lower
high-frequency spectra of interest. Alternatively, the invention
can tune an intermediate frequency signal produced by analog mixing
without requiring a coarse-tunable local oscillator.
The near-baseband passband can include a frequency range extending
from a lower frequency F1-FA to an upper frequency F2+FA, where FA
is a given frequency adjustment. While the actual frequencies F1
and F2, selected as described above, will vary with the particular
application, it is currently preferred that F1 be at least about W,
where W is the bandwidth of the channels to be received or the
bandwidth of channelized signals to be received from a channelized
spectrum. Also preferred is that, in general, F2 be not more than
about 150 kHz. In some applications, however, F2 may be many times
this generalized upper limit. It is currently preferred that F2-F1
be at least about 20 kHz. In embodiments with full-range digital
tuning, it is currently preferred that F2-F1 be within the range of
about 3 W to about 5 W. The frequency adjustment FA can be equal
to, for example, the quantity (1/2) (W--C+Wft), the quantity W/2,
or the quantity W/2+FH, where C is the channel spacing of a
channelized spectrum and Wft is of the width of any fine-tuning
performed.
Another significant aspect of the present invention is the
preferred use of a type-III Hilbert transform in the image
rejection processing in the digital domain. A type III Hilbert
transform enjoys nearly a 2:1 efficiency advantage over a similar
standard type IV Hilbert transform, because every other impulse
response sample is zero. The performance envelope of the type III
Hilbert transform is symmetrical and centered on f.sub.s/4 (where
f.sub.s is the sampling frequency employed), falling off
symmetrically approaching DC and f.sub.s/2. While the performance
of the type III falls off relative to the type IV as frequencies
approach the Nyquist frequency of f.sub.s/2, the present invention
avoids any disadvantage from this characteristic as will be seen
below with respect to FIG. 7.
Due to the preferred spacing from DC of the near-baseband passband
of the present invention as illustrated for example in FIG. 2, the
near-baseband passband is sufficiently separated from DC for an
efficient and accurate Hilbert transform to be performed. The
relatively wide transition band to DC also affords relaxed filter
specifications. To take advantage of the type III transform's
efficiency and to provide even more relaxed filter specifications,
the present invention preferably employs a type III Hilbert
transform with a sampling rate R entering the Hilbert transform
equal to 2(F.sub.1+F.sub.2). This is equivalent to centering the
near-baseband passband at R/4. Some of the advantages of this
arrangement are illustrated for the case k=1 in FIG. 7.
FIG. 7 shows the near-baseband passband P of the present invention
located to encompass a digital tuning range between F.sub.1 and
F.sub.2 with F.sub.1=k(F.sub.2-F.sub.1) with k being a positive
integer, in this case 1. The step size S of the analog local
oscillator is also shown for reference. The use of a type III
Hilbert transform with an entering sampling frequency
R=2(F.sub.1+F.sub.2) results in the illustrated performance curve H
for the preferred type III Hilbert transform. The performance curve
H is symmetrical with the best performance at the location of the
near-baseband passband P, with symmetrically reduced performance
toward DC and the Nyquist frequency of R/2.
The near-baseband passband is also situated so as to substantially
avoid 1/f noise represented by the N.sub.1/f spectrum shown, and
quantization noise Q from a presently most preferred delta-sigma
analog to digital conversion. The transition bands T are also
sufficiently broad to relax filtering requirements in both the
analog and digital domains as will be shown in greater detail
below.
A pair of preferred embodiments of the device of the present
invention implementing the methods and having the characteristics
and advantages discussed above are shown in greater detail in FIG.
8. The device 10 shown in FIG. 8 corresponds to the device 10 shown
in FIG. 1, but with details of presently preferred embodiments
shown in the digital portion 14 of FIG. 8. Accordingly, analog
portion 12 shown in FIG. 8 is as described above with reference to
FIG. 1.
The analog I and Q signals are received into digital portion 14
from the analog portion 12 of the device 10 and are converted into
digital signals by delta-sigma modulators 30, 32 most preferably
third-order delta-sigma modulators, with one-bit wide output. The
delta-sigma modulators sample the I and Q signals at an
over-sampling rate R.sub.o. Decimation filters 34 and 36 filter the
output of the delta-sigma modulators so as to substantially reject
frequencies which would alias into the near-baseband passband on
decimation, and decimate the signal, such that the output sample
rate is equal to R, the desired input sampling frequency at a
Hilbert transform pair, comprised of a Hilbert transform 38 and
allpass filter 40, which follows.
An alternate embodiment, shown in FIG. 8 by the dashed-line
alternate signal paths I.sub.A and Q.sub.A, does not employ
oversampling. Instead, the I and Q signals are sampled by analog to
digital converters 42 and 44 at the rate R, the input sampling
frequency at the Hilbert transform pair 38 and 40, and converted
into digital signals preferably 12 to 16 bits wide, depending on
the dynamic range requirements of the application. Thus no
decimation is required between analog to digital converters 42 and
44 and Hilbert transform pair 38, 40. For this alternate
embodiment, the near-baseband passband of the present invention
provides somewhat relaxed anti-aliasing lowpass filter
specifications, as illustrated in FIG. 9.
The near-baseband passband P of the present invention, for the case
k=1, is shown in FIG. 9. P ends at (k+1)S/2+F.sub.A. The region
AR.sub.R is the first (lowest frequency) region to alias into P at
a sampling rate of R. AR.sub.R begins at R-(k+1)S/2-F.sub.A.
Accordingly, the passband of the anti-aliasing filter represented
by response curve 46 must extend at least to (k+1)S/2+F.sub.A,
while the stop band must begin at or before R-(k+1)S/2-F.sub.A.
This prevents aliasing into P while allowing a fairly relaxed
transition band between the passband and stop band. A highpass
filter would preferably be employed with a passband beginning at
the lower edge of P, which is given by kS/2-F.sub.A. These two
filters together then comprise filter 26, for example, in FIG. 8.
The lowpass filter can be an eighth order switched-capacitor
elliptical lowpass filter, for example. The passband of the filter
26 preferably extends even beyond the edges of P, such that the
corners of the filter, with their typically large group delay, are
not within P.
The relatively high order low-pass filters typically needed for
moderately relaxed transition bands such as the transition band in
response curve 46 of FIG. 9 can cause less efficient image
rejection due to small variations in pole and zero locations
between the filters 26 and 28 in the device 10 of FIG. 8. In the
most preferred embodiment shown in FIG. 8 by the I and Q solid line
signal paths, oversampling allows use of much lower order
anti-aliasing filters, with corresponding improvements in image
rejection.
The relaxed anti-aliasing filter transition band obtainable with
oversampling is illustrated in FIG. 9, where Ro is the oversampling
sampling rate, with R.sub.O=MR where M is the rate of oversampling.
M=3 is shown for illustration purposes in FIG. 9. AR.sub.Ro is then
the first aliasing region, i.e., the lowest frequency region to
alias into P at a sampling rate of R.sub.O. AR.sub.Ro begins at
R.sub.O-(k+1)S/2-F.sub.A. Accordingly, the stopband of the
anti-aliasing filter represented by response curve 48 must begin at
or before R.sub.O-(k+1)S/2-F.sub.A, with the same passband region
as response curve 46. Response curve 48, together with
oversampling, thus prevents aliasing into P while allowing a very
relaxed transition band between the passband and stop band of the
anti-aliasing filter. In practice, even greater oversampling rates
than 3 are desirable, with M=32 currently most preferred. A 2-pole
Chebychev type I low pass filter is then preferred for the low pass
filter portion of filters 26 and 28.
Note that, as discussed with reference to FIG. 26, the frequency
adjustment F.sub.A may have differing values at the upper and lower
edges of the near-baseband passband P.
In the most preferred embodiment, decimating filters 34 and 36
follow the delta-sigma modulators 30 and 32, respectively. One of
the decimating filters 34 and 36 preferably includes a group delay
correction. The output of the delta-sigma modulators 30 and 32 is
preferably one bit wide, allowing group delay correction to be
implemented with a variable shift register in the signal path.
One-bit signal width, together with the near-baseband passband and
other features of the present invention, also makes practical an
efficient single stage implementation of filters 34 and 36 with no
multiplication required.
The aliasing regions of concern in the design of filters 34 and 36
are illustrated for example in FIG. 10. The output of filters 34
and 36 is to be sampled at a rate R which is equal to R.sub.O/M,
where R.sub.O is the over-sampling sampling rate. M=3 is used in
FIG. 10 for illustration purposes. The first aliasing region
AR.sub.R is the first, i.e. lowest frequency, region to alias into
P due to the sampling at rate R. Subsequent aliasing regions AR are
also shown in FIG. 10 to the right of AR.sub.R. The desired
decimating filter should thus have a passband at P and stopbands of
at least the same width as P at each aliasing region. All other
frequency regions may be left unconstrained in the filter design
process. Leaving regions which do not alias into the near-baseband
passband P unconstrained, particularly with the size and position
of P relative to R as preferred in the present invention, allows
significant reduction in filter order and/or length such that a
single stage decimation filter with good performance and reasonably
low processing and memory requirements can be implemented.
A preferred design for a single stage decimation filter for use as
filter 34 and/or 36 is shown in FIG. 11. The filter includes:
32-bit registers 50a 50i, operators 52a 52d, look-up tables 54a 54d
with a look-up table address generator 56, a 22-bit accumulator 58,
and a truncator 60 and a decimator 62.
The 32-bit register 50a receives signal bits from the associated
upstream one-bit delta-sigma modulator until the register 50a is
full. Each time register 50a is full, the contents of each of the
32-bit registers 50a 50h are shifted into the 32-bit registers 50b
50i respectively. Because of the one-bit signal width and the
symmetrical filter coefficients and folded-over filter
architecture, the operators 52a d can be used to efficiently
determine the filter output without multiplication.
In the operators 52a d, each of the 32 signal bits from one
associated register is exclusive or-ed with the signal bit at the
same distance from the center of the filter's delay line from the
other respectively associated register. If the bits are not equal,
a zero is added to the contents of the accumulator 58. If the bits
are equal and positive, twice the value of the applicable
coefficient is added to the contents of the accumulator 58, and if
the bits are equal and negative, negative twice the value of the
applicable coefficient is added to the contents of the accumulator
58. This can be easily implemented by storing not the actual filter
coefficient values in the look-up tables 54a 54d, but twice the
actual coefficient values. Then if two signal bits compared in the
operator 52a for example are equal, the sign of one can be used as
the sign bit to be sent to the accumulator 58 along with the
doubled coefficient value from the look-up table 54a.
Each of operators 52a 52d operates in parallel on two of the 32-bit
registers 50b 50i, and sends its output to accumulator 58 in
parallel. Once all coefficients have been summed in accumulator 58,
truncator 60 takes only the 16 most significant bits from
accumulator 58. Decimator 62 represents the decimation performed in
the operation of this filter.
Table I below contains Matlab.RTM. code for generating filter
coefficients for the filter illustrated in FIG. 11 for use with the
near-baseband passband of the present invention with k=1 and the
near-baseband passband centered at 1/4 of the Nyquist frequency.
(Matlab.RTM. is software for digital signal processing analysis and
development available from The MathWorks, Inc., Natick, Mass.,
U.S.A.) In the code in Table I, the variable fs is the sampling
frequency entering the Hilbert transform and is set to 128 kHz. N
is the filter order, which is set to 255, resulting in 256 FIR
filter taps, which number is desirable as a power of 2 giving
easier implementation in a DSP, and because it provides sufficient
taps to significantly reduce noise at each alias of the
near-baseband passband. R is the weight of the stopband constraint
versus passband constraint, and is set to 100, resulting in very
high stopband rejection at the expense of some passband ripple. Mds
is the over-sampling and decimation ratio, and is set to 32.
Table II below gives an example of doubled filter coefficient
values for use in the look-up tables 54a 54d. Note that look-up
tables 54a and 54b require 32.times.13 bits of storage, while
look-up table 54c needs 32.times.14, and look-up table 54d needs
32.times.16.
The resulting simulated frequency response of the filter in FIG. 11
is shown in FIGS. 12 and 13. In FIG. 12, the filter response at the
near-baseband passband, located at 21.33 42.67 kHz in this example,
may be seen. In FIG. 13 with a smaller scale, the repeating
stopbands at aliasing regions of the near-baseband passband may be
seen, including stopbands at about 80 100 kHz, 140 160 kHz,
etc.
One important criteria for judging the performance of the filter of
FIG. 11 is the reduction of quantization noise from the delta-sigma
modulator, particularly from higher aliasing regions which would
alias into the near-baseband passband. FIG. 14 shows the noise due
to quantization after filtering and decimation without (lower
trace) and with (upper trace) the aliased quantization noise. Noise
floors in the near-baseband passband located in this case at 21.33
42.67 kHz are still at quite acceptable levels, even with the
addition of the aliased noise.
The preferred design of the Hilbert transform 38 of the device 10
in FIG. 8 is of course type III, but with at least one
modification. Type III Hilbert transforms have an odd number of
taps, with the center tap, and taps displaced an even number of
taps from the center tap, set to zero. The Hilbert transform 38 is
modified by having a variable non-zero coefficient present at the
center tap, i.e., at the sample of its impulse response the index
of which corresponds to half the length of the transform delay
line. This modification enables the Hilbert transform 38 to
function as if in parallel with an all pass filter with variable
gain, as shown schematically in FIG. 15. As the contribution from
the allpass portion increases or decreases from zero, the phase
change caused by the Hilbert transform is varied up or down from 90
degrees, allowing efficient correction of phase errors. The other
coefficients of the Hilbert Transform may also be varied along with
the central coefficient to implement correction of amplitude errors
between the I and Q channels. Variable gain for amplitude error
correction may also be implemented in the allpass filter 40 if
desired.
In implementing any type of error correction between the I and Q
channels, the errors should be corrected not to maximize coherence
of the desired signal but to maximize rejection of unwanted mixing
images at and near the frequency of the desired signal. This is
illustrated for phase error correction in FIG. 16. An undesired Q
phasor UQP is already displaced by amount "a" toward an exact
opposite phase relation with the I phasors IP. The Hilbert
transform is accordingly employed to rotate the undesired Q phasor
UQP and the desired Q phasor DQP by a phase correction amount PC
such that PC=90.degree.-a. This rotation moves UQP into direct
phase opposition to the I phasors IP, while DQP is not completely
phase corrected, being out of phase by amount "a" plus amount
"b."
All error correction between the I and Q channels is preferably
implemented by running a characterization of each device upon
completion of device fabrication, and then storing desired
correction factors in a memory associated with the digital portion
of the device. Other techniques such as techniques to continuously
detect and correct such errors may also be employed, if desired.
Temperature sensing capability may also be provided if desired,
such that correction factors may be dependent on temperature for
optimized image rejection under various climatic conditions.
Allpass filter 40 is designed with nominal group delay equal to the
group delay of Hilbert transform 38. The Hilbert transform 38 or
the allpass filter 40 is also enabled to change the sign of its
output, in order to switch from rejecting the image of the upper
high frequency spectrum of interest to rejecting the image of the
lower high frequency spectrum of interest, and vice versa. As
explained above, this switching, combined with the correct step
size S of the local oscillator 24 and with an appropriately sized
and located digital tuning range and/or near-baseband passband,
results in twice the local oscillator step size S that would
otherwise be possible for a given tuning range or a given channel
spacing of a channelized spectrum.
Particularly for the embodiment of the device 10 in FIG. 8
employing the alternate signal paths I.sub.a and Q.sub.a, group
delay correction may also be performed in the Hilbert transform
pair, if desired, by providing the allpass filter 40 with variable
coefficients corresponding to variably offset samples of the sinc
function. (The sinc function is defined as:)
.times..times..noteq..times..times..times..times. ##EQU00001##
For zero time shift, the coefficients are given by samples of the
sinc function at zero+n.pi. with n an integer, which results in
values of zero everywhere except at n=0, where the sinc function
returns a value of 1. Coefficients for a time offset equal to 1/4
of one sample at any given sampling frequency may be generated by
sampling the sinc function at n.pi./4, the central 7 samples of
which are shown in FIG. 17. These seven samples give seven
coefficient values, with n.pi./4 more obtainable as desired by
extending the sinc function sampling further in both directions. An
appropriate window (such as Hamming, Blackman, or Kaiser) should,
of course, be applied to the coefficient values.
Table III below contains Matlab.RTM. code for generating the
coefficients for the modified Hilbert transform 38 of FIG. 8. In
the code, fs is the variable for the sampling frequency entering
the Hilbert transform and is set to 128 kHz. The fbw variable
represents the bandwidth of the signal of interest, in this case
set to 6400 for an 8000 bps QPSK square-root raised-cosine digital
signal with an excess bandwidth setting (Beta) of 0.6. The fref
variable is a reference frequency of the local oscillator equal to
the local oscillator step size which is in this case 42.67 kHz. The
fref variable is used in this code to define the passband of the
transform according the preferred embodiment. Nh is the filter
order, set to 16, resulting in 17 filter taps. (Note that this code
applies the transform to the Q channel rather than the I
channel--either is fine, as long as the other channel has a
0.degree. allpass.)
After the Hilbert transform pair 38, 40 of the device 10 of FIG. 8,
the signals from the I and Q channels are combined by adder 64
resulting in a real, image-rejected near-baseband signal. This
signal is fed to a variable band-pass decimating filter 66.
The variable band-pass decimating filter 66 is designed by first
designing a prototype filter to have a passband of width W
straddling DC, where W is the bandwidth of the desired signal.
Similarly to the preferred embodiment of decimating filters 34 and
36, stopbands also of width W are defined for the prototype filter
only at locations aliased to the passband by the decimation
sampling rate R.sub.D. Transition bands may again be left
unconstrained during filter design. To provide adequate transition
band width while preventing undesired aliasing, R.sub.D must be
somewhat greater than W.
Once the prototype filter coefficients are obtained, the position
of the passband and the stop bands are varied as desired by
multiplication of the filter coefficients by a complex exponent to
select from the near-baseband passband a desired signal spectrum of
width W. The aliasing caused by the decimation then translates the
selected spectrum to within R.sub.D/2 of baseband. The variable
band-pass decimating filter thus performs a tuning function with a
resolution of R.sub.D/2.
Matlab.RTM. code for determining the coefficients of a filter
useable as the variable bandpass decimating filter 66 is presented
below in tables IV and V. The code in table IV determines the
coefficients for a prototype filter with a passband at DC of width
W and seven stopbands of width W at intervals of R.sub.D to either
side of DC. In the code in table IV, N is the filter order and is
set to 63, resulting in 64 FIR filter taps, providing adequate
interference attenuation with a power of 2 length which is
typically more easily implemented in a DSP. R is the relative
emphasis on stopband performance relative to passband performance
and is set to 50, resulting in good stopband rejection with
reasonable levels of passband ripple. Variable f1 represents the
sampling frequency at the Hilbert transform pair and is set to 128
kHz. Variable f2 represents the output sampling frequency of filter
66 and is set to 16 kHz, giving a decimation ratio of M=8. Variable
fbw represents the bandwidth of the signal of interest, in this
case a 8000 bps QPSK square-root raised-cosine digital signal with
an excess bandwidth setting (Beta) of 0.6.
The code in table V adjusts the coefficients generated in the code
in table IV, which are contained in variable b. Variable fs is the
sampling frequency at the Hilbert transform pair, set to 128 kHz
here. Variable fshift is the frequency to which the passband of the
filter 66 is to be shifted.
Final fine-tuning is performed after filter 66 by fine-shifting by
mixing with a complex exponential signal. This fine shifting brings
the desired signal to baseband from the location within R.sub.D/2
of baseband to which it was aliased by filter 66. The complex
exponential signal is supplied by a digital quadrature local
oscillator 68 and mixed with the complex signals by digital mixer
70. The complex signals are then filtered and decimated at a
decimation rate of M=2 by filters 72, 74 matched to the pulse of
the desired signal, which filters reject frequencies in the
transition bands of the variable bandpass decimating filter and in
regions aliasing into the desired signal. Significant suppression
of transition bands is thus effectively postponed until the signal
reaches filters 72, 74, at which point the sampling frequency has
been reduced to R.sub.D=R/8, and the spectrum of interest has been
reduced to within R.sub.D/2 of baseband, allowing for relatively
efficient sharp-cutoff filtering. The resulting signals are then
demodulated by a quadrature demodulator. For other types of
signals, other typical demodulation procedures and devices may be
used after the fine-shifting operation.
Simulated frequency response curves for the embodiment of the
device 10 of FIG. 8 not employing oversampling are seen in FIGS. 18
20.
FIG. 18 shows the continuous-time filtering frequency response
curve CT together with the Hilbert transform frequency response
curve HT. The CT curve shows the desired attenuation of frequencies
near DC, together with anti-aliasing low pass filtering with a
transition band from about 2.25 to about 3. Beginning the
transition band above 2, the upper boundary of the near-baseband
passband in this embodiment, avoids including the corner of the
lowpass filter within the near-baseband passband, thereby avoiding
significant group delay variations which can increase intersymbol
interference. The beginning of the stopband at 3 could actually be
relaxed, allowing the stopband to begin as late as 4 (minus
F.sub.A) without resulting in aliasing into the near-baseband
passband at 1 to 2, given a sampling frequency of R=6 as preferred
with a 1 to 2 near-baseband passband. The HT curve shows rejection
of the mixing image at -1 to -2 on the x axis.
FIG. 19 shows a variable passband decimating filter frequency
response curve VDF and a matched filter frequency response curve
MF. The VDF curve shows a passband centered at 1 with seven
stopbands to either side at intervals of 0.75=R/8=R.sub.D. The
matched filter frequency response curve MF is shown aligned with
the VDF curve to reject signals within the transition band of the
VDF curve. Translation to baseband is not shown.
FIG. 20 shows the system frequency response resulting from the
cascade of the frequency responses shown in FIGS. 18 and 19.
FIG. 21 shows an envelope detector output resulting from simulated
envelope detection of the simulated output of the device 10 of FIG.
8. Inter-symbol interference is -28.55 dB, well below the maximum
allowable in most digital modulation schemes.
FIGS. 22 25 show simulated frequency response curves for the
embodiment of the device 10 of FIG. 8 employing oversampling, but
with M=16 (16 times oversampling) for illustration purposes rather
than M=32 as currently most preferred.
FIG. 22 shows the continuous-time filtering response curve CT, with
the very relaxed upper transition bands employable with
oversampling. The frequency curve HT response of the Hilbert
transform and the frequency response curve DF of the decimating
filters 34, 36 are also shown. The DF curve shows the desired
passband at about 1 to 2 on the x axis with stopbands of the same
width repeating at intervals of 3 on either side.
FIG. 23 shows the curves of FIG. 22 on a smaller scale. The
unconstrained transition bands of the DF curve may be seen, as well
as the image rejection of the HT curve at 1 to 2.
FIGS. 24 and 25 show a simulated system frequency response
resulting from the embodiment of device 10 in FIG. 8 using
oversampling at M=16. Attenuation of unwanted signals and noise in
this simulated embodiment meets the requirements of most
commercially available mobile radio equipment (about 75 dB).
While the above described preferred embodiments are only the
presently most preferred embodiments, certain additional general
advantages of the present invention may be seen therein.
The particular division of functions between analog and digital
portions of the device 10 allows sufficiently relaxed requirements
for both the analog and digital portions that each can be
implemented individually on a single integrated circuit. The
processing power and memory requirements of the embodiment not
employing oversampling are low enough to allow implementation of
the entire digital portion in a current general purpose DSP. Even
the oversampling embodiment may potentially be implemented in
next-generation general purpose DSPs, or in an ASIC with no more
complexity or power requirements than a general purpose DSP, or in
a current DSP with a discrete component or two for performing the
delta-sigma modulation. Single chip implementation of the entire
device is even possible with adequate shielding of the analog
portions from digital portion noise.
While not required, all of the filters in the digital domain may be
implemented as single stage filters due in part to the location of
the near-baseband passband of the present invention, and to the use
of non-constrained transition bands. Single stage filtering is
advantageous in the variable bandpass decimating filter 66, since
only a single stage of coefficients must be varied to alter the
passband location. The passband could thus be varied in real time
to follow variations in a particular signal of interest. Single
stage filtering is also very advantageous in the oversampling
decimating filters 34, 36 because it allows elimination of
multipliers and implementation with adders only.
The preferred use of a modified type III Hilbert transform allows
particularly easy and efficient correction of phase errors between
the quadrature I and Q signals. The use of a one bit wide signal
path in the oversampling embodiment also allows easy correction of
group delay differences between the I and Q signals.
As known to those of skill in the art, modulation and transmission
of RF signals may be performed essentially by reversing the
demodulation process. The device of the present invention may
accordingly be adapted by those of skill in the art for use as a
transmitter/receiver, if desired. In this case, the signal flow
shown in FIG. 8 would be reversed. I and Q signals from a baseband
modulator would be sent through transmit stages analogous to the
receive stages shown. For example, a splitter would be substituted
for the adder, interpolating filters substituted for the decimating
filters, and digital to analog converters substituted for the
analog to digital converters. The Hilbert transform pair and local
oscillator(s) would function for transmission in the same manner as
they function for reception. This substitution of analogous
transmit stages for receive stages should be readily apparent to
those of skill in the art.
Having illustrated and described the principles of the invention in
a preferred embodiment, it should be apparent to those skilled in
the art that the embodiment can be modified in arrangement and
detail without departing from such principles. For example, while
device 10 of a preferred embodiment discussed above includes a
digital portion that corrects phase and amplitude errors, an RF
receiver according to various aspects of the invention can include
just the following: (1) a local oscillator coarse-tunable in steps
of step size S for producing a local oscillator signal; (2)
continuous-time quadrature mixers for quadrature mixing with the
local oscillator signal an incoming channel of interest from a
channelized spectrum having channel spacing C, to produce I and Q
signals approximately in quadrature, thereby translating the
channel of interest to a near-baseband passband; and (3) a digital
signal processing device for rejecting an unwanted mixing image
within the near-baseband passband. The digital signal processing
device can translate any one of N channels of the channelized
spectrum from the near-baseband passband to baseband, where N is a
constant positive integer equal to the number of channels of the
channelized spectrum contained simultaneously within the
near-baseband passband, wherein S is at least 2(N-1)C.
Alternatively, it can translate to baseband a signal of interest
within the near-baseband passband, said signal of interest within
the near baseband passband having essentially any center frequency
within a range extending from a lower frequency F1 to an upper
frequency F2 inclusive, wherein S is about 2(F2-F1). In view of the
many possible embodiments to which the principles of the invention
may be applied, it should be recognized that the illustrated
embodiment is only a preferred example of the invention and should
not be taken as a limitation on the scope of the invention. Rather,
the invention is defined by the following claims. I therefore claim
as my invention all such embodiments that come within the scope and
spirit of the following claims.
The disclosure of originally filed claims 1 42 of parent
application Ser. No. 10/032,526, being part of the specification
thereof, is incorporated herein by reference.
TABLE-US-00001 TABLE I % Define the delta-sigma oversampling
frequency % from the oversampling ratio % and the discrete-time
system sampling frequency % (input to the Hilbert transform pair)
fds = fs * Mds; % Define weight of passband as 1/R and weight of
all % stopbands as 1 wt = [1/R ones(1,floor(Mds)-1]; % Define
passband of filter f = [fs/6 fs/3 ]; m = [1 1 ]; % Define stopbands
of filter only at frequency regions % which would alias into
passband for k = 1:ceil(Mds)-1, % Stopbands fs/2 apart because real
filter f(2*k+1:2*k+2) = [ -fs/12 fs/12] + . . .
(fs/2*k+fs/4)*ones(1,2); m(2*k+1:2*k+2) = [ 0 0 ]; end % Adjust for
1 = Nyquist freq. f = f ./ (0.5*fds); % Compute filter using Remez
exchange algorithm bds = remez(Nds,f,m,wt);
TABLE-US-00002 TABLE II LOOK-UP TABLE COEFFICIENTS 54a 54b 54c 54d
164 4454 -6504 7308 222 4538 -7064 9174 276 4602 -7626 11106 348
4646 -8146 13098 426 4668 -8638 15138 514 4664 -9092 17224 608 4636
-9508 19342 710 4582 -9876 21486 820 4498 -10194 23648 936 4384
-10456 25816 1060 4238 -10656 27980 1190 4060 -10790 30134 1328
3850 -10852 32264 1472 3604 -10838 34362 1622 3324 -10742 36418
1778 3008 -10562 38420 1940 2658 -10292 40360 2106 2272 -9930 42228
2276 1852 -9474 44016 2450 1398 -8920 45712 2624 912 -8266 47310
2802 394 -7510 48798 2978 -156 -6652 50172 3154 -732 -5692 51424
3328 -1334 -4630 52546 3498 -1960 -3468 53532 3664 -2604 -2204
54378 3822 -3266 -844 55076 3972 -3940 612 55630 4112 -4624 2160
56028 4240 -5304 3794 56288 4354 -5996 5512 56372
TABLE-US-00003 TABLE III % Define the zero degree delay as a unit
sample in % the center of an FIR filter of equal length to the % 90
degree Hilbert transform filter. Only the % samples before the unit
sample need to be % implemented in practice. bhI =
[zeros(1,(Nh-1)/2) 1 zeros(1,(Nh-1)/2)]; % Define passband of the
Hilbert transform fhilb = [(fref/2 - fbw/2) (fref + fbw/2)] /
(fs/2); % Define the 90 degree Hilbert transform using Remez %
exchange algorithm bhQ = remez(Nh,fhilb,[1 1], `Hilbert`); % Scale
amplitude of Q channel coefficients for gain % imbalance
compensation bhQv = QG .* bhQ .* SB; % Adjust amplitude of center Q
channel coefficient to % vary phase from 90 degrees. This provides
phase % imbalance compensation. bhQv((Nh/2)+1) = tan((2*pi)/360 *
QP);
TABLE-US-00004 TABLE IV function b = dbf(N,R,f1,f2,fbw) % b =
dbf(N,R,f1,f2,fbw) % Decimating Bandpass Filter % Nth-order
bandpass FIR with decimation and % asymmetrical frequency response
% R parameter (50 suggested) determines relative % importance of
passband and stopbands % f1 is input sampling rate % f2 is output
sampling rate % fbw is 2-sided bandwidth of interest % Calculate
cutoff frequency of prototype LPF (1/2 BW % of interest) fc =
fbw/2; % Iterate to get all stopband regions except at f=1 M =
f1/f2; % Parks McClellan: define bands %
---------------------------------------------------- % Define
passband of filter f = [ 0 fc ] ; m = [ 1 1 ] ; % Define weight of
stopband vs. passband based on R parameter % 50 gives Rp<0.01dB
with Rs<-100dB % Define weight of passband as 1/R and weight of
all % stopbands as 1 wt = [ 1/R ones(1,f1oor(M/2))]; % Define
stopbands of filter only at frequency regions % which would alias
into passband for k = 1:ceil(M/2)-1, f(2*k+1:2*k+2) = [ -fc fc ] +
f2*k*ones(1,2); m(2*k+1:2*k+2) = [0 0 ]; end % If M is even, append
a fixed stopband at Nyquist % frequency if ceil(M/2)==M/2
f(M+1:M+2) = [ f1/2-fc f1/2 ]; m(M+1:M+2) = [ 0 0 ]; end % Adjust
for 1 = Nyquist freq. f = f ./ (0.5*f1); % Compute filter using
Remez exchange algorithm if N>=3 b = remez(N,f,m,wt); else
%Order less than 3 is defined to be just a %zero-order %allpass b =
1 end % Define transfer function denominator coefficients as %
simply a one followed by zeroes a = [1 zeros(1,max(size(b))-1))]; %
Make sure H(0)=1 k = freqz(b,a,linspace(0,pi)); b = b ./
max(abs(k)); %end of function end
TABLE-US-00005 TABLE V n = 1:length(b); b = b . *
exp(i*2*pi(fshift/fs)*n));
* * * * *
References