Progressive feedback for high resolution limited feedback wireless communication
A system and method is proposed for progressively quantizing channel state information for application in a MIMO (multiple input multiple output) communication system. A method includes computing an estimate of a communications channel between a subscriber unit and a base station, quantizing the estimate with a first codebook, thereby producing a first quantized estimate, quantizing an (n−1)-th quantized estimate with an n-th codebook, thereby producing an n-th quantized estimate, where n is an integer value ranging from 2 to R, R is a total number of quantizations of the estimate, wherein the n-th codebook is a localized codebook. The method also includes incrementing n, repeating the quantizing an (n−1)-th quantized estimate until n=R, and transmitting information based on the R quantized estimates to the base station.
1. A method for subscriber unit operation in a wireless communications system, the wireless communications system having a base station, the method comprising:
computing an estimate of a communications channel between the subscriber unit and the base station;
quantizing the estimate with a first codebook, thereby producing a first quantized estimate;
scaling an n-th codebook;
quantizing an (n−1)-th quantized estimate with the scaled n-th codebook, thereby producing an n-th quantized estimate, where n is an integer value ranging from 2 to R and n initially being equal to 2, and where R is a total number of quantizations of the estimate, wherein the n-th codebook is a localized codebook;
incrementing n;
repeating the quantizing an (n−1)-th quantized estimate until n>R; and
transmitting information based on the R quantized estimates to the base station.
2. The method of claim 1 , further comprising after the scaling the n-th codebook, rotating the n-th codebook.
3. The method of claim 1 , further comprising after the scaling the n-th codebook, rotating the (n−1)-th quantized estimate.
4. The method of claim 1 , further comprising prior to the quantizing an (n−1)-th quantized estimate:
scaling the (n−1)-th quantized estimate; and
rotating the (n−1)-th quantized estimate.
5. The method of claim 4 , wherein the n-th codebook and the (n−1)-th codebook are identical.
6. The method of claim 1 , wherein the first codebook is a base codebook.
7. The method of claim 6 , wherein the first codebook comprises a Grassmannian codebook, a Kerdock codebook, a mutually unbiased base codebook, or a vector quantization derived codebook.
8. The method of claim 6 , wherein the base station has two transmit antennas, wherein the first codebook is expressible as:
F
3
GPP
,
2
=
{
[
1
0
]
,
[
0
1
]
,
1
2
[
1
1
]
,
1
2
[
1
-
1
]
,
1
2
[
1
j
]
,
1
2
[
1
-
j
]
}
.
9. The method of claim 6 , wherein the base station has three transmit antennas, wherein the first codebook is expressible as:
F
Kerdock
,
3
=
1
3
{
[
1
1
1
]
,
[
1
ⅇ
j
2
π
/
3
ⅇ
j
4
π
/
3
]
,
[
1
ⅇ
j
4
π
/
3
ⅇ
j
2
π
/
3
]
,
[
1
ⅇ
j
2
π
/
3
ⅇ
j
2
π
/
3
]
,
[
1
ⅇ
j
4
π
/
3
1
]
,
[
1
1
ⅇ
j
4
π
/
3
]
,
[
1
ⅇ
j4π
/
3
ⅇ
j
4
π
/
3
]
,
[
1
ⅇ
j
2
π
/
3
1
]
,
[
1
1
ⅇ
j
2
π
/
3
]
,
[
3
0
0
]
[
0
3
0
]
[
0
0
3
]
}
.
10. The method of claim 6 , wherein the base station has four transmit antennas, wherein the first codebook is expressible as:
F
3
GPP
,
4
=
1
2
{
[
1
-
1
-
1
-
1
]
,
[
1
-
j
1
j
]
,
[
1
1
-
1
1
]
,
[
1
j
1
-
j
]
,
[
1
(
-
1
-
j
)
/
2
-
j
(
1
-
j
)
/
2
]
,
[
1
(
1
-
j
)
/
2
j
(
-
1
+
j
)
/
2
]
,
[
1
(
1
+
j
)
/
2
-
j
(
-
1
+
j
)
/
2
]
,
[
1
(
-
1
+
j
)
/
2
j
(
1
+
j
)
/
2
]
,
[
1
-
1
1
1
]
,
[
1
-
j
-
1
-
j
]
,
[
1
1
1
-
1
]
,
[
1
j
-
1
j
]
,
[
1
-
1
-
1
1
]
,
[
1
-
1
1
-
1
]
,
[
1
1
-
1
-
1
]
,
[
1
1
1
1
]
}
.
11. The method of claim 6 , wherein the base station has four transmit antennas, wherein the first codebook is expressible as:
F
Kerdock
,
4
=
1
2
{
[
2
0
0
0
]
,
[
0
2
0
0
]
,
[
0
0
2
0
]
,
[
0
0
0
2
]
,
[
-
j
1
-
j
-
1
]
,
[
-
j
-
1
-
j
1
]
,
[
-
j
1
j
1
]
,
[
-
j
-
1
j
-
1
]
,
[
-
1
-
j
-
j
1
]
,
[
-
1
-
j
j
-
1
]
,
[
-
j
-
1
-
1
j
]
,
[
j
1
-
1
j
]
,
[
-
1
-
1
j
-
j
]
,
[
j
j
-
1
1
]
,
[
j
-
j
-
1
-
1
]
,
[
1
-
1
-
j
-
j
]
,
[
j
j
j
j
]
,
[
1
-
1
-
1
1
]
,
[
j
j
-
1
-
1
]
,
[
-
1
1
1
-
1
]
}
.
12. The method of claim 1 , wherein the n-th codebook comprises a scaled version of the (n−1)-th codebook.
13. The method of claim 1 , wherein the n-th codebook comprises a ring codebook, a concentric ring codebook, a concentric-rotated ring codebook, or a disc codebook.
14. The method of claim 1 , wherein the base station has two transmit antennas, and wherein the n-th codebook is a ring codebook with vectors of the form
w
ℓ
=
[
1
-
γ
0
2
γ
0
ⅇ
j
θ
ℓ
]
with a set of uniform phases
θ
ℓ
=
2
π
ℓ
N
l
-
1
for l=0,1, . . . , N l −2.
15. The method of claim 1 , wherein the base station has four transmit antennas, and wherein the n-th codebook is a ring codebook expressible as:
S
2
=
{
[
1
0
]
,
1
2
[
1
1
]
,
1
2
[
1
j
]
,
1
2
[
1
-
1
]
,
1
2
[
1
-
j
]
}
.
16. The method of claim 1 , wherein the base station has two transmit antennas, and wherein the n-th codebook is a ring codebook with vectors of the form
w
ℓ
=
[
1
-
γ
0
2
w
~
ℓ
γ
0
ⅇ
j
θ
ℓ
]
with a set of uniform phases
θ
ℓ
=
2
π
ℓ
N
l
-
1
for l=0,1, . . . , N l −2.
17. The method of claim 1 , wherein the base station has three transmit antennas, and wherein the n-th codebook is a ring codebook expressible as:
S
3
=
1
3
{
[
3
0
0
]
,
[
1
1
1
]
,
[
1
ⅇ
j2π
/
3
ⅇ
j4π
/
3
]
,
[
1
ⅇ
j4π
/
3
ⅇ
j2π
/
3
]
,
[
1
ⅇ
j2π
/
3
ⅇ
j2π
/
3
]
,
[
1
ⅇ
j4π
/
3
1
]
,
[
1
1
ⅇ
j4π
/
3
]
,
[
1
ⅇ
j4π
/
3
ⅇ
j4π
/
3
]
,
[
1
ⅇ
j2π
/
3
1
]
,
[
1
1
ⅇ
j2π
/
3
]
}
.
18. The method of claim 1 , wherein the base station has four transmit antennas, and wherein the n-th codebook is a ring codebook with
γ
0
=
3
2
,
the ring codebook is expressible as:
S
4
=
1
2
{
[
2
0
0
0
]
,
[
-
j
1
-
j
-
1
]
,
[
-
j
-
1
-
j
1
]
,
[
-
j
1
j
1
]
,
[
-
j
-
1
j
-
1
]
,
[
1
-
j
-
j
1
]
,
[
-
1
-
j
j
-
1
]
,
[
-
j
-
1
-
1
j
]
,
[
j
1
-
1
j
]
,
[
-
1
-
1
j
-
j
]
,
[
j
j
-
1
1
]
,
[
j
-
j
-
1
-
1
]
,
[
1
-
1
-
j
-
j
]
,
[
j
j
j
j
]
,
[
1
-
1
-
1
1
]
,
[
j
j
-
1
-
1
]
,
[
-
1
1
1
-
1
]
}
.
19. The method of claim 1 , wherein R is based on a mobility of the subscriber unit.
20. The method of claim 1 , wherein the information comprises a concatenation of indices of a result of each of the R quantizations into their respective codebooks.
21. The method of claim 1 , wherein the information comprises a combination of indices of a result of each of the R quantizations into their respective codebooks.
22. The method of claim 1 , wherein the information comprises a concatenation of indices of a result of each of the n-th quantizations into their respective codebooks.
23. The method of claim 1 , wherein there are multiple subscriber units in the wireless communications system, and wherein R is set independently for each subscriber unit.
24. The method of claim 1 , wherein the first codebook comprises a localized codebook.
25. The method of claim 1 , further comprising prior to the transmitting the information, applying an error correcting code to the information.
26. The method of claim 1 , wherein the first codebook and an n-th codebook are combined in a composite codebook, wherein n is equal to two (2).
27. A method for subscriber unit operation in a wireless communications system, the wireless communications system having a base station, the method comprising:
computing an estimate of a communications channel between the subscriber unit and the base station;
quantizing the estimate with a first codebook, thereby producing a first quantized estimate;
scaling the (n−1)-th quantized estimate;
quantizing an (n−1)-th quantized estimate with an n-th codebook, thereby producing an n-th quantized estimate, where n is an integer value ranging from 2 to R and n initially being equal to 2, and where R is a total number of quantizations of the estimate, wherein the n-th codebook is a localized codebook;
incrementing n;
repeating the quantizing an (n−1)-th quantized estimate until n>R; and
transmitting information based on the R quantized estimates to the base station.
28. The method of claim 27 , further comprising, after the scaling, rotating the (n−1)-th quantized estimate.
29. The method of claim 27 , wherein the n-th codebook and the (n−1)-th codebook are identical.
30. The method of claim 27 , wherein the first codebook is a base codebook.
31. The method of claim 30 , wherein the first codebook comprises a Grassmannian codebook, a Kerdock codebook, a mutually unbiased base codebook, or a vector quantization derived codebook.
32. The method of claim 27 , wherein the n-th codebook comprises a scaled version of the (n−1)-th codebook.
33. The method of claim 27 , wherein the n-th codebook comprises a ring codebook, a concentric ring codebook, a concentric-rotated ring codebook, or a disc codebook.
34. The method of claim 27 , wherein R is based on a mobility of the subscriber unit.
35. The method of claim 27 , wherein the information comprises a concatenation of indices of a result of each of the R quantizations into their respective codebooks.
36. The method of claim 27 , wherein the information comprises a combination of indices of a result of each of the R quantizations into their respective codebooks.
37. The method of claim 27 , wherein the information comprises a concatenation of indices of a result of each of the n-th quantizations into their respective codebooks.
38. The method of claim 27 , wherein there are multiple subscriber units in the wireless communications system, and wherein R is set independently for each subscriber unit.
39. The method of claim 27 , wherein the first codebook comprises a localized codebook.
40. The method of claim 27 , further comprising prior to the transmitting the information, applying an error correcting code to the information.
41. The method of claim 27 , wherein the first codebook and an n-th codebook are combined in a composite codebook, wherein n is equal to two (2).
42. A method for subscriber unit operation in a wireless communications system, the wireless communications system having a base station, the method comprising:
computing an estimate of a communications channel between the subscriber unit and the base station;
quantizing the estimate with a first codebook, thereby producing a first quantized estimate;
quantizing an (n−1)-th quantized estimate with an n-th codebook, thereby producing an n-th quantized estimate, where n is an integer value ranging from 2 to R and n initially being equal to 2, and where R is a total number of quantizations of the estimate, wherein the n-th codebook is a localized codebook, and wherein the n-th codebook comprises a scaled version of the (n−1)-th codebook;
incrementing n;
repeating the quantizing an (n−1)-th quantized estimate until n>R; and
transmitting information based on the R quantized estimates to the base station.
43. A method for subscriber unit operation in a wireless communications system, the wireless communications system having a base station, the method comprising:
computing an estimate of a communications channel between the subscriber unit and the base station;
quantizing the estimate with a first codebook, thereby producing a first quantized estimate;
quantizing an (n−1)-th quantized estimate with an n-th codebook, thereby producing an n-th quantized estimate, where n is an integer value ranging from 2 to R and n initially being equal to 2, and where R is a total number of quantizations of the estimate, wherein R is based on a mobility of the subscriber unit, and wherein the n-th codebook is a localized codebook;
incrementing n;
repeating the quantizing an (n−1)-th quantized estimate until n>R; and
transmitting information based on the R quantized estimates to the base station.
44. The method of claim 43 , wherein the first codebook is a base codebook.
45. The method of claim 44 , wherein the first codebook comprises a Grassmannian codebook, a Kerdock codebook, a mutually unbiased base codebook, or a vector quantization derived codebook.
46. The method of claim 43 , wherein the n-th codebook comprises a scaled version of the (n−1)-th codebook.
47. The method of claim 43 , wherein the n-th codebook comprises a ring codebook, a concentric ring codebook, a concentric-rotated ring codebook, or a disc codebook.
48. The method of claim 43 , wherein there are multiple subscriber units in the wireless communications system, and wherein R is set independently for each subscriber unit.
49. The method of claim 43 , wherein the first codebook comprises a localized codebook.
50. The method of claim 43 , further comprising prior to the transmitting the information, applying an error correcting code to the information.