Low complexity soft detection in multiple transmit and receive antenna systems with M-QAM modulations
This invention discloses a method for performing soft detection of transmitted signals modulated by M-QAM when a transmitter equipped with one or more transmit antennas, and the receiver has one or more receive antennas. This invention is built based on the fact that soft value of a single transmitted bit (or symbol) has a piece-wise linear behavior as a function of the received signal(s). The methodology to obtain such piece-wise linear functions are given for some M-QAM modulations in single transmit and single receive antenna systems and arbitrary constellation mapping. Also, the methodology is explained for the case where the number of transmit antennas is more than one by an example for 4-QAM modulation and two transmit antennas. A further required process to expand above embodiments to multiple receive antennas are also given.
1 . A method for performing soft detection of transmitted signals modulated by M-QAM, the method comprising:
calculating a first and a second probability, respectively, that a selected bit of transmitted symbol of the transmitted signal is equal to 0 and 1 according to
λ
k
,
i
(
r
,
b
)
=
log
∑
s
∈
S
b
k
,
i
Pr
(
r
|
s
,
h
)
≡
log
∑
s
∈
S
b
k
,
i
exp
(
-
r
-
<
h
,
s
>
2
2
σ
2
)
,
wherein r is a received signal, h is a channel gain, b is 0 or 1, S b k,i represents a subset of an expanded modulation whose symbols have the i th bit of the k th signal equal to bε{0, 1}, and σ 2 is a normal noise variance;
estimating a first and second sub-optimum probabilities, respectively, based on the first and second probabilities according to
log
∑
j
x
j
≈
max
j
log
x
j
;
and
obtaining one or more soft detection values based on a difference between the first and second sub-optimum probabilities.
2 . The method of claim 1 further comprising:
transmitting the signals by a first predetermined number of transmit antennas;
receiving the transmitted signals by a second predetermined number of receive antennas;
calculating the soft detection value for signals received by each receive antenna; and
summing all the soft detection values calculated from each receive antenna to obtain a true soft detection value.
3 . The method of claim 2 , wherein the first predetermined number is one.
4 . The method of claim 2 further comprising obtaining the transmitted signals by combining all the received signals by a single receive antenna according to
r
=
∑
k
=
1
T
h
k
S
k
+
n
,
where h k is the channel gain of the k th transmit antenna, and n is the k=1 white normal noise, when the first predetermined number of transmit antenna is greater than one.
5 . The method of claim 2 , wherein the second predetermined number is one.
6 . The method of claim 2 , wherein the second predetermined number is greater than one.
7 . A method for performing soft detection of transmitted signals modulated by M-QAM, the method comprising:
transmitting the signals by a first predetermined number of transmit antennas;
receiving the transmitted signals by a second predetermined number of receive antennas;
calculating a first and second probabilities, respectively, that a selected bit of transmitted symbol of the transmitted signal is equal to 0 and 1 according to
λ
k
,
i
(
r
,
b
)
=
log
∑
Pr
(
r
❘
s
,
h
)
≡
log
∑
s
∈
S
b
k
,
i
exp
(
-
r
-
<
h
,
s
>
2
2
σ
2
)
,
wherein r is a received signal, h is a channel gain, b is 0 or 1, S b k,i represents a subset of an expanded modulation whose symbols have the i th bit of the k th signal equal to bε{0,1}, and σ 2 is a normal noise variance;
estimating a first and second sub-optimum probabilities, respectively, based on the first and second probabilities according to
log
∑
j
x
j
≈
max
j
log
x
j
;
obtaining one or more soft detection values based on a difference between the first and second sub-optimum probabilities for each receive antenna independently; and
summing all the soft detection values calculated from each receive antenna to obtain a true soft detection value.
8 . The method of claim 7 , wherein the first predetermined number is one.
9 . The method of claim 7 further comprising obtaining the transmitted signals by combining all the received signals by a single receive antenna according to
r
=
∑
k
=
1
T
h
k
S
k
+
n
,
where h k is the channel gain of the k th transmit antenna, and n is the white normal noise, when the first predetermined number of transmit antenna is greater than one.
10 . The method of claim 7 , wherein the second predetermined number is one.
11 . The method of claim 7 , wherein the second predetermined number is greater than one.
12 . A method for performing soft detection of transmitted signals modulated by M-QAM, the method comprising:
transmitting the signals by a plurality of transmit antennas;
receiving the transmitted signals by a single receive antennas;
combining all the received transmitted signals according to
r
=
∑
k
=
1
T
h
k
S
k
+
n
,
where h k is a channel gain of the k th transmit antenna, and n is a white normal noise;
calculating a first and second probabilities, respectively, that a selected bit of transmitted symbol of the transmitted signal is equal to 0 and 1 according to
λ
k
,
i
(
r
,
b
)
=
log
∑
s
∈
S
b
k
,
i
Pr
(
r
❘
s
,
h
)
≡
log
∑
s
∈
S
b
k
,
i
exp
(
-
r
-
<
h
,
s
>
2
2
σ
2
)
,
wherein r is a received signal, h is a channel gain, b is 0 or 1, S b k,i represents a subset of an expanded modulation whose symbols have the i th bit of the k th signal equal to bε{0,1}, and σ 2 is a normal noise variance;
estimating a first and second sub-optimum probabilities, respectively, based on the first and second probabilities according to
log
∑
j
x
j
≈
max
j
log
x
j
;
and
obtaining one or more soft detection values based on a difference between the first and second sub-optimum probabilities.