Computer implemented method for reducing adaptive beamforming computation using a Kalman filter

1. A computer implemented method for reducing adaptive beamforming computation resources for estimating and updating a model of beam weights, comprising:

a) estimating, through a computer device by a base station, optimal beam pattern weights of an antenna electromagnetic element signal duration, using an adaptive beamforming algorithm for at least 3 time steps of the antenna electromagnetic element signal, wherein a time step is a time interval between reference signal transmissions;

b) creating, through the computer, an initial linear model for either magnitude or phase components of the optimal beam pattern weights computed from the adaptive beamforming algorithm estimates;

c) estimating, through the computer, for each time step, a measurement of the optimal beam pattern weights, using a reduced set of data comprising 5-20% of first samples of data generated by the antenna electromagnetic element signal duration; and

d) computing new beam pattern weights, through the computer, using a magnitude state estimation filter and/or phase state estimation filter, wherein the computation resources required by the adaptive beamforming algorithm to obtain the new beam pattern weights are reduced by 80 to 90%.

2. The computer implemented method of claim 1 , further comprising, for each antenna electromagnetic element signal duration, time step, and magnitude or phase state estimation filter;

a) forming an estimator matrix;

b) predicting the state of beam weight model coefficients;

c) calculating error covariance;

d) calculating state estimation filter gain;

e) estimating beam weight model coefficients;

f) calculating a new beam pattern weight using the estimate for the beam weight model coefficients; and

g) computing error covariance.

3. A computer implemented method for reducing adaptive beamforming computation resources for estimating and updating a linear model of unwrapped beam weights, comprising:

a) estimating, through a computer device by a base station, optimal beam pattern weights of an antenna element signal, using an adaptive beamforming algorithm for at least 3 time steps of the antenna electromagnetic element signal, wherein a time step is a time interval between reference signal transmissions;

b) creating, through the computer, an initial linear model for either magnitude or phase components of the optimal beam pattern weights computed from the adaptive beamforming algorithm estimates;

c) estimating, through the computer, for each time step, a measurement of the optimal beam pattern weights, using a reduced set of data comprising 5-20% of first samples of data generated by the adaptive beamforming algorithm; and

d) computing Kalman factor state filter measurements, through the computer, wherein the computation resources required by the adaptive beamforming algorithm to obtain a new beam pattern weights are reduced by 80 to 90%.

4. The computer implemented method of claim 3 , further comprising, for each antenna element signal and each time step;

a) forming a linear estimator matrix;

b) predicting the state of beam weight linear model coefficients;

c) calculating error covariance;

d) calculating Kalman gain;

e) estimating beam weight linear model coefficients;

f) calculating a new beam pattern weight using the estimate for the beam weight linear model coefficients; and

g) computing error covariance.

5. The computer implemented method of claim 3 , wherein step b) employs the

h

=

(

H

′

⋆

H

)

-

1

⁢

H

′

⋆

Z

=

[

h

1

(

t

)

h

2

(

t

)

]

;

following equation:

Step c) employs the following equations: d=s *w est and w est (t)=(s′*s) −1 s′*d; and

Step d) employs the following equation m mag =|w est (t)| for the magnitude KF and the following equation m phase =unwrap (∠w est ) for the phase KF.

6. The computer implemented method of claim 4 , wherein

step a) uses the following equation: v=[x(k−1, n)1];

step b) uses the following equation: hp(k)=A*h(k−1,n);

step c) uses the following equation: Pp=A*P(k−1,n)*A T +Q;

step d) uses the following equation:

K

⁡

(

k

,

n

)

=

Pp

⋆

v

′

R

+

v

⋆

Pp

⋆

v

′

;

step e) uses the following equation: h(k,n)=hp(k)+K(k,n)*[m(k,n)−v*hp(k,n)];

step f) uses the following equation: x(k,n)=v*h(k,n); and

step g) uses the following equation: P(k,n)=I−K(k,n)*v*Pp.

7. A computer implemented method for reducing adaptive beamforming computation resources for estimating and updating a linear model of unwrapped beamforming weights, comprising:

a) estimating, through a computer device by a base station, the optimal beam pattern weights of an antenna element signal, using an adaptive beamforming algorithm for at least 3 time steps of the antenna electromagnetic element signal, wherein a time step is a time interval between reference signal transmissions;

b) creating, through the computer, an initial linear model for either magnitude or phase components of the optimal beam pattern weights computed from the adaptive beamforming algorithm estimates, using the following equation:

h

=

(

H

′

⋆

H

)

-

1

⁢

H

′

⋆

Z

=

[

h

1

(

t

)

h

2

(

t

)

]

;

c) estimating, through the computer, for each time step, a measurement of the optimal beam pattern weights, using a reduced set of data comprising 5-20% of first samples of data generated by the adaptive beamforming algorithm, using the following equations:

d=s*w est and W est (t)=(s′*s) −1 s′*d;   

d) computing Kalman factor state filter measurements, through the computer, using the following equation for the magnitude KF:

m mag =|w est (t)|  

and the following equation for the phase KF:

m phase =unwrap( w est ); and   

e) for each antenna element signal and each time step;

i) forming a linear estimator matrix;

ii) predicting the state of the beam pattern weight linear model coefficients;

iii) calculating error covariance;

iv) calculating Kalman gain;

v) estimating beam pattern weight linear model coefficients;

vi) calculating a new beam pattern weight using the estimate for the beam pattern weight linear model coefficients; and

vii) computing error covariance, wherein the computation resources required by the adaptive beamforming algorithm to obtain new beam pattern weights are reduced by 80 to 90%.

8. The computer implemented method of claim 7 , wherein

step i) uses the following equation: v=[x (k−1,n)1];

step ii) uses the following equation: hp(k)=A*h(k−1,n);

step iii) uses the following equation: Pp=A*P(k−1,n)* A T +Q;

step iv) uses the following equation:

K

⁡

(

k

,

n

)

=

Pp

⋆

v

′

R

+

v

⋆

Pp

⋆

v

′

;

step v) uses the following equation: h(k,n)=hp(k)+K(k,n)*[m(k,n)−v*hp(k,n)];

step vi) uses the following equation: x(k,n)=v*h(k,n); and

step vii) uses the following equation: P(k,n)=I−K(k,n)*v*Pp.