Abstract:
Several (in some cases many dozen) small antennae are integrated into or over a full body suit or clothing. These antennae preferably include an intra-suit or clothing wired connection to one or more small Ultra-Wide-Band (UWB) radios, e.g., in the 3-10 GHz range. In some cases, each antenna connection includes a variable delay, e.g., a few nanoseconds with picoseconds-scale resolution on the delays, thus allowing for the body-suit ensemble to act as a directional phased-array. One claim recites a radio wearable by a human comprising: a phased-array antenna including a plurality of antennae, the array being configured for wearing over or on a human body, the plurality of antennae provided for spatially positioning in multiple different regions over or on the human body; an RF radio; and a controller configured for: i) determining relative spatial position information for antennae within the phased-array antenna; and ii) using at least the relative spatial position information, controlling the radio to produce a directional UWB beam through the phased-array antenna. Another claim includes an antenna having a plurality of metamaterial elements. Of course, other claims and combinations are provided as well.

Description:
This application claims the benefit of U.S. Provisional Application No. 61/670,568, filed Jul. 11, 2012, which is hereby incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates generally to the field of wireless communications. In some embodiments the disclosure relates more particularly to phased-array antenna systems. In still further embodiments the disclosure relates to body-wearable phased-array antenna systems. Such systems find used, e.g., for first responders (e.g., fire fighters, medical personal), law enforcement and military personnel. 
     SUMMARY 
     This disclosure relates to person to person RF (radio frequency) packet communications, most typically using UWB (ultra-wide band), and Wi-Fi or cell protocols of various flavors. Streams of such packets are more and more replacing traditional ‘continuous channel’ forms of radios such as the classic walkie-talkies. The principle of this invention works for continuous channels as well, but it is in packet-based communications where the jam resistance and low probability of detection properties shine more brightly. 
     Others have dabbled in this general ballpark. The company Wearable Antenna Technologies Inc. in Gallatin, Tenn., USA, claims to have developed a Tactical Vest Antenna System that is a concealable antenna designed for military applications. The radiating elements slide over small arms protective insert plates inside a plate carrier, placing a whip antenna out of enemy&#39;s sight, and out of the radio operator&#39;s way. The antenna system consists of two antenna inserts, two interconnecting cables, and a cable for radio connection. The radio operates in the 30-512 MHz range and provides an omnidirectional radiation pattern. 
     Pharad, LLC in Glen Burnie, Md., USA, claims to offer a wearable UWB (ultra wide band) antenna. This body wearable antenna is fabricated using a thin flexible material for placement next to the exterior of body armor or tactical vests. UWB link performance is maintained supposedly without hindering the user&#39;s vision or movement. A SMA connector allows these antennas to connect to standard radios. This antenna operates in the 3-10 GHz range and provides a near omni-directional pattern. 
     Other body-wearable antennae examples are found in U.S. Pat. Nos. 7,450,077; 7,629,934; and 7,642,963, which are each hereby incorporated herein by reference in their entirety. Several publications also address this space, e.g., Lee, et al., “Omnidirectional Vest-Mounted Body-Worn Antenna System for UHF Operation,” IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, VOL. 10, 2011, pg. 581-583; “Yang, et al., “Wearable Ultra-Wideband Half Disk Antennas,” IEEE, 2005, pp. 500-503; and D. Psychoudakis, “Body-Worn Diversity Antennas for Squad Area Networks (SAN),” 2008 URSI General Assembly, Chicago, Ill., each of which is hereby incorporated herein by reference in its entirety. 
     What we do not see in these prior works is a body-worn phased-array antenna in the manner described in this patent document. Other features and advantages discussed herein are also missing. 
     As a brief summary, several (in some cases many dozen) small antennae are integrated into, over and/or throughout a full body suit or clothing. These antennae preferably include an intra-suit or clothing wired connection to one or more small Ultra-Wide-Band (UWB) radios, e.g., in the 3-10 GHz range, or controllers associated with the radios. In some cases, each antenna connection includes a variable (sometimes selectable) delay, e.g., a few nanoseconds with picoseconds-scale resolution on the delays, thus allowing for the body-suit ensemble to act as a directional phased-array. Two or more such suits can combine to create a high reliability, low probability of intercept and nearly jam-proof network between people wearing such directional phased-array systems. Features of these include narrow focused beams—preferably not omni-directional—and low power level and sparse packet rates. 
     Active phasing of cooperative antennae can ‘beam’ RF energy in specific directions. E.g., an example of a directional beam transmission is shown in  FIG. 4 . Aspects of this disclosure present pragmatic approaches to treating the body and limbs of a person as a phased array antenna. There are a variety of novelties to make this approach function, including, e.g., dealing with the rapid and ever-changing configuration of the human body in motion, especially in extreme forms of motion and position. In order to phase the sub-antennae draped around a person&#39;s body correctly, one preferably knows how those antennae spatially relate to each other generally, e.g., at the tenth-of-a-second time scale or even finer. Approaches are presented which can do this to, generally, centimeter and sub-centimeter precision. When one considers standard communications frequency bands in the GHz and even greater than 10 GHz ranges, such spatial knowledge can be fundamental to proper phasing. The actual phasing of the signals then proceeds on the order of low double-digit picoseconds in delay-control or even finer. 
     The foregoing and other features, aspects and advantages of the present technology will be even more readily apparent from the following detailed description, which proceeds with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates a wearable antennae array system. 
         FIG. 2  illustrates a wearable phased-array system with a human outline removed. 
         FIG. 3  shows that micro antennae or loops of antennae can be configured to transmit at different signal amplitude levels. 
         FIG. 4  illustrates an example of a directional beam transmission. 
         FIG. 5  illustrates a corresponding signal pattern to the FIGS phased-array system. 
     
    
    
     DETAILED DESCRIPTION 
     An efficient and non-burdensome way to directly send an RF packet from one person to another is to treat their entire bodies as an antenna array. One way to accomplish this is to augment their clothing, suit, vest or uniform with micro-antennae—preferably over a majority of their body region—and treat the whole body as a tuned phased array. Phased arrays have long been known to be a preferred way to ‘beam’ RF energy from one specific point to another, in a directional manner. 
     With reference to  FIG. 1 , a wearable antennae array system is illustrated. The array includes a plurality of antenna arranged over the body, e.g., as integrated into or carried by clothing worn by a human. The array preferably includes a plurality of micro-antenna arranged over the body. The micro antennae can be grouped or arranged in loops (e.g., around the legs, arms, neck, etc.) or variously placed (e.g., torso) to help achieve a phased-array. The system includes one or more RF radios. The radio may be constructed from various hardware components (e.g., mixers, RF front end, filters, amplifiers, modulator/demodulators, detectors, transceivers, etc.) or be constructed as a so-called “software-define radio” (SDR) in which many of the traditional hardware components are provided in software or embedded computing devices, in connection with various amplifiers. Of course, the radio can include both hardware and software components. SDR&#39;s have some advantages including allowing designers to forgo limited assumptions associated with traditional hardware. For example, using an SDR for ultra wideband techniques allow several transmitters to transmit in the same place on the same frequency with very little interference, typically combined with one or more error detection and correction techniques to fix all the errors caused by such interference. Regardless of the implementation, the system radio preferably operates in the 3-10 GHz range. Of course, other frequency ranges will similarly benefit from the inventive techniques disclosed herein. 
     The micro-antennae themselves can be constructed with thin (e.g., think smaller than human hair) and lightweight wiring. In some cased nanoantenna technology could be used. 
       FIG. 2  illustrates a wearable phased-array system with the human outline removed. The x, y &amp; z axis are in meters. 
     The radio includes or cooperates with a controller. The controller can be constructed with hardware, programmed microprocessors and/or specialized integrated circuits (ICs), e.g., digital signal processors (DSPs). The controller may include or cooperate with an IC delay unit. The controller is preferably in communication with each micro antenna and/or with groups of antennae. For example, the controller communicates with the micro-antennae over wired lines or via a low power wireless connection. 
     In some examples the controller facilitates: 1) determining and maintaining knowledge of relative body positions, e.g., arm to leg or arm to torso, etc. (and, hence, relative antennae positions)—helping to, 2) ‘picophase’ signals going out to all the transmission points (micro antennae) on the body such that the system&#39;s combined RF transmission signal becomes a highly directional beam aimed toward some receiving person. The person receiving such beamed RF packets can also ‘tune’ their reception in a similar phased-array manner, increasing the overall energy efficiency of the established communications, making those communications approach the limits of jam resistance and improbability of detection. 
     Let&#39;s take these above operations, 1 &amp; 2, in turn. 
     First, determining and maintaining relative antennae positioning across the body is helpful in order to properly time signal phase and amplitude transmission across the wearable phased-array antenna. A phased-array antennae system typically includes a plurality of radiating elements (in our case, micro antennae, or in some cases groups of micro-antennae). Beams can be formed by shifting the phase and/or amplitude of the signal emitted from each radiating element, to provide constructive/destructive interference so as to steer the beams in a desired direction. 
     There are several ways to determine relative antenna positioning. 
     For example, the controller can cause a micro-antenna, e.g., positioned over the left leg, to transmit a lower frequency signal or “chirp” (e.g., 100 MHz). The controller can monitor the receipt of the chirp at each micro antenna across the system (or at select antenna in each antenna loop or group across the system). Reception timing at different micro antennae will allow for the calculation of relative distances between the chirping antenna and the receiving antennae. (Of course, the system can be calibrated to take into account line transmission delays from the controller across various system circuitry and communication lines to each of the micro-antennae and/or groups of antennae. This delay time in connection with chirp signal reception timing can allow for precise relative distance calculations based on time of flight/transmission.) Calculated distances for each node relative to other nodes or group of nodes can be stored for use when sending out phase transmission signals and appropriate delays. This is an efficient approach since, e.g., 30 loops (of 12 micro-antennae each) can be chirped in less than 1 ms. Timing of the chirps can be controlled to help conserve battery consumption. For example, the system will exercise a complete antennae chirp process at predetermined intervals, or when the system senses system movement or partial movement (e.g., input from one or more gyroscopes and/or accelerometers). 
     Each micro-antenna may include both a transmitter and receiver, with the receiver monitoring chirps and other communication. Time multiplex arrangements can also be used to transition a transceiver between transmit and receive modes. 
     Of course, other techniques (e.g., from the near field communications field) can be used to help determine relative antennae positioning. 
     Returning to the second operation—picophasing—the controller controls signaling to the various transmission points (micro antennae) over the body such that the system&#39;s combined RF transmission signal becomes a highly directional beam aimed toward some receiving station or person. A receiver can also ‘tune’ their reception in a similar phased-array manner, increasing the overall energy efficiency of the established communications, making those communications approach the limits of jam resistance and improbability of detection. 
     One approach delays signals to corresponding micro-antennae by fixed amounts corresponding to roughly where on the body they are spatially located (mid-thigh, for example), then further pico-delayed by a value determined by the direction from the body the overall beam dictates. Think ‘1 o&#39;clock forward’, which then translates into micro-antennae in the back part of the thigh pulsing just slightly ahead of those on the forward part of the thigh, together forming a beam heading in the selected 1 o&#39;clock direction. On reception, this active picophasing can occur either in the physical domain of tuned delay lines OR in the digital signal processing realm of individually recorded waveforms of the micro-antennae. 
     As mentioned above the controller can include or cooperate with a delay circuit. The delay circuit may include, e.g., a tapped delay circuit in which differing delay paths/times can be selected based on different circuit taps. For example, the circuit may provide signal delays in a range of 50 picoseconds (ps) to 550 ps in 1 ps or more increments. Of course other delay paths with different ranges can be used to help provide appropriate timing. Knowing the relative spatial antennae alignment and the inherent system transmission delays, the controller can select an appropriate delay when sending an RF signal for each of the various micro-antennae or for groups (or loops) of antennae. Thus, the controller provides picophasing to operate the wearable antennae system to operate as a phased-array providing a highly directional beam. 
     Using voltage amplitude triggered responses can also be used to help regulate timing. With reference to  FIG. 3 , the micro antennae or loops of antennae can be configured to transmit at different signal amplitude levels. The controller can send the signal variously to the transmission nodes so as to transmit in a phased timing. 
     The directionality of the body-worn phased array can be improved by accounting for and minimizing various transmission anomalies, e.g., unwanted transmission sidelobes. For example, the phased-array can be modeled—even across multiple body orientations (e.g., lying prone, running, kneeling, standing, etc.)—to account for constructive/deconstructive interference and high amplitude sidelobes. For example, EZNEC antenna software by W7EL, which is a front end to the NEC-2 and NEC-4 antenna modeling engines developed by Lawrence Livermore Lab, can be used to model array signal properties. Then, knowing the modeling of a particular configuration, the controller can use various techniques to maximize beam directionality and efficiencies, e.g., by minimize sidelobes. For example, the controller may apply digital phase shifters as discussed in Gotto et al.&#39;s, “Sidelobe-Reduction Techniques for Phased Arrays Using Digital Phase Shifters,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, Vol. AP-18, NO. 6, November 1970, pgs. 769-773, which is hereby incorporated herein by reference. Different correction or different models may be used to approximate the current body position. Such models will also allow for accounting of the dielectric effect of the human body. 
     The controller can also account and compensate for different polarizations between the antennae that may be variously present as the orientation of the micro antennae change with body movement. (E.g., consider a leg as it bends to kneel. While kneeling, the antennae over that leg may include different polarizations based on leg positions, e.g., horizontal or vertical positions.) Knowing the relative positioning of the various micro antennae can help the controller account for differing polarization across the array. 
     The controller may also facilitate initial startup communication and reinitializing communication (e.g., if a dropped signal occurs). To initialize communication, the controller may issue a low level (even omni-directional) pilot signal. Key-based spread spectrum communications may to be used with the pilot signal. A receiving radio may handshake with the controller once a pilot signal is received, or the controller may lock onto a pilot signal of another radio. 
     If a signal is lost, the controller may default back to issuing an omni-directional pilot signal or may slowly broaden the directionality of a narrow beam until communications are reestablished. 
     The controller and radio discussed herein can include or cooperate with multiple sub-radios and sub-controllers arranged over the system. Processes can be assigned or divided between different controllers to improve signal and gain efficiencies. 
     For GHz and above frequencies, the degree of classic ‘gain’ that can be impressed into a reasonably narrow yet error-tolerant beam begins at the 20 dB (or 10× power gain) level and possibly even much better than that. Actual radio performance has and always will be a matter of testing and using, not theory. 
     The practical trade-off in this approach will be beam width (and its inherent gain—the narrower the beam the higher the gain) against precise knowledge and maintenance of where the beam should pointed. Too narrow of a beam, without the proper beam-locking mechanisms, and communications will unlikely occur. So there will be an inherent tension between gain and dynamic pointing, certainly once a cluttered non-line-of-sight environment enters the picture. 
     The controller can also cooperate with one or more nearby body phased arrays (e.g., worn by a nearby humans) to enhance transmission and reception of RF signals. Phased-timing between the two or more suits is controlled to have them operate as one larger phased array antenna. 
     Appendix A includes MATLAB code that is used to model the phased array shown in  FIG. 2 . A corresponding signal pattern is shown in  FIG. 5 . (Of course, other signals waveforms could be used besides a dual-lobed wave.) 
     In alternative embodiments, metamaterial antennas are utilized for body-worn antenna systems. Metameterials and antenna using such materials are discussed, e.g., in U.S. Pat. Nos. 6,859,114; 6,958,729; 7,522,124; 7,538,946; 7,710,664; 7,764,232; 7,855,696; 7,872,812; 8,081,138; 8,164,837; 8,207,907; 8,384,600; 8,451,183; and 8,462,063, which are each hereby incorporated by reference in its entirety. 
     In some metamaterial antennas, one or more radio waves propagate along a surface of low-loss material comprising individual metamaterial elements. Each of those elements (or groups of elements) can be controlled to resonate or emit at a specific frequency and in specific directions. As the surface wave passes beneath the elements, waves of radiation emit from the surface at different angles depending on how each individual element (or groups of elements) is tuned. Constructive and destructive interference patterns can transmit in a desired direction and shape. 
     A body-worn uniform (e.g., clothing, suit, vest, helmet and/or jacket) is configured to include one or more metamaterial antenna. Such antenna preferably includes one or more array(s) of metamaterial elements arranged to be provided on or over a human body. Such elements (or groups of elements, or the arrays themselves) are controlled (e.g., with local or master suit controllers) to cooperatively emit waveforms. The elements (and/or arrays) can be controlled with timing signals to produce constructive and/or destructive interference patterns to facilitate directional communication. 
     In some implementations, transmission signals are locally generated under the control of timing signals coordinating the local firing of such transmission signals (or waveforms). 
     A controller can be used to account and compensate for different interference between the arrays of metamaterial elements that may be variously present as the orientation and location of the metamaterial antennae change with body movement.
     boxlight—now cylinder—now loopy loopy loopy!!!   % create a random 3-D distribution of UWB emitters on the surface of a % body-dimension cylinder   % loopy: two ring loops per major limb bone, giving 8 rings on the arms % and legs; then belt loop, midriff, and just below the armpits; one loop % mid-shoulder and a final loop at the neck collar; total loops: 21!!! % perfect; how bout 12 antennae per loop a la the zodiac, 252 antennae % altogether; loopy perfect   % crudely model the body as one stick waist to collar, then two sticks each % for the four limbs. The body stick will have five loops, each limb-stick % will have two loops each; use various ellipse shapes as the loops % ellipse: x(t)=a cos(t) y(t)=b sin(t)   body_len=1.0; % meters   leg_len=0.5; % lower AND upper leg both   arm_len=0.6; % ditto, lower and upper   antennae_per_loop=12;   % lower left leg   stick_end=[0 0.15 0.1];   stick_vect=[0 0 leg_len];   forward=[1 0 0];   forward=forward/norm(forward);   crosss=cross(stick_vect,forward);   crosss=crosss/norm(crosss);   loops_per_stick=3;   ant_loc=zeros(4*loops_per_stick*antennae_per_loop,3);   cnt=0;   a=0.05; b=0.04;   for i=1:loops_per_stick
       cent=stick_end+(i−1)*stick_vect/(loops_per_stick−1);   for t=1: antennae_per_loop
           cnt=cnt+1;   tt=2*pi*(t/antennae_per_loop);   ant_loc(cnt,:)=cent+a*cos(tt)*forward+b*sin(tt)*crosss;   
           end   
       end   % lower right leg   stick_end=[0 −0.15 0.1];   stick_vect=[0 0 leg_len];   forward=[1 0.2 −0.1];   forward=forward/norm(forward);   crosss=cross(stick_vect,forward);   crosss=crosss/norm(crosss);   a=0.05; b=0.04;   for i=1:loops_per_stick
       cent=stick_end+(i−1)*stick_vect/(loops_per_stick−1);   for t=1: antennae_per_loop
           cnt=cnt+1;   tt=2*pi*(t/antennae_per_loop);   ant_loc(cnt,:)=cent+a*cos(tt)*forward+b*sin(tt)*crosss;   
           end   
       end   % upper left leg   stick_end=[0 −0.15 0.7];   stick_vect=[0 0 leg_len];   forward=[1 −0.25 −0.3];   forward=forward/norm(forward);   crosss=cross(stick_vect,forward);   crosss=crosss/norm(crosss);   a=0.07; b=0.05;   for i=1:loops_per_stick
       cent=stick_end+(i−1)*stick_vect/(loops_per_stick−1);   for t=1: antennae_per_loop
           cnt=cnt+1;   tt=2*pi*(t/antennae_per_loop);   ant_loc(cnt,:)=cent+a*cos(tt)*forward+b*sin(tt)*crosss;   
           end   
       end   % upper right leg   stick_end=[0 0.15 0.73];   stick_vect=[0 0 leg_len];   forward=[1 0.1 0.3];   forward=forward/norm(forward);   crosss=cross(stick_vect,forward);   crosss=crosss/norm(crosss);   a=0.07; b=0.05;   for i=1:loops_per_stick
       cent=stick_end+(i−1)*stick_vect/(loops_per_stick−1);   for t=1: antennae_per_loop
           cnt=cnt+1;   tt=2*pi*(t/antennae_per_loop);   ant_loc(cnt,:)=cent+a*cos(tt)*forward+b*sin(tt)*crosss;   
           end   
       end   % lower left arm   stick_end=[0.03 0.35 0.7];   stick_vect=[0 0 arm_len];   forward=[1 0.3 −0.3];   forward=forward/norm(forward);   crosss=cross(stick_vect,forward);   crosss=crosss/norm(crosss);   loops_per_stick=3;   a=0.04; b=0.03;   for i=1:loops_per_stick
       cent=stick_end+(i−1)*stick_vect/(loops_per_stick−1);   for t=1: antennae_per_loop
           cnt=cnt+1;   tt=2*pi*(t/antennae_per_loop);   ant_loc(cnt,:)=cent+a*cos(tt)*forward+b*sin(tt)*crosss;   
           end   
       end   % lower right arm   stick_end=[−0.02 −0.38 0.75];   stick_vect=[0 0 arm_len];   forward=[1 0.1 0];   forward=forward/norm(forward);   crosss=cross(stick_vect,forward);   crosss=crosss/norm(crosss);   loops_per_stick=3;   a=0.04; b=0.03;   for i=1:loops_per_stick
       cent=stick_end+(i−1)*stick_vect/(loops_per_stick−1);   for t=1: antennae_per_loop
           cnt=cnt+1;   tt=2*pi*(t/antennae_per_loop);   ant_loc(cnt,:)=cent+a*cos(tt)*forward+b*sin(tt)*crosss;   
           end   
       end   % upper left arm   stick_end=[0.05 0.36 1.4];   stick_vect=[0 0 arm_len];   forward=[1 0.2 −0.2];   forward=forward/norm(forward);   crosss=cross(stick_vect,forward);   crosss=crosss/norm(crosss);   loops_per_stick=3;   a=0.06; b=0.04;   for i=1:loops_per_stick
       cent=stick_end+(i−1)*stick_vect/(loops_per_stick−1);   for t=1: antennae_per_loop
           cnt=cnt+1;   tt=2*pi*(t/antennae_per_loop);   ant_loc(cnt,:)=cent+a*cos(tt)*forward+b*sin(tt)*crosss;   
           end   
       end   % upper right arm   stick_end=[0.01 −0.37 1.5];   stick_vect=[0 0 arm_len];   forward=[1 0.1 −0.2];   forward=forward/norm(forward);   crosss=cross(stick_vect,forward);   crosss=crosss/norm(crosss);   loops_per_stick=3;   a=0.06; b=0.04;   for i=1:loops_per_stick
       cent=stick_end+(i−1)*stick_vect/(loops_per_stick−1);   for t=1: antennae_per_loop
           cnt=cnt+1;   tt=2*pi*(t/antennae_per_loop);   ant_loc(cnt,:)=cent+a*cos(tt)*forward+b*sin(tt)*crosss;   
           end   
       end   % body waist through neck   stick_end=[0.01 −0.03 1.4];   stick_vect=[0 0 body_len];   forward=[1.1 −0.05];   forward=forward/norm(forward);   crosss=cross(stick_vect,forward);   crosss=crosss/norm(crosss);   loops_per_stick=6;   a=0.08; b=0.22;   for i=1:loops_per_stick
       cent=stick_end+(i−1)*stick_vect/(loops_per_stick−1);   if i==5
           a=0.08;b=0.35;   
           else if i==6
           a=0.04;b=0.04;   
           end   for t=1: antennae_per_loop
           cnt=cnt+1;   tt=2*pi*(t/antennae_per_loop);   ant_loc(cnt,:)=cent+a*cos(tt)*forward+b*sin(tt)*crosss;   
           end   
       end   cyl_height=1.8; % meters   cyl_radius=0.3; % meters   num_uwbs=100;   % uwb_location=(boxlength*rand(num_uwbs,3))−(boxlength/2);   uwb_location=zeros(num_uwbs,3);   uwb_location(:,3)=cyl_height*rand(num_uwbs,1)−cyl_height/2;   din=2*pi*rand(num_uwbs,1);   uwb_location(:,1)=cyl_radius*sin(dirr);   uwb_location(:,2)=cyl_radius*cos(dirr);   wavelength=0.06; % in meters, 0.1 is roughly 3 GHz   waves=1.5; % one half-wave with 50% positive energy, and two with 25% energy   wave_lut=zeros(76,1); % simple lut on a sine wave   for i=1:76
       ii=i−1;   amp=cos(2*pi*ii/100);   if i&lt;26
           wave_lut(i)=2*amp;   
           else
           wave_lut(i)=amp;   
           end   
       end   opt_dist=100;   optimized_pt=[opt_dist,0,0];   cyl_height_angle=180*a tan(cyl_height/opt_dist)/pi;   cyl_width_angle=180*a tan(2*cyl_radius/opt_dist)/pi;   % find light time between opt and all uwb_loc   % c=299792458;   advance_retard=zeros(num_uwbs,1);   for i=1:num_uwbs
       dist1=(uwb_location(i,1)−optimized_pt(1))^2;   dist2=(uwb_location(i,2)−optimized_pt(2))^2;   dist3=(uwb_location(i,3)−optimized_pt(3))^2;   dist=sqrt(dist1+dist2+dist3);   advance_retard(i)=dist−opt_dist;   
       end   % now produce the EM-field vector and intensity ‘shell’ about the opt_pt   % in tenth wavelength slices   shellslice=0.025; % meters   shellwidth=50;   theta_sampling=1.3; % degrees   theta_limit=3.9; % degrees   theta_dim=floor(2*(theta_limit/theta_sampling)+1);   field_val=zeros(shellwidth*2+1,theta_dim,theta_dim);   observation_pt=zeros(3,1);   tot_pts=(shellwidth*2+1)*theta_dim*thetadim;   obs_quiver_base=zeros(tot_pts,3);   obs_fieldvector=zeros(tot_pts,1);   dummy=zeros(tot_pts,1);   shellcount=0;   overall_count=0;   for dist_shell=−shellwidth:shellwidth
       shellcount=shellcount+1   r=opt_dist+dist_shell*shellslice*wavelength;   r2=r*r;   ycount=0;   for y=−theta_limit:theta_sampling:theta_limit
           ycount=ycount+1;   observation_pt(2)=r*sin(pi*y/180);   ob2=observation_pt(2)^2;   zcount=0;   for z=−theta_limit:theta_sampling:theta_limit
               zcount=zcount+1;   overall_count=overall_count+1;   observation_pt(3)=r*sin(pi*z/180);   ob3=observation_pt(3)^2;   observation_pt(1)=sqrt(r2−ob2−ob3);   % what is the combined EM field &amp; intensity at this observation   totamp=0;   for i=1:num_uwbs
                   dist1=(uwb_location(i,1)−observation_pt(1))^2;   dist2=(uwb_location(i,2)−observation_pt(2))^2;   dist3=(uwb_location(i,3)−observation_pt(3))^2;   dist=sqrt(dist1+dist2+dist3);   amp=1/dist;   wave_pt=floor(100*(dist-opt_dist-advance_retard(i))/wavelength);   if wave_pt&gt;−76    if wave_pt&lt;76    if wave_pt&lt;0    wave_pt=−wave_pt;    end    wave_pt=wave_pt+1;    totamp=totamp+amp*wave_lut(wave_pt);    end   end   
                   end   field_val(shellcount,ycount,zcount)=totamp;   obs_fieldvector(overall_count)=totamp;   obs_quiver_base(overall_count,1)=observation_pt(1);   obs_quiver_base(overall_count,2)=observation_pt(2);   obs_quiver_base(overall_count,3)=observation_pt(3);   
               end   
           end   
       end   foo=zeros(theta_dim);   foo(:,:)=field_val((shellcount+1)/2,:,:);   imagesc(foo);   % quiver3(obs_quiver_base(:,1),obs_quiver_base(:,2),obs_quiver_base(:,3), . . .   % dummy,dummy,obs_fieldvector,2,‘ShowArrowHead’,‘off’,‘Marker’,‘.’);   quiver3(obs_quiver_base(:,1),obs_quiver_base(:,2),obs_quiver_base(:,3), . . .   dummy,dummy,obs_fieldvector,3,‘ShowArrowHead’,‘off’);   axis([99 101 −8 8 −8 8]);   grid off   xlabel(‘meters distant’);   ylabel(‘lateral meters’);   zlabel(‘height meters’);   

     CONCLUDING REMARKS 
     Having described and illustrated the principles of the technology with reference to specific implementations, it will be recognized that the technology can be implemented in many other, different, forms. To provide a comprehensive disclosure without unduly lengthening the specification, applicants incorporate by reference the patents and documents referenced above. 
     The methods, processes, and systems described above may be implemented in hardware, software or a combination of hardware and software. The particular combinations of elements and features in the above-detailed embodiments are exemplary only; combinations between the different implementations and embodiments is expressly considered; the interchanging and substitution of these teachings with other teachings in this and the incorporated-by-reference patents/documents are also contemplated.