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| United States Patent Application |
20020136327 |
| Kind Code |
A1 |
| El-Gamal, Hesham ; et
al. |
September 26, 2002 |
Method and system for utilizing space-time codes for block fading
channels
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 message signal, and an encoder that is configured to
generate a code word in response to the message signal. The code word is based
upon a stacking construction that is generalized for the communication channel.
The communication channel is characterized as a multi-input multi-output (MIMO)
block fading channel. The transmitter also includes a modulator that is
configured to modulate the code word for transmission over the communication
channel. Further, the transmitter includes a plurality of transmit antennas that
are configured to transmit the modulated code word over the communication
channel. The system also includes a receiver, which has a plurality of receive
antennas. The receiver is configured to receive the transmitted code word via
the plurality of receive antennas.
| Inventors: |
El-Gamal,
Hesham; (Dublin, OH) ; Hammons, A. Roger JR.; (N.
Potomac, MD) |
| Correspondence Name and Address: |
Hughes Electronics Corporation
Patent Docket Administration
P.O. Box 956
Bldg. 1, Mail Stop A109
El Segundo
CA
90245-0956
US
|
| Serial No.: |
011831 |
| Series Code: |
10 |
| Filed: |
November 5, 2001 |
| U.S. Current Class: |
375/308 |
| U.S. Class at Publication: |
375/308 |
| Intern'l Class: |
H04L 027/20 |
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 message signal; and generating a code word in response to the
message signal, the code word being based upon a stacking construction that is
generalized for the communication channel, the communication channel being
characterized as a multi-input multi-output (MIMO) block fading channel.
2. The method according to claim 1, wherein the code word in the
generating step satisfies a block fading baseband rank criterion that maximizes
transmit diversity, d, over all pairs of distinct code words c, e.epsilon.C and
a block fading product distance criterion that maximizes coding advantage, .mu.,
over all pairs of distinct code words c, e.epsilon.C, C being a linear
L.sub.t.times.n space-time code with n.gtoreq.L.sub.t, wherein L.sub.t
represents the number of transmit antennas in the communication system, e being
an alternate code word of c.
3. The method according to claim 2, 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.
4. The method according
to claim 3, wherein BPSK modulation is used in the modulating step, the code
word being a part of C that is a linear L.sub.t.times.n space-time code with
n.gtoreq.L.sub.t, wherein L.sub.t represents the number of transmit antennas in
the communication system, C achieving at least r levels of transmit diversity, r
being the largest integer such that.A-inverted.G.epsilon.G, . . . ,
G.sub.m.epsilon.G, 0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t+r+1), . . .
,0.ltoreq.m.sub.M.ltoreq.min(L.sub.t, ML.sub.t-r+1), and
.SIGMA..sub.m=1.sup.Mm.sub.i=ML.sub.t-r+1, R.sub.m.sub..sub.1.sub., . . . ,
m.sub..sub.M(G.sub.1, . . . ,G.sub.m)=.left brkt-bot.R.sub.0(G.sub.1), . . . ,
R.sub.m.sub..sub.1(G.sub.1), R.sub.0(G.sub.2), . . . ,
R.sub.m.sub..sub.2(G.sub.2), . . . , R.sub.m.sub..sub.M(G.sub.M).right brkt-bot.
having a full rank k over a binary field F,G defining a set of binary fall rank
matrices {G:G=.left brkt-bot.g.sub.i, j.right
brkt-bot..sub.L.sub..sub.1.sub.xL.sub..sub.2} resulting from applying row
operations to an identity matrix, I.sub.L.sub..sub.t, M representing the number
of blocks per code word.
5. The method according to claim 2, wherein for
every non-zero code word c.epsilon.C, .SIGMA..sub.m=1.sup.Mrank(c[m]).gtoreq.d,
wherein the rank is over a binary field F and d is the largest possible integer,
the space-time code C achieving a diversity level of at least dL.sub.r, L.sub.r
being the number of receive antennas in the communication system, M representing
the number of blocks per code word.
6. The method according to claim 2,
wherein C is a linear L.sub.t.times.n space-time code over Z.sub.4, Z.sub.4={0,
.+-.1, 2}, for every non-zero code word c.epsilon.C, at least one of
.SIGMA..sub.m=1.sup.Mrank{(c[m])}.- gtoreq.d, and
.SIGMA..sub.m.times.1.sup.Mrank{.PSI.(c[m])}.gtoreq.d holds true, wherein the
rank is over a binary field and d is the largest possible integer, being a
row-based indicant projection, .PSI. being a column-based indicant projection,
the space-time code C achieving a diversity level of at least dL.sub.r, L.sub.r
being the number of receive antennas in the communication system, M representing
the number of blocks per code word.
7. The method according to claim 1,
wherein the generalized stacking construction in the generating step specifies C
as a linear L.sub.t.times.n space-time code, the space-time code being of
dimension k including code word matrices, 26 c = [ x _ M 1 x _ M 2 x _ M L t ]
wherein x denotes an arbitrary k-tuple of information bits and n.gtoreq.L.sub.t,
M.sub.1, M.sub.2 , . . . , M.sub.L.sub..sub.t are binary matrices of dimension
k.times.n, n.ltoreq.k, and L.sub.t represents the number of transmit antennas in
the communication system.
8. The method according to claim 1, further
comprising: transmitting the code word via a plurality of transmit antennas to a
plurality of receive antennas, wherein the number of receive antennas is less
than the number of transmit antennas.
9. An apparatus for encoding
signals for transmission over a communication channel of a communication system,
the apparatus comprising: a source configured to output a message signal; and an
encoder configured to generate a code word in response to the message signal,
the code word being based upon a stacking construction that is generalized for
the communication channel, the communication channel being characterized as a
multi-input multi-output (MIMO) block fading channel.
10. The apparatus
according to claim 9, wherein the code word satisfies a block fading baseband
rank criterion that maximizes transmit diversity, d, over all pairs of distinct
code words c, e.epsilon.C and a block fading product distance criterion that
maximizes coding advantage, .mu., over all pairs of distinct code words c,
e.epsilon.C, C being a linear L.sub.t.times.n space-time code with
n.gtoreq.L.sub.i, wherein L.sub.t represents the number of transmit antennas in
the communication system, e being an alternate code word of c.
11. The
apparatus according to claim 10, further comprising: a modulator configure 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.
12. The apparatus according to claim 11,
further comprising: a plurality of transmit antennas configured to transmit the
modulated code word, wherein the modulator modulates the code word using BPSK
modulation, the code word being a part of C that is a linear L.sub.t.times.n
space-time code with n.gtoreq.L.sub.t, wherein L.sub.t represents the number of
the plurality of transmit antennas in the communication system, C achieving at
least r levels of transmit diversity, r being the largest integer such
that.A-inverted.G.epsilon.G, . . . , G.sub.m.epsilon.G,
0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t-r+1), . . . ,
0.ltoreq.m.sub.M.ltoreq.min(L.sub.t, ML.sub.t-r+1), and
.SIGMA..sub.m=1.sup.Mm.sub.t=ML.sub.t-r+1, R.sub.m.sub..sub.t.sub., . . . ,
m.sub..sub.M(G.sub.1, . . . , G.sub.m)=.left brkt-bot.R.sub.0(G.sub.1), . . . ,
R.sub.m.sub..sub.l(G.sub.1), R.sub.0(G.sub.2), . . . ,
R.sub.m.sub..sub.2(G.sub.2), . . . , R.sub.m.sub..sub.M(G.sub.M).right brkt-bot.
having a full rank k over a binary field F,G defining a set of binary full rank
matrices {G:G=.left brkt-bot.g.sub.i, j.right
brkt-bot..sub.L.sub..sub.i.sub.xL.sub..sub.t} resulting from applying row
operations to an identity matrix, I.sub.L.sub..sub.1, M representing the number
of blocks per code word.
13. The apparatus according to claim 10,
wherein for every non-zero code word c.epsilon.C,
.SIGMA..sub.m=1.sup.Mrank(c[m]).gtoreq.d, wherein the rank is over a binary
field F and d is the largest possible integer, the space-time code C achieving a
diversity level of at least dL.sub.r, L.sub.r being the number of receive
antennas in the communication system, M representing the number of blocks per
code word.
14. The apparatus according to claim 10, further comprising:
a plurality of transmit antennas configured to transmit the modulated code word,
wherein C is a linear L.sub.t.times.n space-time code over Z.sub.4, Z.sub.4={0,
.+-.1, 2}, for every non-zero code word c.epsilon.C, at least one of
.SIGMA..sub.m=1.sup.Mrank{(c[m])}.gtoreq.d, and
.SIGMA..sub.m-1.sup.Mrank{.PSI.(c[m])}.gtoreq.d holds true, wherein the rank is
over a binary field and d is the largest possible integer, being a row-based
indicant projection, .PSI. being a column-based indicant projection, the
space-time code C achieving a diversity level of at least dL.sub.r, L.sub.r
being the number of receive antennas in the communication system, M representing
the number of blocks per code word.
15. The apparatus according to claim
9, wherein the generalized stacking construction specifies C as a linear
L.sub.t.times.n space-time code, the space-time code being of dimension k
including code word matrices, 27 c = [ x _ M 1 x _ M 2 x _ M L t ] wherein x
denotes an arbitrary k-tuple of information bits and n.gtoreq.L.sub.t, M.sub.1,
M.sub.2, . . . , M.sub.L.sub..sub.t are binary matrices of dimension k.times.n,
n.ltoreq.k, and L.sub.t represents the number of transmit antennas in the
communication system.
16. The apparatus according to claim 9, further
comprising: a plurality of transmit antennas configured to transmit the code
word to a plurality of receive antennas, wherein the number of receive antennas
is less than the number of transmit antennas.
17. An apparatus for
encoding signals for transmission over a communication channel of a
communication system, the apparatus comprising: means for receiving a message
signal; and means for generating a code word in response to the message signal,
the code word being based upon a stacking construction that is generalized for
the communication channel, the communication channel being characterized as a
multi-input multi-output (MIMO) block fading channel.
18. The apparatus
according to claim 17, wherein the code word satisfies a block fading baseband
rank criterion that maximizes transmit diversity, d, over all pairs of distinct
code words c, e.epsilon.C and a block fading product distance criterion that
maximizes coding advantage, .mu., over all pairs of distinct code words c,
e.epsilon.C, C being a linear L.sub.t.times.n space-time code with
n.gtoreq.L.sub.t, wherein L.sub.t represents the number of transmit antennas in
the communication system, e being an alternate code word of c.
19. The
apparatus according to claim 18, further comprising: a modulator configure 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.
20. The apparatus according to claim 19,
further comprising: a plurality of transmit antennas configured to transmit the
modulated code word, wherein the modulator modulates the code word using BPSK
modulation, the code word being a part of C that is a linear L.sub.t.times.n
space-time code with n.gtoreq.L.sub.t, wherein L.sub.t represents the number of
the plurality of transmit antennas in the communication system, C achieving at
least r levels of transmit diversity, r being the largest integer such
that.A-inverted.G.epsilon.G, . . . , G.sub.m.epsilon.G,
0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t-r+1), . . . ,
0.ltoreq.m.sub.M.ltoreq.min (L.sub.t, ML.sub.t-r+1), and
.SIGMA..sub.m=1.sup.Mm.sub.i=ML.sub.t-r+1, R.sub.m.sub..sub.i.sub., . . . ,
m.sub..sub.M(G.sub.1, . . . , G.sub.m)=.left brkt-bot.R.sub.0(G.sub.1), . . . ,
R.sub.m.sub..sub.1(G.sub.1), R.sub.0(G.sub.2), . . . ,
R.sub.m.sub..sub.2(G.sub.2), . . . , R.sub.m.sub..sub.M(G.sub.M).right brkt-bot.
having a full rank k over a binary field F,G defining 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.xL.sub..sub.t} resulting from applying row
operations to an identity matrix, I.sub.L.sub..sub.t, M representing the number
of blocks per code word.
21. The apparatus according to claim 18,
wherein for every non-zero code word c.epsilon.C,
.SIGMA..sub.m=1.sup.Mrank(c[m]).gtoreq.d, wherein the rank is over a binary
field F and d is the largest possible integer, the space-time code C achieving a
diversity level of at least dL.sub.r, L.sub.r being the number of receive
antennas in the communication system, M representing the number of blocks per
code word.
22. The apparatus according to claim 18, further comprising:
a plurality of transmit antennas configured to transmit the modulated code word,
wherein C is a linear L.sub.t.times.n space-time code over Z.sub.4, Z.sub.4={0,
.+-.1, 2}, for every non-zero code word c.epsilon.C, at least one of
.SIGMA..sub.m=1.sup.Mrank{(c[m])}.gtoreq.d, and
.SIGMA..sub.m=1.sup.Mrank{.PSI.(c[m])}.gtoreq.d holds true, wherein the rank is
over a binary field and d is the largest possible integer, being a row-based
indicant projection, .PSI. being a column-based indicant projection, the
space-time code C achieving a diversity level of at least dL.sub.r, L.sub.r
being the number of receive antennas in the communication system, M representing
the number of blocks per code word.
23. The apparatus according to claim
17, wherein the generalized stacking construction specifies C as a linear
L.sub.t.times.n space-time code, the space-time code being of dimension k
including code word matrices, 28 c = [ x _ M 1 x _ M 2 x _ M L t ] wherein x
denotes an arbitrary k-tuple of information bits and n.gtoreq.L.sub.t, M.sub.1,
M.sub.2, . . . , M.sub.L.sub..sub.t are binary matrices of dimension k.times.n,
n.ltoreq.k, and L.sub.t represents the number of transmit antennas in the
communication system.
24. The apparatus according to claim 17, further
comprising: a plurality of transmit antennas configured to transmit the code
word to a plurality of receive antennas, wherein the number of receive antennas
is less than the number of transmit antennas.
25. A communication system
for transmitting encoded signals over a communication channel, the system
comprises: a transmitter including, a source configured to output a message
signal, an encoder configured to generate a code word in response to the message
signal, the code word being based upon a stacking construction that is
generalized for the communication channel, the communication channel being
characterized as a multi-input multi-output (MIMO) 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.
26. The system according to claim 25, wherein the codeword satisfies a
block fading baseband rank criterion that maximizes transmit diversity, d, over
all pairs of distinct code words c, e.epsilon.C and a block fading product
distance criterion that maximizes coding advantage, .mu., over all pairs of
distinct code words c, e.epsilon.C, C being a linear L.sub.t.times.n space-time
code with n.gtoreq.L.sub.t, wherein L.sub.t represents the number of the
plurality of transmit antennas, e being an alternate code word of c.
27.
The system according to claim 26, wherein the modulator modulates 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.
28. The system according to claim 27, wherein modulator
utilizes BPSK modulation, the code word being a part of C that is a linear
L.sub.t.times.n space-time code with n.gtoreq.L.sub.t, wherein L.sub.t
represents the number of the plurality of transmit antennas, C achieving at
least r levels of transmit diversity, r being the largest integer such
that.A-inverted.G.epsilon.G, . . . , G.sub.m.epsilon.G,
0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t-r+1), . . . ,
0.ltoreq.m.sub.M.ltoreq.min (L.sub.t, ML.sub.t-r+1), and
.SIGMA..sub.m=1.sup.Mm.sub.i=ML.sub.t-r+1, R.sub.m.sub..sub.1.sub., . . . ,
m.sub..sub.M(G.sub.1, . . . , G.sub.m)=.left brkt-bot.R.sub.0(G.sub.1), . . . ,
R.sub.m.sub..sub.1(G.sub.1), R.sub.0(G.sub.2), . . . ,
R.sub.m.sub..sub.2(G.sub.2), . . . , R.sub.m.sub..sub.M(G.sub.M).right brkt-bot.
having a full rank k over a binary field F,G defining 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.xL.sub..sub.t} resulting from applying row
operations to an identity matrix, I.sub.L.sub..sub.t, M representing the number
of blocks per code word.
29. The system according to claim 26, wherein
for every non-zero code word c.epsilon.C,
.SIGMA..sub.m=1.sup.Mrank(c[m]).gtoreq.d, wherein the rank is over a binary
field F and d is the largest possible integer, the space-time code C achieving a
diversity level of at least dL.sub.r, L.sub.r being the number of the plurality
of receive antennas, M representing the number of blocks per code word.
30. The system according to claim 26, wherein C is a linear
L.sub.t.times.n space-time code over Z.sub.4, Z.sub.4={0, .+-.1, 2}, for every
non-zero code word c.epsilon.C, at least one of
.SIGMA..sub.m=1.sup.Mrank{(c[m])}.gtoreq.d, and .SIGMA..sub.m=1.sup.Mrank-
{.PSI.(c[m])}.gtoreq.d holds true, binary field and d is the largest possible
integer, being a row-based indicant projection, .PSI. being a column-based
indicant projection, the space-time code C achieving a diversity level of at
least dL.sub.r, L.sub.r being the number of the plurality of receive antennas, M
representing the number of blocks per code word.
31. The system
according to claim 25, wherein the generalized stacking construction in the
generating step specifies C as a linear L.sub.t.times.n space-time code, the
space-time code being of dimension k including code word matrices, 29 c = [ x _
M 1 x _ M 2 x _ M L t ] wherein x denotes an arbitrary k-tuple of information
bits and n.gtoreq.L.sub.t, M.sub.1, M.sub.2 , . . . , M.sub.L.sub..sub.t are
binary matrices of dimension k.times.n, n.ltoreq.k, and L.sub.t represents the
number of the plurality of transmit antennas.
32. The system according
to claim 25, wherein the number of the plurality of receive antennas is less
than the number of the plurality of transmit antennas.
33. A waveform
signal for transmission over a communication channel of a communication system,
the waveform signal comprising: a code word being that is based upon a stacking
construction that is generalized for the communication channel, the
communication channel being characterized as a multi-input multi-output (MIMO)
block fading channel.
34. The signal according to claim 33, wherein the
code word satisfies a block fading baseband rank criterion that maximizes
transmit diversity, d, over all pairs of distinct code words c, e.epsilon.C and
a block fading product distance criterion that maximizes coding advantage, .mu.,
over all pairs of distinct code words C, e.epsilon.C, C being a linear
L.sub.t.times.n space-time code with n.gtoreq.L.sub.t, wherein L.sub.t
represents the number of transmit antennas in the communication system, e being
an alternate code word of c.
35. The signal according to claim 34,
wherein the code word is modulated using at least one of BPSK (binary
phase-shift keying) modulation and QPSK (quadrature phase-shift keying)
modulation.
36. The signal according to claim 35, wherein the code word
is BPSK modulated, the code word being a part of C that is a linear
L.sub.t.times.n space-time code with n.gtoreq.L.sub.t, wherein L.sub.t
represents the number of transmit antennas in the communication system, C
achieving at least r levels of transmit diversity, r being the largest integer
such that.A-inverted.G.epsilon.G, . . . , G.sub.m.epsilon.G,
0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t-r+1), . . . ,
0.ltoreq.m.sub.M.ltoreq.min (L.sub.t, ML.sub.t-r+1), and
.SIGMA..sub.m=1.sup.Mm.sub.i=ML.sub.t-r+1, R.sub.m.sub..sub.i.sub., . . . ,
m.sub..sub.M(G.sub.1, . . . , G.sub.m)=.left brkt-bot.R.sub.0(G.sub.1), . . . ,
R.sub.m.sub..sub.1(G.sub.1), R.sub.0(G.sub.2), . . . ,
R.sub.m.sub..sub.2(G.sub.2), . . . , R.sub.m.sub..sub.M(G.sub.M).right brkt-bot.
having a full rank k over a binary field F,G defining a set of binary full rank
matrices {G:G=.left brkt-bot.g.sub.i, j.right
brkt-bot..sub.L.sub..sub.i.sub.xL.sub..sub.t} resulting from applying row
operations to an identity matrix, I.sub.L.sub..sub.t, M representing the number
of blocks per code word.
37. The signal according to claim 34, wherein
for every non-zero code word c.epsilon.C,
.SIGMA..sub.m=1.sup.Mrank(c[m]).gtoreq.d, wherein the rank is over a binary
field F and d is the largest possible integer, the space-time code C achieving a
diversity level of at least dL.sub.r, L.sub.r being the number of receive
antennas in the communication system, M representing the number of blocks per
code word.
38. The signal according to claim 34, wherein C is a linear
L.sub.t.times.n space-time code over Z.sub.4, Z.sub.4={0, .+-.1, 2}, for every
non-zero code word c.epsilon.C, at least one of
.SIGMA..sub.m-1.sup.Mrank{(c[m])}.gtoreq.d, and .SIGMA..sub.m=1.sup.Mrank-
{.PSI.(c[m])}.gtoreq.d holds true, wherein the rank is over a binary field and d
is the largest possible integer, being a row-based indicant projection, .PSI.
being a column-based indicant projection, the space-time code C achieving a
diversity level of at least dL.sub.r, L.sub.r being the number of receive
antennas in the communication system, M representing the number of blocks per
code word.
39. The signal according to claim 33, wherein the generalized
stacking construction specifies C as a linear L.sub.t.times.n space-time code,
the space-time code being of dimension k including code word matrices, 30 c = [
x _ M 1 x _ M 2 x _ M L t ] wherein x denotes an arbitrary k-tuple of
information bits and n.gtoreq.L.sub.t, M.sub.1, M.sub.2, . . . , M.sub.r are
binary matrices of dimension k.times.n, n.ltoreq.k, and L.sub.t represents the
number of transmit antennas in the communication system.
40. 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 message signal; and
generating a code word in response to the message signal, the code word being
based upon a stacking construction that is generalized for the communication
channel, the communication channel being characterized as a multi-input
multi-output (MIMO) block fading channel.
41. The computer-readable
medium according to claim 40, wherein the code word in the generating step
satisfies a block fading baseband rank criterion that maximizes transmit
diversity, d, over all pairs of distinct code words c, e.epsilon.C and a block
fading product distance criterion that maximizes coding advantage, u, over all
pairs of distinct code words c, e.epsilon.C, C being a linear L.sub.t.times.n
space-time code with n.gtoreq.L.sub.t, wherein L.sub.t represents the number of
transmit antennas in the communication system, e being an alternate code word of
c.
42. The computer-readable medium according to claim 41, 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.
43. The computer-readable medium according to claim 42,
wherein BPSK modulation is used in the modulating step, the code word being a
part of C that is a linear L.sub.t.times.n space-time code with
n.gtoreq.L.sub.t, wherein L.sub.t represents the number of transmit antennas in
the communication system, C achieving at least r levels of transmit diversity, r
being the largest integer such that.A-inverted.G.epsilon.G, . . . ,
G.sub.m.epsilon.G, 0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t-r+1), . . . ,
0.ltoreq.m.sub.M.ltoreq.min (L.sub.t, ML.sub.t-r+1), and
.SIGMA..sub.m=1.sup.Mm.sub.i=ML.sub.t-r+1, R.sub.m.sub..sub.1.sub., . . . ,
m.sub..sub.M(G.sub.1, . . . , G.sub.m)=.left brkt-bot.R.sub.0(G.sub.1), . . . ,
R.sub.m.sub..sub.1(G.su- b.1), R.sub.0(G.sub.2), . . . ,
R.sub.m.sub..sub.1(G.sub.2), . . . , R.sub.m.sub..sub.M(G.sub.M).right brkt-bot.
having a full rank k over a binary field F,G defining a set of binary full rank
matrices {G:G=.left brkt-bot.g.sub.i, j.right
brkt-bot..sub.L.sub..sub.i.sub.xL.sub..sub.t} resulting from applying row
operations to an identity matrix, I.sub.L.sub..sub.t, M representing the number
of blocks per code word.
44. The computer-readable medium according to
claim 41, wherein for every non-zero code word c.epsilon.C,
.SIGMA..sub.m=1.sup.Mrank(c[m]).gtoreq.d, wherein the rank is over a binary
field F and d is the largest possible integer, the space-time code C achieving a
diversity level of at least dL.sub.r, L.sub.r being the number of receive
antennas in the communication system, M representing the number of blocks per
code word.
45. The computer-readable medium according to claim 41,
wherein C is a linear L.sub.t.times.n space-time code over Z.sub.4, Z.sub.4={0,
.+-.1, 2}, for every non-zero code word c.epsilon.C, at least one of
.SIGMA..sub.m=1.sup.Mrank {(c[m])}.gtoreq.d, and .SIGMA..sub.m=1.sup.Mran-
k{.PSI.(c[m])}.gtoreq.d holds true, wherein the rank is over a binary field and
d is the largest possible integer, being a row-based indicant projection, .PSI.
being a column-based indicant projection, the space-time code C achieving a
diversity level of at least dL.sub.r, L.sub.r being the number of receive
antennas in the communication system, M representing the number of blocks per
code word.
46. The computer-readable medium according to claim 40,
wherein the generalized stacking construction in the generating step specifies C
as a linear L.sub.t.times.n space-time code, the space-time code being of
dimension k including code word matrices, 31 c = [ x _ M 1 x _ M 2 x _ M L t ]
wherein x denotes an arbitrary k-tuple of information bits and n.gtoreq.L.sub.t,
M.sub.1, M.sub.2, . . . , M.sub.L.sub..sub.t are binary matrices of dimension
k.times.n, n.ltoreq.k, and L.sub.t represents the number of transmit antennas in
the communication system.
47. The computer-readable medium according to
claim 40, wherein the one or more processors further perform the step of:
transmitting the code word via a plurality of transmit antennas to a plurality
of receive antennas, wherein the number of receive antennas is less than the
number of transmit antennas.
48. 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, wherein
the code word being based upon a stacking construction that is generalized for
the communication channel, the communication channel being characterized as a
multi-input multi-output (MIMO) block fading channel; and a decoder configured
to decode the code word and to output a message signal.
49. The
apparatus according to claim 48, wherein the code word satisfies a block fading
baseband rank criterion that maximizes transmit diversity, d, over all pairs of
distinct code words C, e.epsilon.C and a block fading product distance criterion
that maximizes coding advantage, .mu., over all pairs of distinct code words c,
c.epsilon.C, C being a linear L.sub.t.times.n space-time code with
n.gtoreq.L.sub.t, wherein L.sub.t represents the number of transmit antennas in
the communication system, e being an alternate code word of c.
50. The
apparatus according to claim 49, wherein the received signal is modulated using
at least one of BPSK (binary phase-shift keying) modulation and QPSK (quadrature
phase-shift keying) modulation.
51. The apparatus according to claim 50,
wherein the received signal is modulated using BPSK modulation, the code word
being a part of C that is a linear L.sub.t.times.n space-time code with
n.gtoreq.L.sub.t, wherein L.sub.t represents the number of the plurality of
transmit antennas in the communication system, C achieving at least r levels of
transmit diversity, r being the largest integer such
that.A-inverted.G.epsilon.G, . . . , G.sub.m.epsilon.G,
0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t-r+1), . . . ,
0.ltoreq.m.sub.M.ltoreq.min (L.sub.t, ML.sub.t-r+1), and
.SIGMA..sub.m=1.sup.Mm.sub.i=ML.sub.t-r+1, R.sub.m.sub..sub.1.sub., . . . ,
m.sub..sub.M(G.sub.1, . . . , G.sub.m)=.left brkt-bot.R.sub.0(G.sub.1), . . . ,
R.sub.m.sub..sub.1(G.su- b.1), R.sub.0(G.sub.2), . . . ,
R.sub.m.sub..sub.2(G.sub.2), . . . , R.sub.m.sub..sub.M(G.sub.M).right brkt-bot.
having a full rank k over a binary field F,G defining 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.xL.sub..sub.t} resulting from applying row
operations to an identity matrix, I.sub.L.sub..sub.t, M representing the number
of blocks per code word.
52. The apparatus according to claim 49,
further comprising: a plurality of receive antennas coupled to the demodulator
and configured to receive the signal, wherein for every non-zero code word
c.epsilon.C, .SIGMA..sub.m=1.sup.Mrank(c[m]).gtoreq.d, the rank is over a binary
field F and d is the largest possible integer, the space-time code C achieving a
diversity level of at least dL.sub.r, L.sub.r being the number of the plurality
of receive antennas, M representing the number of blocks per code word.
53. The apparatus according to claim 49, further comprising: a plurality
of receive antennas coupled to the demodulator and configured to receive the
signal, wherein C is a linear L.sub.t.times.n space-time code over Z.sub.4,
Z.sub.4={0, .+-.1, 2}, for every non-zero code word c.epsilon.C, at least one of
.SIGMA..sub.m=1.sup.Mrank{(c[m])}.gtoreq.d, and
.SIGMA..sub.m=1.sup.Mrank{.PSI.(c[m])}.gtoreq.d holds true, wherein the rank is
over a binary field and d is the largest possible integer, being a row-based
indicant projection, .PSI. being a column-based indicant projection, the
space-time code C achieving a diversity level of at least dL.sub.r, L.sub.r
being the number of the plurality of receive antennas, M representing the number
of blocks per code word.
54. The apparatus according to claim 48,
wherein the generalized stacking construction specifies C as a linear
L.sub.t.times.n space-time code, the space-time code being of dimension k
including code word matrices, 32 c = [ x _ M 1 x _ M 2 x _ M L t ] wherein x
denotes an arbitrary k-tuple of information bits and n.gtoreq.L.sub.t, M.sub.1,
M.sub.2, . . . , M.sub.L.sub..sub.t are binary matrices of dimension k.times.n,
n.ltoreq.k, and L.sub.t represents the number of transmit antennas in the
communication system.
55. The apparatus according to claim 48, further
comprising: a plurality of receive antennas coupled to the demodulator and
configured to receive the signal, wherein the number of the plurality of receive
antennas is less than the number of transmit antennas in the communication
system.
56. The apparatus according to claim 48, further comprising: a
memory configured to store channel state information of the communication
channel, wherein the code word is decoded based upon the channel state
information.
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-200343), filed Nov. 6, 2000,
entitled "Method and Constructions for Space-Time Codes for Block Fading
Channels," 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 having spatial
diversity and temporal 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 visa 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 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] 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) block 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 spacetime codes that can enhance system reliability
and throughput in a multiple antenna system is highly desirable.
SUMMARY
OF THE INVENTION
[0009] The present invention addresses the above stated
needs by providing space-time codes to optimally exploit the spatial and
temporal diversity available in the multi-input multi-output (MNO) block fading
channels.
[0010] 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 message signal, and
generating a code word in response to the message signal. The code word is based
upon a stacking construction that is generalized for the communication channel.
The communication channel is characterized as a multi-input multi-output block
fading channel. Under this approach, spatial diversity and temporal diversity
are enhanced, without sacrificing transmission rate.
[0011] According to
another sect of the invention, an apparatus for encoding signals for
transmission over a communication channel of a communication system is provided.
The apparatus comprises a source that is configured to output a message signal,
and an encoder that is configured to generate a code word in response to the
message signal. The code word is based upon a stacking construction that is
generalized for the communication channel. The communication channel is
characterized as a multi-input multi-output block fading channel. The above
arrangement advantageously improves system throughput and system reliability of
a communication system.
[0012] 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 message signal, and means for generating a code word in response to
the message signal. The code word is based upon a stacking construction that is
generalized for the communication channel. The communication channel is
characterized as a multi-input multi-output block fading channel. The above
arrangement advantageously provides increased system capacity.
[0013]
According to another aspect of the invention, a communication system for
transmitting encoded signals over a communication channel is disclosed. The
system includes which has a source that is configured to output a message
signal, and an encoder that is configured to generate a code word in response to
the message signal. The code word is based upon a stacking construction that is
generalized for the communication channel, he communication channel is
characterized as a multi-input multi-output block fading channel. The
transmitter also includes a modulator that is configured to modulate the code
word for transmission over the communication channel. Further, the transmitter
includes a plurality of transmit antennas that are configured to transmit the
modulated code word over the communication channel. The system also includes a
receiver, which has a plurality of receive antennas; the receiver is configured
to receive the transmitted code word via the plurality of receive antennas. The
above arrangement advantageously maximizes spatial and temporal diversity.
[0014] 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 is based upon a
stacking construction, which is generalized for the communication channel. The
communication channel is characterized as a multi-input multi-output block
fading channel. The above approach minimizes data transmission errors.
[0015] 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 message signal.
Another step includes generating a code word in response to the message signal.
The code word is based upon a stacking construction that is generalized for the
communication channel. The communication channel is characterized as a
multi-input multi-output block fading channel. This approach advantageously
provides simplified receiver design.
[0016] 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,
wherein the code word being based upon a stacking construction that is
generalized for the communication channel. The communication channel is
characterized as a multi-input multi-output block fading channel. The apparatus
also 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
[0017] 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:
[0018] FIG. 1 is a
diagram of a communication system configured to utilize space-time codes,
according to an embodiment of the present invention;
[0019] FIG. 2 is a
diagram of an encoder that generates space-time codes, in accordance with an
embodiment of the present invention;
[0020] FIG. 3 is a diagram of a
decoder that decodes space-time codes, according to an embodiment of the present
invention;
[0021] FIG. 4 is a flow chart of the process of constructing
space-time codes used in the system of FIG. 1;
[0022] FIG. 5 is a
diagram of a wireless communication system employing the space-time codes,
according to an embodiment of the present invention; and
[0023] FIG. 6
is a diagram of a computer system that can perform the processes of encoding and
decoding of space-time codes, in accordance with an embodiment of the present
invention.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0024] 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.
[0025] Although the present invention is discussed with
respect to MMO block fading channels, the present invention has applicability to
communication channels with other channel characteristics.
[0026] 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. As a result, receiver 105 must
be able to compensate for the attenuation that is introduced by channel 03. 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.
[0027] FIG. 2 shows a diagram of an encoder that
generates space-time codes, in above, possesses a message source 201 that
generates k signals from a discrete alphabet, X'. Encoder 032 then generates
signals from alphabet Y to a modulator 25. 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 segmented into L.sub.t data
streams and then simultaneously transmitted over the antennas 207.
[0028] FIG. 3 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. 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.
[0029] FIG. 4 shows a flow chart of the process of constructing
space-time codes used in the system of FIG. 1. As stated previously, some
research have explored the availability of multiple transmit antennas in
designing channel codes that exploit spatial transmit diversity. The present
invention focuses on a quasi-static fading model of the communication channel
103 in which the path gains remain fixed throughout the code word. Specifically,
in the present invention, the more general block fading model is examined, based
upon the quasi-static fading channel. In the present model, the code word is
composed of multiple blocks. The fading coefficients are constant over one
fading block but are independent from block to block. The number of fading
blocks per code word can be regarded as a measure of the interleaving delay
allowed in the system 100, so that systems subject to a strict delay constraint
are usually characterized by a small number of independent blocks. The
information theoretic capacity of multiple antenna systems 100 in block fading
channels has been studied by Biglieri et al [3]; assuming the availability of
channel state information (CSI) at both the transmitter 101 and receiver 105, it
is noted that antenna diversity can be a substitute for time diversity. However,
this conclusion does not hold when CSI is only available at the receiver 105.
The code design of the present invention exploits both spatial and temporal
diversity.
[0030] Spatial and temporal diversity can be achieved through
the construction of space-time codes, as described in FIG. 4. In step 401, a
baseband design criteria that determine the diversity and coding advantage
achieved over block fading channels are developed. As will be more fully
described, this design criteria, as in [1] [2], for quasi-static and fast fading
channels are special cases of the new criteria. Then, according to step 403, the
diversity advantage baseband design criterion is translated into binary rank
criteria for PSK modulated codes; this approach is more fully detailed in a
paper by A. R. Hammons Jr. and H. El Gamal, entitled "On the theory of
space-time codes for PSK modulation" IEEE Trans. Info. Theory, March 2000, which
is incorporated herein by reference in its entirety. Next, the binary rank
criteria are then used to develop an algebraic framework for space-time code
design in block fading design, per step 405. Such an algebraic framework permits
construction of space-time codes that realize the optimum trade-off between
diversity advantage and transmission rate for arbitrary number of transmit
antennas and fading blocks (step 407). According to the present invention, the
notion of universal space-time coding, which aims at constructing codes that
exploit the spatial and temporal diversity when available, is described. This
notion is a generalization of the smart greedy design principle proposed in [1].
[0031] In addition to its importance in the study of code design in time
varying fading channels, the MIMO block fading model of communications channel
103 is beneficial in the frequency selective scenario. The developed algebraic
framework is employed to construct space-frequency codes that exploit the
frequency diversity available in the MIMO frequency selective fading channels.
[0032] In system 100, maximum likelihood (ML) decoding at receiver 105
is assumed. This assumption represents the case in which only a small number of
receive antennas 303 (FIG. 3) are available so that the receiver signal
processing capabilities are limited. This assumption is more fully explored in a
paper by H. El Gamal and A. R. Hammons Jr., entitled "The Layered Space-Time
Architecture: A New Prospective [sic]" IEEE Trans. Info. Theory, 1999, which is
incorporated herein by reference in its entirety. In the case in which a
relatively large number of receive antennas are available, more efficient signal
processing techniques can be employed to separate the different transmit antenna
signals. The code design criterion is different in both scenarios. The present
invention develops a coding approach for systems 100 with small number of
receive antennas 303.
[0033] Before discussing the construction of
space-time codes of the present invention, it is instructive to discuss the
concepts of space-time code design in general. First, a system model is
discussed, and then the design criteria for space-time code design in
quasi-static and fast fading channels, respectively, are described.
[0034] The system model, according to an embodiment of the present
invention, the source 201 of transmitter 200 generates k information symbols
from the discrete alphabet X, which are encoded by the error control code C via
encoder 203 to produce code words of length N=nL.sub.t over the symbol alphabet
Y. The encoded symbols are parsed among L.sub.t transmit antennas 207 and then
mapped by the modulator into constellation points from the discrete
complex-valued valued signaling constellation .OMEGA. for transmission across
the channel 103. The modulated streams for all antennas 207 are transmitted
simultaneously.
[0035] At the receiver 303, there are L.sub.r receive
antennas 303 to collect the incoming transmissions. The received baseband
signals are subsequently decoded by the space-time decoder 305. Each spatial
channel (the link between one transmit antenna (e.g., 207) and one receive
antenna (e.g., 303)) is assumed to experience statistically independent flat
Rayleigh fading. Receiver noise is assumed to be AWGN (Additive White Gaussian
Noise).
[0036] A space-time code is defined to include an underlying
error control code together with a spatial parser. An L.sub.t.times.n space-time
code C of size S consists of an (L.sub.tn, S) error control code C and a spatial
parser that maps each code word vector c.epsilon.C to an L.sub.t.times.n matrix
c, whose entries are a rearrangement of those of c. Except as noted to the
contrary, it is assumed that the standard parser maps the following
c=(c.sub.1.sup.1, c.sub.1.sup.2, . . . , c.sub.1.sup.L.sup..sub.t,
c.sub.2.sup.1, c.sub.2.sup.2, . . . , c.sub.2.sup.L.sup..sub.t, c.sub.n.sup.1,
c.sub.n.sup.2, . . . , c.sub.n.sup.L.sup..sub.t).epsilon.C
[0037] to the
matrix 1 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] In this notation, it is understood that c.sub.t.sup.i is the code
symbol assigned to transmit antenna i (e.g., 207) at time t.
[0039]
Assuming that .function.: Y.fwdarw..OMEGA. is the modulator mapping function,
then s=.function.(c) is the baseband version of the code word as transmitted
across the channel 103. For this system, we have the following baseband model of
the received signal: 2 y t j = E s i = 1 L t ij s t i + n t j
[0040]
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 (e.g.,
207) to receive antennaj (e.g., 303) at time t,
s.sub.t.sup.i=.function.(c.sub.t.sup.i) is the transmitted constellation point
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 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.
[0041] The fading model of primary interest
is that of a block flat Rayleigh fading process in which the code word
encompasses M fading blocks. The complex fading gains are constant over one
fading block but are independent from block to block. The quasi-static and fast
fading models are special cases of the block fading model in which M=1, and M=n,
respectively. For simplicity, it is assumed that M divides n.
[0042] For
the quasi-static flat Rayleigh fading channel, the pairwise error probability is
given by [1][2]: 3 P ( c e ) ( 1 i = 1 d ( 1 + i E S / 4 N 0 ) ) L r P ( c e ) (
E s 4 N 0 ) - d L r
[0043] where d=rank(.function.(c)-.function.(e)) and
.mu.=(.lambda..sub.1 .lambda..sub.2 . . . .lambda..sub.d).sup.1/d is the
geometric mean of the nonzero eigen-values of
A=(.function.(c)-.function.(e))(.function.(c)-.fu- nction.(e)).sup.H. The
exponent dL.sub.t is, also referred to as the "diversity advantage," while the
multiplicative factor .mu. is known as the "coding advantage."The parameter d is
the diversity provided by the multiple transmit antennas 207.
[0044]
Accordingly, the rank and equivalent product distance criteria for space-time
codes in quasi-static channels [1] results. Specifically, the rank criterion
specifies that the transmit diversity advantage
d=rank(.function.(c)-.function.(e)) be maximized over all pairs of distinct code
words c, e.epsilon.C. Further, the product distance criterion requires the
maximization of the coding advantage .mu.=(.lambda..sub.1 .lambda..sub.2 . . .
.lambda..sub.d).sup.1/d over all pairs of distinct code words c, e.epsilon.C.
The rank criterion is the more important of the two criteria, as it determines
the asymptotic slope of the performance curve as a function of E.sub.s/N.sub.0.
[0045] The binary rank criterion for BPSK (Binary Phase-Shift
Keying)-modulated, binary space-time codes are now developed. It is assumed that
C is a linear L.sub.t.times.n space-time code with underlying binary code C of
length N=nL.sub.t, wherein n>L.sub.t. It is also assumed that every non-zero
code word c is a matrix of fall rank over the binary field F. Thus, for BPSK
transmission over the quasi-static fading channel, the space-time code C
achieves full spatial diversity L.sub.tL.sub.r.
[0046] Using the above
binary rank criterion, the following general construction for space-time codes,
which is referred to as the "stacking construction"is developed. It is assumed
that M.sub.1, M.sub.2 . . . , M.sub.L.sub..sub.t are binary matrices of
dimension k.times.n, n.gtoreq.k, and C is a L.sub.t.times.n space-time code of
dimension k consisting of the code word matrices 4 c = [ x _ M 1 x _ M 2 x _ M L
t ]
[0047] where x denotes an arbitrary k-tuple of information bits and
L.sub.t<n. Consequently, C satisfies the binary rank criterion, and thus, for
BPSK transmission over the quasi-static fading channel, achieves full spatial
diversity L.sub.tL.sub.r, if and only if M.sub.1, M.sub.2 . . . ,
M.sub.L.sub..sub.t have the property that
.A-inverted.a.sub.1, a.sub.2,
. . . , a.sub.L.sub..sub.t.epsilon.F:
M=a.sub.1M.sub.1.sym.a.sub.2M.sub.2.sym. . . .
.sym.a.sub.L.sub..sub.tM.su- b.L.sub..sub.t
[0048] is of full rank k
unless a.sub.1=a.sub.2= . . . =a.sub.L.sub..sub.t=0.
[0049] The
previously described binary rank criteria and stacking construction may lift to
the Z.sub.4 domain, where they describe full diversity QPSK (Quadrature
Phase-Shift Keying)-modulated space-time codes. The stacking construction
encompasses as special cases transmit delay diversity, Tarokh's hand-crafted
trellis codes [1], and certain block and concatenated coding schemes. The
stacking construction is general in the number of transmit antennas 207 and
applies to tail terminated trellis codes as well as block codes. The important
class of rate 1/Lt binary convolutional codes with optimal d.sub.free can
usually be spatially formatted to yield full diversity space-time codes.
[0050] The present invention generalizes the stacking construction in
two different ways. First, a generalization is described that allows for
increasing the transmission rate at the expense of minimal reduction in the
diversity advantage. This construction can then be extended to block fading
channels in which an objective is to optimally exploit the spatial and temporal
diversity available in the channel without compromising the transmission rate.
[0051] With respect to a fast fading channel, the pairwise error
probability that the decoder 305 prefers an alternate code word e to c can be
upper bounded by [1] 5 P ( c e ) ( 1 i = 1 d ( 1 + f ( c _ t ) - f ( e _ t ) 2 E
S / 4 N 0 ) ) L r P ( c e ) ( E s 4 N 0 ) - d L r
[0052] where c.sub.t
is the i.sup.th column of c, e.sub.t is the t.sup.th the column of e, d is the
number of columns c.sub.t that are different from e.sub.t, and 6 = ( .PI. c _ t
e _ t f ( c _ t ) - f ( e _ t ) 2 ) 1 / d
[0053] The diversity advantage
is dL.sub.r; and the coding advantage is .mu.. Thus, the fundamental design
criteria [1] for space-time codes over fast fading channels are as follows. For
the distance criterion, the number of column differences
d=.vertline.{t:{overscore (c)}.sub.t.noteq.{overscore (e)}.sub.t}.vertline. over
all pairs of distinct code words c, e.epsilon.C are maximized. In addition, for
product criterion, the following coding advantage is maximized over all pairs of
distinct code words c, e.epsilon.C: 7 = ( .PI. c _ t e _ t f ( c _ t ) - f ( e _
t ) 2 ) 1 / d
[0054] Because real fading channels are neither
quasi-static nor fast fading, but something in between, Tarokh et al. [1]
suggested the ad-hoc strategy of designing space-time codes based on a
combination of the quasi-static and fast fading design criteria. They refer to
space-time codes designed according to the hybrid criteria as "smart greedy
codes," meaning that the codes seek to exploit both spatial and temporal
diversity whenever available. The present invention introduces the notion of
universal space-time coding that attempts to achieve the same goal, in a
systematic fashion, under the MIMO block fading model.
[0055] The
present invention considers the block fading model and develops a systematic
approach for designing space-time codes that achieve the maximum diversity
advantage for any coding rate, number of transmit antennas 207, and temporal
interleaving depth. First, the design criteria that governs the code performance
in such channels are developed. The baseband design criterion is described.
Under the block fading assumption, the path gains are constant over n/M
consecutive symbol durations. The notation (.)[m] denotes the single or two
dimensional vector of values of parameter (.) for the m.sup.th fading block.
Accordingly, the following parameters are defined:
.alpha..sup.ij[M]=.alpha..sub.(m-ln/M+1).sup.ij= . . .
=.alpha..sub.mn/M.sup.ij,
Y[m]=[y.sub.((m-1)n/M)+1).sup.1, . . . ,
y.sub.mn/M.sup.1, . . . , y.sub.mn/M.sup.L.sup..sub.r],
N[m]=[n.sub.((m-1)n/M)+1.sup.1, . . . , n.sub.mn/M.sup.1, . . . ,
n.sub.mn/M.sup.L.sup..sub.r],
A[m]=[.alpha..sup.11[m], . . . ,
.alpha..sup.L.sup..sub.t.sup.1[m], . . . ,
.alpha..sup.L.sup..sub.f.sup.L.sup..sub.t[m]],
c[m]=[{overscore
(c)}.sub.((m-1)n/M)+1, . . . , {overscore (c)}.sub.mn/M],
[0056] For
1.ltoreq.m.ltoreq.M, the following expression exists:
Y[m]={square
root}{square root over (E.sub.s)}A[m]D.sub.c[m]+N[m]
[0057] If code word
c is transmitted, then the conditional pairwise error probability that the
decoder 305 will prefer the alternate code word e to c is given by the
following:
P(c.fwdarw.e.vertline.{.alpha..sup.ij})=P(V<0.vertline..alpha..sup.ij),
[0058] where 8 V = m = 1 M [ ; A _ [ m ] ( D c [ m ] - D e [ m ] ) + N _
[ m ] r; 2 - ; N _ [ m ] r; 2 ]
[0059] is a Gaussian random variable
with mean 9 E { V } = m = 1 M ; A _ [ m ] ( D c [ m ] - D e [ m ] ) + N _ [ m ]
r; 2
[0060] and variance
Var{V}=2N.sub.0E{V}.
[0061]
Thus, 10 P ( V < 0 { ij } ) = Q ( m = 1 M ; A _ [ m ] ( D c [ m ] - D e [ m ]
) r; 2 N 0 ) 11 1 2 exp { - 1 4 N 0 m = 1 M ; A _ [ m ] ( D c [ m ] - D e [ m ]
) r; 2 }
[0062] Accordingly, the pairwise probability of error can be
manipulated to yield the fundamental bound [1] [2]: 12 P ( c e ) ( E s 4 N 0 ) -
dL r
[0063] where d=.SIGMA..sub.m-1.sup.Md.sub.m,
d.sub.m=rank(.function.(c[m])- -.function.(e[m])),
.mu.=(.pi..sub.m=1.sup.M.lambda..sub.1[m].lambda..sub.- 2[m] . . .
.lambda..sub.d.sub..sub.m[m]).sup.1/d, .lambda..sub.1[m], .lambda..sub.2[m] , .
. . , .lambda..sub.d.sub..sub.m[m] are the nonzero eigenvalues of
.multidot.A[m]=(.function.(c[m])-.function.(e[m])(.functio-
n.(c[m])-.function.(e[m])).sup.H. Hence, the generalized diversity and product
distance criteria for space-time codes over block fading channels are as
follows: for the block fading baseband rank criterion, the transmit diversity
advantage d.sub.m=.SIGMA..sub.m=1.sup.Mrank(.function.- (c[m])-.function.(e[m]))
over all pairs of distinct code words c, e.epsilon.C is maximized, and the block
fading product distance criterion entails maximizing the coding advantage
.mu.=(.pi..sub.m=1.sup.M.lambda..- sub.1[m].lambda..sub.2[m] . . .
.lambda..sub.d.sub..sub.m[m]).sup.1/d over all pairs of distinct code words c,
e.epsilon.C.
[0064] It is straightforward to observe that the design
criteria for quasi-static and fast fading channels can be obtained from the
block fading generalized criteria by simply letting M=1, M=n, respectively. As
in the case of quasi-static fading channels, the fact that the baseband rank
criterion applies to the complex-valued differences between baseband code words
represents a major obstacle to the systematic design of space-time codes that
achieve the maximum possible diversity advantage. It is possible to translate
the baseband criterion into an equivalent binary rank criteria for BPSK and QPSK
modulated space-time codes. These general binary criteria are sufficient to
ensure that a space-time code achieves a certain level of diversity over block
fading channels. To this end, a certain equivalence relation is imposed upon
potential baseband difference matrices. Each equivalence class contains a
special representative that is seen to be a binary projection of a code word
whose rank over the binary field is a lower bound on the rank of any of the
complex matrices in the equivalence class.
[0065] Turning now to the
discussion of the BPSK binary rank criterion, for BPSK modulation, the natural
discrete alphabet is the field F={0, 1} of integers modulo 2. Modulation is
performed by mapping the symbol x.epsilon.F to the constellation point
s=.function.(x).epsilon.{-1, 1} according to the rule s=(-1).sup.x. It is noted
that it is possible for the modulation format to include an arbitrary phase
offset e.sup.i.phi., since a uniform rotation of the BPSK constellation will not
affect the rank of the matrices .function.(c[m])-.function.(e[m])nor the
eigenvalues of the matrices
A[m]=(.function.(c[m])-.function.(e[m])(.function.(c[m])--
.function.(e[m])).sup.H. Notationally, the circled operator .sym. will be used
to distinguish modulo 2 addition from real- or complex-valued (+, -) operations.
[0066] Based on the above discussion, the following result for BPSK
modulated codes over block fading (BF) channels is achieved. It is assumed that
C is a linear L.sub.t.times.n space-time code with n.gtoreq.L.sub.t used in
communication system 100 with L.sub.t transmit antennas 207, L.sub.r receive
antennas 303, and operating over a block fading channel 103 with M blocks per
code word. Additionally, it is supposed that every non-zero binary code word c
.epsilon.C has the property that d is the largest integer such that
.SIGMA..sub.m-1.sup.Mran- k(c[m]).gtoreq.d, where the rank is over the binary
field F. Then, for BPSK transmission, the space-time code C achieves a diversity
level at least as large as dL.sub.r. This result stems from the fact that for
any two code words c, e.epsilon.C, the following expression holds true:
rank(.function.(c[m])-.function.(e[m]).gtoreq.rank(.function.(c[m]).sym..f-
unction.(e[m])),
[0067] where the rank in the left hand side is over the
complex field and in the right hand side is over the binary field. Hence, 13 m =
1 M rank ( f ( c [ m ] ) - f ( e [ m ] ) ) m = 1 M rank ( f ( c [ m ] ) f ( e [
m ] ) )
[0068] Since C is linear, then c.sym.e.epsilon.C and 14 min c ,
e C m = 1 M rank ( f ( c [ m ] ) - f ( e [ m ] ) ) min c C m = 1 M rank ( c [ m
] ) .
[0069] As regards the QPSK binary rank criterion, in QPSK
modulation, the natural discrete alphabet is the ring Z.sub.4={0, .+-.1, 2} of
integers modulo 4. Modulation is performed by mapping the symbol
x.epsilon.Z.sub.4 to the constellation point s.epsilon.{.+-.1, .+-.i} according
to the rule s=i.sup.x, where i={square root}{square root over (-1)}. Again, the
absolute phase reference of the QPSK constellation could have been chosen
arbitrarily without affecting the diversity advantage or coding advantage of a
Z.sub.4-valued space-time code.
[0070] For the Z.sub.4-valued matrix
c[m], the binary-valued indicant projections are defined: (c[m]) and
.PSI.(c[m]). These indicant projections as defined below serve to indicate
certain aspects of the binary structure of the Z.sub.4 matrix in which multiples
of two are ignored. A Z.sub.4-valued matrix c[m] of dimension L.sub.t.times.n/M
is said to be of type 1.sup.l2.sup.L.sub..sub.t.sup.-l if it consists of exactly
l rows that are not multiples of two.
[0071] It is assumed that c[m] is
a Z.sub.4-valued matrix of type 1.sup.12.sup.L.sub..sub.t.sup.-1. After suitable
row permutations if necessary, it has the following row structure: 15 c [ m ] =
[ c _ 1 [ m ] c _ l [ m ] 2 c _ l + 1 ' [ m ] 2 c _ L i ' [ m ] ]
[0072]
The row-based indicant projection (5-projection) is then defined as the
following: 16 ( c [ m ] ) = [ ( c _ 1 [ m ] ) ( c _ l [ m ] ) ( c _ l + 1 ' [ m
] ) ( c _ L i ' [ m ] ) ]
[0073] Similarly, the column-based indicant
projection (.PSI.-projection) is defined as
[.PSI.(c[m])].sup.T=(c[m].sup.T)
[0074] Using the binary
indicants, we have the following result that translates the baseband rank
criterion into binary rank criterion for QPSK modulated codes in a block fading
environment.
[0075] With respect to the QPSK-BF binary rank criterion,
it is assumed that C is a linear L.sub.t.times.n space-time code over Z.sub.4,
with n.gtoreq.L.sub.t in communication system 100 with L.sub.t transmit antennas
207, L.sub.r receive antennas 303, and operating over a block fading channel 103
with M blocks per code word. It is further assumed that, every non-zero code
word c.epsilon.C has the property that d is the largest integer such that
.SIGMA..sub.m=1.sup.Mrank{(c[m])}.gtoreq.d or
.SIGMA..sub.m=1.sup.Mrank{.PSI.(c[m])}.gtoreq.d where the rank is over the
binary field F. Then, for QPSK transmission, the space-time code C achieves a
diversity level at least as large as dL.sub.r.
[0076] The block fading
channel binary rank criteria open the door for developing an algebraic framework
for constructing space-time codes that realize the optimum trade-off between
transmission rate and diversity advantage. First, it is shown that the design of
spec-time codes that realize full diversity is relatively easy using the
multi-stacking construction in
[0077] However, attaining full diversity
entails a significant loss in the transmission rate compared to the quasi-static
scenario, irrespective of the coding scheme used. The more challenging task, as
recognized by the present invention, is to construct space-time codes that
exploit the temporal diversity in a multi-input multi-output (MIMO) block fading
channel without compromising the transmission rate. This coding paradigm can
achieve significant increase in the diversity advantage with a relatively small
number of fading blocks per code word (i.e., a small penalty in terms of
interleaving delay).
[0078] The algebraic framework for BPSK space-time
codes is now described. In a MIMO block fading channel 103 with L.sub.t transmit
antennas 207 and M fading blocks per codeword the maximum transmit diversity is
L.sub.tM. Under this model, the space-time code C is defined to include the
following code words 17 c = [ x _ M 11 x _ M 12 x _ M 1 M x _ M 21 x _ M 22 x _
M 2 M x _ M L t 1 x _ M L t 2 x _ M L t M ]
[0079] where
x.epsilon.F.sup.k, M.sub.ij.epsilon.F.sup.kxn/M. Full diversity is realized in
this channel 103 by the following multi-stacking code construction. The
space-time code C achieves full transmit diversity L.sub.tM if for every i,
1.ltoreq.i.ltoreq.M, the set of matrices {M.sub.1i, M.sub.2i, . . . ,
M.sub.L.sub..sub.t.sub.i} satisfies the stacking construction as discussed
previously.
[0080] The main disadvantage of the above multi-stacking
construction is that the transmission rate is reduced to 1/M bits/sec/Hz; it is
noted that in quasi-static fading channels, the stacking construction supports 1
bits/sec/Hz. This reduction in rate is not a special characteristic of the
multi-stacking construction and any space-time code that achieves fall diversity
in the MIMO block fading channel suffers from this advantage. This fact is
formalized in the following result that serves to establish the fundamental
limit on the transmission rate for space-time codes with a certain level of
diversity advantage in MIMO block fading channels.
[0081] The maximum
transmission rate for BPSK modulation in a communication system 100 with L.sub.t
transmit antennas 207, operating over a block fading channel 103 with M blocks
and using a space-time code that achieves d levels of transmit diversity is 18
ML t - d + 1 M
[0082] bits/sec/Hz. It is observed that the scenario at
hand is strictly more restrictive than the case of single transmit antenna with
ML.sub.t fading block--i.e., a code that achieves d levels of diversity in the
MIMO block fading scenario achieves at least the same diversity order in the
later scenario.
[0083] At this point, the general case of constructing
codes that realize the optimum trade between the transmission rate and diversity
advantage for any arbitrary transmission rate is described. The main result for
space-time code design in MIMO block fading channels is obtained in two steps.
First, a generalization of the stacking construction in quasi-static fading
channels that allows for increasing the transmission rate at the expense of
minimal reduction the diversity advantage is achieved. This important result
introduces the technical machinery necessary for the second step, in which
space-time codes are constructed to optimally exploit the diversity available in
MIMO block fading channels.
[0084] In the first step, the previously
discussed stacking construction is generalized to handle codes that achieve
d<L.sub.t levels of spatial transmit diversity. These codes are capable of
supporting higher transmission rates than full diversity codes. For example,
with BPSK modulation and L.sub.t transmit antennas 207, a d-diversity code can
support .eta..gtoreq.1 bits/sec/Hz, where L.sub.t-d+1.gtoreq..eta..gtoreq-
.L.sub.t-d, over the quasi-static fading channel. Before proceeding further,
certain definitions and terminologies are presented to facilitate the discussion
of the generalized stacking construction.
[0085] The BPSK space-time
code under consideration C is defined as in the previously described stacking
construction with the modification that n can be smaller than k to allow for
higher transmission rates than 1 bits/sec/Hz. G is defined as the set of binary
full rank matrices {G:G=.left brkt-bot.g.sub.i, j.right
brkt-bot..sub.L.sub..sub.t.sub.xL.su- b..sub.t} resulting from applying any
number of simple row operations to the identity matrix, I.sub.L.sub..sub.t.
Also, .A-inverted.G.epsilon.G, x.epsilon.F.sup.K, let 19 Q ( x _ , G ) = G [ x _
M 1 x _ M 2 x _ M L t ] = [ q 1 T ( x _ , G ) , q 2 T ( x _ , G ) , , q L t T (
x _ , G ) ] T
[0086] According to the BPSK binary rank criterion, for C
to achieve at least r levels of diversity, the binary rank for each code word
must be larger than or equal to r. A code word matrix c has a binary rank equal
to r, if and only if all matrices resulting from applying any number of simple
row operations to c have at least r non zero rows (i.e., the number of zero rows
is less than L.sub.t-r+1). Noting that {Q(x G)} is the set of matrices resulting
from applying all possible combinations of simple row operations to the code
word matrix corresponding to the input stream x, the following condition for a
space-time code achieving r levels of diversity results:
.A-inverted.G.epsilon.G, x.epsilon.F.sup.K
.left
brkt-bot.q.sub.1(x, G), q.sub.2(x, G), . . . , q.sub.L.sub..sub.t.sub.-r+1(x,
G).right brkt-bot..noteq.0.sub.1.times.n(L- .sub..sub.t.sub.-r+l)
[0087]
Now, the following relationships are used to obtain the generalized the stacking
construction: 20 q i ( x _ , G ) = x _ [ q t , 1 I k , q t , 2 I k , , q i , L t
I k ] [ M 1 M 2 M L t ] = x _ R i ( G ) ,
[0088] In the generalized
stacking construction, C is assumed to be a linear L.sub.t.times.n space-time
code as defined in the previously described stacking construction with the
exception that n.ltoreq.k is allowed. Then, for BPSK transmission over the
quasi-static fading channel, C achieves at least d levels of transmit diversity
if d is the largest integer such that .A-inverted.G.epsilon.G, R(G)=.left
brkt-bot.R.sub.1(G), R.sub.2(G), . . . , R.sub.L.sub..sub.t.sub.-d+1,.rig- ht
brkt-bot. has a full rank k over the binary field F. It is clear that for
d=L.sub.t, this condition reduces to the previously described stacking
construction. The above generalized stacking construction allows for a
significant increase in throughput. For example, in the case of 4 transmit
antennas 207, the rate can be increased from 1 bits/sec/Hz to 2 bits/sec/Hz at
the expense of a small reduction in diversity advantage from 4 to 3.
[0089] The same idea behind the generalized stacking construction can be
used to design space-time codes for MIMO block fading channels. First, the
following notations are introduced:
.A-inverted.1.ltoreq.m.ltoreq.M,
G.sub.m=[g.sub.i, j(m)].epsilon.G, x.epsilon.F.sup.K, let
[0090] 21 Q (
x _ , G m , m ) = G m [ x _ M 1 m x _ M 2 m x _ M L t m ] = [ q 1 T ( x _ , G m
, m ) , q 2 T ( x _ , G m , m ) , , q L t T ( x _ , G m , m ) ] T
[0091]
Using the block fading channel binary rank criterion and the generalized
stacking construction argument, it is observed that the space-time code C
achieves at least r levels of diversity if it satisfies the following condition:
.A-inverted.G.epsilon.G, . . . , G.sub.m.epsilon.G, x.epsilon.F.sup.K,
0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t-r+1), . . . ,
0.ltoreq.m.sub.M.ltoreq.min(L.sub.t, ML.sub.t-r+1),
[0092] and
.SIGMA..sub.m=1.sup.Mm.sub.i=ML.sub.t-r+1,
[q.sub.0(x, G.sub.1,
1), . . . , q.sub.m.sub..sub.1(x, G.sub.1, 1), q.sub.0(x, G.sub.2, 2), . . . ,
q.sub.m.sub..sub.2(x, G.sub.2,2), . . . , q.sub.m.sub..sub.M(x, G.sub.M,
M).right brkt-bot..noteq.0.sub.1.times.n(L- .sub..sub.t.sub.-r+1)
[0093]
where q.sub.0(x, G.sub.m, m)=[ ] is an empty vector.
[0094] Again the
following fact is utilized: 22 q i ( x _ , G m , m ) = x _ [ g i , 1 ( m ) I k ,
g i , 2 ( m ) I k , , g i , L t ( m ) I k ] [ M 1 m M 2 m M L t m ] = x _ R i (
G m , m ) ,
[0095] for i.gtoreq.1 and R.sub.0(G.sub.m, m) is an empty
matrix, to obtain the result below, which applies the generalized stacking
construction to MIMO block fading channels.
[0096] In the case of a
block fading generalized stacking construction, C is assumed to be a linear
L.sub.t.times.n space-time code. For BPSK transmission over a block fading
channel 103 with M blocks, C achieves at least r levels of transmit diversity if
r is the largest integer such that
.A-inverted.G.epsilon.G, . . . ,
G.sub.m.epsilon.G, 0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t-r+1), . . . ,
0.ltoreq.m.sub.M.ltoreq.min(L.sub.t, ML.sub.t-r+1), and
.SIGMA..sub.m=1.sup.Mm.sub.l=ML.sub.t-r+1, R.sub.m.sub..sub.1.sub., . . . ,
m.sub..sub.M(G.sub.1, . . . , G.sub.m)=.left brkt-bot.R.sub.0(G.sub.1), . . . ,
R.sub.m.sub..sub.1(G.sub.1), R.sub.0(G.sub.2), . . . ,
R.sub.m.sub..sub.2(G.sub.2) , . . . , R.sub.m.sub..sub.M(G.sub.M).right
brkt-bot. has a full rank k over the binary field F.
[0097] It is
straightforward to note that the multi-stacking construction can be obtained by
setting the diversity advantage d=ML.sub.t. Further, it is interesting to
compare the above condition to the threaded stacking construction for layered
space-time systems.
[0098] Space-time layering is suitable for systems
with relatively large number of receive antennas. The large number of receive
antennas allows for the design of efficient signal processing algorithms to
separate the signals from different layers efficiently, and hence, code design
for layered systems can assume no spatial interference for between layers. Based
on this assumption, it is observed that the layered space-time code needs to
satisfy the above condition when every .A-inverted.G.sub.m is a permutation of
the identity matrix. This relaxed constraint constitute the base for the
framework for layered space-time coding in [6], which considers a scenario that
is different from that of the present invention. For example, the present
invention according to one embodiment, considers use of a relatively smaller
number of receive antennas 303 than the number of transmit antennas 207, thereby
limiting the ability to separate the different transmit antenna signals. Hence,
the burden now lays on the code design to account for the fact that the input to
the maximum likelihood decoder 305 is the sum of the different transmit antenna
signals multiplied with the corresponding fading coefficients.
[0099]
The block fading generalized stacking construction permits construction of
space-time codes that optimally exploit the diversity available in MIMO block
fading channels with arbitrary number of transmit antennas 207 and fading blocks
per code word. The special case of designing space-time convolutional codes for
this scenario is now described. Such codes advantageously enables the use of
computationally efficient maximum likelihood decoders (e.g., 305).
[0100] The natural space-time codes associated with binary rate
1/ML.sub.t convolutional codes with periodic bit interleaving are attractive
candidates for the application under consideration in the present invention, as
they can be easily formatted to satisfy the multi-stacking condition, and hence
achieve full diversity. Each output arm from the encoder 203 is assigned to a
distinct pair of transmit antenna 207 and fading block.
[0101] The next
step is to consider the more challenging task of finding rate k/ML.sub.t codes
that achieve the best trade-off between throughput and diversity advantage for
arbitrary choice of the transmission throughput. It is assumed that C is a
binary convolutional code of rate k/ML.sub.t. The encoder 203 processes k binary
input sequences x.sub.1(t), x.sub.2(t), . . . , x.sub.k(t) and produces ML.sub.t
coded output sequences y.sub.1(t), y.sub.2(t), . . . , y.sub.ML.sub..sub.t(t)
which are multiplexed together to form the output code word. A sequence {x(t)}
is often represented by the formal series X(D)=x(0)+x(1)D+x(2)D.su- p.2+ . . .
{x(t)}X(D) is referred to as a D-transform pair. The action of the
binary-convolutional encoder 203 is linear and is characterized by the so-called
impulse responses g.sub.i, l(t)G.sub.i, j(D) associating output y.sub.i(t) with
input x.sub.i(t). Thus, the encoder 203 action is summarized by the matrix
equation:
Y(D)=X(D)G(D),
[0102] where
Y(D)=.left
brkt-bot.Y.sub.1(D)Y.sub.2(D) . . . Y.sub.ML.sub..sub.t(D).sub.- 2.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 , ML t ( D ) G 2 , 1 ( D ) G 2 , 2 ( D ) G 1 , ML t
( D ) G k , 1 ( D ) G k , 2 ( D ) G k , ML t ( D ) ]
[0103] The natural
space-time formatting of C is considered, whereby the output sequence
corresponding to Y.sub.(m-1)L.sub..sub.t.sub.+l(D) is assigned to the l.sup.th
transmit antenna 207 in the m.sup.th fading block, such that the diversity that
can be achieved by this scheme can be characterized. The algebraic analysis
technique considers the rank of matrices formed by concatenating linear
combinations of the column vectors: 24 F l ( D ) = [ G 1 , l ( D ) G 2 , l ( D )
G k , l ( D ) ] ( 15 )
[0104] Using the same approach as in the block
fading generalized stacking construction, the following is defined
.A-inverted.G.sub.m.epsilon.G, 1.ltoreq.i.ltoreq.L.sub.t, 1.ltoreq.m.ltoreq.M 25
R t ( 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 ) ]
( 16 )
[0105] An algebraic framework for designing BPSK space-time
convolutional codes is now established. In a communication system 100 with
L.sub.t transmit antennas 207 operating over a block fading channel 103 with M
blocks, C denotes the space-time code that includes the binary convolutional
code C, whose k.times.ML.sub.t transfer function matrix is G(D)=.left
brkt-bot.F(D).sub.1. . . F.sub.ML.sub..sub.t(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.+l(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.epsilon.G, . . . G.sub.M.epsilon.G,
0.ltoreq.m.sub.1.ltoreq.min(L.sub.t, ML.sub.t-d+1), . . . ,
0.ltoreq.m.sub.M.ltoreq.min(L.sub.t, ML.sub.t-r+1),
[0106] and
.SIGMA..sub.m=1.sup.Mm.sub.i-ML.sub.t=d+1,
R.sub.m.sub..sub.1.sub., . . . , m.sub..sub.M.sup.(G.sup..sub.1.sup., .
. . , G.sup..sub.M.sup.)(D)=.left brkt-bot.R.sub.0.sup.(G.sup..sub.1.sup.,1-
)(D), . . . , R.sub.m.sub..sub.1.sup.(G.sup..sub.1.sup.,1)(D),
R.sub.0.sup.(G.sup..sub.2.sup.,2)(D), . . . , R.sub.m.sub..sub.2.sup.(G.s-
up..sub.2.sup.,2)(D), . . . , R.sub.mM.sup.(G.sup..sub.M.sup.,M)(D).right
brkt-bot.
[0107] has a rank k over the space of all formal series.
[0108] The above result is utilized to construct convolutional
space-time codes that realize the optimum tradeoff between transmission rate and
diversity order for BPSK modulation with arbitrary coding rate, number of
transmit antennas 207, and number of fading blocks. It can be easily seen that
this framework encompasses as special case rate 1/n' convolutional codes with
bit or symbol interleaving across the transmit antennas and fading blocks [6].
[0109] The binary constructions previously proposed for BPSK modulation
can also be used to construct codes for higher order constellations. For QPSK
modulation, linear Z.sub.4 codes can be constructed by "lifting" linear binary
codes to the Z.sub.4 alphabet (i.e., the binary projection of the Z.sub.4 code
generator matrix is the same as the binary generator matrix). Another way for
designing codes for QPSK modulation is to combine two binary codes A, B with the
same diversity advantage in a dyadic format C=A+2B. The resulting Z.sub.4 code
achieves the same diversity advantage as the binary code, however, for QPSK
transmission.
[0110] The present invention considers the design of
space-time codes for MIMO block fading channels. The developed baseband design
criteria determines the diversity and coding advantage achieved by space-time
codes in block fading channels. For BPSK and QPSK modulated codes, the developed
binary rank criteria allow for designing space-time codes that exhibit the
optimum diversity-vs.- throughput tradeoff. These binary criteria are then
utilized to develop general algebraic framework for space-time code design in
MIMO block fading channels. The above construct has applicability in a number of
communication systems; for example, the space-time codes can be deployed in a
wireless communication, as seen in FIG. 5.
[0111] FIG. 5 shows a diagram
of a wireless communication system that utilizes space-time codes, according to
an embodiment 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 a space-time encoder 203 (as shown in FIG. 2) that
generates space-time codes with a block fading generalized stacking
construction. 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. The space-time code construction of the present
invention advantageously permits use of a smaller number of receive antennas
than that of the transmitting terminal 501, thereby resulting in hardware cost
reduction. In an exemplary embodiment, a terminal that is designated as a
receiving unit may possess a smaller quantity of antennas that of the
transmitting unit.
[0112] FIG. 6 shows a diagram of a computer system
that can perform the processes of encoding and decoding of space-time codes, in
accordance with an embodiment 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.
[0113] 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.
[0114] 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.
[0115] Further, the instructions to
support the generation of space-time 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 light waves, such as those generated during radio wave and
infrared data communication.
[0116] 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.
[0117] Various forms of computer readable media may be 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.
[0118] 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 may be 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.
[0119] 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.
[0120] The
techniques described herein provide several advantages over prior approaches to
providing space-time codes for MIMO block fading channels. Such code
construction enhances spatial and temporal diversity without sacrificing
transmission rate.
[0121] 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
[0122] [1] 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.
[0123] [2] 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.
[0124] [3] E. Biglieri, G.
Caire, and G. Taricco. Limiting performance for block-fading channels with
multiple antennas, submitted to IEEE Trans. Info. Theory, September 1999.
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