Method for iterative estimation of global parameters

1. A method for iterative estimation of a set of unknown channel parameters in a beamforming network comprising:

determining a first order estimate of offsets at measurement nodes and a confidence in the initial estimate of the offsets at the measurement nodes; and

iterating, until a desired estimation accuracy is obtained:

determining an improved estimate of a parameter set, and a confidence in the improved estimate, using the prior estimate of the offsets at the measurement nodes; and

determining an improved estimate of the offsets at the measurement nodes, and the associated confidence values, using the prior estimate of the parameter set and the corresponding confidence values, wherein the measurement nodes on a forward link collect channel information corresponding to a Geostationary satellite's forward link, and wherein a Hybrid Matrix assembly is a part of a satellite payload, send the measured channel information to a central beamforming network over a Wide Area Network (WAN) fiber link,

wherein the Hybrid Matrix effects are taken into account and propagation delays are compensated for using a linear predictive scheme in processing of a measurement matrix R L×M prepared using the data on the WAN, and

wherein on a return link, beacon transmitters send pilot signals that are received at the beamforming network, wherein measurements of the pilot signals are used to formulate the matrix R L×M .

2. The method of claim 1 , wherein the parameter estimation extracts the estimates of two different sets, c M×1 and k L×1 , of unknown complex-valued parameters, from their coupled, intermittent and noisy measurements collected in the measurement matrix R L×M .

3. The method of claim 2 , wherein faults and outages in the measurement matrix R L×M are accounted for resulting in graceful performance degradation as the unavailability of the measurements increases.

4. The method of claim 1 , wherein the iterating further comprises passing from one iteration to the next, the estimates of the unknown variables, and the confidence in the estimates.

5. The method of claim 1 , further comprising:

self-initializing by using an arbitrary row or column of an observation matrix as an initial seed; and

iterating using multiple instantiations, where each instantiation uses a different row or column of the observation matrix.

6. The method of claim 1 , wherein one of the measurement nodes and the beacon transmitters are part of one of a beam forming network, a distributed MIMO architecture, and a wireless communication system with macro-diversity.

7. A method for iterative estimation of a set of unknown channel parameters in a beamforming network comprising:

determining a first order estimate of offsets at measurement nodes and a confidence in the initial estimate of the offsets at the measurement nodes; and

iterating, until a desired estimation accuracy is obtained:

determining an improved estimate of a parameter set, and a confidence in the improved estimate, using the prior estimate of the offsets at the measurement nodes; and

determining an improved estimate of the offsets at the measurement nodes, and the associated confidence values, using the prior estimate of the parameter set and the corresponding confidence values,

wherein determining the first order estimate of the measurement offsets comprises:

using an arbitrary m th column of a normalized matrix {tilde over (R)} L×M of measurements to determine a vector {tilde over (k)} m according to {tilde over (k)} m =[{tilde over (R)}(1,m),{tilde over (R)}(2,m), . . . , {tilde over (R)}(L,m)] T , where the vector {tilde over (k)} m represents a parameter m as measured at L measurement nodes and the normalized matrix {tilde over (R)} L×M is a normalized set of measurements.

8. A method for iterative estimation of a set of unknown channel parameters in a beamforming network comprising:

determining a first order estimate of offsets at measurement nodes and a confidence in the initial estimate of the offsets at the measurement nodes;

determining a first order estimate of the channel parameter set, wherein determining the first order estimate comprises:

using an arbitrary 1 th row of a normalized matrix {tilde over (R)} L×M of measurements to determine a vector {tilde over (c)} 1 according to {tilde over (c)} l =[{tilde over (R)}(l,1),{tilde over (R)}(l,2), . . . ,{tilde over (R)}(l,M)] T , where the vector {tilde over (c)} 1 represents the 1 th measurement nodes measurements of M parameters, and the normalized matrix {tilde over (R)} L×M is a normalized set of measurements: and

iterating, until a desired estimation accuracy is obtained:

determining an improved estimate of the channel parameter set, and a confidence in the improved estimate, using the prior estimate of the offsets at the measurement nodes; and

determining an improved estimate of the offsets at the measurement nodes, and the associated confidence values, using the prior estimate of the parameter set and the corresponding confidence values.

9. A method for iterative estimation of a set of unknown channel parameters in a beamforming network comprising:

determining a first order estimate of offsets at measurement nodes and a confidence in the initial estimate of the offsets at the measurement nodes; and

iterating, until a desired estimation accuracy is obtained:

determining an improved estimate of a parameter set, and a confidence in the improved estimate, using the prior estimate of the offsets at the measurement nodes; and

determining an improved estimate of the offsets at the measurement nodes, and the associated confidence values, using the prior estimate of the parameter set and the corresponding confidence values,

wherein determining the improved estimate of the parameter set, using the first order estimate of offsets at the measurement nodes, comprises:

transforming a normalized receiver measurement matrix {tilde over (R)} L×M using a parameter set vector {tilde over (k)} to a form that contains only the unknown c m terms, {tilde over (C)} L×M ={tilde over (K)} L×L −1 ×{tilde over (R)} L×M ˜1 L×M +C M×M where an m th column has L different estimates of a single unknown variable c m , and is represented as

[

c

m

⁡

(

1

)

⋮

c

m

⁡

(

L

)

]

=

[

1

⋮

1

]

L

×

1

⁢

c

m

+

[

n

c

m

⁡

(

1

)

⋮

n

c

m

⁡

(

L

)

]

;

combining the L estimates using a weight vector w whose 1 th element, w 1 is inversely proportional to a variance of a corresponding noise term n c m (1);

collecting M estimates {tilde over (c)} m in a single vector {tilde over (c)}; and

setting a variance σ l,m 2 to a high number, and a Signal to Noise Ratio a low value, if the measurement {tilde over (R)} l,m is not available due to lack of connections or due to a failure of the beacon transmitter.

10. A method for iterative estimation of a set of unknown channel parameters in a beamforming network comprising:

determining a first order estimate of offsets at measurement nodes and a confidence in the initial estimate of the offsets at the measurement nodes; and

iterating, until a desired estimation accuracy is obtained:

determining an improved estimate of a parameter set, and a confidence in the improved estimate, using the prior estimate of the offsets at the measurement nodes; and

determining an improved estimate of the offsets at the measurement nodes, and the associated confidence values, using the prior estimate of the parameter set and the corresponding confidence values,

wherein determining the improved estimate of the offsets at the measurement nodes, using the improved estimate of the parameter set, comprises:

converting an estimated vector {tilde over (c)} to a diagonal matrix {tilde over (C)} M×M ;

transforming a normalized receiver measurement matrix {tilde over (R)} L×M to a form that contains only the unknown k 1 terms, {tilde over (K)} M×L ={tilde over (C)} M×M −1 ×({tilde over (R)} L×M ) T ˜1 M×L +K L×L ;

combining the L estimates using a weight vector w whose 1 th element, w 1 is inversely proportional to a variance of a corresponding noise term n c m (1); and

setting a variance σ l,m 2 to a high number, and a Signal to Noise Ratio a low value, if the measurement {tilde over (R)} l,m is not available due to lack of connections or due to a failure of the beacon transmitter.

11. A system for iterative parameter estimation comprising:

a plurality of measurement nodes on a forward link and a plurality of beacon transmitters on a return link that are geographically separated and have an partial visibility to a full antenna array, and that introduce an unknown offset in a partial measurement of an antenna array channel parameter set; and

a signal processing system, wherein the signal processing system is configured to estimate parameters affecting the antenna array using measurements from the measurement nodes by determining a first order estimate of the offsets due either to the measurement node or the beacon transmitter and confidence in the estimates, and iteratively the prior estimate of the offsets due to the measurement node or the beacon transmitter and the corresponding confidence values to determine an improved estimate of the parameters and the corresponding confidence values, wherein the measurement nodes on the forward link collect channel information corresponding to a Geostationary satellite's forward link, and wherein a Hybrid Matrix assembly is a part of a satellite payload, send the measured channel information to a central beamforming network over a Wide Area Network (WAN) fiber link,

wherein the Hybrid Matrix effects are taken into account and propagation delays are compensated for using a linear predictive scheme in processing of a measurement matrix R L×M prepared using the data on the WAN, and

wherein on the return link, beacon transmitters send pilot signals that are received at the beamforming network, wherein measurements of the pilot signals are used to formulate the matrix R L×M .

12. The system of claim 11 , wherein the signal processing system is further configured to:

repeatedly improve the improved estimate of the offsets and improve the improved estimate of the parameters until an estimate with the desired accuracy is reached.

13. The system of claim 11 , wherein the measurement nodes and the beacon transmitters are part of one of a ground-based beam former, a terrestrial D-MIMO system, and a Wireless Sensor Network (WSN).

14. A system for iterative parameter estimation comprising:

a plurality of measurement nodes on a forward link and a plurality of beacon transmitters on a return link that are geographically separated and have an partial visibility to a full antenna array, and that introduce an unknown offset in a partial measurement of an antenna array channel parameter set; and

a signal processing system, wherein the signal processing system is configured to estimate parameters affecting the antenna array using measurements from the measurement nodes by determining a first order estimate of the offsets due either to the measurement node or the beacon transmitter and confidence in the estimates, and iteratively the prior estimate of the offsets due to the measurement node or the beacon transmitter and the corresponding confidence values to determine an improved estimate of the parameters and the corresponding confidence values,

wherein the signal processing system is configured to determine a first order estimate of a parameter set by:

using an arbitrary m th column of a normalized matrix {tilde over (R)} L×M of measurements to determine a vector {tilde over (k)} m according to {tilde over (k)} m =[{tilde over (R)}(1,m),{tilde over (R)}(2,m), . . . ,{tilde over (R)}(L,m)] T , where the vector {tilde over (k)} m represents a parameter m as measured at L measurement nodes on the forward link and using the beacon transmitters on the return link and the normalized matrix {tilde over (R)} L×M is a normalized set of measurements.

15. A system for iterative parameter estimation comprising:

a plurality of measurement nodes on a forward link and a plurality of beacon transmitters on a return link that are geographically separated and have an partial visibility to a full antenna array, and that introduce an unknown offset in a partial measurement of an antenna array channel parameter set; and

a signal processing system, wherein the signal processing system is configured to estimate parameters affecting the antenna array using measurements from the measurement nodes by determining a first order estimate of the offsets due either to the measurement node or the beacon transmitter and confidence in the estimates, and iteratively the prior estimate of the offsets due to the measurement node or the beacon transmitter and the corresponding confidence values to determine an improved estimate of the parameters and the corresponding confidence values,

wherein the signal processing system is configured to determine a first order estimate of offsets at the beacon transmitters and measurement nodes by:

using an arbitrary 1 th row of a normalized matrix {tilde over (R)} L×M of measurements to determine a vector {tilde over (c)} 1 according to {tilde over (c)} l =[{tilde over (R)}(l,1),{tilde over (R)}(l,2), . . . ,{tilde over (R)}(l,M)] T , where the vector {tilde over (c)} 1 represents the 1 th beacon transmitter or measurement node measurements of M parameters, and the normalized matrix {tilde over (R)} L×M is a normalized set of measurements.

16. A system for iterative parameter estimation comprising:

a plurality of measurement nodes on a forward link and a plurality of beacon transmitters on a return link that are geographically separated and have an partial visibility to a full antenna array, and that introduce an unknown offset in a partial measurement of an antenna array channel parameter set; and

a signal processing system, wherein the signal processing system is configured to estimate parameters affecting the antenna array using measurements from the measurement nodes by determining a first order estimate of the offsets due either to the measurement node or the beacon transmitter and confidence in the estimates, and iteratively the prior estimate of the offsets due to the measurement node or the beacon transmitter and the corresponding confidence values to determine an improved estimate of the parameters and the corresponding confidence values,

wherein the signal processing system is configured to determine an improved estimate of the parameters using the first order estimate of offsets at the beacon transmitters and measurement nodes by:

transforming a normalized receiver measurement matrix {tilde over (R)} L×M using a parameter set vector {tilde over (k)} to a form that contains only the unknown c m terms, {tilde over (C)} L×M ={tilde over (K)} L×L −1 ×{tilde over (R)} L×M ˜1 L×M +C M×M where an m th column has L different estimates of a single unknown variable c m , and is represented as

[

c

m

⁡

(

1

)

⋮

c

m

⁡

(

L

)

]

=

[

1

⋮

1

]

L

×

1

⁢

c

m

+

[

n

c

m

⁡

(

1

)

⋮

n

c

m

⁡

(

L

)

]

;

combining the L estimates using a weight vector w whose 1 th element, w 1 is inversely proportional to a variance of a corresponding noise term n c m (1);

collecting M estimates {tilde over (c)} m in a single vector {tilde over (c)}; and

setting a variance σ l,m 2 to a high number, and a Signal to Noise Ratio a low value, if the measurement {tilde over (R)} l,m is not available due to lack of connections or due to a failure of the beacon transmitter.

17. A system for iterative parameter estimation comprising:

a plurality of measurement nodes on a forward link and a plurality of beacon transmitters on a return link that are geographically separated and have an partial visibility to a full antenna array, and that introduce an unknown offset in a partial measurement of an antenna array channel parameter set; and

a signal processing system, wherein the signal processing system is configured to estimate parameters affecting the antenna array using measurements from the measurement nodes by determining a first order estimate of the offsets due either to the measurement node or the beacon transmitter and confidence in the estimates, and iteratively the prior estimate of the offsets due to the measurement node or the beacon transmitter and the corresponding confidence values to determine an improved estimate of the parameters and the corresponding confidence values,

wherein the signal processing system is configured to determine an improved estimate of the offsets at the measurement nodes using the improved estimate of the parameter set by:

converting an estimated vector {tilde over (c)} to a diagonal matrix {tilde over (C)} M×M ;

transforming a normalized receiver measurement matrix {tilde over (R)} L×M to a form that contains only the unknown k 1 terms, {tilde over (K)} M×L ={tilde over (C)} M×M −1 ×({tilde over (R)} L×M ) T ˜1 M×L +K L×L ; and

combining the L estimates using a weight vector w whose 1 th element, w 1 is inversely proportional to a variance of a corresponding noise term n c m (1).