Multiuser multiple-input multiple-output (MU-MIMO) channel estimation for multicarrier communications
View Patent ↗Provided are a system and method of estimating channels for a plurality of multicarrier signals in a wireless receiver. A receiver accepts a plurality of multicarrier signals, transmitted simultaneously from a plurality of transmitters, with overlapping carrier frequencies and nominally orthogonal reference signals. For each multicarrier signal, a reference signal is recovered including a plurality of adjacent subcarrier frequencies carrying predetermined symbols. A channel estimate is found across the plurality of adjacent subcarrier frequencies, for each multicarrier signal channel, by compensating for a loss of orthogonality between reference signals, in response to assuming a linear phase rotation for each channel across the plurality of adjacent reference signal subcarriers, and a constant amplitude for each channel across the plurality of adjacent reference signal subcarriers. More explicitly, the assumption of linear phase rotation and constant amplitude permits a Direction of Arrival (DoA) algorithm to be used.
1. In a wireless receiver, a method of estimating channels for a plurality of multicarrier signals, the method comprising;
a receiver accepting a plurality of multicarrier signals, transmitted simultaneously from a plurality of transmitters, with overlapping carrier frequencies and nominally orthogonal reference signals;
for each multicarrier signal, recovering a reference signal including a plurality of adjacent subcarrier frequencies carrying predetermined symbols;
finding a channel estimate across the plurality of adjacent subcarrier frequencies for each multicarrier signal channel by compensating for a loss of orthogonality between the reference signals, caused by propagation medium distortion errors, in response to assuming:
a linear phase rotation for each channel across the plurality of adjacent reference signal subcarriers; and,
a constant amplitude for each channel across the plurality of adjacent reference signal subcarriers.
2. The method of claim 1 wherein accepting the plurality of multicarrier signals includes receiving signals in a protocol selected from a group consisting of orthogonal frequency division multiple access (OFDMA), orthogonal frequency division multiplexing (OFDM), and single carrier-frequency division multiple access (SC-FDMA).
3. The method of claim 2 wherein accepting the plurality of multicarrier signals includes accepting Multiuser Multiple-Input Multiple-Output (MU-MIMO) signals.
4. The method of claim 1 wherein recovering the reference signal includes recovering a reference signal where adjacent subcarriers are separated by a frequency of less than about 325 kilohertz.
5. The method of claim 4 wherein recovering the reference signal includes recovering a reference signal with a coherence bandwidth selected from a group consisting of less than 20 megahertz for an indoor propagation medium and less than 200 kilohertz for an outdoor propagation medium.
6. The method of claim 4 wherein finding the channel estimate assuming linear phase rotation and constant amplitude includes finding the channel estimate using an algorithm selected from a group consisting of classic beamforming, Capon beamforming, MUltiple SIgnal Classification (MUSIC), estimation of signal parameters via rotational invariance techniques (ESPRIT), alternating projection, and simplified projection.
7. The method of claim 5 wherein accepting the plurality of multicarrier signals includes accepting the plurality of multicarrier signals via Mr number of receive antennas;
wherein assuming the linear phase rotation and constant amplitude to find the channel estimate is equivalent to:
H k+p,u ≈H k,u e −jpφ u , 0≦ p≦P− 1
where H is a Mr×1 channel vector;
k is a subcarrier index;
p is the index of separation between subcarriers;
φ u is the phase shift in channel response from subcarrier k to subcarrier k+1 (due to timing offset);
u is an index of accepted multicarrier signals; and,
P is the total number of adjacent subcarriers where the assumption of a channel having a linear phase rotation and constant amplitude holds.
8. The method of claim 7 wherein finding the channel estimate includes finding:
[
Z
k
…
Z
k
+
P
-
1
]
=
[
H
k
,
1
…
H
k
,
U
]
[
1
…
ⅇ
j
(
P
-
1
)
θ
1
⋮
⋱
⋮
1
…
ⅇ
j
(
P
-
1
)
θ
U
]
+
[
W
~
k
…
W
~
k
+
P
-
1
]
wherein Z is a Mr×1 received reference signal vector, after removing pre-determined symbol values; and,
{tilde over (W)} is a Mr×1 vector of interference plus noise, where;
θ u =−φ u +2πΔ u /N, 1≦ u≦U;
where Δ u is a known cyclic shift in samples for received multicarrier signal u and φ u is the phase shift in channel response from subcarrier k to subcarrier k+1 (due to timing offset).
9. The method of claim 8 wherein finding the channel estimate includes finding:
[Ĥ k,1 . . . Ĥ k,U ]=[Z k . . . Z k+P−1 ]Â{circumflex over (*)} P ( Â P Â* P +σ 2 I ) −1
where Ĥ is a Mr×1 channel estimate vector;
A
P
=
[
1
…
ⅇ
j
(
P
-
1
)
θ
1
⋮
⋱
⋮
1
…
ⅇ
j
(
P
-
1
)
θ
U
]
;
is a U×P matrix containing the linear phase rotation across adjacent subcarriers;
 P is an estimate of A P ;
σ 2 =is a regularization parameter;
U is the number of simultaneously transmitted multicarrier signals; and,
and I is the U×U identity matrix.
10. The method of claim 1 wherein accepting the plurality of multicarrier signals subject to propagation medium distortion errors includes accepting multicarrier signals subject to propagation medium distortion selected from a group consisting of multipath fading and timing offsets.
11. The method of claim 8 wherein finding the channel estimate includes using a classic beamforming algorithm by forming:
Z
~
=
[
Z
0
…
Z
P
-
1
Z
P
…
Z
2
P
-
1
…
Z
(
N
-
1
)
P
…
Z
NP
-
1
]
where NP is less than a total number of allocated subcarriers M;
computing metrics:
λ(θ)=∥ {tilde over (Z)}a H (θ)∥ 2
a (θ)=[1 . . . e j(P−1)θ ]
where a is the steering vector
peak picking to estimate:
ϕ
^
u
=
arg
max
ϕ
∈
[
ϕ
min
,
ϕ
max
]
λ
(
2
πΔ
u
/
N
-
ϕ
)
;
where Δ u is a known cyclic shift in samples for each multicarrier signal u.
12. The method of claim 8 wherein finding the channel estimate includes using an alternate projection algorithm by forming:
Z
~
=
[
Z
0
…
Z
P
-
1
Z
P
…
Z
2
P
-
1
…
Z
(
N
-
1
)
P
…
Z
NP
-
1
]
;
where NP is less than a total number of allocated subcarriers M and P>U;
for each multicarrier signal, setting initial estimates
{circumflex over (θ)} u ={circumflex over (θ)} u (0) , and iteratively updating the estimates according to {circumflex over (θ)} u =2πΔ u /N−{circumflex over (φ)} u ;
where Δ u is a known cyclic shift in samples for each multicarrier signal;
where
ϕ
^
u
=
arg
max
ϕ
∈
[
ϕ
mi
n
,
ϕ
max
]
λ
u
(
2
πΔ
u
/
N
;
-
ϕ
)
where λ u ( ) is determined by computing a projection matrix
P u =I−A u H ( A u A u H ) −1 A u ;
where
A u =[a H ({circumflex over (θ)} 1 ), . . . , a H ({circumflex over (θ)} u−1 ), a H ({circumflex over (θ)} u+1 ), . . . , a H ({circumflex over (θ)} U )] H ;
projecting and normalizing a steering vector
b
u
(
θ
)
=
a
(
θ
)
P
u
a
(
θ
)
P
u
;
computing λ u (θ)=∥{tilde over (Z)}b u H (θ)∥ 2 , and updating {circumflex over (θ)} u ; and,
repeating the above steps until a stopping criteria is met.
13. The method of claim 8 wherein finding the channel estimate includes using a simplified projection algorithm by forming:
Z
~
=
[
Z
0
…
Z
P
-
1
Z
P
…
Z
2
P
-
1
…
Z
(
N
-
1
)
P
…
Z
NP
-
1
]
where NP is less than a total number of allocated subcarriers M and P>U;
setting initial estimates {circumflex over (θ)} u ={circumflex over (θ)} u (0) for each multicarrier signal;
for each multicarrier signal, using a projection method to estimate {circumflex over (θ)} u , from the initial estimates, where the steering vector is given by:
b
u
(
θ
)
=
a
(
θ
)
P
u
a
(
θ
)
P
u
;
and
,
where
P u =I−A u H ( A u A u H ) −1 A u ;
and,
A u =[a H ({circumflex over (θ)} 1 ), . . . , a H ({circumflex over (θ)} u−1 ), a H ({circumflex over (θ)} u+1 ), . . . , a H ({circumflex over (θ)} U )] H .
14. The method of claim 1 wherein the assumptions of linear phase rotation and constant amplitude across adjacent reference signal subcarriers includes applying the assumptions to every m-th subcarrier frequency, where m is an integer variable greater than, or equal to 2.
15. A wireless receiver with a capability of estimating channels for a plurality of multicarrier signals, the receiver comprising:
a plurality of receive antennas accepting a plurality of multicarrier signals, transmitted simultaneously from a plurality of transmitters, with overlapping carrier frequencies and nominally orthogonal reference signals including a plurality of adjacent subcarrier frequencies carrying predetermined symbols;
a plurality of channel estimation preprocessors, each channel estimation preprocessor having an input to accept multicarrier signals from a corresponding antenna, and an output to supply baseband multicarrier signals;
a channel estimation module having an input connected to each channel estimation preprocessor output, the channel estimation module finding a channel estimate across the plurality of adjacent subcarrier frequencies for each multicarrier signal channel by compensating for a loss of orthogonality between the reference signals, caused as a result of propagation medium distortion errors, in response to assuming:
a linear phase rotation for each channel across the plurality of adjacent reference signal subcarriers; and,
a constant amplitude for each channel across the plurality of adjacent reference signal subcarriers.
16. The receiver of claim 15 wherein the antennas accept signals in a protocol selected from a group consisting of orthogonal frequency division multiple access (OFDMA), orthogonal frequency division multiplexing (OFDM), and single carrier-frequency division multiple access (SC-FDMA).
17. The receiver of claim 16 wherein the antennas accept Multiuser Multiple-Input Multiple-Output (MU-MIMO) signals.
18. The receiver of claim 15 wherein the channel estimation module recovers a reference signal where adjacent subcarriers are separated by a frequency of less than about 325 kilohertz.
19. The receiver of claim 18 wherein the channel estimation module recovers a reference signal with a coherence bandwidth selected from a group consisting of less than 20 megahertz for an indoor propagation medium and less than 200 kilohertz for an outdoor propagation medium.
20. The receiver of claim 18 wherein the channel estimation module uses linear phase rotation and constant amplitude assumptions to find channel estimates using an algorithm selected from a group consisting of classic beamforming, Capon beamforming, MUltiple SIgnal Classification (MUSIC), estimation of signal parameters via rotational invariance techniques (ESPRIT), alternating projection, and simplified projection.
21. The receiver of claim 19 wherein Mr number of antennas accept the plurality of multicarrier signals;
wherein the channel estimation module uses the linear phase rotation and constant amplitude assumptions to find the channel estimate is equivalent to:
H k+p,u ≈H k,u e −jpφ u , 0≦ p≦P− 1
where is a Mr×1 channel vector;
k is a subcarrier index;
p is the index of separation between subcarriers;
φ u is the phase shift in channel response from subcarrier k to subcarrier k+1 (due to timing offset);
u is an index of accepted multicarrier signals; and,
P is the total number of adjacent subcarriers where the assumption of a channel having a linear phase rotation and constant amplitude holds.
22. The receiver of claim 21 wherein the channel estimation module finds the channel estimate as follows:
[
Z
k
…
Z
k
+
P
-
1
]
=
[
H
k
,
1
…
H
k
,
U
]
[
1
…
ⅇ
j
(
P
-
1
)
θ
1
⋮
⋱
⋮
1
…
ⅇ
j
(
P
-
1
)
θ
U
]
+
[
W
~
k
…
W
~
k
+
P
-
1
]
wherein Z is a Mr×1 received reference signal vector, after removing pre-determined symbol values; and,
{tilde over (W)} is a Mr×1 vector of interference plus noise, where;
θ u =−φ u +2πΔ u /N, 1≦ u≦U;
where Δ u is a known cyclic shift in samples for received multicarrier signal u and φ u is the phase shift in channel response from subcarrier k to subcarrier k+1 (due to timing offset).
23. The receiver of claim 22 wherein the channel estimation module finds the channel estimate as follows:
[Ĥ k,1 . . . Ĥ k,U ]=[Z k . . . Z k+P−1 ]Â{circumflex over (*)} P ( Â P Â* P +σ 2 I ) −1
where Ĥ is a Mr×1 channel estimate vector;
A
P
=
[
1
…
ⅇ
j
(
P
-
1
)
θ
1
⋮
⋱
⋮
1
…
ⅇ
j
(
P
-
1
)
θ
U
]
;
is a U×P matrix containing the linear phase rotation across adjacent subcarriers;
 P is an estimate of A P ;
σ 2 =is a regularization parameter;
U is the number of simultaneously transmitted multicarrier signals; and,
and I is the U×U identity matrix.
24. The receiver of claim 15 wherein the antennas accept multicarrier signals subject to propagation medium distortion selected from a group consisting of multipath fading and timing offsets.
25. The receiver of claim 22 wherein the channel estimation module uses a classic beamforming algorithm to find:
Z
~
=
[
Z
0
…
Z
P
-
1
Z
P
…
Z
2
P
-
1
…
Z
(
N
-
1
)
P
…
Z
NP
-
1
]
where NP is less than a total number of allocated subcarriers M;
computing metrics:
λ(θ)=∥ {tilde over (Z)}a H (θ)∥ 2
a (θ)=[1 . . . e j(P−1)θ ]
where a is the steering vector
peak picking to estimate:
ϕ
^
u
=
arg
max
ϕ
∈
[
ϕ
mi
n
,
ϕ
max
]
λ
(
2
πΔ
u
/
N
-
ϕ
)
;
where Δ u is a known cyclic shift in samples for each multicarrier signal u.
26. The receiver of claim 22 wherein the channel estimation module uses an alternate projection algorithm to find:
Z
~
=
[
Z
0
…
Z
P
-
1
Z
P
…
Z
2
P
-
1
…
Z
(
N
-
1
)
P
…
Z
NP
-
1
]
where NP is less than a total number of allocated subcarriers M and P>U;
for each multicarrier signal, setting initial estimates
{circumflex over (θ)} u ={circumflex over (θ)} u (0) , and iteratively updating the estimates according to {circumflex over (θ)} u =2πΔ u /N−{circumflex over (φ)} u ;
where Δ u is a known cyclic shift in samples for each multicarrier signal;
where
ϕ
^
u
=
arg
max
ϕ
∈
[
ϕ
mi
n
,
ϕ
max
]
λ
u
(
2
πΔ
u
/
N
;
-
ϕ
)
where λ u ( ) is determined by computing a projection matrix
P u =I−A u H ( A u A u H ) −1 A u ;
where
A u =[a H ({circumflex over (θ)} 1 ), . . . , a H ({circumflex over (θ)} u−1 ), a H ({circumflex over (θ)} u+1 ), . . . , a H ({circumflex over (θ)} U )] H ;
projecting and normalizing a steering vector
b
u
(
θ
)
=
a
(
θ
)
P
u
a
(
θ
)
P
u
;
computing λ u (θ)=∥{tilde over (Z)}b u H (θ)∥ 2 , and updating {circumflex over (θ)} u ; and,
repeating the above steps until a stopping criteria is met.
27. The receiver of claim 22 wherein the channel estimation module uses a simplified projection algorithm to find:
Z
~
=
[
Z
0
…
Z
P
-
1
Z
P
…
Z
2
P
-
1
…
Z
(
N
-
1
)
P
…
Z
NP
-
1
]
where NP is less than a total number of allocated subcarriers M and P>U;
setting initial estimates {circumflex over (θ)} u ={circumflex over (θ)} u (0) for each multicarrier signal;
for each multicarrier signal, using a projection method to estimate {circumflex over (θ)} u , from the initial estimates, where the steering vector is given by:
b
u
(
θ
)
=
a
(
θ
)
P
u
a
(
θ
)
P
u
;
and
,
where
P u =I−A u H ( A u A u H ) −1 A u ;
and,
A u =[a H ({circumflex over (θ)} 1 ), . . . , a H ({circumflex over (θ)} u−1 ), a H ({circumflex over (θ)} u+1 ), . . . , a H ({circumflex over (θ)} U )] H .
28. The receiver of claim 15 wherein the channel estimation module applies the linear phase rotation and constant amplitude assumptions to every m-th subcarrier frequency, where m is an integer variable greater than, or equal to 2.