System and method for providing first arrival path (FAP) and delay spread estimation (DSE) in wireless communication system
A method for minimizing a time domain mean square error (MSE) of channel estimation (CE) includes estimating, by a processor, a power delay profile (PDP) from a time domain observation of reference signal (RS) channels; estimating, by the processor, a noise variance of the RS channels; and determining, by the processor, a first arrival path (FAP) value and a delay spread estimation (DSE) value based on the estimated PDP and the estimated noise variance for minimizing the MSE of CE.
1. A method for minimizing a time domain mean square error (MSE) of channel estimation (CE), the method comprising:
estimating, by a processor, a power delay profile (PDP) from a time domain observation of reference signal (RS) channels;
estimating, by the processor, a noise variance of the RS channels;
determining, by the processor, a first arrival path (FAP) value and a delay spread estimation (DSE) value based on the estimated PDP and the estimated noise variance; and
determining, by the processor, a minimum value of the time domain MSE based on the estimated PDP, the estimated noise variance, and a length of an uniform PDP.
2. A method for minimizing a time domain mean square error (MSE) of channel estimation (CE), the method comprising:
estimating, by a processor, a power delay profile (PDP) from a time domain observation of reference signal (RS) channels;
estimating, by the processor, a noise variance of the RS channels; and
determining, by the processor, a first arrival path (FAP) value and a delay spread estimation (DSE) value based on the estimated PDP and the estimated noise variance for minimizing the MSE of CE, wherein the time domain MSE is:
MSE
=
1
+
L
σ
2
(
1
+
L
σ
2
)
2
+
[
1
(
1
+
L
σ
2
)
2
-
2
1
+
L
σ
2
]
∑
i
=
F
L
+
F
-
1
P
i
(
1
)
wherein F and L are integers, where:
1
≤
L
≤
3
N
4
,
-
N
4
≤
F
≤
N
4
.
wherein, σ 2 is the noise variance, P i is power of an i-th channel tap or an uniform PDP, F is an index of the FAP, N is a length of the estimated PDP, and L is a length of the uniform PDP.
3. The method of claim 2 , wherein determining the FAP value and the DSE value to minimize the time domain MSE comprises determining, by the processor, a value of F and a value of L, wherein a minimum value of the time domain MSE is determined based on the value of F and the value of L.
4. The method of claim 3 , wherein the value of L is the delay spread value for minimizing the MSE and the estimated noise variance is capped at a signal to noise ratio (SNR)=20 dB.
5. The method of claim 3 , wherein the determining the value of F and the value of L for minimizing the time domain MSE comprises:
assigning, by the processor, a value “0” to the index of the FAP F;
determining, by the processor, a minimized value of MSE and corresponding value of L for each F of a plurality of F values within and
-
N
4
≤
F
<
0
and
0
<
F
≤
N
4
;
determining, by the processor, the value of F and the value of L based on comparing minimized values of MSE for the plurality of F values within
-
N
4
≤
F
<
0
and
0
<
F
≤
N
4
.
6. The method of claim 5 , wherein the value of F and the value of L correspond to the minimum value of the time domain MSE from among the minimized values of MSE for the plurality of F values within
-
N
4
≤
F
<
0
and
0
<
F
≤
N
4
,
wherein the minimized values of MSE and the corresponding values of L are determined using equation (1).
7. The method of claim 5 , further comprising stopping a search of the value of F and the value of L for F >0 or F<0, by the processor, in response to the minimized value of MSE, for F within
-
N
4
≤
F
<
0
or
0
<
F
≤
N
4
,
being increased as |F| increased for n consecutive times, wherein the n is 5.
8. The method of claim 5 , further comprising scaling, by the processor, the value of F and the value of L based on a difference of sampling time between the RS channels and data resource elements (REs) to determine a scaled value of F and a scaled value of L.
9. The method of claim 8 , wherein the scaled value of F is F′, wherein F′=scaling factor×F, and the scaled value of L is L′, wherein L′=scaling factor×L, wherein
scaling
factor
=
Sample
duration
of
RS
PDP
Sample
duration
of
data
REs
=
N
IFFT
×
Δ
f
N
PDP
×
Δ
f
×
12
ρ
wherein N IFFT is a size of Fast Fourier Transform (FFT), N PDP is a length of the estimated PDP, Δf is a subcarrier spacing, and p is a density of RS REs.
10. The method of claim 9 , wherein the method further comprising:
determining, by the processor, CE and a frequency correlation between the RS channels and the data REs, based on F′ and L′.
11. A system for minimizing a time domain mean square error (MSE) of channel estimation (CE), the system comprising:
a memory and a processor in communication with the memory, wherein the processor is configured to:
estimate a power delay profile (PDP) from time domain observation of reference signal (RS) channels;
estimate a noise variance of the RS channels;
determine a first arrival path (FAP) value and a delay spread estimation (DSE) value based on the estimated PDP and the estimated noise variance; and
determine a minimum value of the time domain MSE based on the estimated PDP, the estimated noise variance, and a length of an uniform PDP.
12. The system of claim 11 , wherein the time domain MSE is:
MSE
=
1
+
L
σ
2
(
1
+
L
σ
2
)
2
+
[
1
(
1
+
L
σ
2
)
2
-
2
1
+
L
σ
2
]
∑
L
+
F
-
1
i
=
F
P
i
(
1
)
wherein F and L are integers, where:
1
≤
L
≤
3
N
4
,
-
N
4
≤
F
≤
N
4
.
wherein, σ 2 is the noise variance, P i is power of an i-th channel tap or the uniform PDP, F is an index of the FAP, N is a length of the estimated PDP, and L is the length of the uniform PDP.
13. The system of claim 12 , wherein the processor is further configured to:
determine the FAP value and the DSE value to minimize the time domain MSE based on determining a value of F and a value of L, wherein the processor is further configured to determine the minimum value of the time domain MSE based on the value of F and the value of L.
14. The system of claim 13 , wherein the value of L is the delay spread value for minimizing the MSE and the estimated noise variance is capped at a signal to noise ratio (SNR)=20 dB.
15. The system of claim 13 , wherein the processor is further configured to:
assign a value “0” to the index of the FAP F;
determine a minimized value of MSE and corresponding value of L for each F of a plurality of F values within arm
-
N
4
≤
F
<
0
and
0
<
F
≤
N
4
;
determine the value of F and the value of L based on comparing minimized values of MSE for the plurality of F values within
-
N
4
≤
F
<
0
and
0
<
F
≤
N
4
.
16. The system of claim 15 , wherein the value of F and the value of L correspond to the minimum value of the time domain MSE from among the minimized values of MSE for the plurality of F values within
-
N
4
≤
F
<
0
and
0
<
F
≤
N
4
,
wherein the minimized values of MSE and the corresponding values of L are determined using equation (1).
17. The system of claim 15 , wherein the processor is further configured to stop a search of the value of F and the value of L for F >0 or F<0, by the processor, in response to the minimized value of MSE, for F within
-
N
4
≤
F
<
0
and
0
<
F
≤
N
4
,
being increased as |F| increased for n consecutive times, wherein the n is 5.
18. The system of claim 15 , wherein the processor is further configured to scale the value of F and the value of L based on a difference of sampling time between RS channels and data resource elements (REs) to determine a scaled value of F and a scaled value of L.
19. The system of claim 18 , wherein the scaled value of F is F′, wherein F′=scaling factor×F, and the scaled value of L is L′, wherein L′=scaling factor×L, wherein
scaling
factor
=
Sample
duration
of
RS
PDP
Sample
duration
of
data
REs
=
N
IFFT
×
Δ
f
N
PDP
×
Δ
f
×
12
ρ
wherein N IFFT is a size of Fast Fourier Transform (FFT), N PDP is a length of the estimated PDP, Δf is a subcarrier spacing, and p is a density of RS REs.
20. The system of claim 19 , wherein the processor is further configured to determine CE and a frequency correlation between RS channels and data REs, based on F′ and L′.