Pilot packing using complex orthogonal functions

1. A method for wireless communication, comprising:

generating a pilot signal that is represented as a complex exponential signal having both a first linear phase in a time dimension and a second linear phase in a frequency dimension; and

transmitting the pilot signal over a wireless communication channel using transmission resources that are designated for pilot signal transmission in a legacy transmission network,

wherein the generating the pilot signal comprises generating the pilot signals by delay-Doppler domain packing by:

selecting a time-frequency lattice that meets a target overhead allocation;

packing a number of pilots in a torus corresponding to the time-frequency lattice, the number of pilots being selected to meet target delay and Doppler spreads of a channel in the legacy transmission network; and

transforming the number of pilots in the torus into a delay-Doppler domain by applying a symplectic transform.

2. The method of claim 1 , wherein the selecting the time-frequency lattice corresponds to selecting a finest available time-frequency lattice.

3. The method of claim 1 , wherein the legacy transmission network comprises a long term evolution (LTE) network.

4. The method of claim 3 , wherein the linear phase in the frequency dimension repeats every 14 symbols and the linear phase in the time dimension repeats at multiples of 12 time slots.

5. A method for wireless communication, comprising:

generating a pilot signal that is represented as a complex exponential signal having both a first linear phase in a time dimension and a second linear phase in a frequency dimension; and

transmitting the pilot signal over a wireless communication channel using transmission resources that are designated for pilot signal transmission in a legacy transmission network,

wherein the generating the pilot signal comprises generating the pilot signals by time-frequency packing, including:

choosing a time-frequency pilot lattice to support channel estimation by a receiver based on a single pilot signal;

generating an arrangement of pilot signals by staggering multiple time-frequency pilot lattices with equal distance between lattice points to meet a target overhead;

mapping the single pilot signal to a delay-Doppler torus associated with the time-frequency pilot lattice;

transforming the single pilot signal in the torus into a delay-Doppler domain by applying a symplectic transform;

creating the multiple time-frequency lattices and staggering the multiple time-frequency lattices; and

applying a window function to each time-frequency plane.

6. The method of claim 5 , wherein the choosing the time-frequency pilot lattice comprises choosing a coarsest possible time-frequency pilot lattice.

7. The method of claim 5 , wherein the legacy transmission network comprises a long term evolution (LTE) network.

8. The method of claim 7 , wherein the linear phase in the frequency dimension repeats every 14 symbols and the linear phase in the time dimension repeats at multiples of 12 time slots.

9. A method for wireless communication, comprising:

generating a pilot signal that is represented as a complex exponential signal having both a first linear phase in a time dimension and a second linear phase in a frequency dimension; and

transmitting the pilot signal over a wireless communication channel using transmission resources that are designated for pilot signal transmission in a legacy transmission network,

wherein the generating the pilot signal comprises generating the pilot signals by a latency sensitive pilot packing, including:

choosing a time-frequency pilot lattice that meets a target overhead;

selecting a smallest size pilot observation window in time domain to support one pilot signal in Doppler torus;

packing a number of pilots in a torus corresponding to the time-frequency lattice, the number of pilots being selected to meet target delay and Doppler spreads of a channel in the legacy transmission network;

transforming the delay-Doppler domain to the time-frequency domain by applying a symplectic transform; and

applying a window function in the time-frequency domain.

10. The method of claim 9 , wherein choosing the time-frequency pilot lattice includes choosing a finest possible lattice.

11. The method of claim 9 , wherein the legacy transmission network comprises a long term evolution (LTE) network.

12. The method of claim 11 , wherein the linear phase in the frequency dimension repeats every 14 symbols and the linear phase in the time dimension repeats at multiples of 12 time slots.

13. An apparatus for wireless communication, comprising:

a processor; and

a transmitter communicatively coupled to the processor,

wherein the processor is configured to generate a pilot signal that is represented as a complex exponential signal having both a first linear phase in a time dimension and a second linear phase in a frequency dimension,

wherein the transmitter is configured to transmit the pilot signal over a wireless communication channel using transmission resources that are designated for pilot signal transmission in a legacy transmission network, and

wherein generating the pilot signal is based on delay-Doppler domain packing with the processor being further configured to:

select a time-frequency lattice that meets a target overhead allocation;

pack a number of pilots in a torus corresponding to the time-frequency lattice, the number of pilots being selected to meet target delay and Doppler spreads of a channel in the legacy transmission network; and

transform the number of pilots in the torus into a delay-Doppler domain by applying a symplectic transform.

14. The apparatus of claim 13 , wherein the legacy transmission network comprises a long term evolution (LTE) network.

15. The apparatus of claim 14 , wherein the linear phase in the frequency dimension repeats every 14 symbols and the linear phase in the time dimension repeats at multiples of 12 time slots.