Efficient deterministic nulling method and apparatus
Systems and method for placing nulls at desired locations within a beam pattern of a phased array antenna are provided. According to embodiments of the present disclosure, a weight vector solution for controlling operating parameters of the M elements of the array antenna such that a beam pattern incorporating one or more desired nulls is obtained by performing operations on an N×N matrix, where N is equal to a number of vectors used to describe the nulls. The nulls can be placed at arbitrary locations within the beam pattern, and can be formed with arbitrary depths.
1 . A method for placing nulls in an antenna beam pattern, comprising:
determining a desired beam pattern, wherein the desired beam pattern includes one or more nulls;
determining N vectors a, wherein at least one vector a is determined for each null included in the beam pattern;
storing the N determined vectors a in a matrix A;
performing an N×N eigenvalue decomposition of matrix A, thereby defining a vector space;
using decomposition, constructing an orthonormal basis Y spanning the space of A;
scaling and subtracting basis vectors y that form columns of Y from a fixed quiescent vector b to obtain a weight vector solution w; and
sending the weights w to an antenna system feed network to generate a quiescent beam pattern with each of the one or more nulls placed therein, wherein at least some of the one or more nulls have a location that corresponds to a location of an object.
2 . The method of claim 1 , wherein the antenna beam pattern is formed using an antenna having M elements, and wherein M is greater than 500.
3 . The method of claim 1 , wherein the object includes a communication endpoint.
4 . The method of claim 1 , wherein the object includes a radar endpoint.
5 . The method of claim 1 , wherein a depth of a first one of the nulls is different than a depth of a second one of the nulls.
6 . The method of claim 1 , wherein at least a first one of the one or more nulls includes at least first and second individual nulls, wherein the first individual null is created using a first vector a, wherein the second individual null is created using a second vector a, and wherein an area of the first individual null at least partially overlaps an area of or otherwise interacts with the second individual null.
7 . The method of claim 1 , wherein at least some of the nulls have a selected shape.
8 . The method of claim 1 , wherein at least some of the vectors produce nulls that partially overlap or that otherwise interact with one another.
9 . The method of claim 1 , wherein multiple vectors a are determined for at least a first one of the one or more nulls.
10 . The method of claim 1 , wherein the vectors are produced by any method.
11 . The method of claim 1 , wherein at least one of the vectors is produced by one of an iterative, closed-form, deterministic, static, or adaptive algorithm.
12 . The method of claim 1 , wherein at least one of the vectors is produced by empirical means.
13 . The method of claim 1 , wherein at least a first one of the nulls has an area described by a first array manifold vector that includes a plurality of vectors a, and wherein at least a second one of the nulls has an area described by a second array manifold vector that includes a second plurality of vectors a.
14 . A system for generating an antenna beam having a plurality of nulls, comprising:
an antenna system, including:
an array of antenna elements, wherein a spacing between adjacent antenna elements is known, and wherein the antenna elements lie in a first plane;
a feed network, wherein each element in the array of antenna elements is connected to the feed network;
a radio frequency transceiver, wherein the feed network connects the radio frequency transceiver to each of the antenna elements in the array of antenna elements; and
a processor, wherein the processor is operable to execute instructions to control parameters of the feed network to place the plurality of nulls at desired locations within a beam pattern produced by the antenna system, wherein the instructions include instructions to:
determine N vectors a, wherein at least one vector a is determined for each of the desired null locations;
place each of the N vectors a in a matrix A, thereby defining a vector space;
perform an N×N eigenvalue decomposition on the matrix A;
construct an orthonormal basis Y spanning the space of A;
scale and subtract basis vectors y that form columns of Y from a fixed quiescent vector b to obtain a weight vector solution w; and
apply the weights w to control the feed network and generate a quiescent pattern with the nulls.
15 . The system of claim 14 , wherein the array is a two-dimensional array.
16 . The system of claim 14 , wherein the antenna system includes M antenna elements, and wherein M is greater than 500.
17 . The system of claim 14 , wherein the antenna system is part of a communication endpoint.
18 . The system of claim 14 , wherein the antenna system is part of a radar endpoint.
19 . The system of claim 14 , wherein the processor is provided as part of the antenna system.
20 . A non-transitory, computer-readable medium comprising a set of instructions which, when executed by a processor, causes the processor to control parameters of a feed network of an antenna system to generate an antenna beam having a plurality of nulls placed at desired locations within a beam pattern by:
determining N vectors a, wherein at least one vector a is determined for each of the desired null locations;
placing each of the N vectors a in a matrix A, thereby defining a vector space;
performing an N×N eigenvalue decomposition on the matrix A;
constructing an orthonormal basis Y spanning the space of A;
scaling and subtracting basis vectors y that form columns of Y from a fixed quiescent vector b to obtain a weight vector solution w; and
applying the weights w to control the feed network and generate a quiescent beam pattern with the nulls,
wherein at least one of the nulls has a location that corresponds to a location of an object.