Active array antenna linearization

1. A radio system, comprising:

an antenna array comprising a plurality of active antenna elements;

a plurality of transmit branches comprising a respective plurality of power amplifiers, the plurality of transmit branches operable to transmit a plurality of predistorted transmit signals via the plurality of active antenna elements, respectively;

a predistortion subsystem comprising a plurality of predistorters for the plurality of transmit branches respectively, the plurality of predistorters operable to predistort a respective plurality of transmit signals to provide the plurality of predistorted transmit signals and provide the plurality of predistorted transmit signals to the plurality of transmit branches, respectively;

a receive antenna element;

a transmit observation receiver having an input coupled to the receive antenna element, the transmit observation receiver operable to receive, via the receive antenna element, a combined receive signal; and

an adaptor operable to:

generate a combined reference signal based on the plurality of transmit signals such that the combined reference signal models the combined receive signal; and

configure predistortion parameters input to the plurality of predistorters that define predistortion provided by the plurality of predistorters based on the combined reference signal, the combined receive signal, and known complex valued attenuation factors that define the coupling from the plurality of active antenna elements to the receive antenna element;

wherein:

the predistortion parameters are an estimated predistortion coefficient vector, α k+1 , that defines a common set of predistortion coefficients for the plurality of predistorters; and

in order to configure the predistortion parameters, the adaptor is further configured to compute the estimated predistortion coefficient vector, α k+1 , in accordance with:

α k+1 =α k +η·M k + ·[(Σ n=1 N β n ·x n )− y k ]

where α k is a prior set of predistortion parameters for the plurality of predistorters used to generate the plurality of predistorted transmit signals;

ηis a scaling convergence factor;

β n is a coupling factor between the n-th active antenna element and the receive antenna element;

x n is the transmit signal that is predistorted by the respective predistorter to provide the predistorted transmit signal for the transmit branch for the n-th active antenna element;

y k is the combined receive signal; and

M k + =( M k H ·M k ) −1 ·M k H

where

M k =[ y k y k ·|y k | 2 y k ·|y k | 4 ⋅⋅⋅⋅⋅⋅],which is a measurement matrix for a non-linear model of a power amplifier.

2. The radio system of claim 1 wherein the receive antenna element is a dedicated antenna element for the transmit observation receiver.

3. A method of operation of a radio system to linearize the radio system, comprising:

predistorting a plurality of transmit signals via a respective plurality of predistorters of the radio system to thereby provide a plurality of predistorted transmit signals;

transmitting the plurality of predistorted transmit signals via a respective plurality of active antenna elements in an antenna array of the radio system;

receiving a combined receive signal via a receive antenna;

generating a combined reference signal based on the plurality of transmit signals such that the combined reference signal models the combined receive signal; and

configuring, based on the combined reference signal, the combined receive signal, and known complex valued attenuation factors that define the coupling from the plurality of active antenna elements to the receive antenna element, predistortion parameters input to the plurality of predistorters that define predistortion provided by the plurality of predistorters;

wherein:

the predistortion parameters are an estimated predistortion coefficient vector, α k+1 , that defines a common set of predistortion coefficients for the plurality of predistorters; and

configuring the predistortion parameters comprises compute the estimated predistortion coefficient vector, a k+i , in accordance with:

α k+1 =α k +η·M k + ·[(Σ n=1 N β n ·x n )− y k ]

where

α k is a prior set of predistortion parameters for the plurality of predistorters used to generate the plurality of predistorted transmit signals;

η is a scaling convergence factor;

β n is a coupling factor between the n-th active antenna element and the receive antenna element;

x n is the transmit signal that is predistorted by the respective predistorter to provide the predistorted transmit signal for the transmit branch for the n-th active antenna element;

y k is the combined receive signal; and

M k + =( M k H ·M k ) −1 ·M k H

where

M k =[ y k y k ·|y k | 2 y k ·|y k | 4 ⋅⋅⋅⋅⋅⋅],which is a measurement matrix for a non-linear model of a power amplifier.

4. The method of claim 3 wherein the receive antenna element is a dedicated antenna element for a transmit observation receiver used for receiving the combined receive signal.

5. A base station for a wireless communication system, the base station comprising a radio system comprising:

an antenna array comprising a plurality of active antenna elements;

a plurality of transmit branches comprising a respective plurality of power amplifiers, the plurality of transmit branches operable to transmit a plurality of predistorted transmit signals via the plurality of active antenna elements, respectively;

a predistortion subsystem comprising a plurality of predistorters for the plurality of transmit branches respectively, the plurality of predistorters operable to predistort a respective plurality of transmit signals to provide the plurality of predistorted transmit signals and provide the plurality of predistorted transmit signals to the plurality of transmit branches, respectively;

a receive antenna element;

a transmit observation receiver having an input coupled to the receive antenna element, the transmit observation receiver operable to receive, via the receive antenna element, a combined receive signal; and

an adaptor operable to:

generate a combined reference signal based on the plurality of transmit signals such that the combined reference signal models the combined receive signal; and

configure predistortion parameters input to the plurality of predistorters that define predistortion provided by the plurality of predistorters based on the combined reference signal, the combined receive signal, and known complex valued attenuation factors that define the coupling from the plurality of active antenna elements to the receive antenna element;

wherein:

the predistortion parameters are an estimated predistortion coefficient vector, α k+1 , that defines a common set of predistortion coefficients for the plurality of predistorters; and

in order to configure the predistortion parameters, the adaptor is further configured to compute the estimated predistortion coefficient vector, α k+1 , in accordance with:

α

k

+

1

=

α

k

+

η

·

M

k

+

·

[

(

∑

n

=

1

N

⁢

β

n

·

x

n

)

-

y

k

]

where

α k is a prior set of predistortion parameters for the plurality of predistorters used to generate the plurality of predistorted transmit signals;

η is a scaling convergence factor;

β n is a coupling factor between the n-th active antenna element and the receive antenna element;

x n is the transmit signal that is predistorted by the respective predistorter to provide the predistorted transmit signal for the transmit branch for the n-th active antenna element;

y k is the combined receive signal; and

M k + =( M k H ·M k ) −1 ·M k H

where

M k =[ y k y k ·|y k | 2 y k ·|y k | 4 ⋅⋅⋅⋅⋅⋅], which is a measurement matrix for a non-linear model of a power amplifier.