![[Help]](app5_files/help.gif)
![[Home]](app5_files/home.gif)
![[Boolean Search]](app5_files/boolean.gif)
![[Manual]](app5_files/manual.gif)
![[Number Search]](app5_files/number.gif)
![[PTDLs]](app5_files/ptdl.gif)
![[CURR_LIST]](app5_files/hitlist.gif)
![[PREV_DOC]](app5_files/prevdoc.gif)
![[NEXT_DOC]](app5_files/nextdoc.gif)
![[Shopping Cart]](app5_files/cart.gif)
![[Order Copy]](app5_files/order.gif)
![[Image]](app5_files/image.gif)
| United States Patent Application |
20020141508 |
| Kind Code |
A1 |
| El-Gamal, Hesham ; et
al. |
October 3, 2002 |
Space-time trellis code for orthogonal frequency division
multiplexing (OFDM)
Abstract
A communication system for transmitting encoded signals over a communication
channel is disclosed. The system includes a transmitter, which has a source that
is configured to output a plurality of input signals. The transmitter also
includes an encoder that is configured to generate a plurality of output signals
in response to the plurality of the input signals to output a code word
according to the plurality of output signals, wherein the code word has a
predetermined algebraic construction for space-frequency coding based upon the
communication channel being characterized as a frequency selective block fading
channel. Further, the transmitter includes a modulator that is configured to
modulate the code word for transmission over the communication channel, and a
plurality of transmit antennas that configured to transmit the modulated code
word over the communication channel. The system encompasses a receiver that
includes a plurality of receive antennas, in which the receiver is configured to
receive the transmitted code word via the plurality of receive antennas. The
receiver employs an OFDM-front end to transform the Intersymbol Interference
(ISI) channel characteristics of the communication channel to selective block
fading characteristics.
| Inventors: |
El-Gamal,
Hesham; (Dublin, OH) ; Hammons, A. Roger JR.; (N.
Potomac, MD) |
| Correspondence Name and Address: |
Hughes Electronics Corporation
Patent Docket Administration
Bldg. 1, Mail Stop A109
P.O. Box 956
El Segundo
CA
90245-0956
US
|
| Serial No.: |
011631 |
| Series Code: |
10 |
| Filed: |
November 5, 2001 |
| U.S. Current Class: |
375/267; 375/265; 375/279
|
| U.S. Class at Publication: |
375/267; 375/279; 375/265
|
| Intern'l Class: |
H04L 001/02 |
Claims
What is claimed is:
1. A method for transmitting encoded signals
over a communication channel of a communication system, the method comprising:
receiving a plurality of input signals; generating a plurality of output signals
in response to the plurality of the input signals; and outputting a code word
according to the plurality of output signals, wherein the code word has a
predetermined algebraic construction for space-frequency coding based upon the
communication channel being characterized as a frequency selective block fading
channel.
2. The method according to claim 1, further comprising:
performing an inverse Fourier transform of the plurality of output signals.
3. The method according to claim 1, further comprising: transmitting the
code word via a plurality of transmit antennas over the communication channel.
4. The method according to claim 3, wherein the construction of the code
word in the outputting step defines a matrix equation: Y(D)=X(D)G(D), where
Y(D)=.left brkt-bot.Y.sub.1(D)Y.sub.2(D) . . .
Y.sub.L.sub..sub.t.sub.L.sub..sub.ISI(D).right brkt-bot.,
X(D)=[X.sub.1(D)X.sub.2(D) . . . X.sub.k(D)], and 23 G ( D ) = [ G 1 , 1 ( D ) G
1 , 2 ( D ) G 1 , L t L I S I ( D ) G 2 , 1 ( D ) G 2 , 2 ( D ) G 1 , L t L I S
I ( D ) G k , 1 ( D ) G k , 2 ( D ) G k , L t L I S I ( D ) ] ,wherein X(D) and
Y(D) correspond to the plurality of input signals and the plurality of output
signals, respectively, L, representing the number of transmit antennas,
L.sub.ISI representing the number of fading blocks associated with the
communication channel.
5. The method according to claim 4, wherein the
construction of the code word in the outputting step further defines G as a set
of binary full rank matrices {G:G=.left brkt-bot.g.sub.i<j.right
brkt-bot..sub.L.sub..sub.t.sub..times.L.sub..sub.t} resulting from applying a
number of simple row operations to an identity matrix I.sub.L.sub..sub.t, and 24
R i ( G m , m ) ( D ) = [ g i , 1 ( m ) I k , g i , 2 ( m ) I k , , g i , L t (
m ) I k ] [ F ( m - 1 ) L t + 1 ( D ) F ( m - 1 ) L t + 2 ( D ) F m L t ( D ) ]
,wherein m represents the m.sup.th fading block, and F.sub.l(D) is a column
vector defined as follows, 25 F l ( D ) = [ G 1 , l ( D ) G 2 , l ( D ) G k , l
( D ) ] .
6. The method according to claim 5, wherein the code word in
the outputting step is drawn from a space-frequency code, C, which includes a
binary convolutional code C, whose k.times.L.sub.tL.sub.ISI transfer function
matrix is G(D)=.left brkt-bot.F.sub.1(D) . . .
F.sub.L.sub..sub.t.sub.L.sub..sub.ISI(D)J.right brkt-bot. wherein an output
Y.sub.(m-1)L.sub..sub.t.sub.+1(D)=X(D)F.sub.(m-1)L.sub..sub.t.sub.- +1(D) is
assigned to antenna l in the fading block m.
7. The method according to
claim 6, wherein, for BPSK (Binary Phase-Shift Keying) transmission, C achieves
d levels of transmit diversity if d is the largest integer such that
.A-inverted.G.sub.1.di-elect cons.G, . . . ,G.sub.L.sub..sub.ISI.di-elect
cons.G,0.ltoreq.m.sub.1.ltoreq.min(L.sub.t- , L.sub.ISIL.sub.t-d+1), . . .
,0.ltoreq.m.sub.L.sub..sub.ISI<min(L.sub- .t,L.sub.ISIL.sub.t-d+1), 26 and i
= 1 L I S I m i = L I S I L t - d + 1 , 27 R m 1 , , m L I S I ( G 1 , , G L I S
I ) ( D ) [ R 0 ( G 1 , 1 ) ( D ) , , R m 1 ( G 1 , 1 ) ( D ) , R 0 ( G 2 , 2 )
( D ) , , R m 2 ( G 2 , 2 ) ( D ) , , R m L I S I ( G L I S I , L I S I ) ( D )
] has a rank k over the space of all formal series.
8. The method
according to claim 1, further comprising: modulating the code word for
transmission over the communication channel using at least one of BPSK (binary
phase-shift keying) modulation and QPSK (quadrature phase-shift keying)
modulation.
9. The method according to claim 1, further comprising:
distributing the plurality of output signals across a plurality of transmit
antennas according to an interleaver mapping function z defined as 28 ( i ) = [
i L I S I ] + N L I S I ( i ) L I S I ,wherein L.sub.ISI represents the number
of fading blocks associated with the communication channel, 0.sub.m refers to
the modulo m operation, 0.ltoreq.i.ltoreq.N-1, and N is the length of the code
word, N being a multiple of L.sub.ISI.
10. The method according to claim
1, further comprising: distributing the plurality of output signals across a
plurality of transmit antennas according to an interleaver mapping function .pi.
defined as 29 ( i ) = k = 0 log 2 ( L I S I ( max ) ) a k N 2 k + 1 + [ i L I S
I ( max ) ] , a k = ( ( i ) L I S I ( max ) - j = 0 k - 1 a j 2 j 2 k ) ,wherein
L.sub.ISI represents the number of fading blocks associated with the
communication channel, L.sub.ISI.sup.(max) is the maximum possible number of
paths known, and the number of resolvable paths in the communication channel is
L.sub.ISI=2.sup.r, r being an integer.
11. An apparatus for encoding
signals for transmission over a communication channel of a communication system,
the apparatus comprising: a source configured to output a plurality of input
signals; and an encoder configured to generate a plurality of output signals in
response to the plurality of the input signals to output a code word according
to the plurality of output signals, wherein the code word has a predetermined
algebraic construction for space-frequency coding based upon the communication
channel being characterized as a frequency selective block fading channel.
12. The apparatus according to claim 11, further comprising: logic
coupled to the encoder and configured to performing an inverse Fourier transform
of the plurality of output signals.
13. The apparatus according to claim
11, wherein the code word is transmitted via a plurality of transmit antennas
over the communication channel.
14. The apparatus according to claim 13,
wherein the construction of the code word defines a matrix equation:
Y(D)=X(D)G(D), where Y(D)=.left brkt-bot.Y.sub.1(D)Y.sub.2(D) . . .
Y.sub.L.sub..sub.t.sub.L.sub.ISI(D).r- ight brkt-bot.,
X(D)=[X.sub.1(D)X.sub.2(D) . . . X.sub.k(D)], and 30 G ( D ) = [ G 1 , 1 ( D ) G
1 , 2 ( D ) G 1 , L t L I S I ( D ) G 2 , 1 ( D ) G 2 , 2 ( D ) G 1 , L t L I S
I ( D ) G k , 1 ( D ) G k , 2 ( D ) G k , L t L I S I ( D ) ] ,wherein X(D) and
Y(D) correspond to the plurality of input signals and the plurality of output
signals, respectively, L.sub.t representing the number of transmit antennas,
L.sub.ISI representing the number of fading blocks associated with the
communication channel.
15. The apparatus according to claim 14, wherein
the construction of the code word further defines G as a set of binary full rank
matrices {G:G=.left brkt-bot.g.sub.i,j.right
brkt-bot..sub.L.sub..sub.t.sub..times- .L.sub..sub.t} resulting from applying a
number of simple row operations to an identity matrix I.sub.L.sub..sub.t and
.A-inverted.G.sub.1.di-elect cons.G,
1.ltoreq.i.ltoreq.L.sub.t1.ltoreq.i.ltoreq.L.sub.ISI, 31 R i ( G m , m ) ( D ) =
[ g i , 1 ( m ) I k , g i , 2 ( m ) I k , , g i , L t ( m ) I k ] [ F ( m - 1 )
L t + 1 ( D ) F ( m - 1 ) L t + 2 ( D ) F m L t ( D ) ] ,wherein m represents
the m.sup.th fading block, and F.sub.l(D) is a column vector defined as follows,
32 F l ( D ) = [ G 1 , l ( D ) G 2 , l ( D ) G k , l ( D ) ] .
16. The
apparatus according to claim 15, wherein the code word is drawn from a
space-frequency code, C, which includes a binary convolutional code C, whose
k.times.L.sub.tL.sub.ISI transfer function matrix is G(D)=.left
brkt-bot.F.sub.1(D) . . . F.sub.L.sub..sub.t.sub.L.sub.ISI (D).right brkt-bot.
wherein an output Y.sub.(m-1)L.sub..sub.t.sub.+1(D)=X-
(D)F.sub.(m-1)L.sub..sub.t.sub.+l(D) is assigned to antenna l in the fading
block m.
17. The apparatus according to claim 16, wherein, for BPSK
(Binary Phase-Shift Keying) transmission, C achieves d levels of transmit
diversity if d is the largest integer such that .A-inverted.G.sub.1.di-el- ect
cons.G, . . . , G.sub.L.sub..sub.ISI.di-elect cons.G,0.ltoreq.m.sub.1.-
ltoreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1), . . . ,0.ltoreq.m.sub.L.sub..sub-
.ISI.ltoreq.min(L.sub.t, L.sub.ISIL.sub.t-d+1), and 33 i = 1 L ISI m i = L ISI L
t - d + 1 , 34 R m l , , m L ISI ( G 1 , , G L ISI ) ( D ) = [ R 0 ( G 1 , 1 ) (
D ) , R m 1 ( G 1 , 1 ) ( D ) , R 0 ( G 2 , 2 ) ( D ) , , R m 2 ( G 2 , 2 ) ( D
) , , R m L ISI ( G L ISI , L ISI ) ( D ) ] has a rank k over the space of all
formal series.
18. The apparatus according to claim 11, further
comprising: a modulator coupled to the encoder and configured to modulate the
code word for transmission over the communication channel using at least one of
BPSK (binary phase-shift keying) modulation and QPSK (quadrature phase-shift
keying) modulation.
19. The apparatus according to claim 11, further
comprising: an interleaver coupled to the encoder and configured to distribute
the plurality of output signals across a plurality of transmit antennas
according to an interleaver mapping function .pi. defined as 35 ( i ) = [ i L
ISI ] + N L ISI ( i ) L ISI ,wherein L.sub.ISI represents the number of fading
blocks associated with the communication channel, 0.sub.m, refers to the modulo
m operation, 0.ltoreq.i.ltoreq.N-1, and N is the length of the code word, N
being a multiple of L.sub.ISI.
20. The apparatus according to claim 11,
farther comprising: an interleaver coupled to the encoder and configured to
distribute the plurality of output signals across a plurality of transmit
antennas according to an interleaver mapping function .pi. defined as 36 ( i ) =
k = 0 log 2 ( L ISI ( max ) ) a k N 2 k + 1 + [ i L ISI ( max ) ] , a k = ( ( i
) L ISI ( max ) - j = 0 k - 1 a j 2 j 2 k ) , wherein L.sub.ISI represents the
number of fading blocks associated with the communication channel,
L.sub.ISI.sup.(max) is the maximum possible number of paths known, and the
number of resolvable paths in the communication channel is L.sub.ISI=2.sup.r, r
being an integer.
21. An apparatus for encoding signals for transmission
over a communication channel of a communication system, the apparatus
comprising: means for receiving a plurality of input signals; means for
generating a plurality of output signals in response to the plurality of the
input signals; and means for outputting a code word according to the plurality
of output signals, wherein the code word has a predetermined algebraic
construction for space-frequency coding based upon the communication channel
being characterized as a frequency selective block fading channel.
22.
The apparatus according to claim 21, further comprising: means for performing an
inverse Fourier transform of the plurality of output signals.
23. The
apparatus according to claim 21, further comprising: means for transmitting the
code word via a plurality of transmit antennas over the communication channel.
24. The apparatus according to claim 23, wherein the construction of the
code word defines a matrix equation: Y(D)=X(D)G(D), where Y(D)=.left
brkt-bot.Y.sub.1(D)Y.sub.2(D) . . . Y.sub.L.sub..sub.t.sub.L.sub..sub.ISI-
(D).right brkt-bot., X(D)=[X.sub.1(D)X.sub.2(D) . . . X.sub.k(D)], and 37 G ( D
) = [ G 1 , 1 ( D ) G 1 , 2 ( D ) G 1 , L t L ISI ( D ) G 2 , 1 ( D ) G 2 , 2 (
D ) G 1 , L t L ISI ( D ) G k , 1 ( D ) G k , 2 ( D ) G k , L t L ISI ( D ) ]
,wherein X(D) and Y(D) correspond to the plurality of input signals and the
plurality of output signals, respectively, L.sub.t representing the number of
transmit antennas, L.sub.ISI representing the number of fading blocks associated
with the communication channel.
25. The apparatus according to claim 24,
wherein the construction of the code word further defines G as a set of binary
full rank matrices {G:G=.left brkt-bot.g.sub.i,j.right
brkt-bot..sub.L.sub..sub.t.sub..times- .L.sub..sub.t} resulting from applying a
number of simple row operations to an identity matrix I.sub.L.sub..sub.t, and
.A-inverted.G.sub.1.di-elec- t cons.G,
1.ltoreq.i.ltoreq.L.sub.t1.ltoreq.i.ltoreq.L.sub.ISI, 38 R i ( G m , m ) ( D ) =
[ g i , 1 ( m ) I k , g i , 2 ( m ) I k , , g i , L t ( m ) I k ] [ F ( m - 1 )
L t + 1 ( D ) F ( m - 1 ) L t + 2 ( D ) F m L t ( D ) ] ,wherein m represents
the m.sup.th fading block, and F.sub.l(D) is a column vector defined as follows,
39 F l ( D ) = [ G 1 , l ( D ) G 2 , l ( D ) G k , l ( D ) ] .
26. The
apparatus according to claim 25, wherein the code word is drawn from a
space-frequency code, C, which includes a binary convolutional code C, whose
k+L.sub.tL.sub.ISI transfer function matrix is G(D)=.left brkt-bot.F.sub.1(D) .
. . F.sub.L.sub..sub.t.sub.L.sub..sub.ISI(D).right brkt-bot. wherein an output
Y.sub.(m-1)L.sub..sub.t.sub.+1(D)=X(D)F.sub.(- m-1)L.sub..sub.t.sub.+1(D) is
assigned to antenna l in the fading block m.
27. The apparatus according
to claim 26, wherein, for BPSK (Binary Phase-Shift Keying) transmission, C
achieves d levels of transmit diversity if d is the largest integer such that
.A-inverted.G.sub.1.di-el- ect cons.G, . . . ,G.sub.L.sub..sub.ISI.di-elect
cons.G,0.ltoreq.m.sub.1.l- toreq.min(L.sub.t, L.sub.ISIL.sub.t-d+1), . . .
,0.ltoreq.m.sub.L.sub..sub- .ISI.ltoreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1), and
40 i = 1 L ISI m i = L ISI L t - d + 1 , 41 R m 1 , , m L I S I ( G 1 , , G L I
S I ) ( D ) = [ R 0 ( G 1 , 1 ) ( D ) , , R m 1 ( G 1 , 1 ) ( D ) , R 0 ( G 2 ,
2 ) ( D ) , , R m 2 ( G 2 , 2 ) ( D ) , , R m L I S I ( G L I S I , L I S I ) (
D ) ] has a rank k over the space of all formal series.
28. The
apparatus according to claim 21, further comprising: means for modulating the
code word for transmission over the communication channel using at least one of
BPSK (binary phase-shift keying) modulation and QPSK (quadrature phase-shift
keying) modulation.
29. The apparatus according to claim 21, further
comprising: means for distributing the plurality of output signals across a
plurality of transmit antennas according to an interleaver mapping function .pi.
defined as 42 ( i ) = [ i L I S I ] + N L I S I ( i ) L I S I ,wherein L.sub.ISI
represents the number of fading blocks associated with the communication
channel, 0.sub.m refers to the modulo m operation, 0.ltoreq.i.ltoreq.N-1, and N
is the length of the code word, N being a multiple of L.sub.ISI.
30. The
apparatus according to claim 21, further comprising: means for distributing the
plurality of output signals across a plurality of transmit antennas according to
an interleaver mapping function .pi. defined as 43 ( i ) = k = 0 log 2 ( L I S I
( max ) ) a k N 2 k + 1 + [ i L I S I ( max ) ] , a k = ( ( i ) L I S I ( max )
- j = 0 k - 1 a j 2 j 2 k ) ,wherein L.sub.ISI represents the number of fading
blocks associated with the communication channel, L.sub.ISI.sup.(max) is the
maximum possible number of paths known, and the number of resolvable paths in
the communication channel is L.sub.ISI=2.sup.r, r being an integer.
31.
A communication system for transmitting encoded signals over a communication
channel, the system comprises: a transmitter including, a source configured to
output a plurality of input signals, and an encoder configured to generate a
plurality of output signals in response to the plurality of the input signals to
output a code word according to the plurality of output signals, wherein the
code word has a predetermined algebraic construction for space-frequency coding
based upon the communication channel being characterized as a frequency
selective block fading channel, a modulator configured to modulate the code word
for transmission over the communication channel, and a plurality of transmit
antennas configured to transmit the modulated code word over the communication
channel; and a receiver including a plurality of receive antennas, the receiver
being configured to receive the transmitted code word via the plurality of
receive antennas.
32. The system according to claim 31, wherein the
transmitter further comprises: logic coupled to the encoder and configured to
performing an inverse Fourier transform of the plurality of output signals.
33. The system according to claim 31, wherein the construction of the
code word defines a matrix equation: Y(D)=X(D)G(D), where Y(D)=.left
brkt-bot.Y.sub.1(D)Y.sub.2(D) . . . Y.sub.L.sub..sub.t.sub.L.sub..sub.ISI-
(D).right brkt-bot., X(D)=[X.sub.1(D)X.sub.2(D) . . . X.sub.k(D)], and 44 G ( D
) = [ G 1 , 1 ( D ) G 1 , 2 ( D ) G 1 , L i L I S I ( D ) G 2 , 1 ( D ) G 2 , 2
( D ) G 1 , L i L I S I ( D ) G k , 1 ( D ) G k , 2 ( D ) G k , L i L I S I ( D
) ] ,wherein X(D) and Y(D) correspond to the plurality of input signals and the
plurality of output signals, respectively, L.sub.t representing the number of
transmit antennas, L.sub.ISI, representing the number of fading blocks
associated with the communication channel.
34. The system according to
claim 33, wherein the construction of the code word further defines G as a set
of binary full rank matrices {G:G=.left brkt-bot.g.sub.i,j.right
brkt-bot..sub.L.sub..sub.t.sub..times..sub..sub.- t} resulting from applying a
number of simple row operations to an identity matrix I.sub.L.sub..sub.t, and
.A-inverted.G.sub.1.di-elect
cons.G,1.ltoreq.i.ltoreq.L.sub.t1.ltoreq.i.ltoreq.L.sub.ISI, 45 R i ( G m , m )
( D ) = [ g i , 1 ( m ) I k , g 1 , 2 ( m ) I k , , g i , L i ( m ) I k ] [ F (
m - 1 ) L i + 1 ( D ) F ( m - 1 ) L i + 2 ( D ) F m L i ( D ) ] ,wherein m
represents the m.sup.th fading block, and F.sub.l(D) is a column vector defined
as follows, 46 F l ( D ) = [ G 1 , l ( D ) G 2 , l ( D ) G k , l ( D ) ] .
35. The system according to claim 34, wherein the code word is drawn
from a space-frequency code, C, which includes a binary convolutional code C,
whose k.times.L.sub.tL.sub.ISI, transfer function matrix is G(D)=.left
brkt-bot.F.sub.1(D) . . . F.sub.L.sub..sub.t.sub.L.sub..sub.ISI(D).right
brkt-bot. wherein an output Y.sub.(m-1)L.sub..sub.t.sub.+1(D)=X(D)F.sub.(-
m-1)L.sub..sub.t.sub.+1(D) is assigned to antenna l in the fading block m.
36. The system according to claim 35, wherein, for BPSK (Binary
Phase-Shift Keying) transmission, C achieves d levels of transmit diversity if d
is the largest integer such that .A-inverted.G.sub.1.di-el- ect cons.G, . . . ,
G.sub.L.sub..sub.ISI.di-elect cons.G,0.ltoreq.m.sub.1.-
ltoreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1), . . . ,0.ltoreq.m.sub.L.sub..sub-
.ISI.ltoreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1), and 47 i = 1 L I S I m i = L I S
I L i - d + 1 , 48 R m 1 , , m L I S I ( G 1 , , G L I S I ) ( D ) = [ R 0 ( G 1
, 1 ) ( D ) , , R m 1 ( G 1 , 1 ) ( D ) , , R 0 ( G 2 , 2 ) ( D ) , , R m 2 ( G
2 , 2 ) ( D ) , , R m L I S I ( G L I S I , L I S I ) ( D ) ] has a rank k over
the space of all formal series.
37. The system according to claim 31,
wherein the modulator modulates the code word using at least one of BPSK (binary
phase-shift keying) modulation and QPSK (quadrature phase-shift keying)
modulation.
38. The system according to claim 31, wherein the
transmitter further comprises: an interleaver coupled to the encoder and
configured to distribute the plurality of output signals across a plurality of
transmit antennas according to an interleaver mapping function .pi. defined as
49 ( i ) = [ i L I S I ] + N L I S I ( i ) L I S I ,wherein L.sub.ISI represents
the number of fading blocks associated with the communication channel, 0.sub.m
refers to the modulo m operation, 0.ltoreq.i.ltoreq.N-1, and N is the length of
the code word, N being a multiple of L.sub.ISI.
39. The system according
to claim 31, wherein the transmitter further comprises: an interleaver coupled
to the encoder and configured to distribute the plurality of output signals
across a plurality of transmit antennas according to an interleaver mapping
function .pi. defined as 50 ( i ) = k = 0 log 2 ( L I S I ( max ) ) a k N 2 k +
1 + [ i L I S I ( max ) ] , a k = ( ( i ) L I S I ( max ) - j = 0 k - 1 a j 2 j
2 k ) ,wherein L.sub.ISI represents the number of fading blocks associated with
the communication channel, L.sub.ISI.sup.(max) is the maximum possible number of
paths known, and the number of resolvable paths in the communication channel is
L.sub.ISI=2.sup.r, r being an integer.
40. The system according to claim
31, wherein the receiver comprises: an OFDM front-end configured to transform an
Intersymbol Interference (ISI) channel characteristics of the communication
channel to selective block fading characteristics.
41. The system
according to claim 31, wherein the receiver comprises: logic for performing a
Fourier transform on the received codeword.
42. A waveform signal for
transmission over a communication channel of a communication system, the
waveform signal comprising: a code word having a predetermined algebraic
construction for space-frequency coding based upon the communication channel
being characterized as a frequency selective block fading channel, wherein the
code word is transmitted via a plurality of antennas.
43. The signal
according to claim 42, wherein the construction of the code word defines a
matrix equation: Y(D)=X(D)G(D), where Y(D)=.left brkt-bot.Y.sub.1(D)Y.sub.2(D) .
. . Y.sub.L.sub..sub.t.sub.L.sub..sub.ISI- (D).right brkt-bot.,
X(D)=[X.sub.1(D)X.sub.2(D) . . . X.sub.k(D)], and 51 G ( D ) = [ G 1 , 1 ( D ) G
1 , 2 ( D ) G 1 , L 1 L ISI ( D ) G 2 , 1 ( D ) G 2 , 2 ( D ) G 1 , L 1 L ISI (
D ) G k , 1 ( D ) G k , 2 ( D ) G k , L 1 L ISI ( D ) ] ,wherein X(D) and Y(D)
correspond to the plurality of input signals and the plurality of output
signals, respectively, L.sub.t representing the number of antennas, L.sub.ISI
representing the number of fading blocks associated with the communication
channel.
44. The signal according to claim 43, wherein the construction
of the code word further defines G as a set of binary full rank matrices
{G:G=.left brkt-bot.g.sub.i,j.right
brkt-bot..sub.L.sub..sub.t.sub..times.L.sub..sub- .t} resulting from applying a
number of simple row operations to an identity matrix I.sub.L.sub..sub.t, and
.A-inverted.G.sub.1.di-elect
cons.G,1.ltoreq.i.ltoreq.L.sub.t1.ltoreq.i.ltoreq.L.sub.ISI, 52 R i ( G m , m )
( D ) = [ g i , 1 ( m ) I k , g i , 2 ( m ) I k , , g i , L 1 ( m ) I k ] [ F (
m - 1 ) L 1 + 1 ( D ) F ( m - 1 ) L 1 + 2 ( D ) F mL 1 ( D ) ] ,wherein m
represents the m.sup.th fading block, and F.sub.l(D) is a column vector defined
as follows, 53 F l ( D ) = [ G 1 , l ( D ) G 2 , l ( D ) G k , l ( D ) ] .
45. The signal according to claim 44, wherein the code word is drawn
from a space-frequency code, C, which includes a binary convolutional code C,
whose k.times.L.sub.tL.sub.ISI transfer function matrix is G(D)=.left
brkt-bot.F.sub.1(D) . . . F.sub.L.sub..sub.t.sub.L.sub.ISI (D).right brkt-bot.
wherein an output Y.sub.m-1)L.sub..sub.t.sub.+1(D)=X(D)F.sub.(m-
-1)L.sub..sub.t.sub.+1(D) is assigned to antenna l in the fading block m.
46. The signal according to claim 45, wherein, for BPSK (Binary
Phase-Shift Keying) transmission, C achieves d levels of transmit diversity if d
is the largest integer such that .A-inverted.G.sub.1.di-el- ect cons.G, . . .
,G.sub.L.sub..sub.ISI.di-elect cons.G,0.ltoreq.m.sub.L.s-
ub..sub.ISI.ltoreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1) ,. . .
,0.ltoreq.m.sub.L.sub..sub.ISI.ltoreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1), and 54
i = 1 L ISI m i = L ISI L i - d + 1 , 55 R m 1 , , mL ISI ( G 1 , , G L ISI ) (
D ) = [ R 0 ( G 1 , 1 ) ( D ) , , R m 1 ( G 1 , 1 ) ( D ) , R 0 ( G 2 , 2 ) ( D
) , , R m 2 ( G 2 , 2 ) ( D ) , , R m L ISI ( G L ISI , L ISI ) ( D ) , ] has a
rank k over the space of all formal series.
47. The signal according to
claim 43, wherein the code word is modulated using at least one of BPSK (binary
phase-shift keying) modulation and QPSK (quadrature phase-shift keying)
modulation.
48. A computer-readable medium carrying one or more
sequences of one or more instructions for transmitting encoded signals over a
communication channel of a communication system, the one or more sequences of
one or more instructions including instructions which, when executed by one or
more processors, cause the one or more processors to perform the steps of:
receiving a plurality of input signals; generating a plurality of output signals
in response to the plurality of the input signals; and outputting a code word
according to the plurality of output signals, wherein the code word has a
predetermined algebraic construction for space-frequency coding based upon the
communication channel being characterized as a frequency selective block fading
channel.
49. The computer-readable medium according to claim 48, wherein
the one or more processors further perform the step of: performing an inverse
Fourier transform of the plurality of output signals.
50. The
computer-readable medium according to claim 48, wherein the one or more
processors further perform the step of: transmitting the code word via a
plurality of transmit antennas over the communication channel.
51. The
computer-readable medium according to claim 50, wherein the construction of the
code word in the outputting step defines a matrix equation: Y(D)=X(D)G(D), where
Y(D)=.left brkt-bot.Y.sub.1(D)Y.sub.2(D) . . .
Y.sub.L.sub..sub.t.sub.L.sub..sub.ISI(D).right brkt-bot.,
X(D)=[X.sub.1(D)X.sub.2(D) . . . X.sub.k(D)], and 56 G ( D ) = [ G 1 , 1 ( D ) G
1 , 2 ( D ) G 1 , L 1 L ISI ( D ) G 2 , 1 ( D ) G 2 , 2 ( D ) G 1 , L 1 L ISI (
D ) G k , 1 ( D ) G k , 2 ( D ) G k , L 1 L ISI ( D ) ] ,wherein X(D) and Y(D)
correspond to the plurality of input signals and the plurality of output
signals, respectively, L, representing the number of transmit antennas,
L.sub.ISI representing the number of fading blocks associated with the
communication channel.
52. The computer-readable medium according to
claim 51, wherein the construction of the code word in the outputting step
further defines G as a set of binary full rank matrices {G:G=.left
brkt-bot.g.sub.i,j.right brkt-bot..sub.L.sub..sub.t.sub..times.L.sub.t}
resulting from applying a number of simple row operations to an identity matrix
I.sub.L.sub..sub.t, and .A-inverted.G.sub.1.di-elect cons.G,
1.ltoreq.i.ltoreq.L.sub.t1.ltore- q.i.ltoreq.L.sub.ISI, 57 R i ( G m , m ) ( D )
= [ g i , 1 ( m ) I k , g i , 2 ( m ) I k , , g i , L 1 ( m ) I k ] [ F ( m - 1
) L 1 + 1 ( D ) F ( m - 1 ) L 1 + 2 ( D ) F mL 1 ( D ) ] ,wherein m represents
the m.sup.th fading block, and F.sub.l(D) is a column vector defined as follows,
58 F l ( D ) = [ G 1 , l ( D ) G 2 , l ( D ) G k , l ( D ) ] .
53. The
computer-readable medium according to claim 52, wherein the code word in the
outputting step is drawn from a space-frequency code, C, which includes a binary
convolutional code C, whose k.times.L.sub.tL.sub.ISI transfer function matrix is
G(D)=.left brkt-bot.F.sub.1(D) . . . F.sub.L.sub..sub.t.sub.L.sub.ISI(D).right
brkt-bot. wherein an output Y.sub.(m-1)L.sub..sub.t.sub.+1(D)=X(D)F.sub.(-
m-1)L.sub..sub.t.sub.+1(D) is assigned to antenna l in the fading block m.
54. The computer-readable medium according to claim 53, wherein, for
BPSK (Binary Phase-Shift Keying) transmission, C achieves d levels of transmit
diversity if d is the largest integer such that .A-inverted.G.sub.1.di-el- ect
cons.G, . . . ,G.sub.L.sub..sub.ISI.di-elect cons.G,0.ltoreq.m.sub.L.s-
ub..sub.ISI.ltoreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1) ,. . .
,0.ltoreq.m.sub.L.sub..sub.ISI.ltoreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1), and 59
i = 1 L ISI m i = L ISI L i - d + 1 , 60 R m 1 , , mL ISI ( G 1 , , G L ISI ) (
D ) = [ R 0 ( G 1 , 1 ) ( D ) , , R m 1 ( G 1 , 1 ) ( D ) , R 0 ( G 2 , 2 ) ( D
) , , R m 2 ( G 2 , 2 ) ( D ) , , R m L ISI ( G L ISI , L ISI ) ( D ) , ] has a
rank k over the space of all formal series.
55. The computer-readable
medium according to claim 48, wherein the one or more processors further perform
the step of: modulating the code word for transmission over the communication
channel using at least one of BPSK (binary phase-shift keying) modulation and
QPSK (quadrature phase-shift keying) modulation.
56. The
computer-readable medium according to claim 48, wherein the one or more
processors further perform the step of: distributing the plurality of output
signals across a plurality of transmit antennas according to an interleaver
mapping function s defined as 61 ( i ) = [ i L ISI ] + N L ISI ( i ) L ISI
,wherein L.sub.ISI represents the number of fading blocks associated with the
communication channel, 0.sub.m refers to the modulo m operation,
0.ltoreq.i.ltoreq.N-1, and N is the length of the code word, N being a multiple
of L.sub.ISI.
57. The computer-readable medium according to claim 48,
wherein the one or more processors further perform the step of: distributing the
plurality of output signals across a plurality of transmit antennas according to
an interleaver mapping function .pi. defined as 62 ( i ) = k = 0 log 2 ( L ISI (
max ) ) a k N 2 k + 1 + [ i L ISI ( max ) ] , a k = ( ( i ) L ISI ( max ) - j =
0 k - 1 a j 2 j 2 k ) ,wherein L.sub.ISI represents the number of fading blocks
associated with the communication channel, L.sub.ISI.sup.(max) is the maximum
possible number of paths known, and the number of resolvable paths in the
communication channel is L.sub.ISI=2.sup.r, r being an integer.
58. An
apparatus for receiving signals over a communication channel of a communication
system, the apparatus comprising: a demodulator configured to demodulate a
signal containing a code word transmitted from a plurality of transmit antennas
of the communication system, wherein the code word has a predetermined algebraic
construction for space-frequency coding based upon the communication channel
being characterized as a frequency selective block fading channel; and a decoder
configured to decode the code word and to output a message signal.
59.
The apparatus according to claim 58, further comprising: an OFDM front-end
configured to transform an Intersymbol Interference (ISI) channel
characteristics of the communication channel to selective block fading
characteristics.
60. The apparatus according to claim 58, further
comprising: logic for performing a Fourier transform on the received codeword.
61. The apparatus according to claim 58, wherein the construction of the
code word defines a matrix equation: Y(D)=X(D)G(D), where Y(D)=.left
brkt-bot.Y.sub.1(D)Y.sub.2(D) . . . Y.sub.L.sub..sub.t.sub.L.sub..sub.ISI-
(D).right brkt-bot., X(D)=[X.sub.1(D)X.sub.2(D) . . . X.sub.k(D)], and 63 G ( D
) = [ G 1 , 1 ( D ) G 1 , 2 ( D ) G 1 , L t L ISI ( D ) G 2 , 1 ( D ) G 2 , 2 (
D ) G 1 , L t L ISI ( D ) G k , 1 ( D ) G k , 2 ( D ) G k , L t L ISI ( D ) ]
,wherein X(D) and Y(D) correspond to the plurality of input signals and the
plurality of output signals; respectively, L.sub.t representing the number of
transmit antennas, L.sub.ISI representing the number of fading blocks associated
with the communication channel.
62. The apparatus according to claim 61,
wherein the construction of the code word further defines G as a set of binary
full rank matrices {G:G=.left brkt-bot.g.sub.i,j.right
brkt-bot..sub.L.sub..times.L.sub..sub- .t } resulting from applying a number of
simple row operations to an identity matrix I.sub.L.sub..sub.t, and
.A-inverted.G.sub.1.di-elect cons.G,
1.ltoreq.i.ltoreq.L.sub.t1.ltoreq.i.ltoreq.L.sub.ISI, 64 R i ( G m , m ) ( D ) =
[ g i , 1 ( m ) I k , g i , 2 ( m ) I k , , g i , L t ( m ) I k ] [ F ( m - 1 )
L t + 1 ( D ) F ( m - 1 ) L t + 2 ( D ) F mL t ( D ) ] ,wherein m represents the
m.sup.th fading block, and F.sub.l(D) is a column vector defined as follows, 65
F l ( D ) = [ G 1 , l ( D ) G 2 , l ( D ) G k , l ( D ) ] .
63. The
apparatus according to claim 62, wherein the code word is drawn from a
space-frequency code, C, which includes a binary convolutional code C, whose
k.times.L.sub.tL.sub.ISI transfer function matrix is G(D)=.left
brkt-bot.F.sub.1(D) . . . F.sub.L.sub..sub.t.sub.L.sub..sub.IS- I(D).right
brkt-bot. wherein an output Y.sub.(m-1)L.sub..sub.t.sub.+1(D)=X-
(D)F.sub.(m-1)L.sub..sub.t.sub.+1(D) is assigned to antenna l in the fading
block m.
64. The apparatus according to claim 63, wherein, for BPSK
(Binary Phase-Shift Keying) transmission, C achieves d levels of transmit
diversity if d is the largest integer such that .A-inverted.G.sub.1.di-el- ect
cons.G, . . . ,G.sub.L.sub..sub.ISI.di-elect cons.G,0.ltoreq.m.sub.1.l-
toreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1), . . . ,0.ltoreq.m.sub.L.sub..sub.-
ISI.ltoreq.min(L.sub.t,L.sub.ISIL.sub.t-d+1), and 66 i = 1 L ISI m i = L ISI L t
- d + 1 , 67 R m 1 , , m L ISI ( G 1 , , G L ISI ) ( D ) = [ R 0 ( G 1 , 1 ) ( D
) , , R m 1 ( G 1 , 1 ) ( D ) , R 0 ( G 2 , 2 ) ( D ) , , R m 2 ( G 2 , 2 ) ( D
) , , R m L ISI ( G L ISI , L ISI ) ( D ) ] has a rank k over the space of all
formal series.
Description
CROSS-REFERENCES TO RELATED APPLICATION
[0001] This application
is related to, and claims the benefit of the earlier filing date of U.S.
Provisional Patent Application (Attorney Docket PD-200346), filed November 6,
2000, entitled "Space-Time Trellis Codes for OFDM," the entirety of which is
incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention
relates to coding in a communication system, and is more particularly related to
space-time codes that exploit multiple forms of diversity.
[0004] 2.
Discussion of the Background
[0005] Given the constant demand for higher
system capacity of wireless systems, multiple antenna systems have emerged to
increase system bandwidth vis-a-vis single antenna systems. In multiple antenna
systems, data is parsed into multiple streams, which are simultaneously
transmitted over a corresponding quantity of transmit antennas. At the receiving
end, multiple receive antennas are used to reconstruct the original data stream.
To combat the detrimental effects of the communication channel, communication
engineers are tasked to develop channel codes that optimize system reliability
and throughput in a multiple antenna system.
[0006] To minimize the
effects of the communication channel, which typically is Rayleigh, space-time
codes have been garnered significant attention. Rayleigh fading channels
introduce noise and attenuation to such an extent that a receiver may not
reliably reproduce the transmitted signal without some form of diversity;
diversity provides a replica of the transmitted signal. Space-time codes are two
dimensional channel codes that exploit spatial transmit diversity, whereby the
receiver can reliably detect the transmitted signal. Conventional designs of
space-time codes have focused on maximizing spatial diversity in quasi-static
fading channels and fast fading channels. However, real communication systems
exhibit channel characteristics that are somewhere between quasi-static and fast
fading. Accordingly, such conventional space-time codes are not optimized.
[0007] Further, other approaches to space-time code design assume that
channel state information (CSI) are available at both the transmitter and
receiver. Thus, a drawback of such approaches is that the design requires the
transmitter and receiver to have knowledge of the CSI, which increases
implementation costs because of the need for additional hardware. Moreover,
these approaches view the transmit diversity attending the use of space-time
codes as a substitute for time diversity; consequently, such space-time codes
are not designed to take advantage of other forms of diversity.
[0008]
Notably, information theoretic studies have shown that spatial diversity
provided by multiple transmit and/or receive antennas allows for a significant
increase in the capacity of wireless communication systems operated in a flat
Rayleigh fading environment [1] [2]. Following this observation, various
approaches for exploiting this spatial diversity have been proposed. In one
approach, channel coding is performed across the spatial dimension as well as
time to benefit from the spatial diversity provided by using multiple transmit
antennas [3]. Tarokh et al. coined the term "space-time coding" for this scheme.
One potential drawback of this scheme is that the complexity of the maximum
likelihood (ML) decoder is exponential in the number of transmit antennas.
Another approach, as proposed by Foshini [5], relies upon arranging the
transmitted data stream into multiple independent layers and sub-optimal signal
processing techniques at the receiver to achieve performance that is
asymptotically close to the outage capacity with reasonable complexity. In this
approach, no effort is made to optimize the channel coding scheme.
[0009] Conventional approaches to space-time coding design have focused
primarily on the flat fading channel model. With respect to the treatment of
multi-input multi-output (MIMO) frequency selective channels, one approach
contends the that space-time codes that are designed to achieve a certain
diversity order in flat fading channels achieve at least the same diversity
order in frequency selective fading channels. Such an approach fails to exploit
the spatial and frequency diversity available in the channel.
[0010]
Based on the foregoing, there is a clear need for improved approaches for
providing space-time codes that can be utilized in a multi-input multi-output
(MIMO) selective fading channel. There is also a need to design space-time codes
that can exploit spatial diversity as well as time diversity. There is also a
need to improve system reliability without reducing transmission rate. There is
a further need to simplify the receiver design. Therefore, an approach for
constructing space-time codes that can enhance system reliability and throughput
in a multiple antenna system is highly desirable.
SUMMARY OF THE
INVENTION
[0011] The present invention addresses the above stated needs
by providing space-frequency codes that optimally exploit the spatial and
frequency diversity available in the multi-input multi-output (MIMO) selective
block fading channels. At the receiving end, an OFDM-front end is utilized to
transform the Intersymbol Interference (ISI) channel characteristics of the
communication channel to selective block fading characteristics.
[0012]
According to one aspect of the invention, a method for transmitting encoded
signals over a communication channel of a communication system is provided. The
method includes receiving a plurality of input signals. The method also includes
generating a plurality of output signals in response to the plurality of the
input signals, and outputting a code word according to the plurality of output
signals. The code word has a predetermined algebraic construction for
space-frequency coding based upon the communication channel being characterized
as a frequency selective block fading channel. Under this approach, spatial
diversity and frequency diversity are enhanced, without sacrificing transmission
rate.
[0013] According to another aspect of the invention, an apparatus
for encoding signals for transmission over a communication channel of a
communication system is provided. The apparatus includes a source that is
configured to output a plurality of input signals. The apparatus also includes
an encoder that is configured to generate a plurality of output signals in
response to the plurality of the input signals to output a code word according
to the plurality of output signals. The code word has a predetermined algebraic
construction for space-frequency coding based upon the communication channel
being characterized as a frequency selective block fading channel. The above
arrangement advantageously improves system throughput and system reliability of
a communication system.
[0014] According to one aspect of the invention,
an apparatus for encoding signals for transmission over a communication channel
of a communication system is provided. The apparatus includes means for
receiving a plurality of input signals and means for generating a plurality of
output signals in response to the plurality of the input signals. Additionally,
the apparatus includes means for outputting a code word according to the
plurality of output signals, wherein the code word has a predetermined algebraic
construction for space-frequency coding based upon the communication channel
being characterized as a frequency selective block fading channel. The above
arrangement advantageously provides increased system capacity.
[0015]
According to another aspect of the invention, a communication system for
transmitting encoded signals over a communication channel is disclosed. The
system includes a transmitter, which has a source that is configured to output a
plurality of input signals. The transmitter also includes an encoder that is
configured to generate a plurality of output signals in response to the
plurality of the input signals to output a code word according to the plurality
of output signals, wherein the code word has a predetermined algebraic
construction for space-frequency coding based upon the communication channel
being characterized as a frequency selective block fading channel. Further, the
transmitter includes a modulator that is configured to modulate the code word
for transmission over the communication channel, and a plurality of transmit
antennas that configured to transmit the modulated code word over the
communication channel. The system encompasses a receiver that includes a
plurality of receive antennas, in which the receiver is configured to receive
the transmitted code word via the plurality of receive antennas. The above
arrangement advantageously maximizes spatial and frequency diversity.
[0016] According to another aspect of the invention, a waveform signal
for transmission over a communication channel of a communication system is
disclosed. The waveform signal includes a code word that has a predetermined
algebraic construction for space-frequency coding based upon the communication
channel being characterized as a frequency selective block fading channel,
wherein the code word is transmitted via a plurality of antennas. The above
approach minimizes data transmission errors.
[0017] In yet another
aspect of the invention, a computer-readable medium carrying one or more
sequences of one or more instructions for transmitting encoded signals over a
communication channel of a communication system is disclosed. The one or more
sequences of one or more instructions include instructions which, when executed
by one or more processors, cause the one or more processors to perform the step
of receiving a plurality of input signals. Another step includes generating a
plurality of output signals in response to the plurality of the input signals.
Yet another step includes outputting a code word according to the plurality of
output signals, wherein the code word has a predetermined algebraic construction
for space-frequency coding based upon the communication channel being
characterized as a frequency selective block fading channel. This approach
advantageously provides simplified receiver design.
[0018] In yet
another aspect of the present invention, an apparatus for receiving signals over
a communication channel of a communication system is provided. The apparatus
includes a demodulator that is configured to demodulate a signal containing a
code word transmitted from a plurality of transmit antennas of the communication
system. The code word has a predetermined algebraic construction for
space-frequency coding based upon the communication channel being characterized
as a frequency selective block fading channel. Additionally, the apparatus
includes a decoder that is configured to decode the code word and to output a
message signal. Under this approach, the effective bandwidth of the
communication system is increased.
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] A more complete appreciation of the invention and many of the
attendant advantages thereof will be readily obtained as the same becomes better
understood by reference to the following detailed description when considered in
connection with the accompanying drawings, wherein:
[0020] FIG. 1 is a
diagram of a communication system configured to utilize space-time codes,
according to an embodiment of the present invention;
[0021] FIG. 2 is a
diagram of an encoder that generates space-time codes, in accordance with an
embodiment of the present invention;
[0022] FIGS. 3A and 3B are diagrams
of receivers that employ space-time codes and space-frequency codes,
respectively, according to various embodiments of the present invention;
[0023] FIGS. 4A-4G are graphs of simulation results of the space-time
codes and space-frequency codes, according to the embodiments of the present
invention;
[0024] FIG. 5 is a diagram of a wireless communication system
that is capable of employing the space-time codes and space-frequency codes,
according to embodiments of the present invention; and
[0025] FIG. 6 is
a diagram of a computer system that can perform the processes of encoding and
decoding of space-time codes and space-frequency, in accordance with embodiments
of the present invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0026] In the following description, for the purpose of explanation,
specific details are set forth in order to provide a thorough understanding of
the invention. However, it will be apparent that the invention may be practiced
without these specific details. In some instances, well-known structures and
devices are depicted in block diagram form in order to avoid unnecessarily
obscuring the invention.
[0027] Although the present invention is
discussed with respect to Binary Phase-Shift Keying (BPSK) and Quadrature
Phase-Shift Keying (QPSK) modulation, the present invention has applicability to
other modulation schemes.
[0028] FIG. 1 shows a diagram of a
communication system configured to utilize space-time codes, according to an
embodiment of the present invention. A digital communication system 100 includes
a transmitter 101 that generates signal waveforms across a communication channel
103 to a receiver 105. In the discrete communication system 100, transmitter 101
has a message source that produces a discrete set of possible messages; each of
the possible messages have a corresponding signal waveform. These signal
waveforms are attenuated, or otherwise altered, by communications channel 103.
One phenomena of interest is Intersymbol Interference (ISI), in which the
channel 103 causes the overlap of signal pulses, resulting in the lost of signal
orthogonality. As described with respect to the construction of space-frequency
codes, the channel ISI characteristics are minimized. It is evident that
receiver 105 must be able to compensate for the attenuation that is introduced
by channel 103.
[0029] To assist with this task, transmitter 101 employs
coding to introduce redundancies that safeguard against incorrect detection of
the received signal waveforms by the receiver 105. To minimize the impact of the
communication channel 103 on the transmission signals, channel coding is
utilized. An algebraic design framework for layered and non-layered space-time
codes in flat fading channels are in the following: A. R. Hammons Jr. and H. El
Gamal. "On the theory of space-time codes for PSK modulation," IEEE Trans. Info.
Theory, March 2000; and H. El Gamal and A. R. Hammons Jr. "The layered
space-time architecture: a new prospective," IEEE Trans. Info. Thleory, 1999;
each of which is incorporated herein by reference in its entirety.
[0030] Based upon the algebraic design framework for space-time coding
in flat fading channels in "On the Theory of Space-Time Codes for PSK
Modulation," A. R. Hammons Jr. and H. El Gamal, IEEE Trans. Info. Theory, March
2000, the present invention extends this framework to design algebraic codes for
multi-input multi-output (MIMO) frequency selective fading channels. The codes,
according to the present invention, optimally exploit both the spatial and
frequency diversity available in the channel. Two design approaches with
different complexity-versus-diversity advantage trade-offs are considered. The
first approach (referred to as "single carrier time domain design" approach or
STC (space-time coding)), which is more fully described below in FIG. 3A, uses
space-time coding and maximum likelihood (ML) decoding to exploit the multipath
nature of the channel. The second approach utilizes an orthogonal frequency
division multiplexing (OFDM) technique to transform the multi-path channel into
a block fading channel (referred to as "OFDM based design" approach or SFC
(space-frequency coding)); this approach is detailed in the discussion of FIG.
3B. The new algebraic framework, according to one embodiment of the present
invention, is then used to construct space-frequency codes that optimally
exploit the diversity available in the resulting block fading channel.
[0031] The two approaches, according to the present invention, differ in
terms of decoder complexity, maximum achievable diversity advantage, and
simulated frame error rate performance. The first approach requires relatively
greater complexity at the receiver 105 over the second approach, in that the
first approach combines algebraic space-time coding with maximum likelihood
decoding to achieve the maximum possible diversity advantage in MIMO frequency
selective channels to achieve the diversity advantage. As a result, this first
approach has a relatively large trellis complexity, as required by the maximum
likelihood receiver 105. The second approach utilizes an orthogonal frequency
division multiplexing (OFDM) front-end to transform an intersymbol-interference
(ISI) fading channel into a flat block fading channel.
[0032] FIG. 2
shows a diagram of an encoder that generates space-time codes, in accordance
with an embodiment of the present invention. A transmitter 200 is equipped with
a channel encoder 203 that accepts input from an information source 201 and
outputs coded stream of higher redundancy suitable for error correction
processing at the receiver 105 (FIG. 1). The information source 201 generates k
signals from a discrete alphabet, X'. Encoder 203 generates signals from
alphabet Y to a modulator 205. Modulator 205 maps the encoded messages from
encoder 203 to signal waveforms that are transmitted to L.sub.t number of
antennas 207, which emit these waveforms over the communication channel 103.
Accordingly, the encoded messages are modulated and distributed among the
L.sub.t antennas 207. The transmissions from each of the L.sub.t transmit
antennas 207 are simultaneous and synchronous.
[0033] FIG. 3A shows a
diagram of a decoder that decodes space-time codes, according to an embodiment
of the present invention. At the receiving side, a receiver 300 includes a
demodulator 301 that performs demodulation of received signals from transmitter
200. These. signals are received at multiple antennas 303. The signal received
at each antenna 303 is therefore a superposition of the L.sub.t transmitted
signals corrupted by additive white Gaussian noise (AWGN) and the multiplicative
intersymbol interference (ISI) fading. After demodulation, the received signals
are forwarded to a decoder 305, which attempts to reconstruct the original
source messages by generating messages, X'. Receiver 300, according to one
embodiment of the present invention, has a memory 307 that stores channel state
information (CSI) associated with the communication channel 103. Conventional
communication systems typically require that CSI be available at both the
transmitter and the receiver. By contrast, the present invention, according to
one embodiment, does not require CSI at the transmitter 200, thus, providing a
more robust design.
[0034] At the receiver 300, the signal r.sub.i.sup.j
received by antenna j at time t is given by 1 r t j = E s l = 0 L ISI - 1 i = 1
L t l ij s t - 1 i + n t j
[0035] where {square root}{square root over
(E.sub.s)}, is the energy per transmitted symbol; a.sub.t.sup.ij is the complex
path gain from transmit antenna i to receive antenna j for the lth path;
L.sub.ISI is the length of the channel impulse response; s; is the symbol
transmitted from antenna i at time t; n.sub.t.sup.j is the additive white
Gaussian noise sample for receive antenna j at time t. The noise samples are
independent samples of circularly symmetric zero-mean complex Gaussian random
variable with variance N.sub.0/2 per dimension. The different path gains
.alpha..sub.t.sup.ij are assumed to be statistically independent. A space-time
code is defined to include an underlying error control code together with a
spatial parsing formatter. Specifically, an L.sub.t.times.l space-time code C of
size M has an (L.sub.tl, M) error control code C and a spatial parser a that
maps each code word vector {overscore (c)}.di-elect cons.C to an L.sub.t.times.l
matrix c whose entries are a rearrangement of those of {overscore (c)}. The
space-time code C is said to be linear if both C and .sigma. are linear.
[0036] It is assumed that the standard parser maps
{overscore
(c)}=(c.sub.1.sup.(1),c.sub.1.sup.(2), . . .
,c.sub.1.sup.(L.sup..sub.t.sup.),c.sub.2.sup.(1),c.sub.2.sup.(2), . . .
,c.sub.2.sup.(L.sup..sub.t.sup.), . . . ,c.sub.l.sup.(1),c.sub.l.sup.(2), . . .
,c.sub.l.sup.(L.sup..sub.t.sup.) ).di-elect cons.C
[0037] to the matrix
2 c = [ c 1 1 c 2 1 c n 1 c 1 2 c 2 2 c n 2 c 1 L t c 2 L t c n L t ]
[0038] The baseband code word f(c) is obtained by applying the
modulation operator f on the components of c. This modulation operator maps the
entries of c into constellation points from the discrete complex-valued
signaling constellation .OMEGA. for transmission across the channel. In this
notation, it is understood that c.sub.t.sup.(i) is the code symbol assigned to
transmit antenna i at time t and 3 s t ( i ) = f ( c t ( i ) ) .
[0039]
The diversity advantage of a space-time code is defined as the minimum absolute
value of the slope of any pairwise probability of error versus signal-to-noise
ratio curve on a log-log scale. To maximize the spatial diversity advantage
provided by the multiple transmit antenna in quasi-static flat fading MIMO
channels, the following rank criterion is utilized [3] [4]: for the baseband
rank criterion, d=rank(f(c)-f(e)) is maximized over all pairs of distinct code
words c, e.di-elect cons.C. Therefore full spatial transmit diversity is
achieved if and only if rank(f(c)-f (e))=L.sub.t for all pairs of distinct code
words c, e.di-elect cons.C. It should be noted that in the presence of L.sub.r
receive antennas 303, the total diversity advantage achieved by this code is
L.sub.tL.sub.r.
[0040] Space-time code constructions for frequency
selective fading channels is based on the concept that in an ISI (intersymbol
interference) environment with L.sub.ISI paths, a space-time system with L.sub.t
transmit antennas 207 is equivalent to a space-time system operating in flat
fading channel with L.sub.tL.sub.ISI, transmit antenna 207. However, in this
equivalent model the code word matrices are restricted to have a certain special
structure. This structure is captured in the following definition for the
baseband code word matrix in ISI environments: 4 f ( c ) ISI = [ f ( c ) 0 _ 0 0
f ( c ) 0 0 0 f ( c ) ]
[0041] where c is the code word matrix as
defined in (2) below, and 0 is the L.sub.t.times.1 all zero vector. From the
equivalent model, it is clear that in the frequency selective fading channels,
space-time codes can be constructed to achieve L.sub.tL.sub.ISI, transmit
diversity order. Therefore, the following baseband design criterion for
space-time codes in the ISJ channel is established: for ISI baseband rank
criterion, d=rank(f.sub.ISI(c)-f.sub.ISI (e)) is maximized over all pairs of
distinct code words c, e.di-elect cons.C. Full transmit diversity in this
scenario is equal to L.sub.tL.sub.ISI, and is achieved if and only if
rank(f.sub.ISI(c)-f.sub.ISI(e))=L.sub.tL.sub.ISI for all pairs of distinct code
words c, e.di-elect cons.C.
[0042] Next, the binary rank criteria is
developed; this criteria facilitate the construction of algebraic space-time
codes for BPSK (Binary Phase-Shift Keying) and QPSK (Quadrature Phase-Shift
Keying) modulated systems with an arbitrary number of transmit antennas 207 and
channel impulse response lengths. A new code word matrix CIS, that captures the
nature of the ISI channel is defined as follows: 5 c ISI = [ c 0 _ 0 0 c 0 0 0 c
]
[0043] It is first observed that in general
f(c.sub.ISI).noteq.f(c).sub.ISI, (2)
[0044] since
f(0).noteq.0
[0045] However, it is noted the diversity advantage
only depends on differences between code words rather than the code words
themselves, and thus
f(c.sub.ISI)-f(e.sub.ISI)=f(c).sub.ISI-f(e).sub.ISI
[0046] for any signaling constellation. The previous result is the key
to the algebraic space-time constructions developed in this section.
[0047] Attention is now turned to the development of BPSK modulated
codes, which may be utilized in the communication system 100 of FIG. 1. For BPSK
modulation, elements in e are drawn from the field F={0, 1} of integers modulo
2. The modulation operator/maps the symbol c.sub.t.sup.(i)=(-1).su-
p.c.sup..sub.t.sup..sup.(i).di-elect cons.F to the constellation point
s.sub.t.sup.(i)=f(c.sub.t.sup.(i)).di-elect cons.{-1,1} according to the rule
f(c.sub.t.sup.(i))=(-1).sup.c.sup..sub.t.sup..sup.(i). The binary rank criterion
for full diversity space-time codes in ISI channels can thus be stated as
follows.
[0048] With respect to the ISI channel binary rank criterion,
it is assumed that C is a linear L.sub.t.times.l space-time code with underlying
binary code C of length N=L.sub.tl operating in an ISI channel with L.sub.ISI
paths, where l.ltoreq.L.sub.tL.sub.ISI. Also, assuming that every non-zero code
word c corresponds to a matrix c.sub.ISI of full rank L.sub.tL.sub.ISI over the
binary field F, then, for BPSK transmission over the frequency selective
quasi-static fading channel 103, the space-time code C achieves full transmit
diversity L.sub.tL.sub.ISI.
[0049] While the previous result was stated
for full transmit diversity codes, it readily generalizes to any order of
transmit diversity less than or equal to L.sub.tL.sub.ISI. The ISI channel
binary rank criterion permits the use of a stacking construction that
establishes an algebraic framework for the design of algebraic space-time codes
for MIMO ISI fading channels. According to an embodiment of the present
invention, the ISI channel stacking construction, M.sub.1,M.sub.2, . . .
,M.sub.L.sub..sub.t are binary matrices of dimension k.times.l,l.gtoreq.k, and C
is the L.sub.t.times.l space-time code of dimension k including the code word
matrices 6 c = [ x _ M 1 x _ M 2 x _ M L t ] ,
[0050] where x denotes an
arbitrary k-tuple of information bits and L.sub.t <l . The following is
denoted
M.sub.n,m=.left
brkt-bot.O.sub.L.sub..sub.t.sub..times.(m-1)M.sub.nO.sub.L-
.sub..sub.t.sub..times.(L.sub..sub.ISI.sub.+1-m),.right brkt-bot.,
[0051] where O.sub.L.sub..sub.t.sub..times.(m-1) is the
L.sub.t.times.(m-1) all zero matrix. Hence, C satisfies the ISI channel binary
rank criterion, and accordingly, for BPSK transmission over the quasi-static
fading channel, achieves full transmit diversity L.sub.tL.sub.ISI, if and only
if M.sub.1,1, M.sub.2,1, . . . M.sub.L.sub..sub.t.sub.L.sub..sub.ISI have the
property that .A-inverted..alpha..sub.1,.alpha..sub.2, . . .
,.alpha..sub.L.sub..sub.t .di-elect cons.F:
[0052]
M=.alpha..sub.1M.sub.1c1.sym..alpha..sub.2M.sub.2,1.sym. . . .
.alpha..sub.L.sub..sub.t.sub.L.sub..sub.ISI is of full rank k unless
.alpha..sub.1= . . . .alpha..sub.L.sub..sub.t.sub.ISI=0. It is noted that 7 c
ISI = [ x _ M 1 , 1 x _ M 1 , 2 x _ M L t , L ISI ] .
[0053] The
stacking construction is general and applies to block codes as well as trellis
codes. An important example of the stacking construction is given by the class
of binary convolutional codes. This class is important because it allows for a
reasonable complexity maximum likelihood decoder. Let C be the binary, rate
l/L.sub.t, convolutional code having transfer function matrix [6]
G(D)=.left brkt-bot.g.sub.1(D),g.sub.2(D),. . .
,g.sub.L.sub..sub.t.sub.1(- D), . . .
,g.sub.L.sub..sub.t.sub.,L.sub..sub.ISI(D).right brkt-bot.,
[0054] then
the natural space-time code C associated with C is defined to include the code
word matrices c(D)=G.sup.T(D)x(D), where the polynomial x(D) represents the
input information bit stream. In other words, for the natural space-time code,
the natural transmission format is adopted, in which the output coded bits
generated by g.sub.i(D) are transmitted via antenna i. It is assumed the trellis
codes are terminated by tail bits [3]. Thus, if x(D) is restricted to a block of
N information bits, then C is an L.sub.t.times.(N+v) space-time code, where
v=max.sub.1.ltoreq.i.lto- req.L.sub..sub.t {degg.sub.i(x)} is the maximal memory
order of the convolutional code C. The following is denoted
G.sub.ISI(D)=[g.sub.1,1(D),g.sub.2,1(D), . . . ,
g.sub.L.sub..sub.t.sub., 1(D), . . . , g.sub.L.sub..sub.t.sub.L.sub..sub.ISI;
(D)]
[0055] where g.sub.n.m=D.sup.(m-1)g.sub.n . The following
characterizes the result of the performance of natural space-time convolutional
codes in ISI channels.
[0056] The natural space-time code C associated
with the rate I/L, convolutional code C satisfies the binary rank criterion, and
thus achieves full transmit diversity for BPSK transmission in an ISI channel
with L.sub.ISI paths, if and only if the transfer function matrix G.sub.ISI(D)
of C has fall rank L.sub.tL.sub.ISI as a matrix of coefficients over F. This
result stems from the observation that 8 1 i L t , 1 j L ISI a i , j g i , j ( D
) x ( D ) = 0
[0057] for some x(D).noteq.0 iff 9 1 i L t , 1 j L ISI a i
, j g i , j ( D ) = 0.
[0058] This observation readily generalizes to
recursive convolutional codes.
[0059] The above result extends to
convolutional codes with arbitrary rates and arbitrary diversity orders. Since
the coefficients of G.sub.ISI(D) form a binary matrix of dimension
L.sub.tL.sub.ISI.times.(v+- L.sub.ISI), and the column rank must be equal to the
row rank, the result provides a simple bound as to how complex the convolutional
code must be in order to satisfy the fall diversity ISI channel binary rank
criterion.
[0060] The maximum diversity order achieved by a space-time
code based on an underlying rate 1/L.sub.t convolutional code C with a maximal
memory order v in a L.sub.ISI paths ISI channel is v+L.sub.ISI. This bound shows
that, for a fixed trellis complexity, increasing the number of antennas beyond
10 L t = v + L ISI L ISI
[0061] will not result in an increase in the
diversity advantage. This fact is supported by the results in Table 1, below,
which lists the diversity advantage for BPSK algebraic space-time codes with
optimal free distance for MIMO frequency selective fading channels:
1TABLE 1 Connection d for d for d for d for L.sub.t .nu. Polynomials
L.sub.ISI = 1 L.sub.ISI = 2 L.sub.ISI = 3 L.sub.ISI = 4 2 2 5, 7 2 4 5 6 3 64,
74 2 4 6 7 4 46, 72 2 4 6 8 5 65, 57 2 4 6 8 6 554, 744 2 4 6 8 3 3 54, 64, 74 3
5 6 7 4 52, 66, 76 3 6 7 8 5 47, 53, 75 3 6 8 9 6 554, 624, 764 3 6 9 10 4 4 52,
56, 66, 76 4 6 7 8 5 53, 67, 71, 75 4 7 8 9 5 5 75, 71, 73, 65, 57 5 7 8 9
[0062] Because the number of paths is not known a priori at the
transmitter 200, it is desirable to construct space-time codes that achieve the
maximum diversity order for arbitrary number of paths. This leads to the notion
of universal space-time codes that combine the maximum spatial diversity with
the ISI channel frequency diversity whenever available. Within the class of
universal space-time codes with maximum diversity advantage, it is ideal to
select the code with the maximum product distance, which measures the asymptotic
coding achieved by the code [3] [4].
[0063] Although BSPK modulation is
discussed, it is recognized that the extension to QPSK modulation can be readily
made. The ISI binary rank criterion and stacking construction for BPSK
modulation can be generalized to obtain similar results for QPSK modulation. As
a consequence of the QPSK ISI binary rank criterion and stacking construction,
it is observed that the binary connection polynomials of Table 1 can be used to
generate linear, Z.sub.4-valued, rate 1/L.sub.t convolutional codes whose
natural space-time formatting achieves full spatial diversity L.sub.tL.sub.ISI
for QPSK modulation. More generally, any set of Z.sub.4-valued connection
polynomials with modulo 2 projections (shown Table 1) may be used. In most cases
under consideration, the best performance was obtained from the lifted Z.sub.4
codes constructed by replacing the zero coefficients by twos. This lifting
produces the codes in Table 2, which lists Z.sub.4 space-time codes for QPSK
modulation in MIMO frequency selective fading channels.
2 TABLE 2
L.sub.t v Connection Polynomials 2 1 1 + 2D, 2 + D 2 1 + 2D + D.sup.2, 1 + D +
D.sup.2 3 1 + D + 2D.sup.2 + D.sup.3, 1 + D + D.sup.2 + D.sup.3 4 1 + 2D +
2D.sup.2 + D.sup.3 + D.sup.4, 1 + D + D.sup.2 + 2D.sup.3 + D.sup.4 5 1 + D +
2D.sup.2 + D.sup.3 + 2D.sup.4 + D.sup.5, 1 + 2D + D.sup.2 + D.sup.3 + D.sup.4 +
D.sup.5 3 2 1 + 2D + 2D.sup.2, 2 + D + 2D.sup.2, 1 + D + 2D.sup.2 3 1 + D +
2D.sup.2 + D.sup.3, 1 + D + 2D.sup.2 + D.sup.3, 1 + D + D.sup.2 + D.sup.3 4 1 +
2D + D.sup.2 + 2D.sup.3 + D.sup.4, 1 + D + 2D.sup.2 + D.sup.3 + D.sup.4, 1 + D +
D.sup.2 + D.sup.3 + D.sup.4 5 1 + 2D + 2D.sup.2 + D.sup.3 + D.sup.4 + D.sup.5, 1
+ 2D + D.sup.2 + 2D.sup.3 + D.sup.4 + D.sup.5, 1 + D + D.sup.2 + D.sup.3 +
2D.sup.4 + D.sup.5 4 3 1 + 2D + 2D.sup.2 + 2D.sup.3, 2 + D + 2D.sup.2 +
2D.sup.3, 2 + 2D + D.sup.2 + 2D.sup.3, 2 + 2D + 2D.sup.2 + D.sup.3 4 1 + 2D +
D.sup.2 + 2D.sup.3 + D.sup.4, 1 + D + 2D.sup.2 + D.sup.3 + D.sup.4, 1 + D +
2D.sup.2 + D.sup.3 + D.sup.4, 1 + D + D.sup.2 + D.sup.3 + D.sup.4 5 1 + 2D +
D.sup.2 + 2D.sup.3 + D.sup.4 + D.sup.5, 1 + D + 2D.sup.2 + D.sup.3 + D.sup.4 +
D.sup.5, 1 + D + D.sup.2 + 2D.sup.3 + 2D.sup.4 + D.sup.5, 1 + D + D.sup.2 +
D.sup.3 + 2D.sup.4 + D.sup.5 5 4 1 + 2D + 2D.sup.2 + 2D.sup.3 + 2D.sup.4, 2 + D
+ 2D.sup.2 + 2D.sup.3 + 2D.sup.4, 2 + 2D + D.sup.2 + 2D.sup.3 + 2D.sup.4, 2 + 2D
+ 2D.sup.2 + D.sup.3 + 2D.sup.4, 2 + 2D + 2D.sup.2 + 2D.sup.3 + D.sup.4 5 1 + D
+ D.sup.2 + D.sup.3 + 2D.sup.4 D.sup.5, 1 + D + D.sup.2 + 2D.sup.3 + 2D.sup.4 +
D.sup.5, 1 + D + D.sup.2 + 2D.sup.3 + D.sup.4 + D.sup.5, 1 + D + 2D.sup.2
D.sup.3 + 2D.sup.4 + D.sup.5, 1 + 2D + D.sup.2 + D.sup.3 + 2D.sup.4 + D.sup.5
[0064] The described single carrier time domain design approach requires
the use of a relatively more complex maximum likelihood decoder 305 to account
for the multi-input multi-output ISI nature of the channel 103. In an exemplary
embodiment, this maximum likelihood decoder 305 can be realized using a Viterbi
decoder with trellis complexity proportional to 2.sup.(L.sup..sub.ISI.sup.+v)
and 4.sup.(L.sup..sub.ISI.sup.+v) for BPSK and QPSK modulations, respectively
(wherein v is the maximal memory order of the underlying convolutional code).
[0065] If receiver complexity presents an issue, which is conceivable in
certain applications, then a second design approach may be implemented. Such an
approach uses space-frequency codes. In particular, to reduce the complexity of
the receiver 300, an OFDM front-end 313 is utilized to transform the ISI channel
into a flat, however, selective fading channel. The baseband signal assigned to
each antenna 207 is passed through an inverse fast Fourier transform (IFFT)
before transmission. The transmitted signal from antenna i at the nth interval
is given by 11 x n i = k = 0 N - 1 s k i exp ( - j 2 k n N ) ,
[0066]
where N is block length. A cyclic prefix of length L.sub.ISI-1 is added to
eliminate the ISI between consecutive OFDM symbols. At the receiver end, the
signal y.sub.n.sup.j received by antenna j at time t is given by 12 y n j = E s
l = 0 L ISI - 1 i = 1 L t l ij x t - 1 j + n t j = E s l = 0 L ISI - 1 i = 1 L t
k = 0 N - 1 l ij s k j exp ( - j 2 k ( n - 1 ) N ) + n t j
[0067] The
fast Fourier transform (FFT) operator is then applied to the received signal to
yield 13 r t j = n = 0 N - 1 y k j exp ( - j 2 n t N ) = i = 1 L t ( l = 0 L ISI
- 1 l ij exp ( - j 2 n t N ) ) s t i + N t j = i = 1 L t H t ( ij ) s t i + N t
j ,
[0068] where N.sub.t.sup.j are independent noise samples of
circularly symmetric zero-mean complex Gaussian random variable with variance
N.sub.0/2 per dimension. The complex fading coefficients of the equivalent
channel model H.sub.t.sup.ij have the following auto-correlation function:
R(i.sub.1-i.sub.2, j.sub.1-j.sub.2,
t.sub.2)=E(H.sub.t.sub..sub.1.sup.(t.s-
up..sub.1.sup.j.sup..sub.1.sup.)H.sub.t.sub..sub.2.sup.(i.sub..sub.2.sup.j-
.sub..sub.2.sup.)*)
[0069] 14 = ( i 1 - i 2 , j 1 - j 2 ) l = 0 L ISI -
1 exp ( - j 2 l ( t 1 - t 2 ) N ) ,
[0070] where .delta.(i, j) is the
dirac-delta function. It is clear that the fading coefficients of the equivalent
channel are spatially independent [6] and that 15 R ( 0 , 0 , kN L ISI ) = 0
[0071] for k=1,2, . . . ,L.sub.ISI-1. This observation suggests that the
equivalent fading channel can be approximated by the piece-wise constant block
fading channel. In this model the code word encompasses L.sub.ISI fading blocks.
It is assumed that the complex fading gains are constant over one fading block,
but are independent from block to block. Another type of receiver may be
utilized in the event that receiver complexity presents a key design concern, as
shown in FIG. 3B.
[0072] FIG. 3B shows a diagram of a receiver that
employs space-frequency codes, according to an embodiment of the present
invention. As with receiver 300 of the space-time code approach, receiver 311
processes signals via antennas 309 and includes a demodulator 315, a decoder
317, and a memory 319. Unlike receiver 300, receiver 311 employs an OFDM
front-end 313, and includes a fast Fourier transform (FFT) logic 321 that may
operate in parallel with the demodulator 315.
[0073] The design of
space-frequency codes for the OFDM based design approach is described below.
These space-frequency codes optimally exploit both spatial and
frequency-selective diversity available in the multi-input-multi-output (MINO)
block fading channel. As in the single carrier time domain design approach,
attention is focused on trellis based codes because of the availability of
reasonable complexity ML decoders. For the purpose of explanation, the
discussion pertains to BPSK modulated systems; however, it is recognized by one
of ordinary skill in the art that QPSK codes can be obtained by lifting the BPSK
codes, as described previously.
[0074] The general case in which C is a
binary convolutional code of rate k/L.sub.tL.sub.ISI.is considered. The encoder
203 processes k binary input sequences x.sub.1(t),x.sub.2(t), . . . , x.sub.k(t)
and produces L.sub.tL.sub.ISI coded output sequences y.sub.1(t),y.sub.2(t), . .
. , y.sub.L.sub..sub.t.sub.L.sub..sub.ISI (t), which are multiplexed together to
form the output code word. The encoder action is summarized by the following
matrix equation
Y(D)=X(D)G(D),
where Y(D).left
brkt-bot.Y.sub.1(D).sup.Y.sub.2(D) . . .
Y.sub.L.sub..sub.t.sub.L.sub.ISI(D).right brkt-bot., X(D)=[X.sub.1(D)X.sub.2(D)
. . . X.sub.k(D.)], and 16 G ( D ) = ( G 1 , 1 ( D ) G 1 , 2 ( D ) G 1 , L t L
ISI ( D ) G 2 , 1 ( D ) G 2 , 2 ( D ) G 1 , L t L ISI ( D ) G k , 1 ( D ) G k ,
2 ( D ) G k , L t L ISI ( D ) )
[0075] The natural space-time formatting
of C is such that the output sequence corresponding to
Y.sub.(m-1)L.sub..sub.t+1, (D) is assigned to the l.sup.th transmit antenna in
the m.sup.th fading block. The algebraic analysis technique considers the rank
of matrices formed by concatenating linear combinations of the column vectors 17
F l ( D ) = ( G 1 , l ( D ) G 2 , l ( D ) G k , l ( D ) )
[0076] G is
defined to be the set of binary full rank matrices {G:G=.left
brkt-bot.g.sub.t,j.right brkt-bot..sub.L.sub..sub.t.sub..times.L.sub..sub- .t }
resulting from applying any number of simple row operations to the identity
matrix I.sub.L.sub..sub.t; and
.A-inverted.G.sub.1.di-elect cons.G,
1.ltoreq.i.ltoreq.L.sub.t1.ltoreq.i.l- toreq.L.sub.ISI,
[0077] 18 R i (
G m , m ) ( D ) = [ g i , 1 ( m ) I k , g i , 2 ( m ) I k , , g i , L t ( m ) I
k ] ( F ( m - 1 ) L t + 1 ( D ) F ( m - 1 ) L t + 2 ( D ) F m L t ( D ) )
[0078] Accordingly, the following algebraic construction for BPSK
space-frequency convolutional codes results. In a MIMO OFDM based communication
system with L, transmit antennas 207 operating over a frequency selective block
fading channel with L.sub.t blocks, C denotes the space-frequency code that
includes the binary convolutional code C, whose k.times.L.sub.tL.sub.ISI
transfer function matrix is G(D)=.left brkt-bot.F.sub.1(D) . . .
F.sub.L.sub..sub.t.sub.L.sub.ISI (D).right brkt-bot. and the spatial parser
.sigma. in which the output
Y.sub.(m-1)L.sub..sub.t.sub.+1(D)=X(D)F.sub.(m-1)L.sub..sub.t.sub.+1 (D) is
assigned to antenna l in fading block m. Then, for BPSK transmission, C achieves
d levels of transmit diversity if d is the largest integer such that
.A-inverted.G.sub.1.di-elect cons.G, . . .
,G.sub.L.sub..sub.ISI.di-elect cons.G,0.ltoreq.m.sub.1.ltoreq.min(L.sub..sub.t,
L.sub.ISIL.sub.t-d+1), . . .
,0.ltoreq.m.sub.L.sub..sub.ISI.ltoreq.min(L.sub..sub.t,L.sub.ISIL.sub- .t-d+1),
[0079] and 19 i = 1 L ISI m i = L ISI L t - d + 1 , 20 R m 1 , , m L ISI
( G 1 , , G L ISI ) ( D ) = [ R 0 ( G 1 , 1 ) ( D ) , , R m 1 ( G 1 , 1 ) ( D )
, R 0 ( G 2 , 2 ) ( D ) , , R m 2 ( G 2 , 2 ) ( D ) , , R m L ISI ( G L ISI , L
ISI ) ( D ) ]
[0080] has a rank k over the space of all formal series.
[0081] The above result allows for constructing convolutional
space-frequency codes that realize the optimum tradeoff between transmission
rate and diversity order for BPSK modulation with arbitrary coding rate, number
of transmit antenna, and number of fading blocks. It is readily seen that this
framework encompasses as a special case rate 1/n' convolutional codes with bit
or symbol interleaving across the transmit antennas and frequency fading blocks.
[0082] Similar to the space-time coding approach, rate I/L,
convolutional codes are considered, wherein the same transmission throughput is
achieved. The output sequence from the ith arm Y.sub.i(D) is assigned to the ith
antenna. The input assigned to each antenna 207 is then distributed across the
different fading blocks using a periodic bit interleaver 209. The design of
interleaver 209 depends largely on whether the number of resolvable paths is
available at the transmitter 200. In the case in which this information is
available at the transmitter 200, the interleaver mapping function .pi. is
defined as 21 ( i ) = [ i L I S I ] + N L I S I ( i ) L I S I ,
[0083]
where 0.sub.m refers to the modulo m operation, 0.ltoreq.i.ltoreq.N-1, and N is
the code word length, which is assumed to be a multiple of L.sub.ISI.
[0084] In the absence of the prior information on the number of
resolvable paths in the channel 103, an interleaving scheme that is capable of
exploiting all the frequency diversity, whenever available, for an arbitrary
unknown number of paths is needed. In the special case in which the number of
paths is restricted to L.sub.ISI=2.sup.r (for any arbitrary integer r) and the
maximum possible number of paths L.sub.ISI.sup.(max) is known at the transmitter
200, the following construction for the universal interleaving map is provided:
22 ( i ) = k = 0 log 2 ( L I S I ( max ) ) a k N 2 k + 1 + [ i L I S I ( max ) ]
, a k = ( ( i ) L I S I ( max ) - j = 0 k - 1 a j 2 j 2 k )
[0085] This
interleaving scheme distributes the input sequence periodically among the
L.sub.ISI fading blocks for any L.sub.ISI=2.sup.r and L.sub.ISI
.ltoreq.L.sub.ISI.sup.(max). In practical applications, L.sub.ISI.sup.(max) may
be chosen to be larger than the maximum number of resolvable paths expected in
this particular application, and hence, the transmitter 200 does not need
feedback from the receiver 300. This does not result in any loss of performance.
If the number of paths is not a power of two, then the diversity advantage is
lower bounded by that achieved with the number of paths equal to
L.sub.ISI.sup.(approx) such that L.sub.ISI.sup.(approx)2.sup.r<L.sub.ISI.
[0086] Table 3 shows the diversity advantage that is achieved by the
optimal free distance codes when used as space-frequency codes in this scenario.
Specifically, Table 3 lists the diversity advantage for BPSK algebraic
space-frequency codes with optimal free distance for MIMO frequency selective
fading channels.
3TABLE 3 Connection d for d for d for d for L.sub.t
.nu. Polynomials L.sub.ISI = 1 L.sub.ISI = 2 L.sub.ISI = 3 L.sub.ISI = 4 2 2 5,
7 2 4 5 6 3 64, 74 2 4 6 7 4 46, 72 2 4 6 8 5 65, 57 2 4 6 8 6 554, 744 2 4 6 8
3 3 54, 64, 74 3 4 -- -- 4 52, 66, 76 3 3 5 -- 5 47, 53, 75 3 -- -- -- 6 554,
624, 764 3 -- -- -- 4 4 52, 56, 66, 76 4 -- -- -- 5 53, 67, 71, 75 4 -- -- -- 5
5 75, 71, 73, 65, 57 5 -- -- --
[0087] While, the codes in Table 3 may
not realize the maximum possible diversity advantage under all circumstances,
these codes a compromise between the diversity advantage and coding gain.
[0088] The OFDM based approach addresses the need for a lower complexity
maximum likelihood receiver 300. This approach recognizes the fact that the
maximum likelihood decoder 317 complexity in the OFDM approach does not increase
exponentially with the number of resolvable paths, contrary to the space-time
coding approach. It should be noted that this does not mean, however, that
complexity of the decoder 317 does not depend on the number of paths. As shown
in Table 3, as the number of paths increases, the codes with larger constraint
lengths are needed to efficiently exploit the diversity available in the channel
103. Unlike the space-time coding approach, it is possible to trade diversity
advantage for a reduction in complexity by choosing a code with a small
constraint length. This trade-off is not possible in the space-time coding
approach because, irrespective of the constraint length of the code, the
complexity of the (ML) decoder 305 grows exponentially with the number of
resolvable paths. The OFDM based approach, however, provides a relatively lower
diversity advantage over the space-time coding approach.
[0089] The
maximum transmit diversity advantage achieved in a BPSK OFDM MIMO wireless
system with L.sub.t transmit antennas 207 and L.sub.ISI resolvable paths/antenna
supporting a throughput of 1 bps/Hz is L.sub.ISI(L.sub.t-1)+1. It is clear that
the maximum diversity advantage under this approach is lower as compared to the
space-time coding approach (i.e, L.sub.tL.sub.ISI). The results in Tables 1 and
3 compare the diversity advantage achieved by space-time codes and
space-frequency codes for different values of L.sub.t and L.sub.ISI. As will be
evident from the discussion below, this loss in diversity advantage may not
always lead to a performance loss in the frame error rate range of interest.
[0090] FIGS. 4A-4H show graphs of simulation results of the channel
codes, in accordance with the various embodiments of the present invention.
Specifically, these figures show the simulated frame error rate performance
results for the two coding approaches, concentrating on the codes presented in
Tables 1, 2, and 3. In all cases, the frame length corresponds to 100
simultaneous transmissions from all antennas 207. Joint maximum likelihood
decoding and equalization that accounts for the ISI nature of the channel is
assumed at the receiver (e.g., 300 and 311). In most cases, the simulated frame
error rates were restricted to less than 1% because of the practical
significance of this range and to limit the simulation time.
[0091]
FIGS. 4A-4G report the performance of the two proposed approaches in BPSK
systems with different numbers of transmit antennas L.sub.t, receive antennas
L.sub.r, resolvable paths L.sub.ISI, and receiver trellis complexity. The number
of states in the figures represents the maximum likelihood decoder trellis
complexity. For the OFDM approach, this number is equal to the number of states
in the underlying convolutional codes; however, for the space-time coding
approach, this number accounts for the additional complexity dictated by the ISI
nature of the channel. In the figures, the single carrier approach with
space-time coding is referred to as (STC), whereas the OFDM approach with
space-frequency coding is referred to as (SFC).
[0092] In FIGS. 4A and
4B, the gain in performance of the two approaches are shown with respect to an
increasing number of resolvable paths. In the single carrier approach, this
improvement provides a concomitant increase in receiver complexity as the number
of states in the maximum likelihood receiver grows exponentially with the number
of resolvable paths. In contrast, for the space-frequency coding approach, the
performance improvement does not entail any increase in complexity. It is noted
that the improvement in performance in the SFC approach is marginal when
L.sub.ISI increases from one to two because, as shown in Table 1; the diversity
advantage of the 4-state code used is the same in both scenario.
[0093]
FIGS. 4C-4F provides a comparison between the STC and SFC approaches. It is
shown that when the same code is used in both schemes, the STC approach always
provides a gain in performance, however, at the expense of higher receiver
complexity. Whereas, if the receiver complexity is fixed in both approaches, the
SFC approach sometimes offers better performance. This may seem in contrary to
the intuition based on the superiority of the STC approach in terms of diversity
advantage; this seeming contradiction can be attributed to two reasons. First,
the same receiver complexity allows the SFC approach to utilize more
sophisticated codes that offer larger coding gains. Second, the effect of the
STC superior diversity advantage may only become apparent at significantly
larger signal-to-noise ratios. This observation, however, indicates that the SFC
approach may yield superior performance in some practical applications.
[0094] FIG. 4G highlights the importance of careful design in optimizing
the diversity advantage. In this figure, the 4-state (5,7) optimal free distance
SFC is compared with the 4state (6,7) in a system with L.sub.t=-2, L.sub.r=I,
and L.sub.ISI=2,3. As reported in Table 1, the (5,7) code achieves d=2,3 for
L.sub.ISI=2,3, respectively. Whereas, the (6,7) code achieves d=3 in both codes;
it is noted that in the L.sub.ISI, d=3 is the maximum possible diversity
advantage for this throughput. As shown in the figure, for the L.sub.ISI=2 case,
the superior diversity advantage of the (6,7) is apparent in the steeper frame
error rate curve slope. This results in a gain of about 1 dB at 0.01 frame error
rate. On the other hand, for the L.sub.ISI=3 case, it is shown that the (5,7)
code exhibits a superior product distance that accounts for about 1 dB gain
compared with the (6,7) code.
[0095] The above construct has
applicability in a number of communication systems; for example, the developed
channel codes can be deployed in a wireless communication, as seen in FIG. 5.
[0096] FIG. 5 shows a diagram of a wireless communication system that
utilizes the channel codes, according to the various embodiments of the present
invention. In a wireless communication system 500, multiple terminals 501 and
503 communicate over a wireless network 505. Terminal 501 is equipped with an
encoder 203 (as shown in FIG. 2) that generates space-time or space-frequency
codes. Terminal 501 also includes multiple transmit antennas 207 (as shown in
FIG. 2). In this example, each of the terminals 501 and 503 are configured to
encode and decode the space-time codes; accordingly, both of the terminals 501
and 503 possess the transmitter 200 and receiver 300. However, it is recognized
that each of the terminals 501 and 503 may alternatively be configured as a
transmitting unit or a receiving unit, depending on the application. For
example, in a broadcast application, terminal 501 may be used as a head-end to
transmit signals to multiple receiving terminals (in which only receiving
terminal 503 is shown). Consequently, terminal 503 would only be equipped with a
receiver 300. Alternatively, each of the terminals 501 and 503 may be configured
to operate using space-frequency codes. As mentioned previously, the choice of
space-time codes versus space-frequency codes depends largely on the trade-off
between receiver complexity and the desired diversity advantage.
[0097]
FIG. 6 shows a diagram of a computer system that can perform the processes of
encoding and decoding of the channel codes, in accordance with the embodiments
of the present invention. Computer system 601 includes a bus 603 or other
communication mechanism for communicating information, and a processor 605
coupled with bus 603 for processing the information. Computer system 601 also
includes a main memory 607, such as a random access memory (RAM) or other
dynamic storage device, coupled to bus 603 for storing information and
instructions to be executed by processor 605. In addition, main memory 607 may
be used for storing temporary variables or other intermediate information during
execution of instructions to be executed by processor 605. Computer system 601
further includes a read only memory (ROM) 609 or other static storage device
coupled to bus 603 for storing static information and instructions for processor
605. A storage device 611, such as a magnetic disk or optical disk, is provided
and coupled to bus 603 for storing information and instructions.
[0098]
Computer system 601 may be coupled via bus 603 to a display 613, such as a
cathode ray tube (CRT), for displaying information to a computer user. An input
device 615, including alphanumeric and other keys, is coupled to bus 603 for
communicating information and command selections to processor 605. Another type
of user input device is cursor control 617, such as a mouse, a trackball, or
cursor direction keys for communicating direction information and command
selections to processor 605 and for controlling cursor movement on display 613.
[0099] According to one embodiment, channel code generation within
system 100 is provided by computer system 601 in response to processor 605
executing one or more sequences of one or more instructions contained in main
memory 607. Such instructions may be read into main memory 607 from another
computer-readable medium, such as storage device 611. Execution of the sequences
of instructions contained in main memory 607 causes processor 605 to perform the
process steps described herein. One or more processors in a multi-processing
arrangement may also be employed to execute the sequences of instructions
contained in main memory 607. In alternative embodiments, hard-wired circuitry
may be used in place of or in combination with software instructions. Thus,
embodiments are not limited to any specific combination of hardware circuitry
and software.
[0100] Further, the instructions to support the generation
of space-time codes and space-frequency codes of system 100 may reside on a
computer-readable medium. The term "computer-readable medium" as used herein
refers to any medium that participates in providing instructions to processor
605 for execution. Such a medium may take many forms, including but not limited
to, non-volatile media, volatile media, and transmission media. Non-volatile
media includes, for example, optical or magnetic disks, such as storage device
611. Volatile media includes dynamic memory, such as main memory 607.
Transmission media includes coaxial cables, copper wire and fiber optics,
including the wires that comprise bus 603. Transmission media can also take the
form of acoustic or lightwaves, such as those generated during radio wave and
infrared data communication.
[0101] Common forms of computer-readable
media include, for example, a floppy disk, a flexible disk, hard disk, magnetic
tape, or any other magnetic medium, a CD-ROM, any other optical medium, punch
cards, paper tape, any other physical medium with patterns of holes, a RAM, a
PROM, and EPROM, a FLASH-EPROM, any other memory chip or cartridge, a carrier
wave as described hereinafter, or any other medium from which a computer can
read.
[0102] Various forms of computer readable media maybe involved in
carrying one or more sequences of one or more instructions to processor 605 for
execution. For example, the instructions may initially be carried on a magnetic
disk of a remote computer. The remote computer can load the instructions
relating to encoding and decoding of space-time codes used in system 100
remotely into its dynamic memory and send the instructions over a telephone line
using a modem. A modem local to computer system 601 can receive the data on the
telephone line and use an infrared transmitter to convert the data to an
infrared signal. An infrared detector coupled to bus 603 can receive the data
carried in the infrared signal and place the data on bus 603. Bus 603 carries
the data to main memory 607, from which processor 605 retrieves and executes the
instructions. The instructions received by main memory 607 may optionally be
stored on storage device 611 either before or after execution by processor 605.
[0103] Computer system 601 also includes a communication interface 619
coupled to bus 603. Communication interface 619 provides a two-way data
communication coupling to a network link 621 that is connected to a local
network 623. For example, communication interface 619 may be a network interface
card to attach to any packet switched local area network (LAN). As another
example, communication interface 619 maybe an asymmetrical digital subscriber
line (ADSL) card, an integrated services digital network (ISDN) card or a modem
to provide a data communication connection to a corresponding type of telephone
line. Wireless links may also be implemented. In any such implementation,
communication interface 619 sends and receives electrical, electromagnetic or
optical signals that carry digital data streams representing various types of
information.
[0104] Network link 621 typically provides data
communication through one or more networks to other data devices. For example,
network link 621 may provide a connection through local network 623 to a host
computer 625 or to data equipment operated by a service provider, which provides
data communication services through a communication network 627 (e.g., the
Internet). LAN 623 and network 627 both use electrical, electromagnetic or
optical signals that carry digital data streams. The signals through the various
networks and the signals on network link 621 and through communication interface
619, which carry the digital data to and from computer system 601, are exemplary
forms of carrier waves transporting the information. Computer system 601 can
transmit notifications and receive data, including program code, through the
network(s), network link 621 and communication interface 619.
[0105] The
techniques described herein provide several advantages over prior approaches to
providing space-time codes. The two approaches of designing space-time codes and
space-frequency codes optimally exploits both the spatial and frequency
diversity available in the channel.
[0106] Obviously, numerous
modifications and variations of the present invention are possible in light of
the above teachings. It is therefore to be understood that within the scope of
the appended claims, the invention may be practiced otherwise than as
specifically described herein.
REFERENCES
[0107] E. Teletar.
Capacity of Multi-Antenna Gaussian Channels. Technical Report, AT&T-Bell
Labs, June 1995.
[0108] G. J. Foschini and M. Gans. On the Limits of
Wireless Communication in a Fading Environment When Using Multiple Antennas.
Wireless Personal Communication, 6:311-335, March 1998.
[0109] V.
Tarokh, N. Seshadri, and A. R. Calderbank. Space-Time Codes for High Data Rate
Wireless Communication: Performance Criterion and Code Construction. IEEE Trans.
Info. Theory, IT-44:774-765, March 1998.
[0110] J. -C. Guey, M. R. Bell
M. P. Fitz, and W. -Y. Kuo. Signal Design for Transmitter Diversity, Wireless
Communication Systems over Rayleigh Fading Channels. IEEE Vehicular Technology
Conference, pages 136-140, Atlanta, 1996.
[0111] G. J. Foschini. Layered
Space-Time Architecture for Wireless Communication in Fading Environments When
Using Multiple Antennas. Bell Labs Tech. J, 2, Autumn 1996.
[0112] S.
Lin and Jr. D. J. Costello. Error Control Coding: Fundamentals and Applications.
Prentice-Hall, New Jersey, 1983.
* * * * *
