System and method for enhancing throughput in an additive gaussian noise channel with a predetermined rate set and unknown interference
View Patent ↗A system for, and method of, determining channel throughput achievable under superposition coding given a finite, predetermined set of allowed transmission rates and a related system for, and method of, maximizing channel throughput. In one embodiment, the system includes: (1) a noise level calculator configured to calculate associated optimal noise levels for at least some rate subsets of the set of allowed transmission rates and (2) a code feasibility calculator associated with the noise level calculator and configured to determine whether feasible superposition codes exist for the at least some rate subsets given the associated optimal noise levels and thereby identify ones of the at least some rate subsets that are suitable for subsequent wireless transmissions.
1. A system for determining channel throughput achievable under superposition coding given a finite, predetermined set of allowed transmission rates, comprising:
a noise level calculator configured to calculate associated optimal noise levels for at least some rate subsets of said set of allowed transmission rates; and
a code feasibility calculator associated with said noise level calculator and configured to determine whether feasible superposition codes exist for said at least some rate subsets given said associated optimal noise levels and thereby identify ones of said at least some rate subsets that are suitable for subsequent wireless transmissions.
2. The system as recited in claim 1 wherein said noise level calculator is configured to calculate said associated optimal noise levels using an equation that at least approximates:
q
π
(
i
)
=
γ
π
(
i
)
∏
j
=
i
+
1
K
(
1
+
γ
π
(
j
)
)
,
1
≤
i
≤
K
,
where:
K is a number of rates in a subset R k of said predetermined set of allowed transmission rates,
γ π(i) =exp(2R π(i) )−1, for a permutation π of said subset, and
R π(i) is the i th transmission rate in said permutation.
3. The system as recited in claim 1 wherein said noise level calculator is configured to calculate said associated optimal noise levels using an equation that at least approximates:
x
π
(
i
)
=
1
α
log
(
R
π
(
i
+
1
)
R
π
(
i
)
γ
π
(
i
)
(
1
+
γ
π
(
i
+
1
)
)
γ
π
(
i
+
1
)
)
,
where:
α is an adjustable parameter,
γ π(i) =exp(2R π(i) )−1, for a permutation π of a subset R k of said predetermined set of allowed transmission rates, and
R π(i) is an i th transmission rate in said permutation.
4. The system as recited in claim 1 wherein said noise level calculator is configured to calculate relationships between noise levels using equations that at least approximate:
N
1
*
=
P
-
∑
j
=
1
K
-
1
(
∑
i
=
j
+
1
K
q
π
(
i
)
)
x
π
(
i
)
∑
j
=
1
K
q
π
(
j
)
and
N
i
*
=
N
1
*
+
∑
j
=
1
i
-
1
x
π
(
j
)
,
where:
P is a total received power,
K is a number of rates in a subset R k of said predetermined set of allowed transmission rates,
q
π
(
i
)
=
γ
π
(
i
)
∏
j
=
i
+
1
K
(
1
+
γ
π
(
j
)
)
,
1
≤
i
≤
K
,
x
π
(
j
)
=
1
α
log
(
R
π
(
i
+
1
)
R
π
(
i
)
γ
π
(
i
)
(
1
+
γ
π
(
i
+
1
)
)
γ
π
(
i
+
1
)
)
,
α is an adjustable parameter,
γ π(i) =exp(2R π(i) )−1, for a permutation π of said subset, and
R π(i) is an l th transmission rate in said permutation.
5. The system as recited in claim 1 wherein said code feasibility calculator is further configured to determine throughputs associated with said ones of said at least some rate subsets.
6. The system as recited in claim 5 wherein said code feasibility calculator is configured to determine throughputs using an equation that at least approximates:
T
*
(
R
1
,
…
,
R
K
,
π
)
=
∑
i
=
1
K
[
1
-
ⅇ
-
α
N
i
*
]
R
π
(
i
)
,
where:
R k is a k th transmission rate in a subset of K of said predetermined set of allowed transmission rates,
π is a permutation of said subset,
R π(i) is an i th transmission rate in said permutation,
α is an adjustable parameter, and
N i * is a noise power level associated with said i th transmission rate, wherein a set of N 1 * , . . . ,N k * is associated with a maximum of said channel throughput.
7. The system as recited in claim 5 wherein said code feasibility calculator is further configured to select a one of said at least some rate subsets having a maximum associated throughput.
8. The system as recited in claim 1 wherein said code feasibility calculator is further configured to calculate power allocations for rates in at least one of said at least some rate subsets.
9. The system as recited in claim 8 wherein said code feasibility calculator is further configured to calculate said power allocations using an equation that at least approximates:
P
π
(
k
)
=
γ
π
(
k
)
[
∑
i
=
1
k
-
1
P
π
(
i
)
+
N
k
]
,
where:
γ π(k) =exp(2R π(k) )−1, for a permutation π of a subset R k of said predetermined set of allowed transmission rates,
P π(i) is an allocated power associated with an i th transmission rate in said permutation, and
N k is a noise power level associated with a k th transmission rate in said subset.
10. The system as recited in claim 1 wherein said at least some rate subsets include subsets of single rates.
11. The system as recited in claim 1 wherein said noise level calculator is configured to calculate associated optimal noise levels for all rate subsets of said set.
12. The system as recited in claim 1 wherein a transmission standard determines said set.
13. A method of determining channel throughput achievable under superposition coding given a finite, predetermined set of allowed transmission rates, comprising:
calculating associated optimal noise levels for at least some rate subsets of said set of allowed transmission rates; and
determining whether feasible superposition codes exist for said at least some rate subsets given said associated optimal noise levels and thereby identifying ones of said at least some rate subsets that are suitable for subsequent wireless transmissions.
14. The method as recited in claim 13 wherein said calculating comprises calculating said associated optimal noise levels using an equation that at least approximates:
q
π
(
i
)
=
γ
π
(
i
)
∏
j
=
i
+
1
K
(
1
+
γ
π
(
j
)
)
,
1
≤
i
≤
K
,
where:
K is a number of rates in a subset R k of said predetermined set of allowed transmission rates,
γ π(i) =exp(2R π(i) )−1, for a permutation π of said subset, and
R π(i) is the i th transmission rate in said permutation π.
15. The method as recited in claim 13 wherein said calculating comprises calculating said associated optimal noise levels using an equation that at least approximates:
x
π
(
i
)
=
1
α
log
(
R
π
(
i
+
1
)
R
π
(
i
)
γ
π
(
i
)
(
1
+
γ
π
(
i
+
1
)
)
γ
π
(
i
+
1
)
)
,
where:
α is an adjustable parameter,
γ π(i) =exp(2R π(i) )−1, for a permutation π of a subset R k of said predetermined set of allowed transmission rates, and
R π(i) is an i th transmission rate in said permutation.
16. The method as recited in claim 13 wherein said calculating comprises calculating relationships between noise levels using equations that at least approximate:
N
1
*
=
P
-
∑
j
=
1
K
-
1
(
∑
i
=
j
+
1
K
q
π
(
i
)
)
x
π
(
i
)
∑
j
=
1
K
q
π
(
j
)
and
N
i
*
=
N
1
*
+
∑
j
=
1
i
-
1
x
π
(
j
)
,
where:
P is a total received power,
K is a number of rates in a subset R k of said predetermined set of allowed transmission rates,
q
π
(
i
)
=
γ
π
(
i
)
∏
j
=
i
+
1
K
(
1
+
γ
π
(
j
)
)
,
1
≤
i
≤
K
,
x
π
(
j
)
=
1
α
log
(
R
π
(
i
+
1
)
R
π
(
i
)
γ
π
(
i
)
(
1
+
γ
π
(
i
+
1
)
)
γ
π
(
i
+
1
)
)
,
α is an adjustable parameter,
γ π(i) =exp(2R π(i) )−1, for a permutation π of said subset, and
R π(i) is an i th transmission rate in said permutation.
17. The method as recited in claim 13 wherein said determining comprises determining throughputs associated with said ones of said at least some rate subsets.
18. The method as recited in claim 17 wherein said determining comprises determining throughputs using an equation that at least approximates:
T
*
(
R
1
,
…
,
R
K
,
π
)
=
∑
i
=
1
K
[
1
-
ⅇ
-
α
N
i
*
]
R
π
(
i
)
,
where:
R k is a k th transmission rate in a subset of K of said predetermined set of allowed transmission rates,
π is a permutation of said subset,
R π(i) is an i th transmission rate in said permutation,
α is an adjustable parameter, and
N i * is a noise power level associated with said i th transmission rate, wherein a set of N 1 * , . . . ,N k * is associated with a maximum of said channel throughput.
19. The method as recited in claim 17 further comprising selecting a one of said at least some rate subsets having a maximum associated throughput.
20. The method as recited in claim 13 wherein said determining comprises calculating power allocations for rates in at least one of said at least some rate subsets.
21. The method as recited in claim 20 wherein said calculating comprises calculating said power allocations using an equation that at least approximates:
P
π
(
k
)
=
γ
π
(
k
)
[
∑
i
=
1
k
-
1
P
π
(
i
)
+
N
k
]
,
where:
γ π(k) =exp(2R π(k) )−1, for a permutation π of a subset R k of said predetermined set of allowed transmission rates,
P π(i) is an allocated power associated with an i th rate in said permutation, and
N k is a noise power level associated with a k th transmission rate in said subset.
22. The method as recited in claim 13 wherein said at least some rate subsets include subsets of single rates.
23. The method as recited in claim 13 further comprising calculating associated optimal noise levels for all rate subsets of said set.
24. The method as recited in claim 13 wherein a transmission standard determines said set.