Computational methods for use in a short-code spread-spectrum communications system
View Patent ↗The invention provides methods and apparatus for multiple user detection (MUD) processing that have application, for example, in improving the capacity CDMA and other wireless base stations. One aspect of the invention provides a multiprocessor, multiuser detection system for detecting user transmitted symbols in CDMA short-code spectrum waveforms. A first processing element generates a matrix (hereinafter, “gamma matrix”) that represents a correlation between a short-code associated with one user and those associated with one or more other users. A set of second processing elements generates, e.g., from the gamma matrix, a matrix (hereinafter, “R-matrix”) that represents cross-correlations among user waveforms based on their amplitudes and time lags. A third procesing element produces estimates of the user transmitted symbols as a function of the R-matrix.
1. A method of processing spread spectrum waveforms transmitted by a plurality of users of a spread spectrum system, comprising:
computing a matrix representing cross correlations among the waveforms, said computing step including
performing matrix calculation on at least a first one of two matrix components related by a symmetry property defined in accord with the relation:
R l,k ( m )=ξ R k,l (− m )
wherein
R lk (m) and R kl (m) refer to (l,k) and (k,l) elements of the cross correlation matrix, respectively, and
ξ is a proportionality constant,
computing a second one of the two matrix components as a function of the first matrix component by applying said symmetry property, and
generating estimates of symbols transmitted by the users and encoded in said waveforms as a function of the cross correlation matrix
wherein the step of computing the cross-correlation matrix comprises computing a matrix (herein referred to as Γ-matrix) that represents correlations among short code sequences associated with the respective users in accord with the relation:
Γ
l
k
[
m
]
≡
1
2
N
l
∑
n
=
0
N
-
1
c
l
*
[
n
]
·
c
k
[
n
-
m
]
wherein
c l * [n] represents complex conjugate of the short code sequence associated with the l th user,
c k [n−m] represents the short code sequence associated with k th user,
N represents the length of the code, and
N l represents the number of non-zero length of the code
wherein the step of computing the cross-correlation matrix comprises computing a matrix (herein referred to as C matrix) representing cross-correlations among time lags associated with the transmitted waveforms and correlations among the short code sequences of the respective users as a function of the Γ-matrix in accord with the relation:
C
l
k
q
q
′
[
m
′
]
=
∑
m
g
[
m
N
c
+
τ
]
·
Γ
l
k
[
m
]
wherein
g is a pulse shape vector,
N 0 is the number of samples per chip,
τ is a time lag,
m is a symbol period, and
Γ represents the aforesaid Γ matrix.
2. The method of claim 1 , wherein the step of computing the cross-correlation matrix (herein referred to as r-matrix) comprises calculating the r matrix as a function of the C matrix in accord with the relation:
r
lk
[
m
′
]
=
∑
q
=
1
L
∑
q
′
=
1
L
Re
{
a
^
lq
*
a
kg
1
·
C
lkqg
′
[
m
′
]
}
=
Re
{
a
l
H
·
C
lk
[
m
′
]
·
a
k
}
wherein
â lq * is an estimate of a lq * which is the complex conjugate of one multipath amplitude component of the l th user,
a kq′ is one multipath amplitude component associated with the k th user, and
C denotes to aforesaid C matrix
m′ is an index, indicating a symbol period,
Re denotes the real part of a complex expression, and
a k is a columnar matrix representing multipath amplitude components associated with the k th user.
3. The method of claim 2 , further comprising the step of computing detection statistics corresponding to transmitted symbols as a function of the r matrix.
4. The method of claim 3 , wherein the step of computing detection statistics comprises performing calculation in accord with the relation:
y
l
[
m
]
=
r
ll
[
0
]
b
l
[
m
]
+
∑
k
=
1
K
v
r
lk
[
-
1
]
b
k
[
m
+
1
]
+
∑
k
=
1
K
v
[
r
lk
[
0
]
-
r
ll
[
0
]
δ
lk
]
b
k
[
m
]
+
∑
k
=
1
K
v
r
lk
[
1
]
b
k
[
m
-
1
]
+
η
l
[
m
]
wherein
y l [m] represents detection statistic for the m th symbol transmitted by l th user,
r ll [0]b l [m] represents a signal of interest, and
the remaining terms represent Multiple Access Interference (MAI) and noise.
5. The method of claim 4 , further comprising the step of generating estimates corresponding to the transmitted symbols by applying a multi-stage decision-feedback interference cancellation (MDFIC) algorithm to the detection statistics.
6. The method of claim 5 , wherein the step of applying the MDFIC algorithm comprises utilizing the relation:
b
^
l
[
m
]
=
sign
{
y
l
[
m
]
-
∑
k
=
1
K
v
r
lk
[
-
1
]
b
^
k
[
m
+
1
]
-
∑
k
=
1
K
v
[
r
lk
[
0
]
-
r
ll
[
0
]
δ
lk
]
b
^
k
[
m
]
-
∑
k
=
1
K
v
r
lk
[
1
]
b
^
k
[
m
-
1
]
}
wherein
{circumflex over (b)} l [m] represents an estimate of the m th symbol transmitted by the l th user.