Abstract:
A wireless telecommunications system that mitigates infrasymbol interference due to Doppler-shift and multipath and enables multiple access in one radio channel. Embodiments of the present invention are particularly advantageous for wireless telecommunications systems that operate in high-mobility environments, including high-speed trains and airplanes.

Description:
STATEMENT OF RELATED APPLICATIONS 
     This application claims benefit to provisional application No. 62/316,243, filed on 31 Mar. 2016, entitled “Robust Wireless Telecommunications System,”. 
     This application claims benefit to provisional application No. 62/316,298, filed on 31 Mar. 2016, entitled “Orthogonal Time Frequency Space,”. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to wireless telecommunications in general, and, more particularly, to a wireless telecommunications system that can detect and mitigate impairments to its radio signals. 
     BACKGROUND OF THE INVENTION 
     A radio signal can be impaired as it propagates from a transmitter to a receiver, and the value of a wireless telecommunications system is substantially dependent on how well the system mitigates the effects of those impairments. In some cases, the transmitter can take steps to address the impairments, and in some cases the receiver addresses the impairments. In all cases, however, the nature of each impairment must be detected quickly and accurately so that it can be mitigated. 
     SUMMARY OF THE INVENTION 
     The present invention is a wireless telecommunications system that avoids some of the costs and disadvantages of wireless telecommunications systems in the prior art. In particular, the illustrative embodiment of the present invention is able to discriminate between direct-path and multipath images, which (substantially) prevents infrasymbol interference and enables the remediation of intersymbol interference. Embodiments of the present invention are particularly advantageous in radio channels with multi-path and Doppler-shift impairments. 
     Furthermore, embodiments of the present invention enable a plurality of transmitters to simultaneously transmit (radiate) into the same radio channel to a single receiver in such a way that the receiver can separate the individual transmissions and properly associate them with their respective transmitters. This is widely called “multiple access” and is well known in other telecommunications systems (e.g., frequency-division multiple access, time-division multiple access, code-division multiple-access, etc.). 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  depicts a block diagram of the salient components of wireless telecommunications system  100  in accordance with the illustrative embodiment of the present invention. 
         FIG. 1B  depicts a block diagram of the salient components of base station  120  in accordance with the illustrative embodiment of the present invention. 
         FIG. 1C  depicts a block diagram of the salient components of wireless terminal  130 - 1  in accordance with the illustrative embodiment of the present invention. 
         FIG. 2  depicts a flowchart of the salient tasks performed by base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2  in accordance with the illustrative embodiment of the present invention. 
         FIG. 3  depicts a waveform array Φ is based on M orthogonal M-ary stepped-pulse waveforms. 
         FIG. 4  depicts the composition of waveform array Φ (M=3 and N=4) for any set of orthogonal basic waveforms. 
         FIG. 5  depicts the composition of waveform array Φ (M=3 and N=4) for the stepped-pulse waveform. 
         FIG. 6  depicts a time-frequency plot for one of the waveforms—waveform φ(1,1)—in the illustrative waveform array Φ (M=3 and N=4). 
         FIG. 7  depicts a time-frequency plot for a different one of the waveforms—waveform φ(2,2)—in the illustrative waveform array Φ (M=3 and N=4). 
         FIG. 8  depicts a time-frequency plot for the transmission of one data item in a frequency-division multiplexed/frequency-division multiple access (“FDM/FDMA”) scheme. 
         FIG. 9  depicts a time-frequency plot for the transmission of one data item in a time-division multiplexed/time-division multiple access (“TDM/TDMA”) scheme. 
         FIG. 10  depicts a time-frequency plot for the transmission of one data item in a code-division multiplexed/code-division multiple access (“CDM/CDMA”) scheme. 
         FIG. 11  depicts a time-frequency plot in which a Doppler-shifted multipath image of waveform φ(2,2) causes infra-symbol interference. 
         FIG. 12  depicts a time-frequency plot in which a Doppler-shifted multipath image of waveform φ(2,2) does not cause infra-symbol interference given the same delay spread as in  FIG. 11 . 
         FIG. 13  depicts a flowchart of the salient tasks performed by base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2  in accordance with the performance of task  201 . 
         FIG. 14  depicts the waveforms of waveform array Φ can be represented in tabular form. 
         FIGS. 15A, 15B, and 15C  depict three alternative partitions of the waveforms in waveform array Φ such that each waveform φ(m,n) is assigned to wireless terminal  130 - 1 , wireless terminal  130 - 2 , or to neither (i.e., to be reserved as a guard waveform). 
         FIG. 16  depicts a flowchart of the salient tasks performed by wireless terminal  130 - a  in accordance with the performance of task  202 - a.    
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1A  depicts a block diagram of the salient components of wireless telecommunications system  100  in accordance with the illustrative embodiment of the present invention. Wireless telecommunications system  100  comprises: base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2 , all of which are situated in geographic region  110 . 
     In accordance with the illustrative embodiment, base station  120  provides bi-directional wireless telecommunications service to wireless terminal  130 - 1  and wireless terminal  130 - 2 . 
     In accordance with the illustrative embodiment, base station  120  provides telecommunications service by exchanging “data items” with wireless terminal  130 - 1  and wireless terminal  130 - 2 , which data items represent sound, images, video, data, and signaling. It will be clear to those skilled in the art how to make and use base station  120 , wireless terminal  130 , and wireless terminal  130 - 2  so that they can de-construct sound, images, video, data, and signaling into data items, and it will be clear to those skilled in the art how to make and use base station  120 , wireless terminal  130 , and wireless terminal  130 - 2  so that they can re-construct sound, images, video, data, and signaling from those data items. 
     In accordance with the illustrative embodiment, each data item is represented by a complex number that corresponds to one symbol in a 16 quadrature-amplitude (“16 QAM”) signal constellation modulation scheme. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which each data item corresponds to a symbol in any digital modulation scheme (e.g., frequency-shift keying, amplitude-shift keying, phase-shift keying, etc.). 
     In accordance with the illustrative embodiment, wireless telecommunications system  100  comprises one base station and two wireless terminals, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that comprise any number of base stations and any number of wireless terminals. Furthermore, it will be clear to those skilled in the art how to partition the radio spectrum in an area into radio channels and to assign those channels to the base stations. 
     In accordance with the illustrative embodiment, base station  120  is stationary and terrestrial, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which each base station  120  is mobile or airborne, or mobile and airborne. 
     In accordance with the illustrative embodiment, wireless terminal  130 - 1  and wireless terminal  130 - 2  are mobile, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which each wireless terminal is either mobile or stationary. 
     In accordance with the illustrative embodiment, geographic region  110  comprises natural and man-made radio-frequency objects (not shown) that reflect, refract, and diffract the carrier signals that propagate between base station  120  and wireless terminal  130 - 1  and wireless terminal  130 - 2 . Furthermore, some of the radio-frequency objects are stationary (e.g., trees, hills, buildings, etc.) and some are mobile (e.g., trucks, ships, airplanes, etc.). 
     In accordance with the illustrative embodiment, the parameters that characterize the signal-path impairments in the radio channel between base station  120  and wireless terminal  130 - 1  and wireless terminal  130 - 2  are dynamic (i.e., change with respect to time). It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention in which the characteristics of the radio channel and the nature of the signal-path impairments are static (i.e., do not change with respect to time). 
     In accordance with the illustrative embodiment, base station  120  and wireless terminal  130 - 1  and wireless terminal  130 - 2  exchange modulated radio-frequency carrier signals in a radio channel that is B=10 MHz wide. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the radio channel has a different bandwidth (e.g., 2.5 MHz, 5.0 MHz, 12.5 MHz, 15 MHz, 20 MHz, 40 MHz, 80 MHz, etc.). 
       FIG. 1B  depicts a block diagram of the salient components of base station  120  in accordance with the illustrative embodiment of the present invention. Base station  120  comprises: encoder  121 , modulator  122 , power amplifier  123 , and antenna  124 , low-noise amplifier  125 , demodulator  126 , decoder  127 , and processor  128 . 
     Encoder  121  comprises the hardware and software necessary to compress, encrypt, and add forward error correction to the data items to be transmitted to wireless terminal  130 - 1  and wireless terminal  130 - 2 . It will be clear to those skilled in the art how to make and use encoder  121 . 
     Modulator  122  comprises the hardware and software necessary to modulate a radio-frequency carrier signal with the data items from encoder  121  to generate a modulated radio-frequency carrier signal. The construction and operation of modulator  122  is described in detail herein and in the accompanying figures. 
     Power amplifier  123  comprises the hardware necessary to increase the power of the modulated radio-frequency carrier signal for transmission via antenna  124 . It will be clear to those skilled in the art how to make and use power amplifier  123 . 
     Antenna  124  comprises the hardware necessary to facilitate the radiation of the modulated radio-frequency carrier signal wirelessly through space to wireless terminal  130 - 1  and wireless terminal  130 - 2 . It will be clear to those skilled in the art how to make and use antenna  124 . 
     Low-Noise amplifier  125  comprises the hardware necessary to increase the power of the modulated radio-frequency carrier signal received via antenna  124 . It will be clear to those skilled in the art how to make and use low-noise amplifier  125 . 
     Demodulator  126  comprises the hardware and software necessary to:
         i. demodulate the modulated radio-frequency carrier signal received by antenna  124 , which is the sum of a first modulated radio-frequency carrier signal transmitted by wireless terminal  130 - 1  and a second modulated radio-frequency carrier signal transmitted by wireless terminal  130 - 2 , and   ii. recover one or more data items transmitted by wireless terminal  130 - 1  that are embodied in the modulated radio-frequency carrier signal and to associate those data items with wireless terminal  130 - 1 , and   iii. recover one or more data items transmitted by wireless terminal  130 - 2  that are embodied in the modulated radio-frequency carrier signal and to associate those data items with wireless terminal  130 - 2 .
 
It will be clear to those skilled in the art, after reading this disclosure, how to make and use demodulator  126 .
       

     Decoder  127  comprises the hardware and software necessary to decompress, decrypt, and correct the data items transmitted by wireless terminal  130 - 1  and wireless terminal  130 - 2 . It will be clear to those skilled in the art how to make and use decoder  127 . 
     Processor  128  comprises the hardware and software necessary to operate base station  120  and to interface with the cellular infrastructure (not shown in  FIG. 1B ). It will be clear to those skilled in the art, after reading this disclosure, how to make and use processor  128 . 
       FIG. 1C  depicts a block diagram of the salient components of wireless terminal  130 - a , wherein aε{1, 2}, in accordance with the illustrative embodiment of the present invention. Wireless terminal  130 - a  comprises: encoder  131 - a , modulator  132 - a , power amplifier  133 - a , and antenna  134 - a , low-noise amplifier  135 - a , demodulator  136 - a , decoder  137 - a , processor  138 - a , and user interface  139 - a.    
     Encoder  131 - a  comprises the hardware and software necessary to compress, encrypt, and add forward error correction to the data items to be transmitted to base station  120 . It will be clear to those skilled in the art how to make and use encoder  131 - a.    
     Modulator  132 - a  comprises the hardware and software necessary to modulate a radio-frequency carrier signal with the data items from encoder  131 - a  to generate a modulated radio-frequency carrier signal. The construction and operation of modulator  132 - a  is described in detail herein and in the accompanying figures. 
     Power amplifier  133 - a  comprises the hardware necessary to increase the power of the modulated radio-frequency carrier signal for transmission via antenna  134 - a . It will be clear to those skilled in the art how to make and use power amplifier  133 - a.    
     Antenna  134 - a  comprises the hardware necessary to facilitate the radiation of the modulated radio-frequency carrier signal wirelessly through space to base station  120 . It will be clear to those skilled in the art how to make and use antenna  134 - a.    
     Low-Noise amplifier  135 - a  comprises the hardware necessary to increase the power of the modulated radio-frequency carrier signals received via antenna  134 - a . It will be clear to those skilled in the art how to make and use low-noise amplifier  135 - a.    
     Demodulator  136 - a  comprises the hardware and software necessary to demodulate a modulated radio-frequency carrier signal transmitted by base station  120  to recover the data items transmitted by base station  120 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use demodulator  136 - a.    
     Decoder  137 - a  comprises the hardware and software necessary to decompress, decrypt, and correct the data items transmitted by base station  120 . It will be clear to those skilled in the art how to make and use decoder  137 - a.    
     Processor  138 - a  comprises the hardware and software necessary to operate wireless terminal  130 - a  and to interface with user interface  139 - a . It will be clear to those skilled in the art, after reading this disclosure, how to make and use processor  138 - a.    
     User interface  139 - a  comprises the hardware and software necessary to enable a user (not shown) to interact with wireless terminal  130 - a . It will be clear to those skilled in the art how to make and use user interface  139 - a.    
       FIG. 2  depicts a flowchart of the salient tasks performed by base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2  in accordance with the illustrative embodiment of the present invention. 
     At task  201 , base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2  establish the parameters of waveform array Φ with which they will communicate. Task  201  is described in detail below and in the accompanying figures. 
     At task  202 , wireless terminal  130 - 1  and wireless terminal  130 - 2  each transmit (radiate) a modulated radio-frequency signal in a radio channel to base station  120  in accordance with the parameters of waveform array Φ established in task  201 . Task  202  is described in detail below and in the accompanying figures. 
     At task  203 , base station  120  receives a modulated radio-frequency signal from the radio channel that is a sum of the modulated radio-frequency signals (and their respective multipath images, if any) radiated by wireless terminal  130 - 1  and wireless terminal  130 - 2 . As part of task  203 , base station  120  demodulates and decodes the modulated radio-frequency signal to recover one or more data items transmitted by wireless terminal  130 - 1  (and to associate those data items with wireless terminal  130 - 1 ) and one or more data items transmitted by wireless terminal  130 - 2  (and to associate those data items with wireless terminal  130 - 2 ). It will be clear to those skilled in the art, after reading this disclosure, how to make base station  120  to be able to perform task  203 . 
     At task  204 , base station  120  transmits one or more data items associated with wireless terminal  130 - 1  and one or more data items associated with wireless terminal  130 - 2  to the cellular infrastructure (e.g., a mobile switching center, etc.), which is not shown in  FIG. 1B . 
       FIG. 13  depicts a flowchart of the salient tasks performed by base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2  in the performance of task  201 . As part of task  120 , the parameters of waveform array Φ are chosen to both:
         i. mitigate infra-symbol interference caused by Doppler-shift and multipath interference, and   ii. enable simultaneous multiple access by both wireless terminal  130 - 1  and wireless terminal  130 - 2  to base station  120 .       

     At task  1301 , the parameters of waveform array Φ are established once, before the time when base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2  first establish communication, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the radios periodically or sporadically re-establish the parameters of waveform array Φ. For example and without limitation, base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2  can re-establish the parameters of waveform array Φ as:
         i. traits of the signal path from change, or   ii. the type of data represented by the data items changes, or   iii. the latency tolerance of the data items changes, or   iv. any combination of i, ii, and iii.       

     In accordance with the illustrative embodiment, base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2  convey data items using one waveform array Φ, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use any number of waveform arrays (e.g., two waveform arrays Φ1 and Φ2; three waveform arrays, Φ1, Φ2, and Φ3; four waveform arrays, Φ1, Φ2, Φ3, and Φ4; etc.) to convey data items. For example and without limitation, base station  120 , wireless terminal  130 - 1 , and wireless terminal  130 - 2  use different waveform arrays for:
         i. different conditions of the signal path between base station  120  and wireless terminal  130 - 1  and wireless terminal  130 - 2 , or   ii. different types of data items, or   iii. different latency tolerance of the data items, or   iv. any combination of i, ii, and iii.       

     Basic Waveforms— 
     Waveform array Φ is based on an extension of M basic waveforms b(1), . . . , b(m), . . . , b(M) that are orthogonal in M-dimensional vector space, where M is a positive integer greater than 1, and m is a positive integer in the range mε{1, . . . , M}. 
     In accordance with the illustrative embodiment, basic waveform b(m) is a waveform m of a M-ary stepped-pulse waveform scheme, as depicted in  FIG. 3 . In accordance with the illustrative embodiment, each pulse is a band-limited raised-cosine pulse but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which each pulse has a different shape. 
     Each pulse in basic waveform b(m) is band-limited, and, therefore, the duration of each pulse is 1/B seconds, wherein B is the bandwidth of the channel. Furthermore, the centers of adjacent pulses are separated by 1/B seconds. And still furthermore, the total duration of each basic waveform b(m) is M/B seconds (as depicted in  FIG. 3 ). 
     Although the illustrative embodiment uses stepped-pulse waveforms as the basic waveforms, it will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which waveform array Φ is based on any set of M orthogonal waveforms, b(1), . . . , b(M). 
     Structure of Waveform Array Φ— 
     Waveform array Φ comprises M·N waveforms that are orthogonal in M·N-dimensional vector space, wherein N is a positive integer greater than 1. The M·N waveforms of waveform array Φ are φ(1,1), . . . , φ(m,n), . . . , φ(M,N), where n is a positive integer in the range nε{1, . . . , N}. 
     Each waveform φ(m,n) is identically partitioned into N time slots 1, . . . , p, . . . , N, where p is a positive integer in the range pε{1, . . . , N}. 
     Each waveform φ(m,n) is the sum of N waveforms y(m,n,1), . . . , y(m,n,p), . . . , y(m,n,N). Waveform y(m,n,p) occupies time slot p in waveform φ(m,p) and equals:
 
 y ( m,n,p )= b ( m )· u ( n,p )  (Eq. 1)
 
wherein u(n,p) is a phasor that equals:
 
 u ( n,p )=exp(2π( n− 1)( p− 1) i/N )  (Eq. 2)
 
The duration of waveform y(m,n,p) defines the duration of time slot p.
 
     An illustrative waveform array Φ (M=3 and N=4) is depicted in  FIG. 4  and  FIG. 5 , and the phasors u(n,p) associated with the array are depicted in Table 1. 
     
       
         
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Phasors u(n, p) for Each Waveform y(m, n, p) in  
               
               
                 Waveform Array Φ (M = 3 and N = 4) 
               
             
          
           
               
                   
                 time slot 
                 time slot 
                 time slot 
                 time slot 
               
               
                   
                 p = 1 
                 p = 2 
                 p = 3 
                 p = 4 
               
               
                   
               
               
                 y(m, 1, p) 
                 1 + 0i 
                 1 + 0i 
                  1 + 0i 
                 1 + 0i 
               
               
                 y(m, 2, p) 
                 1 + 0i 
                 0 + 1i 
                 −1 + 0i 
                 0 − 1i 
               
               
                 y(m, 3, p) 
                 1 + 0i 
                 −1 + 0i  
                  1 + 0i 
                 −1 + 0i  
               
               
                 y(m, 4, p) 
                 1 + 0i 
                 0 − 1i 
                 −1 + 0i 
                 0 + 1i 
               
               
                   
               
             
          
         
       
     
     A salient characteristic of the illustrative embodiment is that each waveform φ(m,n) deposits energy into: 
     i. unique time-frequency portions the radio channel, and 
     ii. 1/M·N th  of the radio channel. 
     This is illustrated in  FIGS. 6 and 7 . 
     For example,  FIG. 6  depicts a plot of where the energy associated with waveform φ(1,1) of waveform array Φ (M=3 and N=4) is deposited into the 10 MHz radio channel. In  FIG. 6  the radio channel depicted is divided into twelve 833.3 KHz frequency bands (B=10 MHz/M·N=12) and twelve (M·N=12) intervals. In  FIG. 6 , it can be seen that energy exists only in those intervals when the raised-cosine pulse exists and only in the frequency sub-bands 0-0.833 MHz, 3.333-4.167 MHz, and 6.667-7.500 MHz (i.e., the diagonally-striped blocks) in the channel. 
     Similarly,  FIG. 7  depicts a plot of where the energy associated with waveform φ(2,2) of waveform array Φ (M=3 and N=4) is deposited into the 10 MHz radio channel. In  FIG. 7 , it can be seen that energy exists only in those intervals when the raised-cosine pulse exists and only in the frequency sub-bands 0.833-1.667 MHz, 4.167-5.000 MHz, and 7.500-8.333 MHz (i.e., the diagonally-striped blocks) in the channel. It will be clear to those skilled in the art, after reading this disclosure, how to determine where the energy associated with any waveform φ(m,n) is deposited for an M and N. 
     For comparison,  FIG. 8  depicts an analogous time-frequency plot for the transmission of one data item in a frequency-division multiplexed/frequency-division multiple access (“FDM/FDMA”) scheme. In  FIG. 8 , the striped portion of the time-frequency plot indicates which portion of the channel is occupied by the waveform that transmits the data item. 
     As another example,  FIG. 9  depicts an analogous time-frequency plot for the transmission of one data item in a time-division multiplexed/time-division multiple access (“TDM/TDMA”) scheme. In  FIG. 9 , the striped portion of the time-frequency plot indicates which portion of the channel is occupied by the waveform that transmits the data item. 
     As another example,  FIG. 10  depicts a time-frequency plot for the transmission of one data item in a code-division multiplexed/code-division multiple access (“CDM/CDMA”) scheme. In  FIG. 10 , the entire time-frequency plot is partially striped to indicate that energy is deposited throughout all of the channel all of the time by the waveform that transmits one data item. 
       FIG. 11  depicts a plot of where the energy associated with waveform φ(2,2) of waveform array Φ (M=3 and N=4) is received from the 10 MHz radio channel. In particular,  FIG. 11  depicts: 
     (i) a direct-path image of waveform φ(2,2), and 
     (ii) a Doppler-shifted multipath image of waveform φ(2,2). 
     From  FIG. 11 , it can be seen that the Doppler-shifted multipath image partially overlaps—and causes infrasymbol interference to—the direct-path image. Furthermore, the Doppler-shifted multipath image partially overlaps—and causes intersymbol interference to the direct-path images of waveforms φ(1,2), φ(1,3), and φ(3,2). When the receiver can discriminate between the direct-path and multipath images, the infrasymbol interference can be avoided and the intersymbol interference can be eliminated. 
     In particular, the ability of embodiments of the present invention to discriminate between direct-path and multipath images of waveform φ(m,n) is a function of the values of M and N. In general, larger values of M and N enable higher resolution, and, therefore, greater discrimination between direct-path and multipath images. In particular, larger values of M enable greater discrimination in frequency (i.e., between Doppler-shifted images) and larger values of N enable greater discrimination in time (i.e., between delayed images). As a general rule of thumb, values of M should be much larger than the largest expected delay spread in the radio channel and values of N should be larger than the largest expected Doppler-shift in the radio channel. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention with any value of M, any value of N, and a set of M basic waveforms b(1), . . . , b(M).  FIG. 12  depicts a time-frequency plot in which a Doppler-shifted multipath image of waveform φ(2,2) does not cause infra-symbol interference given the same delay spread as in  FIG. 11 . 
     As part of task  1301 , base station  120  assigns:
         i. one or more of the waveforms of waveform array Φ to wireless terminal  130 - 1  to be used by wireless terminal  130 - 1  for transmitting data items to base station  120 , and   ii. one or more of the waveforms of waveform array Φ to wireless terminal  130 - 2  to be used by wireless terminal  130 - 2  for transmitting data items to base station  120 , and   iii. one or more of the waveforms of waveform array Φ as guard waveforms that are not used by either wireless terminal  130 - 1  or wireless terminal  130 - 1  and shield the waveforms transmitted by each wireless terminal from interference by waveforms transmitted by another wireless terminal.       

     As explained above, each waveform array Φ comprises M·N waveforms that are identified as φ(1,1), . . . , φ(m,n), . . . , φ(M,N). The rectangular nature of waveform array Φ can be represented in tabular form as depicted in  FIG. 14 . 
       FIGS. 15A, 15B, and 15C  depict three alternative partitions of the waveforms in waveform array Φ such that each waveform φ(m,n) is assigned to wireless terminal  130 - 1 , wireless terminal  130 - 2 , or to neither (i.e., to be reserved as a guard waveform). 
     In  FIG. 15A , wireless terminal  130 - 1  has been assigned waveforms φ(1,1), . . . , φ(M−4,N), wireless terminal  130 - 2  has been assigned waveforms φ(M−1,1), . . . , φ(M,N), and waveforms φ(M−2,1), . . . , φ(M−2,N) have been reserved as guard waveforms. 
     In  FIG. 15B , wireless terminal  130 - 1  has been assigned waveforms φ(1,1), . . . , φ(M,N−2), wireless terminal  130 - 2  has been assigned waveforms φ(1,N), . . . , φ(M,N), and waveforms φ(1,N−1), . . . , φ(M,N−1) have been reserved as guard waveforms. 
     In  FIG. 15C , wireless terminal  130 - 1  has been assigned waveforms φ(1,1), . . . , φ(1,N) and φ(M−2,1), . . . , φ(M−2,N), wireless terminal  130 - 2  has been assigned waveforms φ(3,1), . . . , φ(3,N) and φ(M,1), . . . , φ(M,N), and the remainder of the waveforms have been reserved as guard waveforms. 
     It will be clear to those skilled in the art, after reading this disclosure, how to partition the waveforms in waveform array Φ among any number of wireless terminals and guard waveforms. 
     At task  1302 , base station  120  transmits the waveform array Φ parameters to wireless terminal  130 - 1  and wireless terminal  130 - 2  along with a command to transmit into the radio channel using the assigned waveforms. 
     At task  1303 , wireless terminal  130 - 1  receives the waveform array Φ parameters and the command to use the waveforms assigned to it. 
     At task  1304 , wireless terminal  130 - 2  receives the waveform array Φ parameters and the command to use the waveforms assigned to it. 
       FIG. 16  depicts a flowchart of the salient tasks associated with task  202 - a , wherein aε{1, 2}, in accordance with the illustrative embodiment of the present invention. 
     At task  1601 , wireless terminal  130 - a  establishes a one-to-one relationship between each data item it will transmit to base station  120  and each waveform φ(m,n) in waveform array Φ that has been assigned to it. As part of task  1601 , wireless terminal  130 - a  modulates a radio-frequency carrier signal with each waveform assigned to it and the corresponding data item to generate a modulated radio-frequency carrier signal. It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  1601 . 
     At task  1602 , the modulated radio-frequency carrier signal is radiated into the radio channel via antenna  134 - a  for reception by base station  120 . It will be clear to those skilled in the art, after reading this disclosure, how to make and use embodiments of the present invention that perform task  1602 . 
     MARKMAN DEFINITIONS 
     Orthogonal—For the purpose of this specification, two waveforms are orthogonal if their inner product is zero over the time interval of interest.