Gain and phase imbalance compensation for OFDM systems
View Patent ↗The present invention includes methods and devices to compensate for gain and phase imbalance for OFDM and other multi-carrier symbol transmission systems. More particularly, methods and devices for determining compensation parameters are provided. This invention may be applied to a variety of standards utilizing OFDM technology, including IEEE 802.11a, Hiperlan/2 and MMAC. Further description of the invention and its embodiments are found in the figures, specification and claims that follow.
1. A method of compensating for transmitter imbalance in a multi-carrier, ODFM symbol transmission system, including:
estimating transmitter gain and phase imbalance by measuring signals on a plurality of carriers of the multi-carrier system, wherein estimating includes
deducing constellation points transmitted from a received signal; and
calculating one or more differences between the received signal and an intended signal corresponding to the deduced constellation points; and
determining compensation parameters from the imbalance;
loading the compensation parameters into the transmitter, whereby the compensation parameters can be used to compensate for transmitter gain and phase imbalance.
2. The method of claim 1 , wherein the estimating step is a frequency domain estimation.
3. The method of claim 1 , wherein the estimating step is a frequency domain estimation performed after processing a received signal through an equalizer.
4. The method of claim 3 , wherein a plurality but fewer than all of the carriers of the multicarrier system are utilized in the estimating step.
5. The method of claim 1 , wherein the estimating step is a frequency domain estimation such that:
a
^
k
=
{
1
2
∑
p
=
0
N
p
-
1
G
p
exp
(
-
j
2
π
f
s
t
p
k
/
N
)
{
cos
(
θ
)
[
(
α
+
β
)
a
k
+
(
α
-
β
)
a
N
-
k
*
]
+
sin
(
θ
)
[
(
α
0
+
β
0
)
a
k
+
(
α
0
-
β
0
)
a
N
-
k
*
]
}
0
≤
k
<
N
/
2
1
2
∑
p
=
0
N
p
-
1
G
p
exp
(
-
j
2
π
f
s
t
p
(
k
-
N
)
/
N
)
{
cos
(
θ
)
[
(
α
+
β
)
a
k
+
(
α
-
β
)
a
N
-
k
*
]
+
sin
(
θ
)
[
(
α
0
+
β
0
)
a
k
+
(
α
0
-
β
0
)
a
N
-
k
*
]
}
N
/
2
≤
k
<
N
,
where
â k is a received value of a constellation point, k being the carrier index among the plurality of carriers;
a k is a transmitted value of the constellation point for a kth carrier;
a * N−k is a complex conjugate of the transmitted value of the constellation point for an N−k th carrier, where N is a total number of carriers;
f s is a sampling rate of an analog to digital converter in a receiver used to process the received value;
t p is a delay measure for the pth carrier, p being an additional carrier index among the plurality of carriers;
α, α 0 , β and β 0 are intermediary values treated as time-invariant:
α=1− jG rx m sin(θ rx m ) β=G tx m G rx m cos(θ tx m −θ rx m )+ jG tx m sin (θ tx m )
α 0 =−jG rx m cos(θ rx m ) β 0 =G tx m G rx m sin(θ tx m −θ rx m )− jG tx m cos(θ tx m )
G rx m is gain imbalance of a receiver's mixer;
G tx m is gain imbalance of the transmitter's mixer;
θ rx m is phase imbalance of the receiver's mixer; and
θ tx m is gain imbalance of the transmitter's mixer.
6. The method of claim 1 , wherein the estimating step is a frequency domain estimation performed after processing a received signal through an equalizer, such that:
G
m
tx
=
β
^
=
(
Re
[
β
^
]
)
2
+
(
Im
[
β
^
]
)
2
and
θ tx m =<{circumflex over (β)}=tan −1 ( Im[{circumflex over (β)}]/Re [{circumflex over (β)}]),
where
β
^
=
-
a
k
+
a
N
-
k
*
-
a
^
k
,
eq
(
TX
)
(
1
+
ρ
k
)
a
k
-
a
N
-
k
*
-
a
^
k
,
eq
(
TX
)
(
1
-
ρ
k
)
and
G tx m is gain imbalance of the transmitter's mixer;
θ tx m is gain imbalance of the transmitter's mixer;
{circumflex over (β)} is an estimated value;
â (TX) k,eq is a received value of a constellation point, including TX transmitter imbalance, after the processing the received signal through the equalizer, k being the carrier index among the multiple carrier channels;
a k is a transmitted value of the constellation point for a k th carrier;
a * N−k is the complex conjugate of the transmitted value of the constellation point for an N−k th carrier, where N is a total number of carriers;
ρ k is a ratio
ρ k =a * N−k /a k
of transmitted symbols used for equalizer training.
7. The method of claim 1 further including communicating from a receiver to the transmitter the receiver's estimates of the transmitter imbalance.
8. The method of claim 1 , wherein the estimating step includes measuring the imbalances prior to delivery of the system to a customer, by analyzing a received signal corresponding to one or more predetermined training packets transmitted according to standard packet conventions.
9. The method of claim 8 , wherein the predetermined training packets include a second symbol that is a sign inverted equivalent of a first symbol.
10. The method of claim 1 , wherein the estimating step further includes:
transmitting one or more predetermined training packets according to standard packet conventions through a substantially noise-free communication channel; and
performing a time-domain analysis of received packets without processing the received packets through an equalizer.
11. The method of claim 10 , wherein the predetermined training packets include a second symbol that is a sign inverted equivalent of a first symbol.
12. The method of claim 1 , wherein the transmitter is adapted to perform time domain compensation for the imbalances, such that:
y I ( n ) =x I ( n )+ x Q ( n )tan(θ tx m )
and y Q ( n )= x Q ( n )[ G tx m cos(θ tx m )] −1
where
x I (n) is an in-phase component of a signal being compensated;
x Q (n) is a quadrature component of the signal being compensated;
y I (n) is an in-phase component of the signal after being compensated;
y Q (n) is a quadrature component of the signal after being compensated;
G tx m is an estimate of the gain imbalance; and
θ tx m is an estimate of the phase imbalance.
13. The method of claim 12 , wherein the compensation parameters are determined iteratively, from a starting estimate, such that:
G tx m ( i+ 1)= G tx m ( f ) Ĝ tx m
and
θ tx m ( i+ 1)=θ tx m ( i )+{circumflex over (θ)} tx m ,
where Ĝ tx m (f) and {circumflex over (θ)} tx m (i) are i-th estimates of residual gain and phase imbalance.
14. The method of claim 1 , wherein the transmitter is adapted to perform frequency domain compensation for the imbalances, such that:
a
^
k
TX
only
=
1
+
β
Δ
2
a
k
+
1
-
β
Δ
2
a
N
-
k
*
where
â k | TX only is a received value of a constellation point, including TX transmitter imbalance, after the processing the received signal through the equalizer, k being the carrier index among the multiple carrier channels;
a k is a transmitted value of the constellation point for a k th carrier;
a * N−k is the complex conjugate of the transmitted value of the constellation point for an N−k th carrier, where N is a total number of carriers; and
β Δ is a residual offset that is compensated for by either concatenating a second compensator to the original or by updating the original coefficients to include the residual offset.
15. The method of claim 14 , wherein the compensation parameters are determined iteratively, from a starting estimate, such that:
C
1
(
i
+
1
)
=
C
1
(
i
)
1
+
β
^
*
(
i
)
β
^
(
i
)
+
β
^
*
(
i
)
-
C
2
*
(
i
)
1
-
β
^
(
i
)
β
^
(
i
)
+
β
^
*
(
i
)
C
2
(
i
+
1
)
=
C
2
(
i
)
1
+
β
^
*
(
i
)
β
^
(
i
)
+
β
^
*
(
i
)
-
C
1
*
(
i
)
1
-
β
^
(
i
)
β
^
(
i
)
+
β
^
*
(
i
)
where
C 1 (0)=1 , C 2 (0)=0
and {circumflex over (β)}(i) is an i-th estimate of residual TX imbalance.
16. A method of compensating for transmitter imbalances in a multi-carrier, OFDM symbol transmission system, including:
estimating transmitter gain and phase imbalance by measuring signals on a plurality of carriers of the multi-carrier system, wherein estimating includes analyzing a received signal corresponding to one or more predetermined training packets transmitted according to standard packet conventions; and
compensating in the transmitter for the transmitter imbalance responsive to the estimated transmitted gain and phase imbalance.
17. A method of compensating for receiver imbalance in a multi-carrier, OFDM symbol transmission system, including:
estimating receiver gain and phase imbalance by measuring signals on a plurality of carriers of the multi-carrier system, utilizing a transmitter having known imbalance characteristics, wherein estimating includes measuring the imbalances prior to delivery of the system to a customer, by analyzing a received signal corresponding to one or more predetermined training packets transmitted according to standard packet conventions;
determining compensation parameters from the receiver imbalances; and
loading the compensating parameters in the receiver to be used to compensate for receiver gain and phase imbalance.
18. The method of claim 17 , wherein the estimating step is a frequency domain estimation.
19. The method of claim 17 , wherein the estimating step is a frequency domain estimation performed after processing a received signal through an equalizer.
20. The method of claim 19 , wherein a plurality but fewer than all of the multiple carrier channels are utilized in the estimating step.
21. The method of claim 17 , wherein the estimating step is a frequency domain estimation, such that:
a
^
k
=
{
1
2
∑
p
=
0
N
p
-
1
G
p
exp
(
-
j
2
π
f
s
t
p
k
/
N
)
{
cos
(
θ
)
[
(
α
+
β
)
a
k
+
(
α
-
β
)
a
N
-
k
*
]
+
sin
(
θ
)
[
(
α
0
+
β
0
)
a
k
+
(
α
0
-
β
0
)
a
N
-
k
*
]
}
0
≤
k
<
N
/
2
1
2
∑
p
=
0
N
p
-
1
G
p
exp
(
-
j
2
π
f
s
t
p
(
k
-
N
)
/
N
)
{
cos
(
θ
)
[
(
α
+
β
)
a
k
+
(
α
-
β
)
a
N
-
k
*
]
+
sin
(
θ
)
[
(
α
0
+
β
0
)
a
k
+
(
α
0
-
β
0
)
a
N
-
k
*
]
}
N
/
2
≤
k
<
N
,
where
â k is a received value of a constellation point, k being the carrier index among the plurality of carriers;
a k is a transmitted value of the constellation point for a kth carrier;
a * N−k is a complex conjugate of the transmitted value of the constellation point for an N−k th carrier, where N is a total number of carriers;
f t is a sampling rate of an analog to digital converter in a receiver used to process the received value;
t p is a delay measure for the pth carrier, p being an additional carrier index among the plurality of carriers;
α, α 0 , β and β 0 are intermediary values treated as time-invariant:
α=1− jG rx m sin(θ rx m ) β= G tx m G rx m cos(θ tx m −θ rx m ) +jG tx m sin (θ tx m )
α 0 =−jG rx m cos(θ rx m ) β 0 =G tx m G rx m sin(θ tx m −θ rx m ) −jG tx m cos(θ tx m )
G rx m is gain imbalance of a receiver's mixer;
G tx m is gain imbalance of the transmitter's mixer;
θ rx m is phase imbalance of the receiver's mixer; and
θ tx m is gain imbalance of the transmitter's mixer.
22. The method of claim 17 , wherein the estimating step is a frequency domain estimation performed after processing a received signal through an equalizer, such that:
a metric ε k ε * N−k | RX only is substantially minimized,
ɛ
k
ɛ
N
-
k
*
RX
only
=
1
-
2
G
m
rx
cos
θ
m
rx
+
G
m
rx
G
m
rx
1
+
2
G
m
rx
cos
θ
m
rx
+
G
m
rx
G
m
rx
and
ɛ
k
(
RX
)
=
a
^
k
,
eq
(
RX
)
-
a
k
a
N
-
k
*
-
a
^
k
,
eq
(
RX
)
ρ
k
,
where
â k is a received value of a constellation point, k being the carrier index among the plurality of carriers;
a k is a transmitted value of the constellation point for a kth carrier;
a * N−k is a complex conjugate of the transmitted value of the constellation point for an N−k th carrier, where N is a total number of carriers;
G rx m is gain imbalance of a receiver's mixer;
θ rx m is phase imbalance of the receiver's mixer; and
ρ k is a ratio ρ k =a * N−k /a k of transmitted symbols used for equalizer training.
23. The method of claim 17 , wherein the estimating step further includes:
deducing constellation points transmitted from a received signal; and
calculating one or more differences between the received signal and an intended signal corresponding to the deduced constellation points.
24. The method of claim 17 , wherein at the predetermined training packets includes a second symbol that is a sign inverted equivalent of a first symbol.
25. The method of claim 17 , wherein the estimating step further includes:
transmitting one or more predetermined packets according to standard packet conventions through a substantially noise-free communications channel; and
performing a time domain analysis of received packets without processing the received packets through an equalizer.
26. The method of claim 25 , wherein at the predetermined training packets includes a second symbol that is a sign inverted equivalent of a first symbol.
27. The method of claim 17 , wherein the receiver is adapted to compensate for the imbalances, such that
{circumflex over (x)} I ( n )= C II ŷ I ( n )+ C IQ ŷ Q ( n )
and
{circumflex over (x)} Q ( n )= C QI ŷ I ( n )+ C QQ ŷ Q ( n )
where the compensator coefficients are
C II =1, C IQ =0
C
QI
=
G
m
rx
sin
θ
m
rx
G
m
rx
cos
θ
m
rx
=
tan
θ
m
rx
,
C
=
1
G
m
rx
cos
θ
m
rx
,
where
x I (n) is an in-phase component of a signal being compensated;
x Q (n) is a quadrature component of the signal being compensated;
y I (n) is an in-phase component of the signal after being compensated;
y Q (n) is a quadrature component of the signal after being compensated;
â k is a received value of a constellation point, k being the carrier index among the plurality of carriers;
a k is a transmitted value of the constellation point for a kth carrier;
a * N−k is a complex conjugate of the transmitted value of the constellation point for an N−k th carrier, where N is a total number of carriers;
G rx m is an estimate of gain imbalance; and
θ rx m is an estimate of phase imbalance.
28. The method of claim 27 , wherein the compensation parameters are determined iteratively, from a starting estimate, such that:
C II (i+1) =C II ( i )=1, C IQ ( i +1) =C IQ ( f )=0
C
QI
(
i
+
1
)
=
-
C
QI
(
i
)
+
Im
[
α
^
(
i
)
]
Im
[
α
^
ij
(
i
)
]
,
C
(
i
+
1
)
=
-
C
(
i
)
Im
[
α
^
0
(
i
)
]
where C II (0)=1, C IQ (0)=0, C QI (0=0, C QQ (0)=1 and {circumflex over (α)}(f) and {circumflex over (α)} 0 (f) are the i-th estimates of the residual imbalance.
29. The method of claim 27 , wherein the compensation parameters are determined iteratively, from a starting estimate, such that
G tx m ( i+ 1)= G tx m ( i ) Ĝ tx m
and
θ tx m ( i+ 1)=θ tx m ( f )+{circumflex over (θ)} tx m ,
where Ĝ tx m (f) and {circumflex over (θ)} tx m (f) are i-th estimates of residual gain and phase imbalance.
30. A method of compensating for transmitter and receiver imbalance in a multi-carrier, OFDM symbol transmission system, including:
estimating combined transmitter and receiver gain and phase imbalance across multiple carrier channels wherein estimating includes deducing constellation points transmitted from a received signal, and calculating one or more differences between the received signal and an intended signal corresponding to the deduced constellation points; and
determining compensation parameters from the combined imbalance; and
loading the compensation parameters in the receiver to be used to compensate for the combined imbalance.
31. The method of claim 30 , wherein the estimating step is a frequency domain estimation, such that:
a
~
k
=
C
1
a
^
k
,
eq
+
C
2
a
^
N
-
k
,
eq
*
,
C
1
=
1
+
ρ
k
ɛ
k
1
-
ɛ
k
ɛ
N
-
k
*
and
C
2
=
-
ɛ
k
(
1
+
ρ
N
-
k
*
ɛ
N
-
k
*
)
1
-
ɛ
k
ɛ
N
-
k
*
where
ɛ
k
(
RX
)
=
a
^
k
,
eq
(
RX
)
-
a
k
a
N
-
k
*
-
a
^
k
,
eq
(
RX
)
ρ
k
.
â (RX) k,eq â k is a received value of a constellation point after processing through an equalizer, k being the carrier index among the plurality of carriers;
a k is a transmitted value of the constellation point for a kth carrier;
a * N−k is a complex conjugate of the transmitted value of the constellation point for an N−k th carrier, where N is a total number of carriers; and
ρ k is a ratio ρ k =a * N−k /a k of transmitted symbols used for equalizer training.
32. The method of claim 30 , wherein the compensation parameters are determined iteratively, from a starting estimate, such that:
C
1
(
i
+
1
)
=
C
1
(
i
)
(
1
+
ρ
k
ɛ
^
k
(
i
)
)
-
C
2
*
(
i
)
ɛ
k
(
i
)
(
1
+
ρ
N
-
k
*
ɛ
^
N
-
k
*
(
i
)
)
1
-
ɛ
^
k
(
i
)
ɛ
^
N
-
k
*
(
i
)
C
2
(
i
+
1
)
=
C
2
(
i
)
(
1
+
ρ
k
ɛ
^
k
(
i
)
)
-
C
1
*
(
i
)
ɛ
k
(
i
)
(
1
+
ρ
N
-
k
*
ɛ
^
N
-
k
*
(
i
)
)
1
-
ɛ
^
k
(
i
)
ɛ
^
N
-
k
*
(
i
)
where C 1 (0)=1, C 2 (0)=0 and {circumflex over (ε)} k (f) is the i-th estimate of a combined imbalance for the k-th subcarrier.
33. The method of claim 30 , wherein a receiver component of the combined imbalance has a predetermined value, the compensation parameters for the receiver component of the combined imbalance are time domain parameters and the compensation parameters for transmitter component of the combined imbalance are frequency domain parameters.
34. The method of claim 33 , wherein the estimating step is a frequency domain estimation, such that:
{tilde under (a)} k =C 1 â k,eq +C 2 â * N−k,eq ,
where
C
1
(
i
+
1
)
=
C
1
(
i
)
(
1
+
ρ
k
)
+
β
^
(
i
)
(
1
-
ρ
k
)
2
(
β
^
(
i
)
+
β
^
*
(
i
)
)
(
1
+
β
^
*
(
i
)
)
-
C
2
*
(
i
)
(
1
+
ρ
N
-
k
*
)
+
β
^
(
i
)
(
1
-
ρ
N
-
k
*
)
2
(
β
^
(
i
)
+
β
^
*
(
i
)
)
(
1
-
β
^
(
i
)
)
C
2
(
i
+
1
)
=
C
2
(
i
)
(
1
+
ρ
k
)
+
β
^
(
i
)
(
1
-
ρ
k
)
2
(
β
^
*
(
i
)
+
β
^
(
i
)
)
(
1
+
β
^
*
(
i
)
)
-
C
1
*
(
i
)
(
1
+
ρ
N
-
k
*
)
+
β
^
*
(
i
)
(
1
-
ρ
N
-
k
*
)
2
(
β
*
(
i
)
+
β
^
(
i
)
)
(
1
-
β
^
(
i
)
)
where C 1 (0)=1, C 2 (0)=0 and β(f) is the f-th estimate of a residual far-end TX imbalance.
35. The method of claim 34 , wherein i takes a single value, i=0, subject to C 1 (0)=1,C 2 (0)=0.
36. The method of claim 33 , wherein the estimating step is a frequency domain estimation, such that
{tilde under (a)} k =C 1 â k,eq +C 2 â * N−k,eq , where
C
1
(
i
+
1
)
=
C
1
(
i
)
1
+
β
^
(
i
)
2
(
β
^
*
(
i
)
+
β
^
(
i
)
)
(
1
+
β
^
*
(
i
)
)
-
C
2
*
(
i
)
1
+
β
^
*
(
i
)
2
(
β
*
(
i
)
+
β
^
(
i
)
)
(
1
-
β
^
*
(
i
)
)
C
2
(
i
+
1
)
=
C
2
(
i
)
1
+
β
^
(
i
)
2
(
β
^
*
(
i
)
+
β
^
(
i
)
)
(
1
+
β
^
*
(
i
)
)
-
C
1
*
(
i
)
1
+
β
^
*
(
i
)
2
(
β
*
(
i
)
+
β
^
(
i
)
)
(
1
-
β
^
(
i
)
)
where C 1 (0)=1, C 2 (0)=0 and {circumflex over (β)}(i) is the i-th estimate of a residual far-end TX imbalance.
37. The method of claim 36 , wherein i takes a single value, i=0 subject to C 1 (0)=1, C 2 (0)=0.
38. The method of claim 30 , wherein the estimating step is a frequency domain estimation performed after processing a received signal through an equalizer, such that:
a metric ε k ε * N−k | TX only is substantially minimized.
ɛ
k
ɛ
N
-
k
*
TZ
only
=
1
-
2
G
m
tx
cos
θ
m
tx
+
G
m
tx
G
m
tx
1
+
2
G
m
tx
cos
θ
m
tx
+
G
m
tx
G
m
tx
and
ɛ
k
=
a
^
k
,
eq
-
a
k
a
N
-
k
*
-
a
^
k
,
eq
ρ
k
,
where
â k is a received value of a constellation point, k being the carrier index among the plurality of carriers;
a k is a transmitted value of the constellation point for a kth carrier;
a * N−k is a complex conjugate of the transmitted value of the constellation point for an N−k th carrier, where N is a total number of carriers;
G rx m is gain imbalance of a receiver's mixer;
θ rx m is phase imbalance of the receiver's mixer; and
ρ k is a ratio ρ k =a * N−k /a k of transmitted symbols used for equalizer training.
39. A system of compensating for transmitter imbalance in a multi-carrier, OFDM symbol transmission system, including:
a receiver including logic to estimate transmitter gain and phase imbalance in a frequency domain across multiple carrier channels and to determine compensation parameters from imbalances,
wherein estimating transmitter gain and phase imbalance in a frequency domain across multiple carrier channels and determining compensation parameters from imbalances includes
deducing constellation points transmitted from a received signal; and
calculating one or more differences between the received signal and an intended signal corresponding to the deduced constellation points; and
a transmitter having memory to store the compensation parameters, whereby the compensation parameters can be used to compensate for transmitter gain and phase imbalance; and
a transmitter parameter loader, coupled to the logic to estimate and to the memory to store the compensation parameter.
40. A system of compensating for transmitter imbalance is a multi-carrier, OFDM symbol transmission system, including:
a transmitter having a frequency domain analyzer section including logic to estimate transmitter gain and phase imbalance across multiple carrier channels from a transmission signal and to determine compensation parameters from the imbalances, wherein estimating transmitter gain and phase imbalance in a frequency domain across multiple carrier channels and determining compensation parameters from imbalances includes
deducing constellation points transmitted from a received signal; and
calculating one or more differences between the received signal and an intended signal corresponding to the deduced constellation points; and
memory to store the compensation parameters, coupled to the transmitter, whereby the compensation parameters can be used to compensate for transmitter gain and phase imbalance; and
logic to load the compensation parameters into memory.
41. A system of compensating for receiver imbalance in a multi-carrier, OFDM symbol transmission system, including:
a receiver including logic to estimate receiver gain and phase imbalance in a frequency domain across multiple carrier channels and to determine compensation parameters from the imbalances,
wherein estimating receiver gain and phase imbalance in a frequency domain across multiple carrier channels and determining compensation parameters from the imbalances includes
deducing constellation points transmitted from a received signal, and
calculating one or more differences between the received signal and an intended signal corresponding to the deduced constellation points; and
memory to store the compensation parameters coupled to the receiver, whereby the compensation parameters can be used to compensate for the imbalances;
a receiver parameter loader, coupled to the logic to estimate and to memory to store the compensation parameters.
42. A system for compensating for transmitter and receiver imbalance in a multi-carrier, OFDM system, including:
a receiver including logic to estimate combined receiver and transmitter gain and phase imbalance in a frequency domain across multiple carrier channels and to determine compensation parameters from the imbalances, wherein estimating combined receiver and transmitter gain and phase imbalance in a frequency domain across multiple carrier channels and determining compensation parameters from the imbalances includes
deducing constellation points transmitted from a received signal, and
calculating one or more differences between the received signal and an intended signal corresponding to the deduced constellation points; and
memory to store the compensation parameters, coupled to the receiver, whereby the compensation parameters can be used to compensate for the imbalances; and
a receiver parameter loader, coupled to the logic to estimate and to the memory to store the compensation parameters.