Patent Publication Number: US-2022239456-A1

Title: Full duplex wireless transmission with self-interference cancellation

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation of, and claims the benefit under 35 U.S.C. § 120 from U.S. patent application Ser. No. 16/936,284, filed Jul. 22, 2020, titled “Full Duplex Wireless Transmission with Self-Interference Cancellation,” which is hereby incorporated herein by reference, and which in turn is a continuation of, and claims the benefit under 35 U.S.C. § 120 from U.S. patent application Ser. No. 15/653,384, filed Jul. 18, 2017, entitled “Full Duplex Wireless Transmission with Self-Interference Cancellation,” which is hereby incorporated herein by reference, and which in turn is a continuation of, and claims the benefit under 35 U.S.C. § 120 from U.S. Pat. No. 9,713,010, issued Jul. 18, 2017, titled “Full Duplex Wireless Transmission with Self-Interference Cancellation,” which in turn is a non-provisional filing of, and claims the benefit under 35 U.S.C. § 119(e) from, U.S. Provisional Patent Application Ser. No. 61/646,312, filed May 13, 2012, and U.S. Provisional Patent Application Ser. No. 61/771,815, filed Mar. 2, 2013, both of which are hereby incorporated herein by reference. In addition, this application is related to the following applications, all of which are also incorporated herein by reference: U.S. application Ser. No. 13/892,296, titled “Wireless Transmission with Channel State Perturbation,” filed May 13, 2013, U.S. application Ser. No. 13/893,297, titled “Full Duplex Wireless Transmission with Channel Phase-Based Encryption,” filed May 13, 2013, and U.S. application Ser. No. 13/893,299, titled “Distributed Collaborative Signaling in Full Duplex Wireless Transceivers,” filed May 13, 2013. 
    
    
     FIELD OF THE INVENTION 
     The present disclosure relates to wireless communications. In particular, the present disclosure relates to systems and methods to establish two-way (full-duplex) wireless links with support for the use of multiple transmit, multiple receive antennas. 
     BACKGROUND OF THE INVENTION 
     A communication link (e.g. between node A and node B) with the capability to support the connection in both directions at the same time is called full-duplex, or two-way. In contrast, a link that can support the connection in only one direction at a time is called one-way or half-duplex. In a network environment with several nodes, it is desirable that communication nodes can simultaneously communicate in both directions, that is, to talk and listen at the same time. 
     Current wireless systems are one-way and rely on either separate time slots (Time Division Duplex) or separate frequency bands (Frequency Division Duplex) to transmit and to receive. These alternatives have their relative pros and cons, but both suffer from lack of ability to transmit and to receive simultaneously and over the entire frequency band. Even in the context of Orthogonal Frequency Division Multiple Access (OFDMA), where different frequency tones are used to simultaneously service multiple users, there is no method known to use the tones in opposite directions. A similar shortcoming exists in the context of Code Division Multiple Access (CDMA) where different codes are used to separate users. It is well known that two-way wireless is theoretically possible, but it is widely believed to be difficult to implement due to a potentially large amount of interference, called self-interference, between transmit and receive chains of the same node. 
     Full-duplex communications is used in many telecommunications technologies, e.g., ordinary wired telephones, Digital Subscriber Line (DSL), wireless with directional antennas, free space optics, and fiber optics. The impact of full-duplex links in these earlier applications is limited to doubling the rate by providing two symmetrical pipes of data flowing in opposite directions. This affects the point-to-point throughput with no direct impact on networking and security issues. In contrast, in multi-user wireless systems, due to the nature of transmission that everyone hears everyone else, full-duplex capability provides new ways to facilitate networking and enhance security. 
     Although full-duplex is currently used for example in wireless systems with highly directional antennas or free space optics, the underlying full-duplex radios are essentially nothing but two independent half-duplex systems separated in space. In fact, the general two-way channel is very difficult to realize in wireless communications due to excessive amounts of self-interference, i.e., the interference each transmitter generates for the receiver(s) in the same node. 
     Other prior art techniques to provide a type communication system that might be referred to as full-duplex are really frequency division duplex (FDD), where separate frequency ranges are used in the transmit and receive (uplink/downlink) directions. As used herein, however, the term full-duplex is intended to refer to simultaneous transmission and reception of signals within the same frequency band. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       The accompanying figures, where like reference numerals refer to identical or functionally similar elements throughout the separate views, together with the detailed description below, are incorporated in and form part of the specification, and serve to further illustrate embodiments of concepts that include the claimed invention, and explain various principles and advantages of those embodiments. 
         FIG. 1  is a block diagram of a wireless communication system in accordance with some embodiments. 
         FIG. 2  is a block diagram of a wireless communication system in accordance with some embodiments. 
         FIG. 3  is a channel diagram of full-duplex transceivers in accordance with some embodiments. 
         FIG. 4  is a block diagram of an interference cancellation signal flow. 
         FIG. 5  is a block diagram of a self-cancellation full-duplex transceiver. 
         FIG. 6  is a block diagram of another embodiment of a self-cancellation full-duplex transceiver. 
         FIG. 7  is a block diagram of another embodiment of a self-cancellation full-duplex transceiver. 
         FIGS. 8-11  are block diagrams of various embodiments of full-duplex transceiver signal processing elements. 
         FIG. 12  is a circuit for directly coupling the self-interference cancellation signal. 
         FIG. 13  is an antenna configuration for with high coupling of the self-interference cancellation signal. 
         FIG. 14  is a MIMO system that computes joint weight values. 
         FIGS. 15-18  show pictorial views of pair-wise symmetrical antennas. 
         FIGS. 19-20  show a pictorial view of triple-wise symmetrical antenna structures. 
         FIGS. 21-23  show examples of MIMO antenna structures in 3-dimensional space. 
         FIG. 24  shows examples for the placement of one antenna set in the plane of symmetry of some other antenna(s) to support MIMO in 2-dimensions. 
         FIGS. 25-27  shows examples of some antenna structures showing that the coupling between antennas can be very strong (−2 dB) due to near field signals unless it is cancelled relying on pair-wise symmetry. 
         FIGS. 28 and 29  show numerical results (2.4 Ghz band using HFSS) for one example of modifying the shape of the antenna. 
         FIGS. 30 and 31  show a schematic view of two pair-wise symmetrical antennas. 
         FIGS. 32 and 33  show a schematic view of two symmetrical antennas. 
         FIGS. 34, 35, 36, 37, and 38  show five configurations wherein antennas have shared arm above ground plane. 
         FIG. 39  shows a schematic view of a MIMO full-duplex node based on a generalization of antenna structure in  FIG. 31 . 
         FIGS. 40, 41  show the generalization for the realization of three-dimensional pair-wise symmetrical antennas in 2.5 dimensions. 
         FIG. 42  shows a method of measuring the self-interference channel response, the self-interference cancellation channel response, and the residual baseband channel response according to one embodiment. 
         FIG. 43  shows a flow diagram of setting the residual baseband response according to one embodiment. 
         FIG. 44  shows a signal processing flow diagram according to one embodiment. 
         FIG. 45  shows a signal processing flow diagram according to an alternative embodiment. 
         FIG. 46  shows a signal plot regarding clipping. 
         FIG. 47  shows a transceiver having nonlinearities. 
         FIGS. 48 and 49  show embodiments of methods to correct for nonlinearities. 
         FIG. 50  is a MIMO embodiment. 
         FIGS. 51, 52, and 53  are embodiments relating to an asynchronous control network. 
         FIG. 54  is a method of operating an asynchronous control network. 
     
    
    
     Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of embodiments of the present invention. 
     The apparatus and method components have been represented where appropriate by conventional symbols in the drawings, showing only those specific details that are pertinent to understanding the embodiments of the present invention so as not to obscure the disclosure with details that will be readily apparent to those of ordinary skill in the art having the benefit of the description herein. 
     DETAILED DESCRIPTION OF THE INVENTION 
     This disclosure relates to the design of a full-duplex radio. In its simplest from, a full-duplex radio has separate antennas for transmission and reception. The transmit and receive antennas may often be placed in the vicinity of each other and consequently a strong self-interference may be observed at the receive antenna. The description herein illustrates systems and methods for practical implementation of full-duplex wireless using a primary transmit signal and auxiliary transmit signal to reduce interference, and a residual self-interference cancellation signal. To this aim, new self-interference cancellation techniques are deployed. 
     In one embodiment, a method of full-duplex communication may comprise: in a full duplex transceiver, generating an interference-reduced signal by combining an analog self-interference cancellation signal to an incoming signal that includes a desired signal and a self-interference signal, wherein the analog self-interference cancellation signal destructively adds to the self-interference signal to create a residual self-interference signal. Then, the method may include further processing the interference-reduced signal to further reduce the residual self-interference signal using a baseband residual self-interference channel estimate. 
     In a further embodiment, the method may comprise: determining an estimate of a self-interference channel response from a primary transmitter of a transceiver to a receiver of the transceiver and determining an estimate of an auxiliary channel response from an auxiliary transmitter of the transceiver to the receiver. Then, the method may include determining a residual self-interference baseband channel response at a baseband processor of the receiver. Full-duplex communication is performed by preprocessing a primary transmit signal and an auxiliary transmit signal with the estimated auxiliary channel response and a negative of the estimated self-interference channel response, respectively, and transmitting the preprocessed primary transmit signal and the preprocessed auxiliary transmit signal in a transmit frequency range, while receiving a desired signal within a receive frequency range substantially overlapping the transmit frequency range, and receiving a residual self-interference signal. Further, the method may reduce the residual self-interference signal using the residual self-interference baseband channel response; and, further processing the desired signal. 
     In a further embodiment, an apparatus may comprise: a weight calculation unit configured to measure a self-interference channel and an auxiliary channel to obtain an estimate of the self-interference channel and an estimate of the auxiliary channel; a full-duplex transceiver having a primary transmitter, an auxiliary transmitter, and a receiver, wherein the primary transmitter and auxiliary transmitter are configured to preprocess a training sequence to generate two transmit signals such that the two transmit signals respectively traverse the self-interference channel and the auxiliary channel and combine to form an analog residual interference signal at the receiver of the full-duplex transceiver; an analog to digital converter and a receiver baseband processor at the receiver being configured to measure a baseband residual self-interference channel response by; and, the transceiver being further configured to cancel self-interference signals using the auxiliary channel and to cancel residual self-interference signals using the measured baseband residual self-interference channel response. In particular, the full-duplex transceiver may communicate in full-duplex by transmitting information in a first frequency band to a second receiver while simultaneously receiving information in the first frequency band from a second transmitter by cancelling self-interference signals using the auxiliary channel and cancelling residual self-interference signals using the measured baseband residual self-interference channel response. 
       FIG. 1  and  FIG. 2  show block diagrams of a communication network in which an access point (AP), which can be, e.g., a base-station in a cellular setup, is communicating with multiple clients with full-duplex links to each client. The access point of  FIG. 1  communicates with multiple clients using OFDMA for sharing the bandwidth among users with full-duplex link over each OFDM tone and with support for multiple transmit and multiple receive antennas. The full duplex communication networks  100 A and  100 B, albeit simplified, show an access point (AP) (e.g.  104  or  108 ) that is communicating with multiple clients ( 106 A,  106  B  106 C and  106 D) with full-duplex links to each client. Access point  108  of  FIG. 2  communicates with multiple clients using OFDMA for sharing the bandwidth among users with full-duplex links over each OFDM tone and with support for multiple transmit and multiple receive antennas  110  (e.g. N×N). Though described as access points, the components  104  and  108  may be configured as base stations (BS) or other communication components such as relays, range extenders, wireless terminals, and wireless nodes involved in ad hoc or wireless mesh networks. 
       FIG. 3  is a block diagram showing the details of one embodiment of each of the communication links in  FIGS. 1 and 2 , including full-duplex flow for data and control where control communications may include one or more of reference for time/frequency/clock synchronization, channel gain/phase, channel matrix in MIMO, beam-forming vectors, beam-forming gains, Automatic Repeat request (ARQ), power control, instruction for adaptive coding and modulation, etc. 
     As explained herein, several techniques in RF and base-band are provided to reduce/cancel the self-interference, as shown in  FIG. 4 . In a first aspect  410 , antenna design is employed to reduce the incidence of self-interference  402  at a full-duplex communication node  400 . Symmetrical (e.g., pair-wise, triple-wise) transmit and receive antennas are relatively positioned to reduce coupling between transmit and receive and thus reduce the incidence of self-interference. Thus, to facilitate full-duplex communications, access points and clients of the communication network are configured to reduce self-interference between a component&#39;s own respective antennas and transmit and receive chains. In the case of two-dimensional structures, it is shown that there exist pairs of symmetrical antennas with substantially zero mutual coupling over the entire frequency range. To simplify implementation and also provide support for MIMO in two dimensions, various embodiments include a second class of antenna pairs with low, but non-zero coupling. This is based on placing one set of antennas in the plane of symmetry of another set. In 3-dimensions, it is shown there exist triple-wise symmetrical antennas with zero coupling between any pair. It is also shown that in 3-dimensions, one can indeed find two sets of antennas (to be used for transmit and receive in a MIMO system) such that any antenna in one set is decoupled (zero coupling over the entire frequency range) from all the antennas in the second set. Furthermore, such three dimensional structures are generalized to the case that antenna arms are placed closely or merged, for example using two-sides or different layers of a PCB, or analogous approaches based on using Integrated Circuit (IC). An example for the implementation of such constructions is based on using patch antennas wherein one antenna arm is generated through reflection of the other antenna arm in the ground plane. Examples of such a construction are presented wherein the same patch is used as the transmit antenna, the receive antenna and the coupler necessary in analog cancellation. Examples are presented to generalize such constructions for MIMO transmission. Hereafter, such constructions are referred to as being in 2.5 dimensions, or simply 2.5 dimensional. 
     Most examples and aspects herein are described based on using separate antennas for transmit and receive. However, most of the techniques described for self-interference cancellation will be still applicable if the same antenna is used for transmit and receive. Known methods for isolating transmit and receive chains may be applied. To describe the systems and methods a basic setup is used herein. For this purpose, aspects relevant to issues like synchronization and equalization are described assuming OFDM, likewise aspects relevant to supporting multiple clients and networking are described assuming OFDMA. However, techniques herein will be applicable if OFDMA is replaced by some other known alternatives, e.g., CDMA, OFDM-CDMA, Direct Sequence (DS)-CDMA, Time-division Multiple Access (TDMA), constellation construction/transmission in time with pulse shaping and equalization, Space Division Multiple Access (SDMA), and their possible combinations. 
     In a second aspect  412 , a corrective self-interference signal  404  is generated and injected into the receive signal at  412 . Weighting coefficients for filtering are calculated for a primary transmit signal and an auxiliary transmit signal comprising the corrective self-interference signal  404 . The corrective self-interference signal may be transmitted by the node to combine in the air with the signal to be received by the node&#39;s receive antenna. Transmission of the corrective self-interference signal can be at power levels comparable with the primary signal using an antenna with comparable functionality as the antenna used to transmit the primary signal. This can be the case if multiple high power transmit antennas are available in the unit. As an alternative, an auxiliary transmit antenna, with high coupling to the receive antenna, may be used to transmit the corrective self-interference signal with low power. The corrective self-interference signal may be coupled (e.g., in RF in the receive chain of the node without the use of an antenna) to the signal received by the receive antenna. In various embodiments, the analog cancellation may take place at an RF coupler  418 , or alternatively it may take place at baseband frequencies using circuit  420 . 
     As shown in  FIG. 4 , another technique for cancelling self-interference is to determine the response of a transmit-to-receive baseband channel, also referred to herein as a residual interference channel, or a residual self-interference baseband channel. The baseband version or frequency domain version of the transmit signal  408  may be provided to the receiver baseband processor  414  for digital correction by processing the transmit signal with the residual self-interference baseband response and then subtracting it from the incoming signal to obtain the received signal  416 . 
     With respect to  FIG. 5 , one embodiment of a full-duplex transceiver is shown. OSDN data  512  is provided to the transmitter baseband processor  510 . This signal will form the basis of the primary transmit signal  526  that is propagated between the transmit antenna and receive antenna with low coupling as described herein. The baseband processor  510  generates OFDM symbols for transmission and passes them to preprocessor unit  508 . Preprocessor unit  508  multiplies the OFDM symbols by the transfer function H 2 , which represents the transmission channel of the auxiliary transmit path  534 . The signal is then converted to a time domain signal and passed through digital to analog converter  506 . Alternatively, transmit baseband processor  510  generates the time domain signal with an IFFT module and preprocessing filter  508  is implemented in the time domain, such as by an FIR filter. The output of preprocessing unit  508  is converted to an RF signal by modulator  504 , and amplified by power amplifier  502 , and finally transmitted to a distant end receiver (not shown). 
     In the auxiliary transmit channel the OFDM data  524  is provided to the auxiliary transmit baseband processor  522 . Similar to the primary transmit chain, the auxiliary preprocessor  520  may alter the OFDM symbols by the transfer function (−H 1 ), which is the negative of the channel response of the interference channel  536 . Alternatively, the output of the auxiliary transmit baseband processor  522  may be time domain signals calculated by an IFFT module, and the preprocessor unit  520  may be an FIR filter to process signals in the time domain. The output of preprocessor  520  is provided to a digital to analog converter  518 , and then to RF modulator  516 , to generate the auxiliary transmit signal  514 , also referred to as the self-interference cancellation signal. The self-interfering signal  526  combines with the self-interference cancellation signal  514  by way of RF addition  528 . 
     In the embodiment of  FIG. 5 , the self interference is cancelled by determining the characteristics, or frequency response, of (i) the self-interference channel H 1  caused by the primary transmit signal as coupled through the primary transmit antenna and the receive antenna, and (ii) the self-interference cancellation channel H 2  caused by the auxiliary transmit path, which conveys the self interference cancellation signal. The channel responses may be determined by channel sounding techniques, including transmitting predetermined tones and measuring the magnitude and phase variations of the tones in the received signal. Note that the channel responses H 1  and H 2  are the responses of the complete channel from the OFDM data at the respective transmitters through their respective chains, through the analog signal propagation/RF channels, the receiver analog front end, all the way to the receiver baseband  538 . The cancellation effect in the embodiment of  FIG. 5  is due to the concatenation of the two channel responses in the primary transmit chain (H 2  from preprocessor  508 , and H 1  from the remainder of the transmission path), and the negative of the concatenation of the two channel responses in the auxiliary transmit chain (−H 1  by preprocessor  520 , and H 2  from the remainder of the auxiliary transmission path). Because of these two concatenations performed by the respective transmission/reception chains, the self-interference signal  526  is substantially reduced by the negative contribution of the self-interference cancellation signal  514 , by way of RF addition  528 . The remaining received signal is then demodulated by RF demodulator  530 , and is sampled by analog-to-digital converter  532 . The sampled signal is then processed by receive baseband processor  538 / 540 . Receive baseband processor  538 / 540  performs an FFT to generate the OFDM symbols  542 . Note that both preprocessors  602 ,  604  may apply the channel responses by operating directly on the OFDM transmit signals by altering the magnitude and phase of the symbols according to the channel response. Alternatively, the preprocessing may be performed in the time domain. 
     In a further embodiment of full-duplex transceiver  600  depicted in  FIG. 6 , it is recognized that the self-interference channel H 1  and the self-interference cancellation channel H 2  as determined by the full-duplex transceiver  600  are only estimates of the actual channel responses and may include errors ΔH 1  and ΔH 2 , respectively, as shown in preprocessing units  602 ,  604 . After the concatenations of the primary transmit signal and the auxiliary transmit signal with their counter channel responses, a residual interference signal remains after the RF addition. This residual signal is separately measured at the receiver baseband processor, as described more fully below, and is referred to herein as the residual self-interference baseband channel response. Note that both preprocessors may apply the channel responses by operating directly on the OFDM transmit signals by altering the magnitude and phase of the symbols according to the channel response. Alternatively, the preprocessing may be performed in the time domain. 
       FIG. 7  depicts an alternative embodiment  700  of pre-processing the auxiliary transmit signal. In this embodiment, only the auxiliary transmit signal is preprocessed by preprocessor  704 . The filter response used by preprocessor  704  is the negative ratio of the channel estimate (H 1 +ΔH 1 ) for the primary self-interference channel H 1  to the channel estimate (H 2 +ΔH 2 ) for the self-interference cancellation channel response H 2 . After the combination of the self-interference signal from the primary transmit chain is combined with the preprocessed auxiliary transmit signal that traverses H 2 , a residual interference signal remains after the RF addition. This residual signal is separately measured at the receiver baseband processor, as described more fully below, and is referred to herein as the residual self-interference baseband channel response. 
       FIGS. 8 to 11  show block diagrams representing transmit and receive chains, in accordance with examples of embodiments of the full-duplex transceivers shown  FIGS. 1 and 2 . These embodiments differ in the method used to construct the axillary corrective signal from the main transmit signal and the method used to couple (add) the corrective signal with the incoming signal. In some embodiments, the cancellation in analog domain due to the corrective signal is performed prior to Low-Noise-Amplifier (LNA). In another embodiment, this is done after the LNA, and before the A/D. In some embodiments, the filtering is performed in time domain. In another embodiment, filtering is performed in the frequency domain. In some embodiments compensation for amplifier nonlinearities is explicitly shown. In other embodiments compensation for amplifier nonlinearities is implicit. 
     The construction of a secondary (corrective) signal uses the data from the primary transmit signal and an instantaneous measurement of the self-interference channel. The corrective signal, or self-interference cancellation signal, is subtracted (in the analog domain) from the incoming signal prior to A/D. This can be achieved by using multiple, in particular two, transmit antennas with proper beam-forming weights such that their signals are subtracted in the air at the receive antenna. The antenna used to transmit the corrective signal can be a fully functional transmit antenna (similar to the other antenna used in the transmission) in the sense that it is connected to a power amplifier and has a low coupling with the corresponding receive antenna. This scenario may be of interest if there are several transmit units available which can be used in different roles depending on the mode of operation. An alternative is to use an antenna that is designed exclusively for the purpose of self-interference cancellation and consequently has a high coupling to the receive antenna and can transmit with a low power. 
     A different approach is based on subtracting such a corrective signal in the receive chain prior to A/D using methods for RF signal coupling. Regardless of which of the above methods for active cancelation are used, the corresponding weights may be referred to as the self-cancellation beam-forming coefficients. To improve mathematical precision by avoiding dividing of numbers, it helps if the weighing is applied to both primary and secondary signals as shown in  FIG. 6  (as opposed to that of  FIG. 7 ), while scaling both to adjust transmit energy. However, an equivalent filtering operation can be applied to only one chain, in particular to the auxiliary corrective signal. Aspects of filtering for construction of the auxiliary corrective signal are mainly explained using frequency domain realization, however, filtering can be also performed in the time domain. In particular, it is preferred that channel impulse responses are measured in the frequency domain, and then converted to a time-domain impulse response or difference equation used to implement the filter in the time domain. Time domain filters may act continually on the signal in the time domain, or account for and compensate for the initial condition due to the filter memory from the previous OFDM symbol. 
       FIGS. 8 to 11  depict various embodiments of analog cancellation through the use of a Secondary (Corrective) Transmit Signal, or a self-interference cancellation signal. That is, after the antenna stage that may be used to reduce the magnitude of the cross-coupling between the primary transmit stage and the receiver chain, self-interference can be further reduced in RF by forming an auxiliary (corrective) signal to cancel the effect of the self interference and subtract it from the incoming signal prior to A/D. This operation is hereafter called “signal injection”, or “corrective beam-forming”. Although the discussion is focused on injecting the corrective signal in RF and in particularly prior to A/D, this operation can be also done at IF, or even at the base-band. 
     Injection of corrective signal can be also achieved by connecting it to a separate transmit antenna such that the subtraction is performed in the air. This alternative can be an attractive option for cases where the unit has several transmit antennas and several modes of operation, for example a high throughput mode in which the transmit antennas send independent data, and a full-duplex mode in which some of the transmit antennas are used to cancel the self-interference. In this case, multiple transmit antennas create a null on the receive antenna(s) relying on beam-forming within the same unit. Note that restriction on antenna spacing will be less than the case of ordinary MIMO as null creation is easier to achieve compared to the independent gain requirement in MIMO. In the case of having several receive antennas, multiple such corrective transmit antennas can be used to create null on all receive antennas. Hereafter, this technique may be referred to as “corrective beam-forming”. 
       FIG. 8  shows one embodiment of a full-duplex transceiver  800 . The transmit data  816  is provided to transmit baseband  814  of primary transmit chain  804 , which formulates OFDM symbols and forwards them to IFFT processing unit  812  for conversion to a time domain signal. The data is then converted to an analog signal by digital to analog converter  810 . The analog signal is then modulated by RF modulator  808 , and amplified by power amplifier  806 . The signal is then transmitted to a distant end receiver (not shown), and the transmission causes a self interfering signal  802  to be received by the receive chain  832 . The transmit data  816  is also provided to auxiliary transmitter  820 , where the baseband processor  830  generates OFDM symbols. The OFDM symbols are converted to a time domain signal by IFFT processor  828 , and then converted to a time domain signal by digital to analog converter  826 . The auxiliary transmit signal is then modulated by RF modulator  824 , and amplified by amplifier  822  for transmission to the receiver chain  832  via path  818 . 
     Note that the preprocessing of the primary transmit signal and the auxiliary transmit signal may be performed by transmit baseband processor  814  and auxiliary transmit baseband processor  830 , respectively. Specifically, the TX base-band component  814  and ATX base-band component  830  receive weights from weights calculation unit  846  to perform the corrective beam forming (when transmitted for combining in the air) or signal injection (i.e. when added in RF on the unit  800 ). The various embodiments of the coupling between the primary transmit chain  804  and the receiver chain  832 , as well as the coupling between auxiliary transmit chain  820  and the receiver chain  832  will be described more fully below with respect to  FIGS. 12, 13, and 15-41 . 
     In the embodiment  800  illustrated, the amplified signal from amplifier  804  is transmitted, via a pair-wise symmetrical transmit antenna whereas the amplified signal from amplifier  820  is output for combining with a received signal from a pair-wise symmetrical receive antenna of receiver  832  via RF coupling unit  834 . A low noise amplifier  836  amplifies the combined received and injected signal. The amplified signal is demodulated (by demodulator  838 ) and analog to digital conversion is performed at A/D Unit  840 . The digital signal is passed to FFT unit  842  and thereafter to RX base-band  844 , which provides received data  848  and information (measurements) to weights calculation unit  846 . 
       FIG. 9  depicts an embodiment where the received signal and the self-interfering signal are first amplified by LNA  906  before being combined with the self-interference cancellation signal from the auxiliary transmitter chain. In a further alternative embodiment, the LNA  904  may be omitted. 
       FIG. 10  depicts an embodiment  1000  where the auxiliary chain  1002  generates a self-interference cancellation signal in the form of an analog baseband signal, which is added in the received chain  1004  by baseband adder  1006 . 
       FIG. 11  depicts an embodiment  1100  wherein the time domain signal from IFFT  1102  is provided to the auxiliary chain for filtering as shown by signal line  1104  for processing by discrete time domain preprocessing digital filter  1106 . Filtering in time can be used to reduce the number of IFFT operations, and also to improve the performance of self-interference cancellation during OFDM cyclic prefix. Filter coefficients can be still computed using frequency domain training. Note that preprocessing filter  1106  can implement the filter of preprocessor  704 . In a further alternative embodiment, an additional time domain filter may be included in primary transmit chain  1108  to implement preprocessor filter  602 , while preprocessing filter  1106  would be configured to implement preprocessing filter  604  in the time domain. 
       FIG. 12  shows a schematic view of one embodiment of how the self-cancelling signal may be injected in the receive chain and coupled to the received signal to cancel the self-interference. The coils  1204  and  1206  around the core  1200  provide the incoming signal and the self-interference cancellation signals, respectively, while the incoming signal with reduce self-interference is provided on output coil  1202 . Thus,  FIG. 12  shows the self-interference cancelling signal being injected to the receive chain through a coupler (instead of being transmitted in the air using an additional transmit antenna) to cancel the self-interference. 
     Configuration  1208  of  FIG. 12  shows that the relative width of the transformer arms and/or number of turns can provide a static relative weighting for the injected self-cancelling signal to increase coupling, in accordance with one example embodiment. In particular, the three signals are shown as being coupled with one side of each of the coils connected to ground. However, in practice, the inputs could be balanced or unbalanced. These are representative pictorial views of sample methods for combining RF signals. The transformer here is just a pictorial view of RF signal coupling and can be realized in various ways known for RF coupling. Generalization to MIMO will be clear to those skilled in the area. Having high coupling for the corrective signal reduces the need for amplification in the corrective chain and consequently helps to maintain linearity in the corrective signal chain. It also helps to avoid deterioration of the received signal to noise ratio, which can be a side effect of signal coupling. 
       FIG. 13  shows a schematic view of another embodiments where the self-cancelling signal is coupled to the received signal with a high coupling to avoid the need for excessive gain in the auxiliary chain and thereby maintaining linearity in the auxiliary chain (corrective signal). In particular,  FIG. 13  shows the use of two transmit (one high power horizontal  1306  and one low power vertical  1302 ) antennas and one receive (vertical  1304 ) antenna where beam-forming at the two transmit antennas  1302 ,  1306  can be used to cancel the self-interference at the receive antenna  1304 . Auxiliary Transmit Antenna has a simple structure, transmits with low power and has a small spacing to RX antenna (high coupling with RX antenna). More generally, the dashed box in  FIG. 13  symbolizes a multi-terminal antenna. Auxiliary Transmit Antenna  1302  can also be one of the antennas used in MIMO mode (as TX or TX/RX with duplexer), which is switched to act as Auxiliary Transmit Antenna, when needed. Multiple Auxiliary Transmit Antennas can be used for MIMO to cancel multiple self-interference terms. 
     In the case of MIMO embodiments, each receive chain has its own corrective, or self-interference cancellation signal. Assuming M transmit antennas, each such corrective signal is computed by forming a linear combination of the M transmit signals based on measuring the corresponding channel gains. The corrective signal is still transmitted from a single highly coupled ATX feed, such as through a power coupler.  FIG. 14  shows a MIMO-based configuration with N radio units. For simplicity, some of the components of transmitters and receivers are omitted and represented by a dash dot line. Weights calculation units  1402  and  1404  jointly compute the weights as indicated by arrow  1406 . Each corrective signal is computed by forming a linear combination of the M transmit signals based on measuring the corresponding channel gains. 
     An antenna configuration is referred to herein as self-symmetrical when its two arms are the image of each other with respect to a plane of symmetry (construction &amp; excitation). Two antennas are referred to herein as pair-wise symmetrical when the following conditions are satisfied: (i) each antenna is self-symmetrical, (ii) the two antennas have different planes of symmetry, and (iii) Each antenna configuration is invariant under reflection in the plane of symmetry of the other one. 
       FIGS. 15-18  show pictorial views of pair-wise symmetrical antennas for components in accordance with examples. The plane of symmetry for the vertical antenna  1502  is the plane passing through the x axis, and the plane of symmetry for the horizontal antenna  1504  passes through the y axis. Note that the dots such as dot  1500  indicate terminals, and that radiating elements  1502  and  1504  are “V” shaped to illustrate the use of physical symmetry, and are not intended to represent actual radiating element geometries.  FIG. 17  shows a 3-dimensional arrangement where the horizontal antenna has its terminals in the XZ plane near the Z axis, with its plane of symmetry being the YZ plane. The vertical antenna has its terminals in the YZ plane, also close to the Z axis but closer to the origin, where the XZ plane is the plane of symmetry.  FIG. 18  shows antenna  1802  is a ring (in the XY plane). 
     The above idea can be generalized to obtain triple-wise symmetrical antennas in 3-dimensional space (e.g. see  FIGS. 19 and 20 ). In this case, each two antennas are pair-wise symmetrical, meaning there is theoretically zero coupling between any pair. For such a configuration, the 3×3 S-matrix is diagonal in theory, or close to diagonal in practice, independent of frequency. 
       FIGS. 21-23  show examples of MIMO antenna structures in 3-dimensional space where every antenna in one subset, is decoupled from all the antennas in the second subset, using pairwise symmetry.  FIG. 21  utilizes the third dimension to stack the parallel and horizontal antennas along the Z axis, while  FIG. 22  staggers each of the horizontal antennas  2202  and the vertical antennas  2200  along the Z axis. Multiple-Input Multiple-Output Antenna systems are based on using multiple antennas at each node and exploit the resulting spatial degrees of freedom to increase the rate and/or increase the diversity order. For a MIMO full-duplex radio, there is a set of TX antennas and a set of RX antennas (See  FIG. 2 ). To satisfy the low coupling requirement, each antenna in TX set may be pair-wise symmetrical with respect to all antennas in RX set and vice versa. To do so, a straightforward approach is to use the symmetry planes of TX and RX antennas to generate more elements in each set, but this configuration results in unwanted distance between antenna arms and thereby affects their radiation efficiency. To improve radiation efficiency in such a configuration, antenna arms can be brought closer by placing antennas on different PCB layers or its equivalent in other forms of realizing antennas in integrated circuit, or multi-layer antennas with layers coupled through air or through other materials with desirable electromagnetic property that can guide or block the wave. 
     On the other hand, MIMO implementation in three dimensions is more flexible (easier to implement). This is due to the observation that a pair-wise symmetrical antenna structure requires two dimensions effectively, and as a result, it is possible to generate more transmit/receive antennas satisfying the required symmetry condition along the third dimension. In such configurations, it is possible to change the order of antennas, and antennas can be of different lengths for multi-band operation. Some example configurations are shown in  FIGS. 21, 23, and 23  of MIMO antenna structures in 3-dimensional space where every antenna in one subset is decoupled from all the antennas in the second subset. Methods structures to realize 3-dimensional antennas with pair-wise symmetry by using 2.5 dimensions may be used, e.g., using opposite sides or different layers of a PCB based on patch antenna structures. Some example configurations are shown in  FIGS. 30-38 . Constructions based on 2.5 dimensions may be used in forming MIMO antenna structures as shown in  FIGS. 32-38 . 
     It remains to find a better solution for implementation of MIMO in two dimensions. Since E-field of a self-symmetrical antenna is orthogonal to its plane of symmetry bisecting its feed terminals, a MIMO full-duplex radio with low (but non-zero) coupling can be realized in two dimensions by placing one set of antennas along the plane of symmetry of the other set. See  FIG. 24  showing a 4×3 arrangement in two dimensions. In this configuration, shape of arms and spacing between antennas can be adjusted to compensate for lack of perfect symmetry, non-zero width of antennas, as well as for MIMO requirements (independence of gains). See  FIGS. 28 and 29  showing numerical results (2.4 Ghz band using HFSS) for modifying the shape of the antenna to compensate for the loss in symmetry. 
     Although the methods of this disclosure are primarily explained in terms of Diploe and Patch antennas, generalization to other forms such as Monopole, Folded Dipole, Loop antennas (implemented using wire, PCB, or Integrated Circuit); Microstrip antennas, Reflector Antennas, e.g. Corner Reflector, Dish Antenna; Travelling Wave Antennas, e.g., Helical Antennas, Yagi-Uda Antennas, Spiral Antennas; Aperture Antennas, e.g., Slot Antenna, Slotted Waveguide Antenna, Horn Antenna; and Near Filed Communication Antennas should be clear to individuals skilled in the art. 
       FIG. 24  shows examples for the placement of one antenna set in the plane of symmetry of some other antenna(s) to support MIMO in 2-dimensional antenna structures in accordance with one example. While the configuration does not contain pairwise symmetry, the four verticals are symmetrical and their associated electric field is orthogonal to plane of symmetry, and the horizontal antennas are in that plane of symmetry, thereby reducing the coupling because the E-field is orthogonal. This configuration of  FIG. 24  may be used for MIMO. 
       FIGS. 25-27  show examples of some antenna structures showing that the coupling between antennas can be very strong (−2 dB) due to near field signals unless it is cancelled relying on pair-wise symmetry where values of RF coupling are obtained using high frequency structural simulator (HFSS) at 2.4 Ghz band. 
       FIGS. 28 and 29  show numerical results (2.4 Ghz band using HFSS) for one example of modifying the shape of the antenna to compensate for the loss in symmetry. This demonstrates that the shape of the radiating elements may be adjusted so as to reduce the coupling. 
       FIGS. 30 and 31  show a schematic view of two pair-wise symmetrical antennas composed of a dipole and a patch antenna which has an arm above ground plane; and wherein diploe can be realized on the middle layer of a PCB sandwiched between the top and bottom surfaces forming the patch and the ground plane. That is,  FIG. 30  shows a 3 dimensional, or 3D structure (also referred to as 2.5D), the radiating elements  3002  are located on either side of a printed circuit board, while elements  3004  are formed in the center of the PCB. This arrangement maintains pairwise symmetry. 
       FIGS. 32 and 33  show a schematic view of two symmetrical antennas which have shared arm above ground plane (patch antenna), one antenna has symmetrical feed with 180 degree phase shift, with the other antenna placed in its plane of symmetry, and wherein the shared arm is possibly shaped by removing its corners to reduce the coupling. 
       FIGS. 34, 35, 36, 37, and 38  show five configurations wherein antennas have a shared arm above ground plane (e.g., patch antenna) and tasks of transmit, receive and signal injection (corrective beam-forming) are combined into a single arm. 
       FIG. 39  shows a schematic view of a MIMO full-duplex node based on a generalization of antenna structure in  FIG. 31  to MIMO and by placing one set of antennas in the plane of symmetry of another set. 
       FIG. 40, 41  show the generalization for the realization of three-dimensional pair-wise symmetrical antennas in 2.5 dimension (using patch structure above ground plane) to MIMO, wherein a single antenna is used for transmit and receive. 
     Antenna design examples herein are provided for the case where physically different antennas are used to transmit and to receive. However, it will be understood that most of the discussions and results are still applicable when the same antenna is used for both transmit and receive (with transmit/receive chains properly isolated). 
     A full-duplex wireless radio can be considered as a two-port network and therefore it can be described it terms of scattering parameters, i.e., S 11 , S 12 =S 21  and S 22 . In some embodiments, an objective may be to provide a small coupling between transmit and receive antenna, i.e., S 12 =S 21  should be a small quantity, including reflections from the surrounding environment, sources of imperfections in hardware realization or additional coupling through parasitic elements. It may also be desired to have small S 11  and S 22 , to provide good antenna efficiency. Moreover, the above two conditions may be satisfied over the entire frequency range of operation. To achieve the desired low coupling, which is heavily affected by reflections from surrounding environment, sources of imperfections in hardware realization or additional coupling through parasitic elements, it is desirable in certain embodiments to have a much lower coupling between antennas themselves. Methods described herein provide such low couplings. 
     It should be pointed out that the low coupling requirement in full-duplex radio is different from that of MIMO systems. A common assumption for the study of MIMO systems is that the channels between different transmit and receive antennas are independent and identically distributed (i.i.d.). This is achieved by spacing the antennas sufficiently far apart. In practice, due to constraints on the physical dimensions of communication devices, the distances between the multiple antennas are usually small. This renders the channel between different antennas correlated. The correlation between the antennas reduces both the capacity and the diversity gains of the MIMO system. As a result, in MIMO systems, antenna gains to a distant antenna should be independent of each other and that is generally difficult to satisfy when antennas are too close. For low coupling in full-duplex radio, however, transmit and receive antennas should induce a small signal on each other (say a coupling of much less than −40 dB). Using the techniques herein, such antennas can be placed close to each other, while having a small coupling (i.e., small value of S 12 =S 21 ) over frequency band of interest. 
     Since transmit and receive units in a full-duplex radio can be very close to each other, the effect of near-field is remarkable. Even though E and H fields&#39; relationship can be very complex in near field, it can be predicted and therefore managed using the Maxwell equations. According to Maxwell&#39;s equations, geometrical symmetry in structure (shape, material, boundary conditions) and excitation (antenna feed terminals) leads to geometrical symmetry in wave. The geometrical symmetry in wave can then be used to cancel self-interference. 
     Remaining degradations in receive signal can be further reduced by forming an appropriate digital or analog corrective signal and applying it in the base-band (or IF). This may be an attractive option to account for the degradations that are caused by non-linear operations such as rounding, lack of precision in FFT/IFFT etc. 
     In addition to above techniques for self-interference cancellation prior to A/D, various embodiments include methods of base-band signal processing to further reduce the self-interference. Note that, unlike A/D, the Digital-to-Analog (D/A) conversion is a linear operation. As a result, the equivalent Transmit-to-Receive Base-band Channel (TRBC) for the remaining self-interference (residual self-interference) is linear and, by measuring this equivalent channel, the remaining amount of self-interference can be subtracted from the receive signal at the base-band. This is achieved by measuring TRBC using pilot tones, which are weighted with self-cancellation beam-forming coefficients to achieve the initial RF signal cancellation. The properly preprocessed tones (using the estimated auxiliary channel response H 2  and the estimated self-interference channel response H 1 ) are used simultaneously (in a manner similar to the primary and auxiliary signals) such that the corresponding self-interference terms are subtracted in RF prior to A/D. After training is complete, knowing the TRBC, also referred to herein as the residual self-interference baseband channel response, as well as the transmit signal, the receiver chain may subtract the residual self-interference in the base-band through an operation similar to equalization (referred to as “self equalization”). A precise measurement for the TRBC is beneficial, and this may be achieved in some embodiments by sending multiple pilots in time and averaging the measured TRBC. Furthermore, adaptive methods may be used to adjust the number of pilots, and also avoid degradation in performance of self-interference cancellation due to imprecise measurement of TRBC. Finally, in case there are additional error components, e.g., due to numerical inaccuracies and rounding, described herein are further methods to reduce such error components in the digital domain. Aspects relevant to self equalization are described assuming OFDM. However, techniques herein will be applicable if OFDM is replaced by some other known alternatives, e.g., CDMA, OFDM-CDMA, DS-CDMA, TDMA, constellation construction/transmission in time with pulse shaping and equalization. 
     Interference reduction in base-band may be achieved by measuring the residual self-interference baseband channel response. Because the self-interference is known, the remaining interference due to digital data truncation at the transmitter can be subtracted digitally. Cancelling self-interference is a simpler task as compared to traditional equalization. The reason is that in cancelling self-interference, the reference of time, frequency, phase, and clock are all local and accurate. 
     Although the injection of the corrective signal can be performed in several ways, in the examples of  FIGS. 42 and 43 , the concepts are expressed in the language of using multiple transmit antennas with corrective beam-forming. The procedure is as follows. Pilots (disjoint in time) are transmitted from each TX antenna to measure their corresponding channel, resulting in 
     
       
      
       H 
       1 
       +ΔH 
       1  
      
     
       and 
     
       
      
       H 
       2 
       +ΔH 
       2  
      
     
     for the first and second coupling channels, respectively. Then, low power self-cancelling (i.e., with proper weighting) pilots are sent simultaneously from the two antennas resulting in: 
         H   1 ( H   2   +ΔH   z )( P+ΔP )− H   2 ( H   1   +ΔH   1 )( P+ΔP )
 
     We have, 
         H   1 (Δ H   2 )(Δ P )− H   2 (Δ H   1 )(Δ P )˜0
 
     The residual self-interference channel is then equal to: 
         H   1 (Δ H   2 )− H   2 (Δ H   1 ))
 
     Under these circumstances, it is assumed that the OFDM data frame, including a possible computational error term, is equal to: 
       (Γ+ΔΓ)
 
     As a result, received signal is: 
         H   1 ( H   2   +ΔH   2 )(Γ+ΔΓ)− H   2 ( H   1   +ΔH   1 )(Γ+ΔΓ)=
 
     In this case, the term: 
         H   1 (Δ H   2 )(Γ)− H   2 (Δ H   1 )(Γ)
 
     is cancelled by base-band self-interference cancellation using the baseband residual self-interference cancellation signal. In some embodiments, the remaining term: 
         H   1 (Δ H   2 )(ΔΓ)− H   2 (Δ H   1 )(ΔΓ)
 
     can be compensated digitally, as all its components are known, and subsequently compensated by the baseband processor. In particular, the ideal signal may contain too many bits of resolution due to the calculations performed by the IFFT, for example. Thus, the digital signals generated at the primary and auxiliary transmitters may be truncated prior to digital to analog conversion. In an alternative embodiment, the analog self-interference cancellation may be performed by pre-processing only the auxiliary transmit signal, rather than both the primary and auxiliary transmit signals. In this embodiment, the auxiliary transmit signal is pre-processed using the combined estimates of H 1  and H 2 : 
     
       
         
           
             - 
             
               
                 
                   H 
                   1 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     H 
                     1 
                   
                 
               
               
                 
                   H 
                   2 
                 
                 + 
                 
                   Δ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     H 
                     2 
                   
                 
               
             
           
         
       
     
     When the pre-processed auxiliary signal passes through the auxiliary channel H 2 , the received interference channel Tx(H 1 ) will be reduced by destructive interference from the auxiliary transmit signal that is received at the receiver after passing through channel H 2 , or, 
     
       
         
           
             
               Tx 
               ⁡ 
               
                 ( 
                 
                   
                     - 
                     
                       
                         
                           H 
                           1 
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             H 
                             1 
                           
                         
                       
                       
                         
                           H 
                           2 
                         
                         + 
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             H 
                             2 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     H 
                     2 
                   
                 
                 ) 
               
             
             , 
           
         
       
     
     which will be close enough to Tx(H 1 ) to significantly reduce the self-interference in the analog domain. The remaining residual error resulting from imperfect channel estimates H 1  and H 2 , can then be determined as described above, by measuring the effective net-residual error at baseband. The residual error may be generally referred to as ΔH NET . 
     Embodiments of methods of training the full-duplex transceiver will now be described. The corrective signal may be implemented in the OFDM base-band and may be obtained by weighting each tone of the primary transmit signal by a proper value to cause the cancellation. In this case, there exist three channels from the base-band of the transmit chain to the base-band of the receive chain within the same full-duplex node. These are: i) the self-interference channel from the primary transmit signal to receive at base-band, denoted as PTX. ii) the self-interference correction channel from the auxiliary (corrective) signal to receive base-band, denoted as ATX. iii) the baseband residual self-interference channel from the combined transmit signal to receive base-band. These measurements are performed in three steps as explained next and shown in the flow chart of  FIG. 42 . 
     With respect to  FIG. 42 , one method  4200  of training the full-duplex transceiver is described. At  4202  the self-interference channel response is estimated by transmitting a training sequence from the primary transmit antenna (PTX) and then measuring the baseband channel response in the receiver baseband. The effect on each tone of the OFDM signal may be measured to obtain H 1 , which may be designated C PR (f), for all frequencies (∀f). Then, the self-interference cancellation channel is measured at  4204  in a similar manner; by transmitting a training sequence from the auxiliary transmit antenna (ATX) and measuring the baseband channel response at the receiver. The effect on each tone of the OFDM signal may be measured to obtain H 2 , which may be designated C AR (f), ∀f. In these first two measurements, it is sufficient to transmit separate pilots to measure the first and the second channels explained above (in each OFDM tone) and then compute the weights such that the two signals cancel each other at the receive base-band. The weights may be combined to form a single set of weights applied to the auxiliary transmit signal. To avoid division, and thereby improve computational accuracy, in some embodiments the transmit signal and the corrective signals may have their own weights. For example, if the two channels are H 1  and H 2 , it is sufficient to use GH 2  and −GH 1  as weights where G is selected to adjust the transmit energy. In particular, in some embodiments to the energy normalization factor may be computed as: 
         G ( f )=1/√{square root over ( C   PR   2 ( f )+ C   AR   2 ( f ))},
 
     and the normalized weights may be applied to the PTX and ATX signals. 
     After this stage of training, a base level of cancellation will be achieved. It is generally not possible to have perfectly accurate measurements for these weights. The reason is that we are dealing with large quantities, while interested in measuring error terms that are relatively small. As a result, various imperfections, including additive noise, affect the accuracy. The operations described herein exploit the property that as D/A is linear, measurements for analog cancellation do not need to be accurate. Any error in these measurements will act as an additional parasitic linear system. As a result, the equivalent channel for the residual self-interference remains linear and can be used in conjunction with OFDM. This means, as long as we fix the filters computed for active cancellation (with whatever error they may contain) and then accurately measure the equivalent channel for the residual self interference including the effects of the added filters, we can successfully apply the final stage of digital cancellation in base-band. 
     The transmit-to-receive channel for the remaining self-interference (residual self-interference) will be the third channel to be measured at  4206 . This channel is separately measured in the third step by using weighted pilots as the primary and secondary signals by using the weights computed in the first two stages of channel measurements explained above. Specifically, new pilot tones are transmitted from the primary and auxiliary channels using the weights (i.e., the channel estimates, or normalized channel estimates H 1 , H 2 ) previously calculated, and the impact of the residual interference is measured at the baseband of the receiver. 
     Knowing this channel, the remaining self-interference can be subtracted at receive base-band during full-duplex operation. A number of embodiments have been explained in terms of using two filters, and performing the filtering in the frequency domain. It will be clear to individuals skilled in the area, that a single filter applied to the auxiliary corrective signal can replace the two filters. It will be also clear to individuals skilled in the area, that filtering can be also performed in the time domain 
     To improve accuracy of measuring the residual self-interference channel, methods described herein such as method  4300  may be used to send several training sequences and repeating the measurement several times to determine averaged results. Method  4300  includes measuring the baseband residual interference channel at  4302 . At  4304  the mean and variance of the measurements of each tone may be calculated. In one embodiment, if the variance of the repeated measurements is below a desired threshold ( 4306 ), then the residual channel coefficients may be set accordingly, and normal full-duplex data transmission may be commenced. Alternatively, a maximum number of residual baseband channel measurements may be reached ( 4306 ) and the training may be terminated. In either case, additional testing may be utilized to set the baseband channel response at  4308 . In one embodiment, the measurements of each tone may be used to generate a metric for comparison to a threshold. In one such embodiment, the baseband processor of the receiver may determine whether the mean (for a given tone) divided by its respective variance is below a threshold. In the event that it is below a threshold then the baseband response may be set to zero, indicating that the contribution of the residual interference is negligible at that frequency. Thus, the first stage of self-interference reduction using analog cancellation may result in cancelling most of the interference, and consequently, the residual self-interference (and weights for its equivalent base-band channel) may become too small. On the other hand, if the ratio is above the threshold, the baseband residual response may be set equal to the calculated mean for that tone, and used as a weighting factor in the subtraction of residual self-interference until the next round of training. 
     A further method  4400  of some embodiments will be described with reference to  FIG. 44 . The method comprises: in a full duplex transceiver, generating an interference-reduced signal at  4402  by combining an analog self-interference cancellation signal to an incoming signal that includes a desired signal and a self-interference signal, wherein the analog self-interference cancellation signal destructively adds to the self-interference signal to create a residual self-interference signal; processing the interference-reduced signal  4404  to further reduce the residual self-interference signal using a baseband residual self-interference channel estimate. 
     The method  4400  may utilize an analog self-interference signal in the radio frequency range. Furthermore, in alternative embodiments, the analog self-interference signal is an intermediate frequency or baseband signal. In still further embodiments, the analog self-interference signal is combined in an inphase signal path and a quadrature signal path. In some embodiments, the self-interference signal incorporates a self-interference channel response and an estimate of an auxiliary channel response, and the self-interference cancellation signal incorporates an auxiliary channel response and an estimate of the self-interference channel response. 
     The method  4400  may also include determining the baseband residual self-interference channel estimate from transmitting test tones that incorporate an estimate of an auxiliary channel response and an estimate of an interference channel response and measuring a corresponding residual error signal. In some embodiments, the test tones also incorporate a power normalization factor. 
     As described herein, the method  4400  may use a coupler to combine the self-interference cancellation signal with the incoming signal, or it may be transmitted from an auxiliary antenna of the full-duplex transceiver. The auxiliary antenna of the full-duplex transceiver is configured to have a high-coupling to a receive antenna of the full-duplex transceiver. 
     The self-interference signal is received over a self-interference channel that includes a propagation path from a primary transmit antenna of the transceiver to a receive antenna of the transceiver, wherein the primary transmit antenna is pair-wise symmetrical to the receive antenna. 
     An alternative method  4500  is described with respect to  FIG. 45 , comprising: determining  4502  an estimate of a self-interference channel response from a primary transmitter of a transceiver to a receiver of the transceiver and determining an estimate of an auxiliary channel response from an auxiliary transmitter of the transceiver to the receiver; determining  4504  a residual self-interference baseband channel response at a baseband processor of the receiver; preprocessing  4506  a primary transmit signal and preprocessing  4508  an auxiliary transmit signal with the estimated auxiliary channel response and a negative of the estimated self-interference channel response, respectively; transmitting  4510  the preprocessed primary transmit signal and the preprocessed auxiliary transmit signal in a transmit frequency range; receiving  4512  a desired signal within a receive frequency range substantially overlapping the transmit frequency range, and receiving a residual self-interference signal; reducing  4514  the residual self-interference signal using the residual self-interference baseband channel response; and, further processing  4516  the desired signal. 
     The method  4500  may include determining an estimate of a self-interference channel response by transmitting a plurality of tones from the primary transmitter and receiving them at the receiver and measuring the effect of the self-interference channel on the tones. In some embodiments, the tones are an orthogonal frequency division multiplexed (OFDM) signal. The method  4500  may include determining an estimate of an auxiliary channel response by transmitting a plurality of tones from the auxiliary transmitter of the transceiver and receiving them at the receiver and measuring the effect of the auxiliary channel on the tones. 
     Further corrections in the 1st stage (e.g., clipping) may also be undertaken. One or more further stages of correction may be applied to the corrected signal in base-band. In a 2nd stage, asynchronous cancellation may be performed in a time domain. In a 3rd stage, synchronous cancellation and equalization may be performed in an OFDM domain. In a 4th stage, compensation for intentional signal clipping in the 1st stage, A/D residual signal correction, and compensation for numerical inaccuracies in operations such as filtering etc. can be performed in a digital time domain. In a further aspect, in the 2nd stage (time domain), the node may listen for signals to detect a request-to-join signal transmitted by a new client who wishes to join the network without prior timing or frequency co-ordination. 
       FIG. 46  shows a schematic view of clipping an incoming signal prior to A/D to reduce its dynamic range, wherein an approximation for the part that is removed is subsequently compensated at the base-band. If needed, the received analog signal can be clipped prior to A/D (not shown) to reduce its dynamic range using clipping thresholds  4602  and provide a clipped signal  4604 . The clipped part can then be digitally compensated (accounting for only the TX signal) in base-band. 
       FIG. 47  shows a transceiver  4700  with non-linear amplifiers  4702 ,  4704 .  FIG. 48  is a flowchart illustrating a method  4800  for training a wireless full-duplex communication device to determine nonlinearities to perform compensation for nonlinearities in accordance with an embodiment. At  4802  the transmitter generates a training sequence for transmission through the primary transmitter chain. The transceiver then measures  4804  the nonlinearity in each tone in terms of its harmonics (magnitude and phase) that leak into other tones. In an alternative embodiment, the training sequence is a periodic triangular signal, and the nonlinear characteristics are captured in terms of a set of parameters such as slope of gain vs. amplitude, or parameters of a Volterra series, or a Volterra series enhanced by vector quantization of error. At  4806  and  4608 , the similar procedure is executed for the auxiliary transmit chain. 
     In practice, components such as Power Amplifier (PA) and LNA exhibit non-linear characteristics. In another aspect of this invention, such nonlinearities are measured through occasional training and their inverse is applied in the construction of the corrective signal such as the resulting signal cancel the effective self-interference in the analog domain. Subsequently, the effect of remaining nonlinearities and other inaccuracies such as those due to mathematical errors in FFT/IFFT calculation and filtering is accounted for in digital domain in the process of digital self-interference removal. The nonlinearities of PA and LNA can be modeled using memory-less polynomials acting in the time domain sample by sample, or their versions with memory known as Volterra series. Models based on polynomials or Volterra series can be used for coarse modeling followed by Vector Quantization (VQ) for modeling the remaining error. This can be also achieved by fitting a model, e.g., models based on Sigmoid Function, or more generally Generalized Logistic Function, and finding the parameters of the model through training and applying its inverse to form the proper corrective signal. As an alternative, the parameters of the inverse function can be directly computed through training. 
     Method  4900  of  FIG. 49  may be used to correct for nonlinearities in the primary transmitter. The OFDM data  4902  may be converted to the time domain by IFFT processor  4904 . The nonlinearity function (as measured) is then applied to the time-domain signal at  4906 . Note that H 1  may be measured as described above by sending low power pilots that do not cause much nonlinear distortion in the power amplifier. The signal may then be preprocessed according to channel response H 1  ( 4908 ) and H 2  ( 4910 ) in the time domain, although frequency domain processing may be performed. To increase accuracy in the cancellation, the filtering may also account for the initial conditions due to the previous OFDM symbols. That is, filtering can be applied continually in time to capture the memory effects. The filtered signal may then be preprocessed  4910  according to the auxiliary channel response (or, more particularly, its negative inverse). Filtering may again be in the time or frequency domain. As this phase of filtering is IIR (infinite impulse response), it may account for the initial condition due to the previous OFDM symbols and first subtracts the effect of this condition prior to filtering or alternative IIR filtering can be applied continually in time to capture the memory effects. Note also that the ATX chain is may be designed with high coupling to avoid the need for amplification in the ATX chain, and consequently the ATX chain is fairly linear. 
     Further corrections may be made to account for numerical errors. Wireless transmission is usually based on using small constellations with a small number of points, for example 16QAM or 64QAM. For this reason, not many bits are needed to represent the constellation values. To limit potential numerical errors, a small number of bits may be required to represent the constellation values, say 3 bits per I/Q in the case of 64QAM. The main operation increasing the number of bits at the transmitter is the operation of iFFT (to convert the OFDM signal to time domain). If calculations lack proper accuracy, then an additional error term is introduced which, as mention above, is known in the digital domain and can be compensated at the final stage. 
     The systems and methods also support the use of Multiple Input Multiple Output (MIMO) antennas, and can handle multiple clients that are separated using OFDMA. This means support for full-duplex connection over each OFDM tone while achieving additional gains, in terms of multiplexing and/or diversity gains, offered by MIMO antennas. In addition, new clients may join the OFDMA network without prior synchronization with other clients. 
       FIG. 50  shows a schematic view of a MISO/SIMO system, where (1) main transmitting node has several independent radios, (2) main receiver node has one radio, (3) each radio has two antennas with low coupling capable of working in TX mode, or in RX mode, and switching between TX and RX modes, (4) antennas in each of the two nodes are grouped into two sets which alternate as transmit and receive antenna sets, (5) the two sets in the transmitting and receiving nodes switch between transmit/teaching and receive/learning modes in subsequent blocks, (6) main transmitter performs beam-forming to reduce transmit energy for the purposes such as energy saving, interference reduction, enhancing security, signaling below noise level, etc. 
     Although this invention is explained in terms of using OFDM for channel equalization similar concepts are applicable to other means of signal equalization such as time domain equalization, pre-coding plus time domain equalization and time domain signaling with frequency domain equalization. Although this invention is explained in terms of using OFDMA for multi-user multiplexing, similar concepts are applicable to other means of multi-user multiplexing, such as CDMA, TDMA and SDMA. 
     Asynchronous Control Network 
     In many applications, it is desirable that new clients, through sending request-to-join signal, can join an existing OFDMA network without prior co-ordination. To handle such situations, this invention includes an additional stage of self-interference cancellation in time domain to enable the Base-Station (BS) or Access Point (AP), or any other node, to continually monitor its incoming signal in search for such a request-to-join signal.  FIGS. 51, 5, and 53  show the block diagrams for three examples of implementing such an additional detection stage. Once such a signal is detected, the node allocates resources to the new client and synchronizes it with the rest (i.e., synchronization within the cyclic prefix of the underling OFDM scheme). Aspects relevant to asynchronous users are described assuming OFDMA. However, techniques herein will be applicable if OFDMA is replaced by some other known alternatives, e.g., CDMA, OFDM-CDMA, DS-CDMA, TDMA, constellation construction/transmission in time with pulse shaping and equalization, Space Division Multiple Access (SDMA), and their possible combinations. 
     This description provides systems and methods wherein control signals are transmitted as part of the return channel. In particular, one of the nodes inserts pilots in its transmit signal to help in synchronizing distant nodes. Note that without such a reference signal, the degradation in effective Signal-to-Noise Ratio (SNR) due to poor synchronization is usually quite significant, even in point-to-point connections. In the past, such issues have limited the use of high order constellations in wireless systems. Methods of this invention pave the road towards implementing large size constellations as used for example in DSL. This invention also includes methods to use part of the return channel to facilitate operations such as Automatic-Repeat-Request (ARQ), power control and adaptive transmission. 
     To handle asynchronous clients, receiving node (e.g., AP) will be always listening to detect a valid request-to-join signal, while supporting full-duplex connections to its current clients. This is made possible by a stage of self-interference cancellation (digital self-equalization) that is implemented in time domain.  FIGS. 51-53  show examples for the implementation of different cancellation stages. This time domain cancellation stage informs the AP of the new incoming client. AP will then perform the necessary procedures such that the new client can join the network synchronized with other clients. 
     In most practical systems, several repetitions of a sequence (i.e., several periods of a periodic sequence) are used as the request-to-join signal. Once such a signal passes through the linear system corresponding to the channel, it results in an almost periodic sequence of the same period. This can be detected at the receiver end by using a simple correlation calculation by sliding two consecutive windows of the length of that period, shifting them through the incoming signal sample by sample, and computing the inner product of the vectors within the two windows. This produces a peak when the periodicity starts, and this peak will continue until the periodicity lasts. The phase at the peak value provides the frequency offset. It should be ensured that the self-interference does not cause complete loss of this correlation peak. The added stage of self-interference cancellation in time domain serves this purpose. 
       FIGS. 51-53  show three schematic views of a middle interference removal stage in time domain to enable a unit to detect a request-to-join signal transmitted by a new client who wishes to join the network without prior timing co-ordination.  FIGS. 51 and 52  show schematic views of a middle interference removal stage in time domain to enable the unit to detect a request-to-join signal transmitted by a new client who wants to join the network without prior timing or frequency co-ordination; 
     Note that correlation calculation on its own provides a significant boost in signal to noise. To make sure this periodicity remains detectable in the presence of self-interference, this invention has included this additional stage of self-interference cancellation in the time domain. The corresponding filter in time domain can be obtained by converting the OFDM filter to time and this filter does not need to completely cancel the self-interference, all that is needed is some reduction in the amount of self-interference such that the periodic signal coming from the new client is detectable. As this added stage is linear, it will not contradict with the property needed to have an OFDM structure such that the channel can be measured in order to cancel the residual self-interference by subtraction in base-band (self equalization). For this reason, in  FIG. 51  the output of this stage is connected to the next stage of cancellation. As mentioned earlier, this concatenation can be avoided and in this case the task of the time domain self-interference cancellation block is merely to inform the unit of the presence of the new client ( FIG. 53 ). An advantage of this setup is that the coefficients of the time-domain cancellation filter could be calculated using the OFDM channel measurements performed for the purpose of self equalization.  FIG. 52  shows a different realization combining some of the features of the methods in  FIGS. 51 and 53 . 
     In the following, the details are explained using  FIG. 51 , but similar statements are applicable to  FIGS. 52 and 53 . As illustrated, Unit A is communicating with client Unit B in full-duplex and client Unit C desires to join and communicate with Unit A. Unit A comprises a transmit unit  1302  and receive unit  1304 , for example comprising pair-wise symmetrical antennas as described. The respective transmit and receive chains are configured to provide 1st stage cancellation  1306  in the RF, for example via auxiliary transmission (ATX) as described. A 2nd stage cancellation  1308 , in the base-band, provides asynchronous cancellation and listening in the time domain. In  FIG. 52  the 2nd stage provides a wake-up signal. A 3rd stage cancellation  1310  in the base-band performs synchronous cancellation and equalization in the OFDM domain while a fourth stage cancellation  1312  in the base-band compensates for intentional clipping ( FIG. 12 ) and any A/D residual signal in the time domain as described. 
       FIG. 54  is a flowchart showing a method with operations for a wireless communication device for establishing and/or handling communications over a Low Throughput Overlaid (LTO) channel asynchronously and in parallel (i.e. with overlap in time and frequency) with communications over a Higher Throughput Main (HTM) data channel in accordance with one embodiment.  FIG. 4  is a flowchart showing a method with operations  5400  for a wireless communication device for establishing and/or handling communications over an LTO channel asynchronously and in parallel with communications over an HTM data channel in accordance with one embodiment. It will be understood that operations  5402 - 5404  relate to HTM data channel communications and operations  5406 - 5422  relate to LTO channel communications. Respective operations may be performed by respective subunits of the wireless communication device.  FIG. 54  applies to either access point, or client. In particular any unit which may get involved in ad-hoc or mesh networking should have equal capabilities in this respect. However, in a simple network setup, clients may use the LTO channel in the uplink to announce their presence, and then listen for response from the AP in the HTM channel. 
     At  5402 , a determination is made whether the communications are over the HTO. If no operations return to the start of operations  5400 . If yes, operations perform self-interference cancellation in frequency domain, OFDMA networking and transmit/receive operations, possibly detecting/cancelling signal from LTO receive channel prior to decoding data. 
     At  5406 , a determination is made whether data is received over LTO channel. If yes, at  5408 , operations perform self-interference cancellation in the time domain and receive data via the LTO channel until all data is received. If data is not received, there may be data to send over the LTO channel (determination at  5410 ). If yes, at  5412 , operations perform self-interference cancellation in the time domain and search for the periodic sequence indicating if the LTO channel is occupied. At  5414  operations determine whether the LTO channel is idle (i.e. available for the communication device). If no, operations return to  5412  to try again. If yes, at  5416  data is transmitted over the LTO channel superimposed on the periodic signal indicating LTO channel occupancy. At  5418 , a determination is made whether more data is to be sent over the LTO channel. If yes, operations return to  5416 . If not, at  5420  the device performs self-interference cancellation in the time domain and searches for the periodic sequence indicating if another node (device) wants to initiate communications over the LTO channel. If at  5422  there is no incoming communication over the LTO channel, operations may continue at  5410 . If yes, operations continue at  5408  as previously described. 
     A further embodiment includes a method of operating a wireless communication network for establishing communication between a Central Node, e.g., Access Point (AP), Base-station (BS), and respective multiple clients with two-way wireless links, i.e., complete or partial overlap in time as well as in frequency, the wireless communication node comprising a Multiple-Input Multiple-Output (MIMO) antenna system The method may comprise: receiving a request-to-join signal from a new client without prior coordination, and with overlap in time and frequency with the existing clients, and wherein, a central node is continually listening to detect a valid incoming request-to-join signal, or other forms of control signaling, of any client while communicating with the multiple clients of the existing network using full-duplex connectivity for both data and control flow. 
     The central node utilizes a first stage of base-band self-interference cancellation is followed by an algorithmic base-band block, which works synchronously with the transmit signal of a central node A to detect the request-to-join signal and subsequently trigger a sequence of operations required for the node B to join the network associated with node A, or perform other network management operation such as bandwidth allocation and scheduling. 
     The method may include the multiple clients being connected to the central node sharing a common spectrum using Orthogonal Frequency Division Multiple Access (OFDMA). The method may also use neighboring nodes, that by listening to each other while transmitting, collaborate in the subsequent transmission symbol(s), or collaborate in subsequent transmission block(s). 
     The method may include part of a return link used as a control channel to, at least one of: send pilots for synchronization; coordinate retransmission of erroneous frames in ARQ without severely interrupting a forward link; coordinate adaptive coding and modulation and power control based on the quality of the forward link, e.g., using channel gain or features of observed multi-user interference across frequency; feedback the channel state (phase, magnitude, polarization) in an asymmetric link wherein transmitter node posses many antennas and rely on beam-forming in terms of channel state (phase, magnitude, polarization) to achieve high reliability with low transmit energy (e.g., below noise level); and, feedback features of its received signal to improve the capacity of the forward link in an interference channel. 
     The method may include the central node using part of a forward link to broadcast a common pilot to be used by other nodes for synchronization and thereby enabling joint decoding in a multiple access channel or in an interference channel. 
     The method may be used in a MIMO-SDMA network environment wherein part of a return link from each receiver node is used to periodically feedback its corresponding channel state, and wherein part of a forward link from a main transmitter node is used to periodically broadcast a common pilot for synchronization. 
     The method may also be used in a network environment wherein nodes periodically listen while transmitting to measure features of their observed multi-user interference terms, for example energy of interference in different frequency segments, and accordingly adjust their transmit/receive strategies. 
     Methods may also include, in a cognitive transmission network, wherein primary users are distinguished by a signature signal, e.g., a periodic preamble, to be sent at the beginning of their transmission, and wherein primary users start transmission without attention to the channel occupancy by the secondary users, secondary users will be continually listening and searching for the signature of the primary users, and, wherein secondary users adjust their transmission parameters once the signature of the primary users is detected, e.g., stop their transmission and continue with the remaining part at a later time when the network becomes once again available to secondary users. 
     Methods may also include users that are distinguished by a signature signal according to their class of service, e.g., CDMA codes which are superimposed on their main signal, and wherein users check for the channel occupancy, detect the class of the users using the channel, and adjust their transmission strategy accordingly. 
     In further embodiments, methods for overlaying a network of Low Throughout Control (LTC) links on top of the High Throughout Main (HTM) data links with overlap in time and frequency may be included, and wherein, to enable cancellation on the HTM channel, transmission on the LTO channel uses signaling schemes with low power and thereby low spectral efficiency. 
     The LTO transmitter may send several periods of a periodic signal in time domain, which are detected by a correlation calculation using sliding windows, and wherein the presence of such a signal indicates incoming control data, and wherein the amplitude and/or phase and/or duration of a basic periodic signal are varied (with respect a starting periodic signal used as a preamble) to embed the control data, and wherein data on LTO includes Forward Error Correction (FEC) with a short block length. 
     To avoid collisions, an overlaid signature signal is used to indicate occupancy of the LTO channel, and wherein nodes which are interested to participate in the overlay control network will sense the LTO channel and transmit if the channel is idle, e.g., by searching for the basic periodic signal as a sign of LTO channel being idle or occupied, and wherein LTO links use a back-off strategy, e.g., similar to the CSMA protocol used in 802.11, among themselves, and wherein, HTM links operate with relatively higher power, and wherein, nodes involved in signaling over HTM links first search for the LTO signal, detect its timing and synchronize with it, perform signal detection on it, and then (partially or fully) cancel the LTO signal to reduce its harmful interference effect on their respective HTM link. 
     The methods may use a full duplex link to form a closed loop between a transmitter and its respective receiver, wherein the control signals (affecting the channel impulse response) are adjusted relying on closed loop feedback, e.g., using methods known in the context of adaptive signal processing. 
     Still further, the methods may be used even when at least one of the clients does not have full-duplex capability. In further embodiments, apparatuses are provided such as a wireless communication node configured to perform a method according to those set forth herein. 
     In the foregoing specification, specific embodiments have been described. However, one of ordinary skill in the art appreciates that various modifications and changes can be made without departing from the scope of the invention as set forth in the claims below. Accordingly, the specification and figures are to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of present teachings. 
     The benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential features or elements of any or all the claims. The invention is defined solely by the appended claims including any amendments made during the pendency of this application and all equivalents of those claims as issued. 
     Moreover in this document, relational terms such as first and second, top and bottom, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms “comprises,” “comprising,” “has”, “having,” “includes”, “including,” “contains”, “containing” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises, has, includes, contains a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by “comprises . . . a”, “has . . . a”, “includes . . . a”, “contains . . . a” does not, without more constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises, has, includes, contains the element. The terms “a” and “an” are defined as one or more unless explicitly stated otherwise herein. The terms “substantially”, “essentially”, “approximately”, “about” or any other version thereof, are defined as being close to as understood by one of ordinary skill in the art, and in one non-limiting embodiment the term is defined to be within 10%, in another embodiment within 5%, in another embodiment within 1% and in another embodiment within 0.5%. The term “coupled” as used herein is defined as connected, although not necessarily directly and not necessarily mechanically. A device or structure that is “configured” in a certain way is configured in at least that way, but may also be configured in ways that are not listed. 
     It will be appreciated that some embodiments may be comprised of one or more generic or specialized processors (or “processing devices”) such as microprocessors, digital signal processors, customized processors and field programmable gate arrays (FPGAs) and unique stored program instructions (including both software and firmware) that control the one or more processors to implement, in conjunction with certain non-processor circuits, some, most, or all of the functions of the method and/or apparatus described herein. Alternatively, some or all functions could be implemented by a state machine that has no stored program instructions, or in one or more application specific integrated circuits (ASICs), in which each function or some combinations of certain of the functions are implemented as custom logic. Of course, a combination of the two approaches could be used. 
     Moreover, an embodiment can be implemented as a computer-readable storage medium having computer readable code stored thereon for programming a computer (e.g., comprising a processor) to perform a method as described and claimed herein. Examples of such computer-readable storage mediums include, but are not limited to, a hard disk, a CD-ROM, an optical storage device, a magnetic storage device, a ROM (Read Only Memory), a PROM (Programmable Read Only Memory), an EPROM (Erasable Programmable Read Only Memory), an EEPROM (Electrically Erasable Programmable Read Only Memory) and a Flash memory. Further, it is expected that one of ordinary skill, notwithstanding possibly significant effort and many design choices motivated by, for example, available time, current technology, and economic considerations, when guided by the concepts and principles disclosed herein will be readily capable of generating such software instructions and programs and ICs with minimal experimentation. 
     The Abstract of the Disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, it can be seen that various features are grouped together in various embodiments for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed embodiment. Thus the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separately claimed subject matter.