Direction-finding for multiple cochannel sources
View Patent ↗Techniques for determining the angles of arrival of multiple simultaneous cochannel sources using only a single RF receiver sampling and downconversion channel is disclosed. This is accomplished by sequentially forming several known mixtures of multiple antenna signals in the RF domain prior to downconversion and digitization. Angle of arrival information is then recovered through the application of higher order statistics and subspace fitting techniques. The same principles can be applied to other P-element receiver arrays (e.g., acoustical receiver array).
1. A method for determining the angles of arrival of multiple simultaneous radio frequency (RF) cochannel signals received at a P-element antenna array, the method comprising:
receiving multiple simultaneous RF cochannel signals at the array;
sequentially forming mixtures of the received RF cochannel signals using RF mixture weights, thereby enabling nonsimultaneously sampled mixtures;
forming a downconverted baseband mixture for each RF mixture using single channel downconversion;
forming data cumulants based on the baseband mixtures; and
searching over appropriate degrees of freedom in a mixture manifold including a set of possible data cumulants associated with the array to establish a best fit between the formed data cumulants and the possible data cumulants, thereby determining angle of arrival (AOA) estimates for each of the received cochannel signals.
2. The method of claim 1 further comprising the preliminary step of:
determining the mixture manifold and appropriate degrees of freedom for searching based on calibrated antenna gains and phases associated with the array, and baseband mixture weights associated with the RF mixture weights.
3. The method of claim 2 further comprising the preliminary steps of:
determining the calibrated antenna gains and phases at desired operating frequencies associated with the array; and
determining the RF mixture weights and associated baseband mixture weights for all desired mixtures of the RF cochannel signals.
4. The method of claim 1 further comprising:
determining the RF mixture weights (m approx ) through a procedure represented by:
m
approx
=
arg
max
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m
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where
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.
5. The method of claim 1 wherein searching over appropriate degrees of freedom in the mixture manifold to establish a best fit between the formed data cumulants and the possible data cumulants includes establishing an optimal mixture matrix (A est ), where
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est
=
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where is the mixture manifold representing the set of possible data cumulants, c y q represents the formed data cumulants, with q representing a particular data cumulant, P A q represents a matrix that projects onto the subspace spanned by Θ q A, where P A q =(Θ q A){(Θ q A) T (Θ q A)} + (Θ q A) T , and w q are nonnegative weights.
6. The method of claim 1 wherein sequentially forming mixtures of the received RF cochannel signals using RF mixture weights includes using analog multiplication and summing of the RF mixture weights prior to single channel downconversion and sampling.
7. The method of claim 1 wherein forming data cumulants based on the baseband mixtures includes calculating moments mathematically related to the data cumulants.
8. The method of claim 1 wherein the array has a response r(ψ,θ) that is completely known and is not required to be steering direction (ψ) invariant, and the mixture manifold is parameterized by N angles of arrival (θ n ), and searching over the θ n enables a best fit between formed data cumulants to possible data cumulants, where N is the number of received multiple simultaneous RF cochannel signals.
9. The method of claim 1 wherein the array has a response r(ψ,θ) that is completely known and steering direction invariant, and in addition to N−1 AOA differences, the mixture manifold is parameterized by M parameters r(ψ 1 ,θ 1 ),K,r(ψ M ,θ 1 ), with an additional constraint that estimated mixture matrix columns be unit-norm, and wherein searching over the resulting N+M−2 degrees of freedom is performed to optimize the estimated mixture matrix, thereby enabling a best fit between formed data cumulants to possible data cumulants, where N represents the number of received multiple simultaneous RF cochannel signals, and M represents the number of formed RF mixtures.
10. The method of claim 1 wherein forming data cumulants based on the baseband mixtures allowing for modeling errors and finite sample effects.
11. The method of claim 1 wherein searching over appropriate degrees of freedom in a mixture manifold includes limiting the search region.
12. The method of claim 1 wherein previous angle of arrival estimates are used to initialize a next search, thus saving computational cost in the searching.
13. The method of claim 12 wherein the search range is reduced by only allowing the searching to be performed within a small angular window of last estimated positions.
14. The method of claim 1 wherein searching over appropriate degrees of freedom in a mixture manifold includes an alternating least squares (ALS) iterative optimization process.
15. The method of claim 1 further comprising:
determining source cumulants (c x q ) thereby enabling source type identification for each received RF cochannel signal.
16. The method of claim 15 wherein determining the source cumulants includes using either ordinary least squares (OLS) or total least squares (TLS).
17. The method of claim 15 further comprising:
determining the number (N) of received RF cochannel signals based on estimated power of a weakest signal relative to the other signals.
18. The method of claim 1 wherein forming a downconverted baseband mixture for each RF mixture using single channel downconversion is carried out for a quadrature downconversion path.
19. The method of claim 1 wherein forming a downconverted baseband mixture for each RF mixture using single channel downconversion is carried out for a real downconversion path.
20. A method for determining the angles of arrival of multiple simultaneous cochannel signals received at a P-element antenna array, the method comprising:
receiving multiple simultaneous cochannel signals at the array;
sequentially forming mixtures of the received cochannel signals using mixture weights, thereby enabling nonsimultaneously sampled mixtures;
forming data cumulants based on the formed mixtures; and
searching over appropriate degrees of freedom in a mixture manifold including a set of possible data cumulants associated with the array to establish a best fit between the formed data cumulants and the possible data cumulants, thereby determining angle of arrival (AOA) estimates for each of the received cochannel signals.
21. The method of claim 20 wherein searching over appropriate degrees of freedom in a mixture manifold includes limiting the search region.
22. The method of claim 20 wherein previous angle of arrival estimates are used to initialize a next search, thus saving computational cost in the searching.
23. The method of claim 22 wherein the search range is reduced by only allowing the searching to be performed within a small angular window of last estimated positions.
24. The method of claim 20 wherein searching over appropriate degrees of freedom in a mixture manifold includes an alternating least squares (ALS) iterative optimization process.
25. The method of claim 20 wherein searching over appropriate degrees of freedom in a mixture manifold includes a general purpose optimization process.
26. A system for determining the angles of arrival of multiple simultaneous cochannel signals received at a P-element receiver array, the system comprising:
two or more elements adapted to receive multiple simultaneous cochannel signals;
a mixture forming section adapted to sequentially form mixtures of the received cochannel signals using mixture weights, thereby enabling nonsimultaneously sampled mixtures;
a form cumulants module adapted to form data cumulants based on the formed mixtures; and
a subspace fitting search module adapted to search over appropriate degrees of freedom in a mixture manifold including a set of possible data cumulants associated with the array to establish a best fit between the formed data cumulants and the possible data cumulants, thereby determining angle of arrival (AOA) estimates for each of the received cochannel signals.