7.8 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Channel state information | 2/2 | https://en.wikipedia.org/wiki/Channel_state_information | reference | science, encyclopedia | 2026-05-05T14:40:08.762067+00:00 | kb-cron |
where
t
r
{\displaystyle \mathrm {tr} }
denotes the trace. The error is minimized when
P
P
H
{\displaystyle \mathbf {P} \mathbf {P} ^{H}}
is a scaled identity matrix. This can only be achieved when
N
{\displaystyle N}
is equal to (or larger than) the number of transmit antennas. The simplest example of an optimal training matrix is to select
P
{\displaystyle \mathbf {P} }
as a (scaled) identity matrix of the same size that the number of transmit antennas.
=== MMSE estimation === If the channel and noise distributions are known, then this a priori information can be exploited to decrease the estimation error. This approach is known as Bayesian estimation and for Rayleigh fading channels it exploits that
vec
(
H
)
∼
C
N
(
0
,
R
)
,
vec
(
N
)
∼
C
N
(
0
,
S
)
.
{\displaystyle {\mbox{vec}}(\mathbf {H} )\sim {\mathcal {CN}}(0,\,\mathbf {R} ),\quad {\mbox{vec}}(\mathbf {N} )\sim {\mathcal {CN}}(0,\,\mathbf {S} ).}
The MMSE estimator is the Bayesian counterpart to the least-square estimator and becomes
vec
(
H
MMSE-estimate
)
=
(
R
−
1
+
(
P
T
⊗
I
)
H
S
−
1
(
P
T
⊗
I
)
)
−
1
(
P
T
⊗
I
)
H
S
−
1
vec
(
Y
)
{\displaystyle {\mbox{vec}}(\mathbf {H} _{\textrm {MMSE-estimate}})=\left(\mathbf {R} ^{-1}+(\mathbf {P} ^{T}\,\otimes \,\mathbf {I} )^{H}\mathbf {S} ^{-1}(\mathbf {P} ^{T}\,\otimes \,\mathbf {I} )\right)^{-1}(\mathbf {P} ^{T}\,\otimes \,\mathbf {I} )^{H}\mathbf {S} ^{-1}{\mbox{vec}}(\mathbf {Y} )}
where
⊗
{\displaystyle \otimes }
denotes the Kronecker product and the identity matrix
I
{\displaystyle \scriptstyle \mathbf {I} }
has the dimension of the number of receive antennas. The estimation MSE is
t
r
(
R
−
1
+
(
P
T
⊗
I
)
H
S
−
1
(
P
T
⊗
I
)
)
−
1
{\displaystyle \mathrm {tr} \left(\mathbf {R} ^{-1}+(\mathbf {P} ^{T}\,\otimes \,\mathbf {I} )^{H}\mathbf {S} ^{-1}(\mathbf {P} ^{T}\,\otimes \,\mathbf {I} )\right)^{-1}}
and is minimized by a training matrix
P
{\displaystyle \mathbf {P} }
that in general can only be derived through numerical optimization. But there exist heuristic solutions with good performance based on waterfilling. As opposed to least-square estimation, the estimation error for spatially correlated channels can be minimized even if
N
{\displaystyle N}
is smaller than the number of transmit antennas. Thus, MMSE estimation can both decrease the estimation error and shorten the required training sequence. It needs however additionally the knowledge of the channel correlation matrix
R
{\displaystyle \mathbf {R} }
and noise correlation matrix
S
{\displaystyle \mathbf {S} }
. In absence of an accurate knowledge of these correlation matrices, robust choices need to be made to avoid MSE degradation.
=== Neural network estimation === With the advances of deep learning there has been work that shows that the channel state information can be estimated using Neural network such as 2D/3D CNN and obtain better performance with fewer pilot signals. The main idea is that the neural network can do a good interpolation in time and frequency.
== Data-aided versus blind estimation == In a data-aided approach, the channel estimation is based on some known data, which is known both at the transmitter and at the receiver, such as training sequences or pilot data. In a blind approach, the estimation is based only on the received data, without any known transmitted sequence. The tradeoff is the accuracy versus the overhead. A data-aided approach requires more bandwidth or it has a higher overhead than a blind approach, but it can achieve a better channel estimation accuracy than a blind estimator.
== See also == Channel sounding
== References ==
== External links == Atheros CSI Tool Linux 802.11n CSI Tool