Restricted euclidean modulation

1. A method for controlling an antenna having a plurality of antenna elements, the method comprising:

determining modulation states for the plurality of antenna elements based on desired modulation states and achievable modulation states that are based on distances from one or more of the desired modulation states, the achievable modulation states being mapped to voltages applied to the antenna elements;

mapping modulation values associated with the achievable modulation states to one or more control parameters; and

controlling radio frequency (RF) radiating antenna elements using the one or more control parameters to perform beam forming.

2. The method of claim 1 wherein the distances are Euclidean distances.

3. The method of claim 1 wherein each achievable modulation state corresponds to voltages applied to the antenna elements of the antenna to induce magnetic dipole moments.

4. The method of claim 1 wherein the one or more control parameters comprise a voltage to be applied to each of the RF radiating antenna elements.

5. The method of claim 1 wherein the RF radiating antenna elements comprise tunable elements in a metasurface.

6. The method of claim 5 further comprising mapping a desired modulation to achievable modulation states comprises approximating a set of required polarizabilities.

7. The method of claim 1 wherein mapping the desired modulation to achievable modulation states comprises selecting points out of achievable polarizabilities that approximate required polarizabilities of the desired modulation.

8. The method of claim 1 further comprising obtaining the desired modulation, the desired modulation being based on one or more of: location of at least a subset of the RF radiating antenna elements; beam pointing direction and polarization; and wave propagation in a feed of the antenna.

9. An antenna comprising:

a metasurface having a plurality of RF radiating antenna elements;

a controller coupled to the metasurface and having modulation logic to:

determine modulation states for the plurality of antenna elements based on desired modulation states and achievable modulation states that are based on distances from one or more of the desired modulation states, the achievable modulation states being mapped to voltages applied to the antenna elements;

map modulation values associated with the achievable modulation states to one or more control parameters; and

drive circuitry coupled to the metasurface and the controller to control the RF radiating antenna elements using the one or more control parameters to perform beam forming.

10. The antenna of claim 9 wherein the distances are Euclidean distances.

11. The antenna of claim 9 wherein each achievable modulation state corresponds to voltages applied to the antenna elements of the antenna to induce magnetic dipole moments.

12. The antenna of claim 9 wherein the one or more control parameters comprise a voltage to be applied to each of the RF radiating antenna elements.

13. The antenna of claim 9 wherein the RF radiating antenna elements comprise tunable elements in a metasurface.

14. The antenna of claim 9 wherein the modulation logic is operable to map a desired modulation to achievable modulation states by approximating a set of required polarizabilities.

15. The antenna of claim 9 wherein the modulation logic is operable to map the desired modulation to achievable modulation states by selecting points out of achievable polarizabilities that approximate required polarizabilities of the desired modulation.

16. The antenna of claim 9 wherein the modulation logic is operable to obtain the desired modulation, the desired modulation being based on one or more of: location of at least a subset of the RF radiating antenna elements; beam pointing direction and polarization; and wave propagation in a feed of the antenna.