Patent Publication Number: US-10312984-B2

Title: Distributed airborne beamforming system

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a U.S. National Stage of PCT application PCT/US2015/026114 filed in the English language on Apr. 16, 2015, and entitled “D ISTRIBUTED  A IRBORNE  B EAMFORMING  S YSTEM ,” WhiCh claims the benefit under 35 U.S.C. § 119 of provisional application No. 61/980,097 filed Apr. 16, 2014, which application is hereby incorporated herein by reference. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This invention was made with Government support under Contract No. FA8721-05-C-0002 awarded by the U.S. Air Force. The Government has certain rights in the invention. 
    
    
     FIELD 
     The concepts, systems, circuits, devices and techniques described herein relate generally to beamforming systems and more particularly to distributed beamforming systems and related techniques utilizing an antenna array comprising aerial relay nodes. 
     BACKGROUND 
     As is known in the art, beamforming systems allow a user having an antenna with multiple transmit/receive elements to adjust delay, phase and amplitude weights applied to each element to create a desired beam pattern. 
     Adaptive beamforming systems allow dynamic adaption of the weights to adjust an antenna pattern and to increase, and ideally maximize, a desired signal-to-noise ratio. Traditional and adaptive beamforming array antennas (or more simply “arrays”) are typically provided having one-half wavelength spacing between antenna elements which make up the array. Distributed beamforming arrays (i.e. beamforming arrays having an element spacing which is not one half wavelength) have more recently gained interest, particularly with respect to distributed sensors which individually are limited in power, but can cooperatively coordinate their communication to gain advantage through beamforming. 
     SUMMARY 
     Described herein is a distributed beamforming array which utilizes independent aerial relay nodes or platforms (i.e. no strict control of relay node position, no communication between the relay nodes, and no coordinated transmission among the relay nodes) to form a distributed beamforming antenna. 
     The aerial relay nodes are not coordinated in position or communication. The beamforming is digitally performed at a processing site (such as a ground-based receiver) and can be used to increase system capacity or to mitigate interference. 
     In an embodiment, a system includes two or more aerial relay nodes, at least one of which can move independently of the other aerial relay node and receiver to receive an analog transmission from each of the two or more aerial relay nodes. The receiver converts the aerial relay node analog transmissions to corresponding digital representations of each transmission at an output thereof. The aerial relay node transmission comprises at least a data message and a reference signature for calculation of the desired beamforming weights. 
     An adaptive beamforming processor, coupled to the output of the receiver, may be configured to: receive a digital representation of the aerial relay node transmission including the reference signature for calculation of desired beamforming weights from each of the two or more aerial relay nodes and generate a set of beamforming weights for the signals received from two or more aerial relay nodes. The weights are based at least in part upon the reference signature signal characteristics received from each respective aerial relay node and the set of weights compensates for at least physical spacing, relative motion, and signal timing of the aerial relay nodes. The adaptive beamforming processor applies the weights to the respective transmission from respective ones of the aerial relay relay nodes to form a desired beam; and the system then processes the signal received to recover the data message from the aerial relay node transmission. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other objects, features and advantages of the concepts. Systems and techniques described herein will be apparent from the following description of particular embodiments, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the concepts, systems, circuits and techniques sought to be protected herein. 
         FIG. 1  is a block diagram of a distributed airborne adaptive beamforming system. 
         FIG. 2  is a block diagram of an adaptive beamforming system including an adaptive beamforming processor. 
         FIG. 2A  is a block diagram of a beamforming processor and related systems. 
         FIG. 2B  is a flowchart of a beamforming process. 
         FIG. 3  is a block diagram of a messaging sequence. 
         FIG. 4  and  FIG. 4A  are flowcharts of a process for generating weighting signals and demodulating a received signal. 
         FIG. 5  is a block diagram of a distributed airborne adaptive beamforming system showing a jammer. 
     
    
    
     DETAILED DESCRIPTION 
     Referring now to  FIG. 1 , communication system  100  includes communication platforms  10   a  and  10   b  which may wish to communicate with one another. As shown in  FIG. 1 , communication platforms  10   a  and  10   b  may be seagoing vessels such as boats or submarines. In other embodiments, one or both of communication platforms  10   a  and  10   b  may be land-based platforms (e.g. cars or trucks, computers, land-based communication stations, mobile radios, cell-phones or other mobile devices, etc.) or sea going vessels (e.g. boats, ships, seaborne platforms, etc.). Although only two communication platforms are shown in the illustrative embodiment of  FIG. 1 , communication system  100  can include more than two communication platforms communicating with each other. 
     A communication signal  16  (also sometimes referred to herein as a user signal) transmitted from platform  10   a  is relayed through one or more aerial relay nodes  12   a - 12   n  to platform  10   b.    
     As will be discussed in more detail below in conjunction with  FIG. 5 , embodiments which include one or more interfering platforms for proper operation of the beamforming system described herein, the number of aerial relay nodes  12   a - 12   n  should be greater than the number of interfering platforms (e.g. interfering platform  502  in  FIG. 5 ). 
     Interfering platforms may be users that are planned by the system to interfere in time and frequency to increase system capacity while allowing the beamforming system to mitigate that planned interference, or the interference sources could be unplanned external sources (e.g. a jammer). In general, it is not necessary to have more aerial relay nodes than communication platforms, however in cases where interfering nodes exist it is desirable that the number of aerial relay nodes be greater than the number of interfering nodes. 
     For example a system with 10 MHz of bandwidth could assign 1 MHz of bandwidth to each of 10 users and this would not result in interference between the users. If 10 more users were subsequently added on top of the existing  10  (so 20 users total) then two relays would be required because each user would have one interference source—one user interfering with them (i.e. each 1 MHz of bandwidth would have two users in it). 
     In the example embodiment of  FIG. 1 , the platforms  10   a  and  10   b  are illustrated as sea vessels and the aerial relay nodes  12   a - 12   n  are illustrated as balloons—e.g. high altitude balloons such as those able to reach heights of 10 km or more. As noted above, the communication platforms may be any mobile or stationary ground-based vehicles (e.g. handheld devices, cars, trucks or buildings) or mobile or stationary water-based vehicles (e.g. stationary platforms or ships or other water-based vehicles) or mobile or stationary near-ground-based vehicles (e.g. low altitude manned or unmanned aircraft or vehicle) or mobile or stationary air-based vehicle (e.g. any manned or unmanned aircraft or vehicle). In short, any platform, below the aerial relay nodes  12   a - 12   n  may act as a communication platform  10   a ,  10   b.    
     Aerial relay nodes  12   a - 12   n  may also be provided as any number of a wide variety of moving or stationary aerial platforms (e.g. high altitude balloons, quadcopters, tethered-balloons or other aircraft, kites or any manned or unmanned air-based vehicle or aircraft or satellite) and they can be a mix of different types of aerial nodes (i.e. all aerial relay nodes may or may not be of the same type). In an embodiment, the aerial relay nodes are balloons or other platforms where at least one of the relay nodes can move independently of the other relay nodes. In other embodiments, there may be two or more relay nodes in an array that are coupled one or more of the platforms (e.g. one or more of the balloons) so that at least some of the relay nodes (i.e. the relay nodes associated with a same balloon) are spatially fixed with respect to each other. 
     As noted above, antennas in a conventional beamforming array are typically spaced at regular intervals, for example half-wavelengths apart. 
     However, the aerial relay nodes  12   a - 12   n  forming the antenna array as described herein are independent (i.e. not physically coupled to each other (i.e. and may move so they are spaced at irregular and unknown spatial intervals. Also, the aerial relay nodes  12   a - 12 N are typically spaced much further apart than one half-wavelength distance. In some embodiments, the aerial relay nodes may be kilometers apart while operating at frequencies up to 106 GHz and above. 
     In one example embodiment, each platform  10   a  and/or  10   b  transmits signals to the aerial platforms  12   a - 12   n  using a broad beam antenna that can simultaneously transmit to multiple aerial platforms, (i.e. an antenna having a radiation pattern which is broad enough to simultaneously transmit to multiple relays). Each aerial relay antenna node  12   a - 12   n  also transmits and receives signals using a broad beam antenna. It is desirable for a user signal or an uplink signal to be received at multiple relay nodes and for an aerial relay node downlink signals to be received at multiple ground-based (or near ground-based) receiver. Using broad beam antennas in both the communication platforms  10   a ,  10   b  and the aerial relay nodes  12   a - 12   n  (collectively “nodes”), allows one antenna in each node to “see” (i.e. receive signals from and/or transmit signals to, as appropriate) all nodes and receive all signals of interest. While the relatively large number of signals could be transmitted and received using directional a relatively large number of antennas, in systems having a large number of nodes, would be required to capture all of the signals and it may be difficult or expensive to provide enough directional antennas for a system that supports a large number of users. 
     In an embodiment, at least some aerial relay nodes are independent of other nodes (i.e. at least some nodes do not communicate with each other to coordinate their position within the antenna array). The aerial relay nodes also may not communicate their position with the communication platforms. In such embodiments, at least some relay nodes do not have information about their own position or motion, the position or motion of other relay nodes, or the position or motion of the communication platforms. Similarly, the communication platforms may not have information about the position or motion of the relay nodes or of other communication platforms. 
     In other embodiments, the aerial relay nodes may communicate with each other to coordinate position, timing, clocks, or other parameters. 
     The aerial relay nodes may be, for example, simple repeaters that receive signal  16  and amplify and re-broadcast or otherwise re-transmit signal  16  as signals  18   a - 18   n . In other embodiments, the aerial relay nodes may include amplifiers, filters, or other signal processing or signal shaping circuits that can operate on signal  16  before re-transmitting the signal. The aerial relay nodes may also include a power source to provide power for transmitting signals  18   a - 18   n.    
     In some embodiments, the transmitted signals  18   a - 18   n  may be frequency modulated, where each relay node uses a unique modulation frequency, so that the receiving platform  10   b  can identify which signal  18   a - 18   n  came from which aerial relay node  12   a - 12   n . In other embodiments, the aerial relay notes may coordinate timing of broadcasted signals  18   a - 18   n  using a time-division multiplexing scheme. The receiving platform  10   b  can then identify which signal  18   a - 18   n  came from which aerial relay node  12   a - 12   n  based on the time or sequence in which the signal  18   a - 18   n  was received. 
     In other embodiments, the system may include a ground-based beam forming antenna that can point an antenna beam at each of the aerial relay nodes individually. The ground-based antenna may substantially simultaneously steer n beams to n different aerial relay nodes which can be repeated by the relay nodes and received by the receiving communication platform  10   b.    
     In other embodiments, the aerial relay nodes can transmit signals  18   a - 18   n  according to a time division multiple access (TDMA) scheme, where each aerial relay node transmits its signal during a predetermined time slot. For example, node  1  may transmit first, node  2  may transmit second, etc. 
     In other embodiments, a space division multiple access scheme, code division multiplexing scheme, or any other method can be used so that receiving platform  10   b  can differentiate the received signals  18   a - 18   n  and identify the aerial relay from which the signal was transmitted. 
     One or more of the communication platforms  10   a  and  10   b  may include an adaptive beamforming processor  15  and/or a receiver/demodulation processor  17 . Beamforming processor  15  and demodulation processor  17  may operate to receive signals  18   a - 18   n  and to recover a message included therein. As will be discussed below, beamforming processor  15  receives reference signature from the aerial relay nodes  12   a - 12   n  so that beamforming processor  15  can generate weight, phase, and delay vectors based on the current state of the antenna array and form a beam from the received signals  18   a - 18   n . Although beamforming processor  15  and demodulation processor  17  are shown as associated with communication platform  10   b , any communication platform that receives signals  18   a - 18   n  from aerial relay nodes  12   a - 12   n  may include a like beamforming processor and/or demodulation processor. 
     Referring now to  FIG. 2 , a beamforming receiver system  20  performs beamforming processing at a receive node (e.g. platform  10   b  in  FIG. 1 ). The beamforming system  20  comprises adaptive beamforming processor  15  and demodulation processor  17 , which are also shown in  FIG. 1 . Beamforming system  20  receives combined, frequency-translated signals  18   a - 18   n  from each of the N aerial relay nodes on N independent frequency channels. The signals  18   a - 18   n  are provided to inputs of analog-to digital converters (ADCs)  22   a - 22   n  which produce a bit-stream representative of the signals provided thereto. In at least some embodiments, the signals  18   a - 18   n  are down-converted from RF frequencies to IF frequencies before being provided to the input of the ADCs  22   a - 22   n . The digital signals are provided to delay, phase and amplitude adjustment circuitry  24   a - 24   n  as well as to adaptive beamforming processor  15 . 
     The adaptive beamforming processor  15  performs signal processing to identify delay, phase, and amplitude weights that increase (and ideally maximize) the signal to noise ratio (SNR) of the desired signal as identified by a reference signature included as part of the received signals. If an interfering node is present, the beamforming processor may also perform signal processing to identify delay, phase, and amplitude weights that decrease (and ideally minimize) the signal-to-noise ratio of the interfering signal. The phase and amplitude adjustment circuits  24   a - 24   n  adjust the delay, phase, and amplitude before combining the signals to maximize the signal to noise ratio based on the delay, phase, and amplitude adjustments provided by adaptive beamforming processor  15 . 
     In embodiments, adaptive beamforming processor  15  may be a circuit that performs the features and functions described herein. In other embodiments, beamforming processor  15  may be a processor that executes software (i.e. software, firmware, or another type of instruction stored in memory that can be executed by a processor) to effectuate the features and functions described herein. Adaptive beamforming processor  15  may also comprise a combination of circuits, processor(s), and software instructions to perform the features and functions described. 
     Phase and amplitude adjustment circuits  24   a - 24   n  provide appropriately weighted and phased signals to a summing circuit  28 . Summing circuit  28  sums the signals provided thereto to form a beam at an output thereof. The output of summing circuit  28  is coupled to an input of a demodulator processor  17  which demodulates the signal provided thereto to provide an output signal  32 . Output signal  32  contains substantially all of the information transmitted by communication platform  10   a . Thus, communication platform  10   a  is able to communicate with communication platform  10   b  (or with any other communication platforms) using the technique(s) described herein. 
     In one example, platform  10   a  transmits a signal via a broad beam antenna. The so transmitted signal is received by two or more of the aerial relay nodes  12   a - 12   n . As noted above, for desired operation, the system requires at least one more aerial relay nodes than interferer so if one interferer exists, then at least two aerial relay nodes are needed. It should be noted that, in general, system performance improves with more aerial relay nodes. As noted above, in one illustrative embodiment, each aerial relay node  12   a - 12   n  that receives the signal from platform  10   a  relays the signal received on a frequency channel different from the frequency channels used by other ones of the other aerial relay nodes. 
     In another example, platform  10   a  transmits a first signal and platform  10   b  transmits a second signal. The first and second signals are received by aerial relay nodes  12   a - 12   n . The aerial relay nodes  12   a - 12   n  mix the first signal and the second signal received and relay the mixed signal (i.e., aerial relay node  12   a  would transmit the mixed signal via a first channel, aerial relay node  12   b  would transmit the mixed signal via a second channel, etc.). The receiver node combines the mixed signals received from the aerial relay nodes on the n channels and extracts the first signal transmitted from platform  10   a  and extracts the second signal transmitted from platform  10   b.    
     In one illustrative embodiment, a user signal is embedded with a reference signature which allows the beamforming processing to improve (and ideally maximize) signal-to-noise (SNR) without knowledge of the user or jammer (i.e. interferer) location. Embodiments of signature embedment may include a predefined pattern of reference bits embedded in the bit-stream identifying the user, a direct sequence spreading sequence identifying the user, or a frequency hopping pattern identifying the user. In other embodiments, the reference signature may comprise a pseudo-random code or signature hopping pattern that is known to the receiver platform. There are multiple options of beamforming processing techniques that can be adapted for use. As one of ordinary skill in the art would recognize, adding additional aerial relay nodes allows the user additional degrees of freedom to attenuate interfering sources and also to recover a user signal at a receiver node. 
     Referring to  FIG. 2A , a block diagram  200  illustrates an end to end system model of a beamforming technique which may be implemented, in whole or in part, by beamforming processor  15 . An uplink signal x may have unity power so that
 
∥ x∥   F   2   =n   s  
 
The uplink signal may be a reference signature that is known by the downlink receiver, e.g. by the adaptive beamforming processor  15 .
 
     The transmitted uplink signal, s, may represent the amplified signal
 
 s =√{square root over ( P   s )} x  
 
where P s  is the energy per sample and may account for all transmit gain in the uplink terminal. A communication channel h between the uplink terminal antenna and the n b  aerial relay antennas is given as:
 
 h∈     n     b     ×1  
 
     The received signal across the array of aerial relay nodes is:
 
 Y =√{square root over ( P   s )} hx+N   b  
 
where the noise internal to the receive array is:
 
 N   b ∈   n     b     ×n     s    
 
     The noise N b  may have circularly symmetric Gaussian distribution with zero mean and covariance such that:
 
ε{ N   b   N   b   −H }=σ b   2   I.  
 
     The i th  aerial relay node may scale its received signal by a factor of γ ii  to the relay node&#39;s maximum transmit dynamic range, before transmitting the result in the i th  slot of the downlink&#39;s TDMA frame (assuming a TDMA scheme is being used). The re-scaled receive array signal may be represented by: 
     
       
         
           
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     In this example, a time-division multiple access (TDMA) scheme may be used for the signals received from the aerial relay nodes, as described above. The TDMA frame Z received at the downlink terminal may be given by: 
                   Z   =       ⁢       G   ⁢           ⁢   Γ   ⁢           ⁢   Y     +     N   d                   =       ⁢           P   s       ⁢   G   ⁢           ⁢   Γ   ⁢           ⁢   hx     +     G   ⁢           ⁢   Γ   ⁢           ⁢     N   b       +     N   d                   =       ⁢     hx   +   N                 where   h =√{square root over ( P   s )} GΓh  
 
and N d  is the noise internal to the downlink receiver and may have circularly symmetric Gaussian distribution with zero mean and covariance. A channel-allocation matrix G allocates the received uplink signals at the n b  relay nodes to the n b  slots of the TDMA downlink frame. G may be represented as:
 
             G   =     [           g   1         0       0           0       ⋱       0           0       0         g   b           ]           
In the matrix above, g i  is the channel coefficient between the i th  relay node&#39;s antenna and the downlink terminal&#39;s antenna. Equivalently, a space-frequency channel-allocation for a frequency diversion multiple access (FDMA), collision detection multiple access (CDMA), or other type of downlink could be used. In an embodiment, the uplink and downlink channels are assumed to be narrowband (i.e. the delay spread of the channel is assumed to be zero).
 
     If an interference node or jammer is present, the jam signal t may have unity power and may be unknown by the receiver. The transmitted jam signal on the uplink channel j may be given by:
 
 j =√{square root over ( P   j )} t  
 
where P j  is the energy per sample. In embodiments, it may be assumed that x and t are independent (i.e. uncorrelated) variables. The channel between the jammer&#39;s antenna and the array of relay nodes may be referred to as k. In the presence of the jammer signal, the received signal across the array of relay modules may be given by:
 
 Y =√{square root over ( P   s )} hx +√{square root over ( P   j )} kt+N   b  
 
and the TDMA frame received at the downlink terminal may be:
 
                   Z   =       ⁢       G   ⁢           ⁢   Γ   ⁢           ⁢   Y     +     N   d                   =       ⁢           P   s       ⁢   G   ⁢           ⁢   Γ   ⁢           ⁢   hx     +         P   j       ⁢   G   ⁢           ⁢   Γ   ⁢           ⁢   kt     +     G   ⁢           ⁢   Γ   ⁢           ⁢     N   b       +     N   d                   =       ⁢     hx   +   kt   +   N                 where   k =√{square root over ( P   j )} GΓk  
 
The respective covariances of the signal-of-interest, the interference signal, and the noise signal at the downlink terminal are:
 
     
       
         
           
             
               
                 
                   
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     Without beamforming, the signal-to-noise plus interference ration (SINR) at the downlink terminal for the relay path through the i th  balloon is: 
     
       
         
           
             
               
                 
                   
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     The output of the beamformer at the downlink terminal is
 
 {circumflex over (x)}=w   H   Z  
 
and the SINR at the output of the beamformer is:
 
     
       
         
           
             
               
                 
                   
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                       ɛ 
                       ⁢ 
                       
                         { 
                         
                           
                              
                             
                               
                                 w 
                                 H 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   kt 
                                   + 
                                   N 
                                 
                                 ) 
                               
                             
                              
                           
                           2 
                         
                         } 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         w 
                         H 
                       
                       ⁢ 
                       
                         R 
                         S 
                       
                       ⁢ 
                       w 
                     
                     
                       
                         
                           w 
                           H 
                         
                         ⁡ 
                         
                           ( 
                           
                             
                               R 
                               j 
                             
                             + 
                             
                               R 
                               N 
                             
                           
                           ) 
                         
                       
                       ⁢ 
                       w 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         w 
                         H 
                       
                       ⁢ 
                       
                         R 
                         S 
                       
                       ⁢ 
                       w 
                     
                     
                       
                         w 
                         H 
                       
                       ⁢ 
                       Qw 
                     
                   
                 
               
             
           
         
       
     
     The beamforming weight vector that maximizes SINR is 
     
       
         
           
             
               
                 
                   w 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         arg 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         max 
                       
                       
                         w 
                         i 
                       
                     
                     ⁢ 
                     
                       SINR 
                       w 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       Q 
                       
                         - 
                         1 
                       
                     
                     ⁢ 
                     h 
                   
                 
               
             
           
         
       
     
     Computing w may require knowledge of parameters in the model that are impractical to acquire. For example, the parameters h, k, and N are related to random physical processes that may be changing and are therefore unknown a priori. This in turn means that Q is random, dynamic and unknown a priori. Furthermore, Q depends on the interference signal, t, which itself may be unknown a priori or, if t it belongs to a known class of signals, there may be significant uncertainty about specific embodiment of the interference signal. Thus, an estimate of w can be computed as follows. The least-squares channel estimate may first be computed as: 
                     h   ^     =       ⁢     Zx   +                 =       ⁢         Zx   H     ⁡     (     xx   H     )         -   1                   =       ⁢       1     n   s       ⁢     Zx   H                   
where the notation x +  denotes the pseudo-inverse of x. An estimate of Q can be computed from the projection of the received signal into a space orthogonal to the desired signal. The orthogonal projection matrix is computed as:
 
     
       
         
           
             
               
                 
                   
                     P 
                     x 
                     + 
                   
                   = 
                     
                   ⁢ 
                   
                     I 
                     - 
                     
                       
                         x 
                         + 
                       
                       ⁢ 
                       x 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     I 
                     - 
                     
                       
                         
                           
                             x 
                             H 
                           
                           ⁡ 
                           
                             ( 
                             
                               xx 
                               H 
                             
                             ) 
                           
                         
                         
                           - 
                           1 
                         
                       
                       ⁢ 
                       x 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     I 
                     - 
                     
                       
                         1 
                         
                           n 
                           s 
                         
                       
                       ⁢ 
                       
                         x 
                         H 
                       
                       ⁢ 
                       x 
                     
                   
                 
               
             
           
         
       
     
     The estimate of Q may then be computed as 
     
       
         
           
             
               
                 
                   
                     Q 
                     ^ 
                   
                   = 
                     
                   ⁢ 
                   
                     
                       1 
                       
                         n 
                         s 
                       
                     
                     ⁢ 
                     
                       ZP 
                       x 
                       + 
                     
                     ⁢ 
                     
                       Z 
                       H 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       1 
                       
                         n 
                         s 
                       
                     
                     ⁢ 
                     
                       Z 
                       ⁡ 
                       
                         ( 
                         
                           I 
                           - 
                           
                             
                               1 
                               
                                 n 
                                 s 
                               
                             
                             ⁢ 
                             
                               x 
                               H 
                             
                             ⁢ 
                             x 
                           
                         
                         ) 
                       
                     
                     ⁢ 
                     
                       Z 
                       H 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         1 
                         
                           n 
                           s 
                         
                       
                       ⁢ 
                       
                         ZZ 
                         H 
                       
                     
                     - 
                     
                       
                         1 
                         
                           n 
                           s 
                           2 
                         
                       
                       ⁢ 
                       
                         Zx 
                         H 
                       
                       ⁢ 
                       
                         xZ 
                         H 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     
                       
                         1 
                         
                           n 
                           s 
                         
                       
                       ⁢ 
                       
                         ZZ 
                         H 
                       
                     
                     - 
                     
                       
                         h 
                         ^ 
                       
                       ⁢ 
                       
                         
                           h 
                           ^ 
                         
                         H 
                       
                     
                   
                 
               
             
           
         
       
     
     Where the estimate of the beamformer is:
 
{circumflex over ( w )}={circumflex over (Q)} −1   ĥ.  
 
     Referring to  FIG. 2B , a process  212 , which may be performed by beamforming processor  15 , for forming a beam from signals transmitted by aerial relay nodes may be the same as or similar to the process described above with respect to  FIG. 2A . In box  214 , signals (which may be converted to digital signals) are received on each of N antenna elements (X) in box  214 . In box  216 , a steering vector is computed to a user signal (v). This vector may correspond to weights used in beamforming applications. In box  218 , a covariance matrix R is computed between every element in the antenna array. 
     The covariance matrix is computed as a matrix whose elements contain the mathematical correlation between the received signal from each of the relay paths (e.g.  18   a ,  18   b , . . . ,  18   n ). Entries in the covariance matrix may include one or more of an average of the product of a chosen vector component and the conjugate of another chosen vector component, given components of mean zero. Entries in the covariance matrix may be indexed by the ordered pair of chosen components. 
     For example, beamforming processor  15  may analyze parameters of the received reference signature to determine the position of aerial relay nodes with respect to each other, clock skew between the aerial relay nodes, Doppler effect of the received signal from an aerial relay node, relative motion of the aerial relay nodes, etc. 
     In box  220 , the user signal may be removed from the covariance matrix so that the covariance matrix contains only noise and interference. In box  222 , a weight vector w=inverse(R)*v is computed. In embodiments, the inverse of the covariance matrix may be used to mitigate interference. 
     In box  224 , future weight vectors may be extrapolated using a series of previously computed weight vectors. In box  226 , the weight signals are applied to the digital signal received from the aerial relay nodes. Additional iterations may be performed in order to improve performance. In an embodiment, the additional iterations may mitigate changes in the signal due to changes in the antenna array—caused by further movement or clock skew of the relay nodes, for example. 
     Referring now to  FIG. 3 , a message sequence  300  includes a data portion comprising messages  302   a - 302   n  and a reference signature  304 . As noted above, a communication platform  10   a  may send a series of transmissions (i.e. messages  302   a - 302   n ) to an antenna array comprising an array of aerial relay nodes  12   a - 12   n . The aerial relay nodes may then re-broadcast the signals so they can be received by communication platform  10   b . The data portion may include unknown data transmitted from a source (e.g. communication platform  10   a ) to one or more destinations (e.g. communication platform  10   b ). This unknown data may include the message that is being communicated from communication platform  10   a  to communication platform  10   b . The reference portion may comprise known data that can be used to derive weighting and phase vectors for the current state and position of the antenna array. In an embodiment, the weighting vectors may include outputs of finite-input-response (FIR) filters. The FIR filters may have frequency shifts applied to its taps if, for example, a delay-Doppler processing receiver is required. 
     Reference signature  304  may be injected periodically in the message stream. In an embodiment, reference signature  304  may be transmitted by the sending communication platform  10   a , or transmitted by the receiving communication platform  10   b , or may be computed by the aerial relay nodes  12   a - 12   n . In each case, the reference signature may be broadcast as a reference signature by the aerial relay nodes and received by the receiving communication platform  10   b . As noted above, the reference signature may be a predetermined data sequence, a pseudo-random data sequence, a signature hopping data sequence, or any other type of data sequence that can be known by receiving platform  10   b  prior to being received by receiving platform  10   b.    
     Once received, beamforming processor  15  may analyze the received reference signature. The position, motion, and clock timing of the transmitting relay node may affect the amplitude, timing, or other parameters of the reference signature sent by the relay node. Beamforming processor  15  may analyze these parameters to generate one or more of amplitude, delay, and phase values or vectors (i.e. weights) that can be applied to the received messages  302   a - 302   n  in order to from a beam from the received messages. Once the weights (e.g. amplitude and phase vectors) are applied and a composite signal is formed, beamforming processor  15  and/or demodulation processor  17  can retrieve the original message sent by the sending communication platform  10   a.    
     As shown in  FIG. 3 , reference signatures (e.g. reference signatures  304  and  306 ), can be transmitted periodically. Because aerial relay nodes may move independently of each other, the amplitude, delay, and phase vectors that are applied to the received signals from the relay nodes may change. Periodically sending a reference signature may allow beamforming processor  15  to periodically recalculate the weights to be applied to the received signals in response to movement of one or more of the aerial relay nodes move. 
     Referring to  FIG. 4  and  FIG. 4A , a process for forming a beam from an array of independent aerial relay nodes includes, in box  402 , transmitting a reference signature to a plurality of aerial platforms (e.g. aerial relay nodes). The reference sequence may be received by all or fewer than the number of aerial platforms to which the reference signature was transmitted. 
     In box  406 , the reference sequence is transmitted from the aerial platforms to a processing platform (e.g. communications platform  10   b ). In box  408 , the received signals are digitized to generate one or more uncompensated digitized signals, which are provided to an adaptive beamforming processor  15  in box  410 . 
     In box  412 , beamforming processor  15  may generate weighting signals (e.g. amplitude, delay, and/or phase scalar values or vectors) as described above. In box  414 , the weighting signals may be applied to the uncompensated digitized signals to generate a reconstructed reference sequence. 
     If the desired result is not achieved in box  416 , for example if the SNR of received messages is too low using the computed weighting signals and/or if the message cannot be accurately extracted from the received signals, the process may proceed to box  418 . If a partial result is to be used to generate the next set of weights, then partial results are obtained in box  420  and the process proceeds to box  412  to again generate the weighting signals. Otherwise, the process proceeds directly from box  418  to box  412  to again generate the weighting signals. The partial results in box  420  may be obtained, for example, from a previous iteration of the process in order to reduce processing overhead during the next iteration of calculation of the weighting vectors. 
     Referring to  FIG. 5 , an interference source  502  may transmit an interfering signal  504  which is received by one or more of the aerial relay nodes  12   a - 12   n . User signal  16  and a jammer signal  15  are transmitted to one or more of the aerial relay nodes  12   a - 12   n . In the case where interference sources exist, the user communication signal may be required to reach more relay nodes than there are interference sources. Those aerial relay nodes which receive the communication signals  16 , which may be all of the aerial relay nodes, combine the signals  16  provided thereto and perform a frequency translation (or another type of multiplexing as described above). The combined, frequency-translated signals  18   a - 18 N (dash-dot lines and also sometime referred to herein as downlink signals) are transmitted from the aerial relay nodes  12   a - 12   n  to the platform  10   b . Each aerial relay node transmits the downlink signal  18   a - 18   n  on a different downlink frequency (or using another multiplexing scheme). Thus, the frequency, timing, and/or encoding of uplink signals  16  to the aerial relay nodes  12   a - 12   n  may be different than that of the downlink signals  18   a - 18   n  transmitted from the aerial relay nodes. 
     Beamforming processor  15  may generate weighting vectors based on the interference signal  504 . This weighting vector can be applied to signals  18   a - 18   n  to reduce interference from the interference source  502  so as to reduce the signal to noise ratio for the interference signal  504 . 
     As noted above, the concepts, systems and techniques described herein are not limited to sea vessels and can apply to any mix of users within communication reach of the relay nodes. For example, each aerial relay node need not be the same and each communication platform need not be the same. Furthermore, the concepts, systems and techniques described herein are not limited to two users, but rather can be deployed with any desired number of users. Each user can communicate with one receiver, or with multiple receivers as desired via the aerial relay nodes. As also noted above, concepts, systems and techniques described herein are not limited to balloon communication relays and can apply to any airborne relay which can provide coverage to a user area of interest. For desired operation in situations where a jammer exists, the concepts, systems and techniques described herein may require more aerial relays than interference sources. This provides the system having sufficient degrees of freedom to attenuate the interference sources. 
     To increase capacity, the number of users occupying the same frequency and time allocation can be increased and in effect create an interference scenario that can be mitigated through the aerial distributed beamforming array to increase capacity. With all of these distributed sparse beamforming arrays there are grating lobes and gain lobes that are created and must be addressed through the beamforming algorithms to optimize the signal to noise ratio. 
     While particular embodiments of the concepts, systems and techniques described herein have been shown and described, it will be apparent to those skilled in the art that various changes and modifications in form and details may be made therein without departing from the spirit and scope of the invention as defined by the following claims. Accordingly, the appended claims encompass within their scope all such changes and modifications.