System and method for estimating the multi-path delays in a signal using a spatially blind antenna array
View Patent ↗A method is described that enables a system to estimate the individual times of arrival of multi-path signals components in a received signal while blind to the particular angular response characteristics of an antenna array. Additionally, a system is described that estimate the impulse response of the modulation channel. The impulse response is used to generate impulse response estimates for all multi-path signal components without reference to the actual angle of arrival of the signal. The impulse response for the multi-path constituents are directly associated with the time delays on each path, providing delay estimates for each path.
1. A method for estimating the multi-path delays τ i in a signal using a spatially blind antenna array comprising k arbitrary antenna elements, comprising the steps of:
generating an impulse response h k for each antenna element k in the antenna array;
determining a vectorized space-time impulse response I over the antenna array;
creating a covariance matrix C;
creating a fictitious array manifold A f , wherein A f is spatially blind and independent of the array characteristics; and
resolving the covariance matrix C with the fictitious manifold A f to thereby estimate the multi-path delays τ i independent of the array characteristics.
2. The method of claim 1 wherein the impulse response estimate h k is determined from the equation:
h k =(ZZ H ) −1 Zr k
where Z is a delay matrix and r k is the column vector of the received signal at antenna element k of the antenna array, where k=1,2, . . . m.
3. The method of claim 2 wherein the space-time impulse response vector I is formed by stacking the individual impulse response estimates h k into a column vector.
4. The method of claim 1 wherein the fictitious manifold A f is the aggregate of all vectors:
a
=
[
a
1
a
2
⋮
a
m
]
,
where a k (k=1,2, . . . m) range over the set of complex numbers, where m is the number of antenna elements in the array.
5. The method of claim 1 wherein the covariance matrix C is generated according to the following equation:
C
=
∑
I
I
H
.
6. The method of claim 1 , wherein the fictitious array manifold A f is used to form the space-time manifold and the space-time manifold operates to resolve the multi-path delays.
7. The method of claim 1 wherein the step of resolving the covariance matrix C to determine multi-path delays τ i uses the method of MUltiple SIgnal Classification (MUSIC) techniques.
8. The method of claim 1 wherein the step of resolving the covariance matrix C to determine multi-path delays τ i uses the Method of Alternating Projection (APM).
9. A method of estimating the multi-path delays τ i of a sequence of j blocks of a signal received at an antenna array of k isotropic antenna elements, independently of the spatial array characteristics of the antenna array, comprising the steps of:
deriving channel impulse response estimates h j,k for each block j at each antenna k;
determining a vectorized aggregate space-time impulse response I for each block j;
forming an estimated covariance matrix for the sequence of j blocks;
providing an array manifold A f void of spatial information; and,
resolving the covariance matrix with the array manifold A f to determine the multi-path delays τ i .
10. The method of claim 9 , wherein the impulse response estimate h j,k for block j is determined from the equation:
h j,k =(Z j Z j H ) −1 Z j r j,k
where Z j is a delay matrix for block j and r jk is the column vector of the received signal for block j at antenna k of the antenna array, where k=1,2, . . . m.
11. The method of claim 10 , wherein the space-time impulse response vector I is formed by stacking the individual impulse response estimates h jk into a column vector.
12. The method of claim 9 , wherein the fictitious manifold A f is the aggregate of all vectors:
a
=
[
a
1
a
2
⋮
a
m
]
,
where a k (k=1,2, . . . m) range over the set of complex numbers, where m is the number of an antenna element in the array.
13. The method of claim 9 , wherein the covariance matrix C is generated according to the following equation:
C
=
∑
j
=
1
J
I
j
I
j
H
.
14. The method of claim 9 , wherein the fictitious array manifold A f is used to form the space-time manifold and the space-time manifold operates to resolve the multi-path delays.
15. The method of claim 9 , wherein the step of resolving the covariance matrix C to determine multi-path delays τ i uses multiple signal classification techniques.
16. The method of claim 9 , wherein the step of resolving the covariance matrix C to determine multi-path delays τ i uses Alternating Projection.
17. A system for estimating the multi-path delays τ i in a signal using a spatially blind antenna array comprising:
an antenna array for receiving the signal;
a means for generating an impulse response h k for each antenna k in the antenna array;
a means determining a vectorized space-time impulse response I over the antenna array;
a means for creating a covariance matrix C
a means for creating a fictitious manifold A f , wherein A f is spatially blind and independent of the array characteristics; and,
a means for resolving the covariance matrix C with the fictitious manifold A f to estimate the multi-path delays τ i independent of the array characteristics.
18. The system of claim 17 , wherein the fictitious array manifold A f in part forms the space-time manifold and a space-time manifold operates to resolve the multi-path delays.