OTFS method of data channel characterization and uses thereof

• US 10,034,184 B2
• Filed: 05/24/2017
• Issued: 07/24/2018
• Est. Priority Date: 05/28/2010
• Status: Active Grant

• Current Assignee: Cohere Technologies Inc
• Original Assignee: Cohere Technologies Inc
• Inventors: Hadani, Ronny, Rakib, Shlomo Selim
• Primary Examiner(s): Elliott, IV, Benjamin H
• Application Number:
  US15/604,072
• Publication Number:
  US 20170303146A1
• Time in Patent Office: 426 Days
• CPC Class Codes: H04B 7/10 Polarisation diversity; Directional diversity
• CPC Class Codes: H04L 25/022 of frequency response
• CPC Class Codes: H04L 25/0224 using sounding signals
• CPC Class Codes: H04L 27/2613 Structure of the reference signals
• CPC Class Codes: H04L 27/2639 Modulators using other transforms, e.g. discrete cosine transforms, Orthogonal Time Frequency and Space [OTFS] or hermetic transforms
• CPC Class Codes: H04L 5/0007 the frequencies being orthogonal, e.g. OFDM(A), DMT
• CPC Class Codes: H04L 5/0023 Time-frequency-space
• CPC Class Codes: H04L 5/0048 Allocation of pilot signals, i.e. of signals known to the receiver
• CPC Class Codes: H04W 24/02 Arrangements for optimising operational condition
• CPC Class Codes: H04W 72/54 based on quality criteria

Abstract

Fiber, cable, and wireless data channels are typically impaired by reflectors and other imperfections, producing a channel state with echoes and frequency shifts in data waveforms. Here, methods of using OTFS pilot symbol waveform bursts to automatically produce a detailed 2D model of the channel state are presented. This 2D channel state can then be used to optimize data transmission. For wireless data channels, an even more detailed 2D model of channel state can be produced by using polarization and multiple antennas in the process. Once 2D channel states are known, the system turns imperfect data channels from a liability to an advantage by using channel imperfections to boost data transmission rates. The methods can be used to improve legacy data transmission modes in multiple types of media, and are particularly useful for producing new types of robust and high capacity wireless communications using non-legacy OTFS data transmission methods.

Claims

1. An automated method of acquiring a 2D channel state of an impaired data channel connecting at least one transmitter and at least one receiver,

said impaired data channel comprising at least one reflector, each said at least one reflector comprising a reflector location, reflector frequency shift, and at least one reflector coefficients of reflection;

each said at least one transmitter comprising a transmitter location and transmitter frequency shift;

each said at least one receiver comprising a receiver location and receiver frequency shift;

wherein said 2D channel state comprises information pertaining to relative locations, frequency shifts, and reflector coefficients of reflection of said at least one transmitters, receivers, and reflectors;

said method comprising;

using said at least one transmitter and at least one processor to transmit direct pilot bursts, said direct pilot bursts comprising a plurality pilot symbols P_pt,pf transmitted as pilot symbol waveform bursts P_pt,pf·

W_p(pt, pf), over a plurality of combinations of times pt and frequencies pf, where each said pt and pf are unique pilot time-frequency coordinates chosen from a two dimensional pilot time-frequency grid, and all said pilot symbol waveform bursts P_pt,pf·

W_p(pt, pf) are mutually orthogonal waveform bursts derived from time and frequency shifted versions of a same pilot basis waveform W_p;

said receiver configured to receive at least said pilot bursts according to at least a two dimensional pilot time-frequency bin structure with bin sizes and bin-coordinate positions proportional to said time-frequency grid;

wherein upon propagation through said impaired data channel, said direct pilot bursts then travel over at least one path, said at least one path comprising at least one of;

a;

direct pilot bursts traveling directly from said at least one transmitter to said at least one receiver; and

b;

replica pilot bursts comprising direct pilot bursts that have reflected off of said at least one reflector before reaching said at least one receiver, thereby producing direct waveform bursts that are further reflector time-delayed and reflector frequency-shifted at said at least one receiver;

wherein at said at least one receiver, a resulting combination of any said transmitter frequency shifted and receiver frequency shifted direct pilot bursts and any said replica pilot bursts produces channel-convoluted pilot bursts;

at said at least one receiver, using said bin structure to receive said channel-convoluted pilot bursts and using at least one processor to determine said 2D channel state of said impaired data channel connecting said at least one transmitter and said at least one receiver.

2. The method of claim 1, wherein prior to transmission, said plurality of pilot symbols P_pt,pf, and two dimensional pilot time-frequency grid and bin structure are chosen so that if, after transmission by said at least one transmitter, said impaired data channel subsequently causes at least some of said pilot symbol waveform bursts P_t1,f1·

W_p(t1, f1) originally transmitted at a first time-frequency coordinate to be projected onto different pilot symbol waveform bursts P_t2,f2·

Wp(t2, f2) originally transmitted at a different time-frequency coordinate, and bins different from those nominally corresponding to said pilot symbol waveform bursts P_t1,f1·

W_p(t1, f1), at least some of said projections will be detectable and quantifiable by said at least one receiver.

3. The method of claim 2, wherein said plurality of pilot symbols P_pt,pf transmitted as pilot symbol waveform bursts P_pt,pf·

W_p(pt, pf) comprise at least one non-null pilot symbol P_pt,pf transmitted as a pilot symbol waveform burst P_pt,pf·

W_p(pt, pf) with sufficient power to be detectable by said at least one receiver; and

any of;

1;

at least some of said plurality of pilot symbols are null pilot symbols intended to create empty pt and pf unique pilot time-frequency coordinates chosen from said two dimensional pilot time-frequency grid, where no waveform burst is transmitted;

or

2;

at least some of said plurality of pilot symbols are background pilot symbols intended to create a uniform background of pt and pf unique pilot time-frequency coordinates chosen from said two dimensional pilot time-frequency grid to enable projections of channel-convoluted non-null pilot bursts onto said uniform background to be detectable and quantifiable by said at least one receiver.

4. The method of claim 1, wherein said 2D channel state is at least partially determined by using at least one 2D impulse response to mathematically describe how said impaired data channel causes at least some of said pilot symbol waveform bursts P_t1,f1·

W_p(t1, f1) transmitted at a first time-frequency coordinate to be projected onto different pilot symbol waveform bursts P_t2,f2·

Wp(t2, f2) originally transmitted at a different time-frequency coordinate, and bins different from those nominally corresponding to said pilot symbol waveform bursts P_t1,f1·

W_p(t1, f1).

5. The method of claim 4, further using a plurality of said 2D impulse responses from a plurality of said bins to at least partially describe said 2D channel state as at least one 2D transform comprising at least one of a 2D Z-transform or other 2D transform.

6. The method of claim 1, wherein said 2D channel state comprises a matrix or other mathematical transform for said impaired data channel, describing how all signals transmitted by said transmitter are coupled with all signals from said transmitter that are received by said receiver.

7. The method of claim 1, wherein said plurality of pilot symbols P_pt,pf are known by said at least one receiver, and wherein said plurality of pilot symbols are further chosen to be any of:

one or two dimensional m-sequences comprising binary maximal-length shift register sequences, delta values P _i,j surrounded by regions of P_pt,pf zero values, one or two dimensional Barker codes, Costas arrays, Walsh matrixes, or other plurality of pilot symbols selected to facilitate acquiring said 2D channel state; and

wherein said bins have time-frequency resolutions that are equal to or more precise than time-frequency resolutions of said grid.

8. The method of claim 1, further transmitting a plurality of data symbols through said impaired data channel by using said at least one transmitter and at least one processor to also transmit at least some of said plurality of data symbols as direct data bursts comprising a plurality of data carrying waveform bursts, and to transmit said direct data bursts along with said direct pilot bursts to said at least one receiver;

wherein said direct data bursts also are reflected off of said at least one reflector, thereby producing replica data bursts comprising time-delayed and reflector frequency-shifted direct data bursts at said at least one receiver, and wherein at said at least one receiver, a resulting combination of any said transmitter frequency shifted and receiver frequency shifted direct data bursts, and replica data bursts, produce channel-convoluted data bursts;

using said 2D channel state and at least one processor to further perform at least one of;

a) precoding at least some of said direct data bursts at said at least one transmitter to pre-compensate for said impaired data channel; and

b) deconvoluting at least some of said channel-convoluted data bursts at said at least one receiver, thereby deriving at least an approximation of said plurality of data symbols.

9. The method of claim 8, wherein at least said data symbols are further arranged in symbol frame portions of a two dimensional data time-frequency grid, said symbol frames being either N×

N or N×

M frames of at least said data symbols, both N and M being integers greater than 1;

wherein, on a per symbol frame basis, said at least one processor spreads information from at least each data symbol across at least all data symbols in said symbol frame using a lossless and invertible transformation, thereby creating a corresponding frame comprising a plurality of symbols and corresponding transformed direct data bursts;

wherein said at least one wireless receiver further receives said channel-convoluted transformed data bursts on a per frame basis, and deconvolutes said plurality of symbols on a per frame basis, thereby creating an approximation of said frame;

further using said at least one processor and an inverse of said transformation to extract at least replica data symbols from said approximation of said frame.

10. The method of claim 8, wherein said direct data bursts transmit at least some of said plurality of data symbols as direct data bursts comprising a plurality of data symbols D_dt,df transmitted as data symbol waveform bursts D_dt,df·

W_d(dt, df) over a plurality of combinations of times dt and frequencies df, where each said dt and df are unique data time-frequency coordinates (dt, df) chosen from a two dimensional data time-frequency grid, and all said data symbol waveform bursts D_dt,df·

W_d(dt,df) comprise originally transmitted data symbols D_dt,df transmitted by mutually orthogonal waveform bursts derived from time and frequency shifted versions of a same data basis waveform W_d, and wherein each data symbol is distributed over a plurality of data symbols D_dt,df;

wherein said channel-convoluted data bursts are channel-convoluted data bursts;

wherein individual data symbols in said plurality of data symbols are encoded into a plurality of data symbols D_dt,df at said transmitter prior to transmission, said encoding configured so that said receiver must successfully receive a plurality of data symbols D_dt,df to provide enough information to determine said individual data symbols;

wherein said plurality of said data symbol waveform bursts D_dt,df·

W_d(dt, df) are mutually orthogonal waveform bursts derived from a same data basis waveform W_d; and

wherein said bin structure further encompasses said two dimensional data time-frequency grid.

11. The method of claim 10, wherein said data symbol waveform bursts D_dt,df·

W_d(dt, df) and said plurality of said pilot symbol waveform bursts P_pt,pf·

W_p(pt, pf) are chosen from a common plurality of times t and frequencies f, where each said t and f are unique time-frequency coordinates (t, f) chosen from a common grid of two dimensional time-frequency coordinates;

wherein said time-frequency coordinates (td, fd) for said data symbol waveform bursts are further chosen to not overlap with the time-frequency coordinates (pt, pf) for said pilot symbol waveform bursts.

12. The method of claim 11, wherein said data carrying data symbol waveform bursts D_dt,df·

W_d(dt,df) and said plurality of pilot symbols P_pt,pf transmitted as pilot symbol waveform bursts P_pt,pf·

W_p(pt, pf) do not occupy all unique time-frequency coordinates (dt, df) chosen from said two dimensional data time-frequency grid.

13. The method of claim 11, wherein said data carrying data symbol waveform bursts D_dt,df·

W_d(dt,df) and said plurality of pilot symbols P_pt,pf transmitted as pilot symbol waveform bursts P_pt,pf·

W_p(pt, pf) are not all transmitted at the same power level, but instead some data symbol waveform bursts or some pilot symbol waveform bursts are sent at power levels chosen according to at least said 2D channel state, distance to said at least one receiver, or sensitivity of said at least one receiver.

14. The method of claim 11, wherein said time-frequency coordinates (td, tf) for said data symbol waveform bursts are further chosen to either surround or to be adjacent to the time-frequency coordinates (pt, pf) for said pilot symbol waveform bursts;

and

wherein said pilot basis waveform W_p and said data basis waveform W_d are chosen to be the same basis waveform.

15. The method of claim 1, wherein said impaired data channel is an optical fiber data channel comprising at least one optical fiber, an electrically conducting wire data channel comprising at least one metallic electrical conductor, or a data channel comprising a fluid.

16. The method of claim 1, wherein said impaired data channel is a wireless data channel, said transmitter is a wireless transmitter, said receiver is a wireless receiver, said reflector is a wireless reflector further comprising a reflector velocity, said reflector frequency shift is a receiver velocity Doppler shift, and said at least one reflector coefficient of reflection is a reflector coefficient of wireless reflection;

said transmitter has a transmitter velocity, and said transmitter frequency is at least partially determined by a transmitter Doppler shift that varies according to said transmitter velocity;

said receiver has a receiver velocity, and said receiver frequency is at least partially determined by a receiver Doppler shift that varies according to said receiver velocity;

said direct pilot bursts comprise a plurality of wireless pilot symbol waveform bursts; and

wherein, said 2D channel state comprises information pertaining to relative locations, velocities, velocity induced frequency shifts caused by transmitter Doppler shifts, receiver Doppler shifts, reflector Doppler shifts, and reflector coefficients of reflection of said at least one transmitters, receivers, and reflectors.

17. An automated method of acquiring a 2D channel state of an impaired data channel connecting at least one transmitter and at least one receiver,

said impaired data channel comprising at least one reflector, each said at least one reflector comprising a reflector location, reflector frequency shift, and at least one reflector coefficients of reflection;

each said at least one transmitter comprising a transmitter location and transmitter frequency shift;

each said at least one receiver comprising a receiver location and receiver frequency shift;

wherein said impaired data channel is a wireless data channel, said transmitter is a wireless transmitter, said receiver is a wireless receiver, said reflector is a wireless reflector further comprising a reflector velocity, said reflector frequency shift is a receiver velocity Doppler shift, said transmitter frequency shift is a transmitter velocity Doppler shift, and said at least one reflector coefficient of reflection is a reflector coefficient of wireless reflection;

wherein said 2D channel state comprises information pertaining to relative locations, frequency shifts, and reflector coefficients of reflection of said at least one transmitters, receivers, and reflectors;

said method comprising;

using said at least one transmitter and at least one processor to transmit direct pilot bursts, said direct pilot bursts comprising a plurality of pilot symbols P_pt,pf transmitted as wireless pilot symbol waveform bursts P_pt,pf·

W_p(pt, pf), over a plurality of combinations of times pt and frequencies pf, where each said pt and pf are unique pilot time-frequency coordinates chosen from a two dimensional pilot time-frequency grid, and all said pilot symbol waveform bursts P_pt,pf·

W_p(pt, pf) are mutually orthogonal waveform bursts derived from time and frequency shifted versions of a same pilot basis waveform W_p;

said receiver configured to receive at least said pilot bursts according to at least a two dimensional pilot time-frequency bin structure with bin sizes and bin-coordinate positions proportional to said time-frequency grid;

wherein upon propagation through said impaired data channel, said direct pilot bursts then travel over at least one path, said at least one path comprising at least one of;

a;

direct pilot bursts traveling directly from said at least one transmitter to said at least one receiver; and

b;

replica pilot bursts comprising direct pilot bursts that have reflected off of said at least one reflector before reaching said at least one receiver, thereby producing direct waveform bursts that are further reflector time-delayed and reflector frequency-shifted at said at least one receiver;

wherein at said at least one receiver, a resulting combination of any said transmitter frequency shifted and receiver frequency shifted direct pilot bursts and any said replica pilot bursts produces channel-convoluted pilot bursts;

at said at least one receiver, using said bin structure to receive said channel-convoluted pilot bursts and using at least one processor to determine said 2D channel state of said impaired data channel connecting said at least one transmitter and said at least one receiver;

wherein, said 2D channel state comprises information pertaining to relative locations, velocities, velocity induced frequency shifts caused by transmitter Doppler shifts, receiver Doppler shifts, reflector Doppler shifts, and reflector coefficients of reflection of said at least one transmitters, receivers, and reflectors.

18. The method of claim 17, further transmitting a plurality of data symbols through said impaired data channel by using said at least one wireless transmitter and at least one processor to also transmit at least some of said plurality of data symbols as direct data bursts comprising wireless data carrying waveform bursts, to said at least one wireless receiver;

wherein said direct data bursts also are reflected off of said at least one wireless reflector, thereby producing replica data bursts comprising direct data bursts that are further reflector time-delayed and reflector velocity Doppler-shifted at said at least one wireless receiver, and wherein at said at least one wireless receiver, a resulting combination of any said transmitter Doppler-shifted and receiver Doppler-shifted direct data bursts and replica data bursts produce channel-convoluted data bursts;

using said 2D channel state and at least one processor to further perform at least one of;

a) precoding at least some of said direct data bursts at said at least one wireless transmitter to pre-compensate for said impaired data channel; and

b) deconvoluting at least some of said channel-convoluted data bursts at said at least one wireless receiver, thereby deriving at least an approximation of said plurality of data symbols;

wherein said data symbols and wireless data carrying waveform bursts are transmitted by any of TDMA, GSM, FDMA, OFDM, CDMA, or other types of wireless waveform bursts.

19. The method of claim 18, wherein at least said data symbols are further arranged in symbol frame portions of a two dimensional data time-frequency grid, said symbol frames being either N×

N or N×

M frames of at least said data symbols, both N and M being integers greater than 1;

wherein, on a per symbol frame basis, said at least one processor spreads information from at least each data symbol across at least all data symbols in said symbol frame using a lossless and invertible transformation, thereby creating a corresponding frame comprising a plurality of symbols and corresponding transformed direct data bursts;

wherein said at least one wireless receiver further receives said channel-convoluted transformed data bursts on a per frame basis, and deconvolutes said plurality of symbols on a per frame basis, thereby creating an approximation of said frame;

further using said at least one processor and an inverse of said transformation to extract at least replica data symbols from said approximation of said frame.

20. The method of claim 18, wherein said precoding or said deconvoluting is done by using at least one 1D projection of said 2D channel state along any of a time axis, frequency axis, or time-frequency axis.

21. The method of claim 18, wherein said at least one wireless transmitter transmits said direct pilot bursts as polarized direct pilot bursts comprising polarized wireless pilot symbol waveform bursts according to at least one polarization direction;

said at least one wireless reflector is a polarization altering wireless reflector that alters a polarization direction of its reflected wireless waveform bursts according to a first reflector polarization operator, thereby producing replica polarized pilot bursts that comprise polarization shifted time-delayed and reflector Doppler-shifted replicas of said polarized direct pilot bursts;

said at least one wireless receiver is further configured to detect a direction of polarization in its received wireless waveforms;

and wherein at said at least one wireless receiver, a resulting combination of any said transmitter Doppler-shifted, receiver Doppler-shifted, and receiver polarized direct pilot bursts and replica polarized pilot bursts produce channel-convoluted polarized pilot bursts;

receiving said channel-convoluted polarized pilot bursts and detecting their direction of polarization;

further using said direction of polarization of said channel-convoluted polarized pilot bursts to further determine said 2D channel state of said impaired data channel.

22. The method of claim 18, wherein said direct data bursts are direct data bursts comprising data symbols transmitted by wireless data symbol waveform bursts;

said wireless transmitter has T uniquely configured transmitting antennas, and said wireless receiver has R uniquely configured receiving antennas, both T and R being greater than 1,and R being greater than or equal to T;

said wireless transmitter configured to use its T transmitting antennas to simultaneously transmit, over a same frequency range, at most T streams of stream identifiable direct data and pilot bursts, each stream identifiable direct data and pilot bursts having at least pilot symbols P_s,pt,pf further chosen to be stream identifiable;

wherein at said at least one wireless receiver antenna R_a, a resulting combination of any said transmitter Doppler-shifted and receiver Doppler-shifted stream identifiable direct data and pilot bursts, and replica stream identifiable direct data and pilot bursts, produce receiving antenna specific channel-convoluted stream identifiable data and pilot bursts;

wherein said T transmitting antennas and R receiving antennas receiving antennas are configured so that said R receiving antennas receive different receiving antenna specific channel-convoluted stream identifiable data and pilot bursts with detectably different 2D channel states;

further improving an efficiency of successfully transmitting said at most T streams of data to said wireless receiver by;

at said receiver, using said R receiving antennas to receive said antenna specific channel-convoluted stream identifiable data and pilot bursts;

for each wireless receiving antenna R and each stream identifiable plurality of pilot symbol waveforms, using a receiver processor to determine said 2D channel state at said receiving antenna, thereby determining stream specific 2D channel states, and use said stream specific 2D channel state to perform at least one of;

a) precoding at least some of said stream identifiable direct data and pilot bursts at said at least one transmitter to pre-compensate for said impaired data channel; and

b) deconvoluting at least some of said antenna specific channel-convoluted stream identifiable data and pilot bursts at said at least one receiver, thereby deriving at least an approximation of said plurality of data symbols.

23. The method of claim 22, wherein determining said 2D channel state further comprises using at least one 2D impulse response to mathematically describe how, for said stream identifiable direct data and pilot bursts, stream-1 pilot symbol waveform bursts P_s1,t1,f1·

Wp(t1,f1) transmitted at a first time-frequency coordinate to be projected onto different stream-2 pilot symbol waveform bursts P_s2,t2,f2·

Wp(t2,f2) originally transmitted at a different time-frequency coordinate, and bins different from those normally corresponding to said stream 1 pilot symbol waveform bursts P_s1,t1,f1·

Wp(t1,f1), according to a receiving antenna specific aspect of said impaired data channel, thereby determining, for each stream, R receiving antenna specific 2D impulse responses;

and using said R receiving antenna specific 2D impulse responses to either precode said streams at said transmitter, or deconvolute said receiving antenna specific channel-convoluted stream identifiable data and pilot bursts.

24. The method of claim 22, wherein at least some of said T uniquely configured transmitting antennas are differently polarized transmitting antennas, and wherein said stream identifiable direct data and pilot bursts are polarized stream identifiable direct data and pilot bursts that are transmitted by said differently polarized transmitting antennas are according to different polarization directions;

said at least one wireless reflector is a polarization altering wireless reflector that alters a polarization direction of its reflected wireless waveform bursts according to a first reflector polarization operator, thereby producing polarized stream identifiable replica data and pilot bursts comprising polarization shifted time-delayed and reflector Doppler-shifted replicas of said polarized stream identifiable direct data and pilot bursts;

said at least one receiver has at least some of its R uniquely configured receiving antennas configured to detect a direction of polarization in its received wireless waveforms;

wherein at said at least one wireless receiver, a resulting combination of any said transmitter Doppler-shifted and receiver Doppler-shifted polarized stream identifiable direct data and pilot bursts, and polarized stream identifiable replica data and pilot bursts, produce antenna specific channel-convoluted stream identifiable polarized data and pilot bursts;

further using at least some of said receiver'"'"'s R uniquely configured receiving antennas to receive and detect the direction of polarization of said antenna specific channel-convoluted stream identifiable polarized data and pilot bursts;

for each wireless receiving antenna R_a and each stream identifiable plurality of pilot symbol waveforms, using a receiver processor to determine said 2D channel state at said receiving antenna R_a, and use said 2D channel states to perform at least one of;

a) precoding at least some of said polarized stream identifiable direct data and pilot bursts at said at least one transmitter to pre-compensate for said impaired data channel; and

b) deconvoluting at least some of said antenna specific channel-convoluted stream identifiable polarized data and pilot bursts at said at least one receiver, thereby deriving at least an approximation of said plurality of data symbols.

25. The method of claim 22, wherein said 2D channel state and said precoding is further used to shape a spatial directionality of the wireless waveforms transmitted by said T uniquely configured transmitting antennas, or wherein said 2D channel state and said deconvoluting is used to shape a spatial directionality of the wireless waveforms received by said R uniquely configured receiving antennas.

26. The method of claim 25, wherein said spatial directionality is achieved by adjusting any of relative phases or angles of the wireless waveforms transmitted by said T uniquely configured transmitting antennas, or wherein said spatial directionality of the wireless waveforms received by said R uniquely configured receiving antennas is achieved by monitoring the relative phases or angles of the wireless waveforms received by said R uniquely configured receiving antennas.

27. The method of claim 22, wherein said at most T different streams are carried by commonly shared carrier waveforms over a same ranges of times and frequencies.

28. The method of claim 22, wherein each said stream identifiable direct data and pilot bursts are not antenna identifiable and not antenna specific, and each transmitting antenna transmits at least one stream of wireless data symbol waveforms along with at least one stream identifiable wireless pilot symbol waveforms.

29. The method of claim 28, wherein each transmitting antenna transmits at least one stream of wireless data symbol waveforms along with at least one stream identifiable wireless pilot symbol waveforms according to a transmitting antenna specific phase or power setting, thereby shaping a spatial directionality of the wireless waveforms transmitted by those transmitting antennas transmitting said stream.

30. The method of claim 22, wherein said stream identifiable direct data and pilot bursts are also antenna identifiable and antenna specific, and each transmitting antenna transmits an antenna specific stream of wireless data symbol waveforms along with a plurality of antenna specific identifiable wireless pilot symbol waveforms.