All The Claims

1. An adjustable insertion assembly for modular electrochemical potential measurement sensors, the assembly comprising:
an elongated electrode holder, configured to receive therein an electrochemical sensor having measurement and reference half cells, the electrochemical sensor configured for electrochemically responding to a process analyte upon contact with a process fluid;
the electrode holder having an aperture disposed in a distal end thereof, to permit process fluid to flow therethrough into contact with the sensor disposed therein;
a receptacle configured to slidably receive the electrode holder therein, wherein the electrode holder is configured for slidable movement within a range of motion extending from fully inserted to fully retracted positions;
the receptacle having an open distal end portion configured for extension through a wall of a process fluid vessel, wherein the aperture of the electrode holder is open to the process fluid when the electrode holder is disposed in the fully inserted position, and closed to the process fluid when in the fully retracted position;
a leverage member coupled to the receptacle, and configured for releasable movement relative to the receptacle;
an extension captured by the leverage member and configured for being moved by the leverage member relative to the receptacle;
the receptacle having an abutment configured to engage the extension in a sliding, interference fit, so that movement of the leverage member in opposite directions alternately clamps and releases the electrode holder relative to the receptacle to substantially prevent and permit movement at substantially any point within the range of movement.
2. The assembly of claim 1, wherein the extension and abutment are configured so that mutual engagement moves at least one of the extension and abutment transversely to the axial direction.
3. The assembly of claim 1, wherein the leverage member comprises a tube nut disposed about, and threadably engaged with a proximal end of the receptacle, the tube nut being configured for threaded, axial movement relative to the receptacle, and the extension includes an axial extension configured for moving axially with the tube nut.
4. The assembly of claim 1, comprising at least one seal disposed between the holder and the receptacle to provide a substantially liquid-tight, sliding engagement therebetween during movement within the range of motion.
5. The assembly of claim 1, comprising at least one seal disposed between the holder and the electrochemical sensor to provide a substantially liquid-tight, sliding engagement therebetween.
6. The assembly of claim 1, wherein the electrode holder is sized and shaped to receive therein, electrochemical sensors of a plurality of sizes.
7. The assembly of claim 6, wherein the electrode holder is sized and shaped to receive therein, electrochemical sensors of a plurality of axial dimensions.
8. The assembly of claim 3, wherein the axial extension comprises a wedge having a cam surface extending obliquely to the axial direction.
9. The assembly of claim 8, wherein the abutment comprises another cam surface extending obliquely to the axial direction, and configured for surface to surface engagement with the cam surface of the wedge.
10. The assembly of claim 9, wherein the receptacle comprises a stepped central channel having a relatively large transverse dimension disposed at a proximal end portion, and a relatively small transverse dimension disposed at a distal end portion thereof.
11. The assembly of claim 10, wherein the distal end portion is configured to form a sliding fit with the electrode holder.
12. The assembly of claim 10, wherein the other cam surface is disposed on a wall of the central channel at the proximal end portion thereof.
13. The assembly of claim 12, comprising a wear surface extending radially between the relatively large and relatively small transverse dimensions.
14. The assembly of claim 13, wherein the wear surface is configured to slidably guide the distal end of the electrode holder towards the center of the channel during insertion thereof into the receptacle.
15. The assembly of claim 1, comprising a flange disposed at the distal end of the electrode holder, the flange configured to engage the distal end of the receptacle when the electrode holder is disposed in its fully retracted position, to close the aperture to the process fluid.
16. The assembly of claim 15, comprising a seal disposed between the flange and the distal end of the receptacle when the electrode holder is disposed in its fully retracted position, wherein the aperture is out of fluid communication with the process fluid.
17. The assembly of claim 1, further comprising the electrochemical sensor.
18. The assembly of claim 17, wherein the electrochemical sensor is configured for being coupled to a process variable transmitter.
19. The assembly of claim 17 wherein the measuring half-cell comprises a pH electrode.
20. The assembly of claim 17 wherein said measuring half-cell comprises a selective ion electrode.
21. The assembly of claim 17 wherein said measuring half-cell comprises a fluoride ion selective electrode.
22. The assembly of claim 17 wherein said measuring half-cell comprises an oxidation-reduction potential electrode.
23. A method of adjustably inserting an electrochemical potential measurement sensors into a process fluid, the method comprising:
(a) providing the insertion assembly of claim 1;
(b) extending the open distal end portion of the receptacle through a wall of a process fluid vessel;
(c) placing the electrochemical sensor into the elongated electrode holder;
(d) slidably placing the electrode holder into the receptacle, wherein the electrode holder is configured for slidable movement within a range of motion extending from a fully inserted position in which the aperture of the electrode holder is open to process fluid within the vessel, to a fully retracted position in which the aperture of the electrode holder is closed to the process fluid;
(e) sliding the electrode holder into a fluid insertion position at any of a plurality of locations within its range of motion;
(f) clamping, with the leverage member, the electrode holder in the fluid insertion position;
(g) operating the electrochemical sensor to detect an analyte associated with the process fluid;
(h) releasing, with the leverage member, the electrode holder;
(i) sliding the electrode holder into the fully retracted position to close the aperture to the process fluid;
(j) clamping, with the leverage member, the electrode holder in the fully retracted position;
(k) removing and replacing the electrochemical sensor; and
(l) repeating said (e)-(g).
24. The method of claim 23, further comprising repeating said (e)-(g) at another of the plurality of locations within the range of motion.

The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

What is claimed is:

1. A brightness enhancing device for an anti-dazzle head lamp of a car which will be used during a device at dust or dawn for which indicating the presence of the car consists of an additional lighting element disposed between a hyperboloid reflecting mirror and a head lens of said anti-dazzle head lamp and operated by the driver to enhancing the brightness therefore.
2. A brightness enhancing device for an anti-dazzle head lamp of a car according to claim 1 wherein said additional lighting element is a neon tube of selective size been installed between a hyperboloid reflecting mirror and a head lens thereof and a head lens thereof and head lamp and operated by the driver to enhancing the brightness thereof.
3. A brightness enhancing device for an anti-dazzle head lamp of a car according to claim 1 wherein said additional lighting element is an additional bulb of selective size been installed between a hyperboloid reflecting mirror and a head lens thereof and a head lens thereof and head lamp and operated by the driver to enhancing the brightness thereof.

1. A method including:
receiving, by a computing device, a definition for a trading strategy, wherein the trading strategy includes a first tradeable object and a second tradeable object;
selecting, by the computing device, a first server to process one or more trade orders for the first tradeable object and a second server to process one or more trade orders for the second tradeable object; and
sending, by the computing device, the definition for the trading strategy to the first server and the second server.
2. The method of claim 1, wherein selecting includes automatically selecting the first and second servers.
3. The method of claim 2, wherein selecting includes automatically selecting based on a distance between the first server and an electronic exchange for the first tradeable object and a distance between the second server and an electronic exchange for the second tradeable object.
4. The method of claim 2, wherein selecting includes automatically selecting based on a performance parameter of the first server and a performance parameter of the second server.
5. The method of claim 1, wherein selecting includes receiving a selection command that defines the first and second servers.
6. The method of claim 1, wherein the first tradeable object is to be traded at a first electronic exchange and a second tradeable object is to be traded at a second electronic exchange.
7. A method including:
receiving, by a computing device, a definition for a trading strategy, wherein the trading strategy includes a first tradeable object and a second tradeable object;
selecting, by the computing device, a first server to process one or more trade orders for the first tradeable object and a second server to process one or more trade orders for the second tradeable object; and
selecting, by the computing device, either the first server or the second server as a control server that reports synthetic trade order data to a trading device; and
notifying, by the computing device, the first server or the second server that was selected as the control server.
8. The method of claim 7, wherein the first server or the second server that was not selected as the control server does not report synthetic trade order data to the trading device.
9. The method of claim 7, wherein the first tradeable object is to be traded at a first electronic exchange and a second tradeable object is to be traded at a second electronic exchange.
10. The method of claim 7, wherein selecting includes automatically selecting the first and second servers.
11. The method of claim 10, wherein selecting includes automatically selecting based on a distance between the first server and an electronic exchange for the first tradeable object and a distance between the second server and an electronic exchange for the second tradeable object.
12. The method of claim 10, wherein selecting includes automatically selecting based on a performance parameter of the first server and a performance parameter of the second server.
13. The method of claim 7, wherein selecting includes receiving a selection command that defines the first and second servers.
14. A system including:
a computing device to facilitate definition of a trading strategy, wherein the trading strategy includes a first tradeable object and a second tradeable object, the computing device to select a first server to process one or more trade orders for the first tradeable object and a second server to process one or more trade orders for the second tradeable object, the computing device to send the definition for the trading strategy to the first server and the second server.
15. The system of claim 14, wherein the trading device comprises an automated trading engine client to facilitate the one or more trade orders with respect to the first server and the second server.
16. The server of claim 14, wherein the computing device is to automatically select the first and second servers.
17. The system of claim 16, wherein the computing device is to automatically select the first and second servers based on a distance between the first server and an electronic exchange for the first tradeable object and a distance between the second server and an electronic exchange for the second tradeable object.
18. The system of claim 16, wherein the computing device is to automatically select the first and second servers based on a performance parameter of the first server and a performance parameter of the second server.
19. The system of claim 14, wherein the computing device is to receive a selection command that defines the first and second servers.
20. The system of claim 14, wherein the first tradeable object is to be traded at a first electronic exchange and a second tradeable object is to be traded at a second electronic exchange.
21. A system including:
a computing device to facilitate definition of a trading strategy, wherein the trading strategy includes a first tradeable object and a second tradeable object, the computing device to select a first server to process one or more trade orders for the first tradeable object and a second server to process one or more trade orders for the second tradeable object, the computing device to send the definition for the trading strategy to the first server and the second server, the computing device to select one of the first server and the second server as a control server to report synthetic trade order data, wherein the computing device is to notify the first server or the second server selected as the control server.
22. The system of claim 21, wherein the first server or the second server that was not selected as the control server is not to report synthetic trade order data to the trading device.
23. The system of claim 21, wherein the trading device comprises an automated trading engine client to facilitate the one or more trade orders with respect to the first server and the second server.
24. The server of claim 21, wherein the computing device is to automatically select the first and second servers.
25. The system of claim 24, wherein the computing device is to automatically select the first and second servers based on a distance between the first server and an electronic exchange for the first tradeable object and a distance between the second server and an electronic exchange for the second tradeable object.
26. The system of claim 24, wherein the computing device is to automatically select the first and second servers based on a performance parameter of the first server and a performance parameter of the second server.
27. The system of claim 21, wherein the computing device is to receive a selection command that defines the first and second servers.
28. The system of claim 21, wherein the first tradeable object is to be traded at a first electronic exchange and a second tradeable object is to be traded at a second electronic exchange
29. A tangible computer readable storage medium including a set of instructions for execution by a processor, the set of instructions, when executed, implement a method including:
receiving a definition for a trading strategy, wherein the trading strategy includes a first tradeable object and a second tradeable object;
selecting a first server to process one or more trade orders for the first tradeable object and a second server to process one or more trade orders for the second tradeable object; and
sending the definition for the trading strategy to the first server and the second server.
30. A tangible computer readable storage medium including a set of instructions for execution by a processor, the set of instructions, when executed, implement a method including:
receiving a definition for a trading strategy, wherein the trading strategy includes a first tradeable object and a second tradeable object;
selecting a first server to process one or more trade orders for the first tradeable object and a second server to process one or more trade orders for the second tradeable object; and
selecting either the first server or the second server as a control server that reports synthetic trade order data to a trading device; and
notifying the first server or the second server that was selected as the control server.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.

1. A receiver for receiving modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over all possible symbol pairs using signals received by a receive antenna from three transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna,
wherein if the modulation symbols are BPSK (Binary Phase Shift Keying) symbols, the first decoder computes parameters
R
1

=

\u2062
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062

1

2
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
+

j
\u2062
\u2062

\u03b2
*

\u2062

1

2
\u2062

r
4
R
3

=

\u2062
\u03b3
\u2062
\u2062

r
2
*
–

j
\u2062
\u2062

\u03b2
*

\u2062

1

2
\u2062

r
1
+
\u03b1
*

\u2062

r
4
–
\u03b2
*

\u2062

1

2
\u2062

r
3
*
R
13

=

\u2062
j
\u2061

(
C
1

+

C
3
)
2
C
1

=

\u2062
–

\u03b1
*
\u2062
\u03b2
\u2062

2
–
\u03b1\u03b2
*

\u2062

2
C
3

=

\u2062
j
\u2062
\u2062

\u03b3
*

\u2062
\u03b2
\u2062

2
–

j
\u2062
\u2062

\u03b3\u03b2
*

\u2062

2
and the second decoder computes parameters
R
2

=

\u2062
\u03b2
*

\u2062

1

2
\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

j
\u2062
\u2062
\u03b2
\u2062

1

2
\u2062

r
3
*
+
\u03b3
*

\u2062

r
4
R
4

=

\u2062
\u03b3
*

\u2062

r
1
–

j
\u2062
\u2062
\u03b2
\u2062

1

2
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

1

2
\u2062

r
4
R
24

=

\u2062
j
\u2061

(
C
2

+

C
4
)
2
C
2

=

\u2062
\u03b1\u03b2
*

\u2062

2
+
\u03b1
*

\u2062
\u03b2
\u2062

2
C
4

=

\u2062
j
\u2062
\u2062

\u03b3\u03b2
*

\u2062

2
–

j
\u2062
\u2062

\u03b3
*

\u2062
\u03b2
\u2062

2
where \u03b1, \u03b2 and \u03b3 are the channel gains and r1, r2, r3 and r4 are the received signals, and R and C are variables,
and the first decoder finds a symbol pair (x1, x3) that minimizes |R1\u2212x1|2+|R3\u2212x3|2+|R13\u2212x1*x3|2, and the second decoder finds a symbol (x2, x4) that minimizes |R2\u2212x2|2+|R4\u2212x4|2+|R24\u2212x2*x4|2.
2. A receiver for receiving modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over all possible symbol pairs using signals received by a receive antenna from three transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna,
wherein if the modulation symbols are QPSK (Quadrature Phase Shift Keying) or 8PSK (8-ary PSK) symbols, the first decoder computes parameters
R
1

=

\u2062
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062

1

2
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
–
v
*

\u2062

\u03b2
*

\u2062

1

2
\u2062

r
4
R
3

=

\u2062
v
\u2062
\u2062
\u03b3
\u2062
\u2062

r
2
*
+
\u03b2
*

\u2062

1

2
\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062

1

2
\u2062

r
3
*
R
13

=

\u2062

–
(
C
1

+

C
3
)

2
C
1

=

\u2062
–

\u03b1
*
\u2062
\u03b2
\u2062
\u2062
v
\u2062

2
+
\u03b1\u03b2
*

\u2062

2
C
3

=

\u2062
\u03b3\u03b2
*

\u2062
v
\u2062

2
–
\u2062
\u03b3
*

\u2062
\u03b2
\u2062

2
and the second decoder computes parameters
R
2

=

\u2062
\u03b2
*

\u2062

1

2
\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b2
\u2062

1

2
\u2062

r
3
*
+
v
*

\u2062

\u03b3
*

\u2062

r
4
R
4

=

\u2062
\u03b3
*

\u2062

r
1
–

v
\u2062
\u2062
\u03b2
\u2062

1

2
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

1

2
\u2062

r
4
R
24

=

\u2062

–
(
C
2

+

C
4
)

2
C
2

=

\u2062
–

\u03b1\u03b2
*
\u2062

2
+

v
\u2062
\u2062

\u03b1
*

\u2062
\u03b2
\u2062

2
C
4

=

\u2062
–
v

\u2062
\u2062

\u03b3\u03b2
*

\u2062

2
+
\u03b3
*

\u2062
\u03b2
\u2062

2
where \u03b1, \u03b2 and \u03b3 are the channel gains, r1, r2, r3 and r4 are the received signals, and v is a phase value by which the transmitter rotates the phases of the symbols, and R and C are variables,
and the first decoder finds a symbol pair (x1, x3) that minimizes |R1\u2212x1|2+|R3\u2212x3|2+|R13\u2212x1*x3|2, and the second decoder finds a symbol pair (x2, x4) that minimizes |R2\u2212x2|2+|R4\u2212x4|2+|R24\u2212x2*x4|2.
3. A receiver for receiving modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over all possible symbol pairs using signals received by a receive antenna from three transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna,
wherein if the modulation symbols are 16QAM (16-ary Quadrature Amplitude Modulation) or 64QAM (64-ary QAM) symbols, the first decoder computes parameters
R
1

=

\u2062
(
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062

1

2
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
–
v
*

\u2062

\u03b2
*

\u2062

1

2
\u2062

r
4
)
K
3
R
3

=

\u2062
(
v
\u2062
\u2062
\u03b3
\u2062
r

2
*
+
\u03b2
*

\u2062

1

2
\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062

1

2
\u2062

r
3
*
)
K
3
R
13

=

\u2062

–
(
C
1

+

C
3
)
2
\u2062

K
3
K
3

=

\u2062
\uf603
\u03b1
\uf604

2

+
\uf603
\u03b2
\uf604

2

+
\uf603
\u03b3
\uf604

2
C
1

=

\u2062
–

\u03b1
*
\u2062
\u03b2
\u2062
\u2062
v
\u2062

2
+
\u03b1\u03b2
*

\u2062

2
C
3

=

\u2062
\u03b3\u03b2
*

\u2062
v
\u2062

2
–
\u03b3
*

\u2062
\u03b2
\u2062

2
and the second decoder computes parameters
R
2

=

\u2062
(
\u03b2
*

\u2062

1

2
\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b2
\u2062

1

2
\u2062

r
3
*
+
v
*

\u2062

y
*

\u2062

r
4
)
K
3
R
4

=

\u2062
(
\u03b3
*

\u2062

r
1
–

v
\u2062
\u2062
\u03b2
\u2062

1

2
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

1

2
\u2062

r
4
)
K
3
R
24

=

\u2062

–
(
C
2

+

C
4
)
2
\u2062

K
3
C
2

=

\u2062
–

\u03b1\u03b2
*
\u2062

2
+
\u03bd\u03b1
*

\u2062
\u03b2
\u2062

2
C
4

=

\u2062
–

\u03bd\u03b3\u03b2
*
\u2062

2
+
\u03b3
*

\u2062
\u03b2
\u2062

2
where \u03b1, \u03b2 and \u03b3 are the channel gains, r1, r2, r3 and r4 are the received signals, and v is a phase value by which the transmitter rotates the phases of the symbols, and R, K and C are variables,
and the first decoder finds a symbol pair (x1, x3) that minimizes |R1\u2212x1|2+|R3\u2212x3|2+|R13\u2212x1*x3|2\u2212|x1|2|x3|2, and the second decoder finds a symbol pair (x2, x4) that minimizes |R2\u2212x2|2+|R4\u2212x4|2+|R24\u2212x2*x4|2\u2212|x2|2|x4|2.
4. A receiver for receiving modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over all possible symbol pairs using signals received by a receive antenna from four transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna,
wherein if the modulation symbols are BPSK (Binary Phase Shift Keying) symbols, the first decoder computes parameters
R
1

=

\u2062
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062
\u2062

r
2
*
+

\u03b6
\u2062
\u2062

r
3
*
+

j
\u2062
\u2062

\u03b3
*

\u2062

r
4
R
3

=

\u2062
\u03b6
\u2062
\u2062

r
2
*
–

j
\u2062
\u2062

\u03b3
*

\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062
\u2062

r
3
*
R
13

=

\u2062

–

(
C
1

+

C
3
)
C
1

=

\u2062
j
\u2062
\u2062

\u03b1
*

\u2062
\u03b3

+

j
\u2062
\u2062

\u03b1\u03b3
*
C
3

=

\u2062
\u03b6
*

\u2062
\u03b2

–

\u03b6\u03b2
*
and the second decoder computes parameters
R
2

=

\u2062
\u03b2
*

\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

j
\u2062
\u2062
\u03b3
\u2062
\u2062

r
3
*
+
\u03b6
*

\u2062

r
4
R
4

=

\u2062
\u03b6
*

\u2062

r
1
–

j
\u2062
\u2062
\u03b3
\u2062
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

r
4
R
24

=

\u2062

–

(
C
2

+

C
4
)
C
2

=

\u2062
\u03b6\u03b2
*

–
\u03b6
*

\u2062
\u03b2
C
4

=

\u2062
–
j

\u2062
\u2062

\u03b1\u03b3
*
–

j
\u2062
\u2062

\u03b3\u03b1
*
where \u03b1, \u03b2, \u03b3 and \u03be are the channel gains and r1, r2, r3 and r4 are the received signals, and R and C are variables,
and the first decoder finds a symbol pair (x1, x3) that minimizes |R1\u2212x1|2+|R3\u2212x3|2+|R13\u2212x1*x3|2, and the second decoder finds a symbol pair (x2, x4) that minimizes |R2\u2212x2|2+|R4\u2212x4|2+|R24\u2212x2*x4|2.
5. A receiver for receiving modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over all possible symbol pairs using signals received by a receive antenna from four transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna,
wherein if the modulation symbols are QPSK (Quadrature Phase Shift Keying) or 8PSK (8-ary PSK) symbols, the first decoder computes parameters
R
1

=

\u2062
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062
\u2062

r
2
*
+

\u03b6
\u2062
\u2062

r
3
*
–
v
*

\u2062

\u03b3
*

\u2062

r
4
R
3

=

\u2062
v
\u2062
\u2062
\u03b6
\u2062
\u2062

r
2
*
+
\u03b3
*

\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062
\u2062

r
3
*
R
13

=

\u2062

–

(
C
1

+

C
3
)
C
1

=

\u2062
–

\u03b1
*
\u2062
\u03b3
\u2062
\u2062
v

+

\u03b1\u03b3
*
C
3

=

\u2062
\u03b6\u03b2
*

\u2062
v

–
\u03b6
*

\u2062
\u03b2
and the second decoder computes parameters
R
2

=
\u03b2
*

\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
+
\u03bd
*

\u2062

\u03b6
*

\u2062

r
4
R
4

=
\u03b6
*

r
1
–

\u03bd\u03b3
\u2062
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

r
4
R
24

=

–

(
C

2
\u2062
+

C
4
)
C
2

=
–

\u03b1\u03b3
*
+
\u03bd\u03b1
*

\u2062
\u03b3
C
4

=
–

\u03bd\u03b6\u03b2
*
+
\u03b6
*

\u2062
\u03b2
where \u03b1, \u03b2, \u03b3 and \u03be are the channel gains, r1, r2, r3 and r4 are the received signals, and v is a phase value by which the transmitter rotates the phases of the symbols, and R and C are variables,
and the first decoder finds a symbol pair (x1, x3) that minimizes |R1\u2212x1|2+|R3\u2212x3|2+|R13\u2212x1*x3|2, and the second decoder finds a symbol pair (x2, x4 that minimizes |R2\u2212x2|2+|R4\u2212x4|2+|R24\u2212x2*x4|2.
6. A receiver for receiving modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over all possible symbol pairs using signals received by a receive antenna from four transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna,
wherein if the modulation symbols are 16QAM (16-ary Quadrature Amplitude Modulation) or 64QAM (64-ary QAM) symbols, the first decoder computes parameters
R
1

=
(
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062
\u2062

r
2
*
+

\u03b6
\u2062
\u2062

r
3
*
–
\u03bd
*

\u2062

\u03b3
*

\u2062

r
4
)
K
4
R
3

=
(
\u03bd\u03b6
\u2062
\u2062

r
2
*
+
\u03b3
*

\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062
\u2062

r
3
*
)
K
4
R
13

=

–
(
C
1

+

C
3
)
K
4
K
4

=

\u2758

\u03b1
\u2062

\u2758
2

\u2062

+

\u2758

\u03b2
\u2062

\u2758
2

\u2062

+

\u2758

\u03b3
\u2062

\u2758
2
C
1

=
–

\u03b1
*
\u2062
\u03b3\u03bd

+

\u03b1\u03b3
*
C
3

=
\u03b6\u03b2
*

\u2062
\u03bd

–
\u03b6
*

\u2062
\u03b2
and the second decoder computes parameters
R
2

=
(
\u03b2
*

\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
+
\u03bd
*

\u2062

\u03b6
*

\u2062

r
4
)
K
4
R
4

=
(
\u03b6
*

\u2062

r
1
–

\u03bd\u03b3
\u2062
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

r
4
)
K
4
R
24

=

–
(
C
2

+

C
4
)
K
4
C
2

=
–

\u03b1\u03b3
*
+
\u03bd\u03b1
*

\u2062
\u03b3
C
4

=
–

\u03bd\u03b6\u03b2
*
+
\u03b6
*

\u2062
\u03b2
where \u03b1, \u03b2, \u03b3 and \u03be are the channel gains, r1, r2, r3 and r4 are the received signals, and v is a phase value by which the transmitter rotates the phases of the symbols, and R, K and C are variables,
and the first decoder finds a symbol pair (x1, x3) that minimizes |R1\u2212x1|2+|R3\u2212x3|2+|R13\u2212x1*x3|2\u2212|x1|2|x3|2, and the second decoder finds a symbol pair (x2, x4) that minimizes |R2\u2212x2|2+|R4\u2212x4|2+|R24\u2212x2*x4|2\u2212x2|2|x4|2.
7. A receiver for receiving PSK (Phase Shift Keying) modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for selecting candidate symbol pairs among all possible symbol pairs using signals received by a receive antenna from three transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna, and detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over the candidate symbol pairs,
wherein the first decoder computes parameters
R
1

=
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062

1

2
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
–
\u03bd
*

\u2062

\u03b2
*

\u2062

1

2
\u2062

r
4
R
3

=
\u03bd\u03b3
\u2062
\u2062

r
2
*
+
\u03b2
*

\u2062

1

2
\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062

1

2
\u2062

r
3
*
R
13

=

–
(
C
1

+

C
3
)

2
C
1

=
–

\u03b1
*
\u2062
\u03b2\u03bd
\u2062

2
+
\u03b1\u03b2
*

\u2062

2
C
3

=
\u03b3\u03b2
*

\u2062
\u03bd
\u2062

2
–
\u03b3
*

\u2062
\u03b2
\u2062

2
and the second decoder computes parameters
R
2

=
\u03b2
*

\u2062

1

2
\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b2
\u2062

1

2
\u2062

r
3
*
+
\u03bd
*

\u2062

\u03b3
*

\u2062

r
4
R
4

=
\u03b3
*

\u2062

r
1
–

\u03bd\u03b2
\u2062

1

2
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

1

2
\u2062

r
4
R
24

=

–
(
C
2

+

C
4
)

2
C
2

=
–

\u03b1\u03b2
*
\u2062

2
+
\u03bd\u03b1
*

\u2062
\u03b2
\u2062

2
C
4

=
\u03bd\u03b3\u03b2
*

\u2062

2
+
\u03b3
*

\u2062
\u03b2
\u2062

2
where \u03b1, \u03b2 and \u03b3 are the channel gains and r1, r2, r3 and r4 are the received signals, and R and C are variables, and the first decoder finds all possible symbol pairs (x1, x3) as the candidate symbol pairs, symbol x3 being a constellation point closest to R3+x1R13, and the second decoder finds all possible symbol pairs (x2, x4) as the candidate symbol pairs, symbol x4 being a constellation point closest to R4x2R24.
8. A receiver for receiving QAM (Quadrature Amplitude Modulation) modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for selecting candidate symbol pairs among all possible symbol pairs using signals received by a receive antenna from three transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna, and detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over the candidate symbol pairs,
wherein the first decoder computes parameters
R
1

=
(
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062

1

2
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
–
\u03bd
*

\u2062

\u03b2
*

\u2062

1

2
\u2062

r
4
)
K
3
R
3

=
(
\u03bd\u03b3
\u2062
\u2062

r
2
*
+
\u03b2
*

\u2062

1

2
\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062

1

2
\u2062

r
3
*
)
K
3
R
13

=

–
(
C
1

+

C
3
)
2
\u2062

K
3
K
3

=

\u2758

\u03b1
\u2062

\u2758
2

\u2062

+

\u2758

\u03b2
\u2062

\u2758
2

\u2062

+

\u2758

\u03b3
\u2062

\u2758
2
C
1

=
–

\u03b1
*
\u2062
\u03b2\u03bd
\u2062

2
+
\u03b1\u03b2
*

\u2062

2
C
3

=
\u03b3\u03b2
*

\u2062
\u03bd
\u2062

2
–
\u03b3
*

\u2062
\u03b2
\u2062

2
and the second decoder computes parameters
R
2

=
(
\u03b2
*

\u2062

1

2
\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b2
\u2062

1

2
\u2062

r
3
*
+
\u03bd
*

\u2062

\u03b3
*

\u2062

r
4
)
K
3
R
4

=
(
\u03b3
*

\u2062

r
1
–

\u03bd\u03b2
\u2062

1

2
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

1

2
\u2062

r
4
)
K
3
R
24

=

–
(
C
2

+

C
4
)
2
\u2062

K
3
C
2

=
–

\u03b1\u03b2
*
\u2062

2
+
\u03bd\u03b1
*

\u2062
\u03b2
\u2062

2
C
4

=
–

\u03bd\u03b3\u03b2
*
\u2062

2
+
\u03b3
*

\u2062
\u03b2
\u2062

2
where \u03b1, \u03b2, \u03b3 and \u03be are the channel gains, r1, r2, r3 and r4 are the received signals, and v is a phase value by which the transmitter rotates the phases of the symbols, and R, K and C are variables,
and the first and second decoders find all possible symbol pairs (x1, x3) and (x2, x4) as the candidate symbol pairs, symbols x3 and x4 being the constellation points closest to R3+x1R13 and R4+x2R24, respectively.
9. A receiver for receiving PSK (Phase Shift Keying) modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for selecting candidate symbol pairs among all possible symbol pairs using signals received by a receive antenna from four transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna, and detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over the candidate symbol pairs,
wherein the first decoder computes parameters
R
1

=
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062
\u2062

r
2
*
+

\u03b6
\u2062
\u2062

r
3
*
–
\u03bd
*

\u2062

\u03b3
*

\u2062

r
4
R
3

=
\u03bd\u03b6
\u2062
\u2062

r
2
*
+
\u03b3
*

\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062
\u2062

r
3
*
R
13

=

–

(
C
1

+

C
3
)
C
1

=
–

\u03b1
*
\u2062
\u03b3\u03bd

+

\u03b1\u03b3
*
C
3

=
\u03b6\u03b2
*

\u2062
\u03bd

–
\u03b6
*

\u2062
\u03b2
and the second decoder computes parameters
R
2

=
\u03b2
*

\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
+
\u03bd
*

\u2062

\u03b6
*

\u2062

r
4
R
4

=
\u03b6
*

\u2062

r
1
–

\u03bd\u03b3
\u2062
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

r
4
R
24

=

–

(
C
2

+

C
4
)
C
2

=
–

\u03b1\u03b3
*
+
\u03bd\u03b1
*

\u2062
\u03b3
C
4

=
–

\u03bd\u03b6\u03b2
*
+
\u03b6
*

\u2062
\u03b2
where \u03b1, \u03b2, \u03b3 and \u03be are the channel gains, r1, r2, r3 and r4 are the received signals, and v is a phase value by which the transmitter rotates the phases of the symbols, and R and C are variables,
and the first decoder finds all possible symbol pairs (x1, x3) as the candidate symbol pairs, symbol x3 being a constellation point closest to R3+x1R13, and the second decoder finds all possible symbol pairs (x2, x4) as the candidate symbol pairs, symbol x4 being a constellation point closest to R4+x2R24.
10. A receiver for receiving QAM (Quadrature Amplitude Modulation) modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for selecting candidate symbol pairs among all possible symbol pairs using signals received by a receive antenna from four transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna, and detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over the candidate symbol pairs,
wherein the first decoder computes parameters
R
1

=
(
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062
\u2062

r
2
*
+

\u03b6
\u2062
\u2062

r
3
*
–
\u03bd
*

\u2062

\u03b3
*

\u2062

r
4
)
K
4
R
3

=
(
\u03bd\u03b6
\u2062
\u2062

r
2
*
+
\u03b3
*

\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062
\u2062

r
3
*
)
K
4
R
13

=

–
(
C
1

+

C
3
)
K
4
K
4

=

\u2758

\u03b1
\u2062

\u2758
2

\u2062

+

\u2758

\u03b2
\u2062

\u2758
2

\u2062

+

\u2758

\u03b3
\u2062

\u2758
2
C
1

=
–

\u03b1
*
\u2062
\u03b3\u03bd

+

\u03b1\u03b3
*
C
3

=
\u03b6\u03b2
*

\u2062
\u03bd

–
\u03b6
*

\u2062
\u03b2
and the second decoder computes parameters
R
2

=
(
\u03b2
*

\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
+
\u03bd
*

\u2062

\u03b6
*

\u2062

r
4
)
K
4
R
4

=
(
\u03b6
*

\u2062

r
1
–

\u03bd\u03b3
\u2062
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

r
4
)
K
4
R
24

=

–
(
C
2

+

C
4
)
K
4
C
2

=
–

\u03b1\u03b3
*
+
\u03bd\u03b1
*

\u2062
\u03b3
C
4

=
–

\u03bd\u03b6\u03b2
*
+
\u03b6
*

\u2062
\u03b2
where \u03b1, \u03b2, \u03b3 and \u03be are the channel gains, r1, r2, r3 and r4 are the received signals, and v is a phase value by which the transmitter rotates the phases of the symbols, and R, K and C are variables,
and the first decoder finds all possible symbol pairs (x1, x3) as the candidate symbol pairs, symbol x3 being a constellation point closest to R3+x1R13, and the second decoder finds all possible symbol pairs (x2, x4) as the candidate symbol pair, symbol x4 being a constellation point closest to R4+x2R24.
11. A receiver for receiving PSK (Phase Shift Keying) modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for selecting candidate symbol pairs among all possible symbol pairs using signals received by a receive antenna from three transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna, and detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over the candidate symbol pairs,
wherein the first decoder computes
R
1

=
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062

1

2
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
–
\u03bd
*

\u2062

\u03b2
*

\u2062

1

2
\u2062

r
4
R
3

=
\u03bd\u03b3
\u2062
\u2062

r
2
*
+
\u03b2
*

\u2062

1

2
\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062

1

2
\u2062

r
3
*
R
13

=

–
(
C
1

+

C
3
)

2
C

1
\u2062
=
–

\u03b1
*
\u2062
\u03b2\u03bd
\u2062

2
+
\u03b1\u03b2
*

\u2062

2
C
3

=
\u03b3\u03b2
*

\u2062
\u03bd
\u2062

2
–
\u03b3
*

\u2062
\u03b2
\u2062

2
where \u03b1, \u03b2 and \u03b3 are the channel gains, r1, r2, r3 and r4 are the received signals, and v is a predetermined phase value by which the transmitter rotates the phases of the symbols, and R and C are variables,
outputs a symbol pair (x1, x3) if x1*x3=x13, x1 being the closest symbol to R13, x3 being the closest symbol to R3, and x13 being the closest symbol to R13, and if x1*x3\u2260x13, computes an angle \u03a6d by dividing the angle between x13 and x1*x3 by 2 and selects symbols whose angles are within \u03a6d from x1 and x3, respectively, as the candidate symbols,
and the second decoder computes
R
2

=
\u03b2
*

\u2062

1

2
\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b2
\u2062

1

2
\u2062

r
3
*
+
\u03bd
*

\u2062

\u03b3
*

\u2062

r
4
R
4

=
\u03b3
*

\u2062

r
1
–

\u03bd\u03b2
\u2062

1

2
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–

\u03b2
\u2062

1

2
\u2062

r
4
R
24

=

–
(
C
2

+

C
4
)

2
C
2

=
–

\u03b1\u03b2
*
\u2062

2
+
\u03bd\u03b1
*

\u2062
\u03b2
\u2062

2
C
4

=
–

\u03bd\u03b3\u03b2
*
\u2062

2
+
\u03b3
*

\u2062
\u03b2
\u2062

2
where \u03b1, \u03b2 and \u03b3 are the channel gains, r1, r2, r3 and r4 are the received signals, and v is the predetermined phase value by which the transmitter rotates the phases of the symbols, and R and C are variables,
outputs a symbol pair (x2, x4) if x2*x4=x24, x2 being the closest symbol to R2, x4 being the closest symbol to R4, and x24 being the closest symbol to R24, and if x2*x4\u2260x13, computes an angle \u03a6d\u2032 by dividing the angle between x24 and x2*x4 by 2 and selects symbols whose angles are within \u03a6d\u2032 from x2 and x4, respectively, as the candidate symbols.
12. A receiver for receiving PSK (Phase Shift Keying) modulation symbols whose phases are rotated once from a transmitter in a wireless communication system, comprising:
first and second decoders for selecting candidate symbol pairs among all possible symbol pairs using signals received by a receive antenna from four transmit antennas for four time periods and channel gains from the transmit antennas to the receive antenna, and detecting symbol pairs that minimize maximum likelihood (ML) decoding metrics over the candidate symbol pairs,
wherein the first decoder computes
R
1

=
\u03b1
*

\u2062

r
1
+

\u03b2
\u2062
\u2062

r
2
*
+

\u03b6
\u2062
\u2062

r
3
*
–
\u03bd
*

\u2062

\u03b3
*

\u2062

r
4
R
3

=
\u03bd\u03b6
\u2062
\u2062

r
2
*
+
\u03b3
*

\u2062

r
1
+
\u03b1
*

\u2062

r
4
–

\u03b2
\u2062
\u2062

r
3
*
R
13

=

–

(
C
1

+

C
3
)
C
1

=
\u03b1
*

\u2062
\u03b3\u03bd

+

\u03b1\u03b3
*
C
3

=
\u03b6\u03b2
*

\u2062
\u03bd

–
\u03b6
*

\u2062
\u03b2
where \u03b1, \u03b2, \u03b3 and \u03be are the channel gains, r1, r2, r3 and r4 are the received signals, and v is a predetermined phase value by which the transmitter rotates the phases of the symbols, and R and C are variables,
outputs a symbol pair (x1, x3) if x1*x3=x13, x1 being the closest symbol to R1, x3 being the closest symbol to R3, and x13 being the closest symbol to R13, and if x1*x3\u2260x13, computes an angle \u03a6d by dividing the angle between x13 and x1*x3 by 2 and selects symbols whose angles are within \u03a6d from x1 and x3, respectively, as the candidate symbols,
and the second decoder computes
R
2

=
\u03b2
*

\u2062

r
1
–

\u03b1
\u2062
\u2062

r
2
*
+

\u03b3
\u2062
\u2062

r
3
*
+
\u03bd
*

\u2062

\u03b6
*

\u2062

r
4
R
4

=
\u03b6
*

\u2062

r
1
–

\u03bd\u03b3
\u2062
\u2062

r
2
*
–

\u03b1
\u2062
\u2062

r
3
*
–
\u03b2
*

\u2062

r
4
R
24

=

–

(
C
2

+

C
4
)
C
2

=
–

\u03b1\u03b3
*
+
\u03bd\u03b1
*

\u2062
\u03b3
C
4

=
–

\u03bd\u03b6\u03b2
*
+
\u03b6
*

\u2062
\u03b2
where \u03b1, \u03b2, \u03b3 and \u03be are the channel gains, r1, r2, r3 and r4 are the received signals, and v is the predetermined phase value by which the transmitter rotates the phases of the symbols, and R and C are variables,
outputs a symbol pair (x2, x4) if x2*x4=x24, x2 being the closest symbol to R2, x4 being the closest symbol to R4, and x24 being the closest symbol to R24, and if x2*x4\u2260x13, computes an angle \u03a6d\u2032 by dividing the angle between x24 and x2*x4 by 2 and selects symbols whose angles are within \u03a6d\u2032 from x2 and x4, respectively as the candidate symbols.