Patent Publication Number: US-2023136372-A1

Title: System and method for time-delay based hybrid beamforming

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS AND CLAIM OF PRIORITY 
     The present application claims priority to U.S. Provisional Patent Application Ser. No. 63/273,786 filed on Oct. 29, 2021 and U.S. Provisional Patent Application Ser. No. 63/337,496 filed on May 2, 2022. The contents of the above-identified patent documents are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates generally to wireless communication systems and, more specifically, the present disclosure relates to a system and method for time-delay based hybrid beamforming. 
     BACKGROUND 
     Due to the rising demand for traffic, wireless systems are moving towards higher frequency of operation, such as millimeter-wave (mm-wave) and terahertz (THz) frequencies, where abundant spectrum is available. However, the higher frequencies also suffer from a high channel propagation loss, and therefore require a large antenna array to create sufficient beamforming gain to ensure sufficient link budget for operation. Thus, these high frequency systems are usually built with a large antenna array at the transmitter and/or the receiver containing many individual antenna elements. At the operating bandwidths of these mm-wave and THz systems, the cost and power consumption of mixed-signal components such as analog-to-digital converters (ADCs) and/or digital-to-analog converters (DACs) also grows tremendously. Thus, fully digital transceiver implementations, where each antenna element is fed by a dedicated radio-frequency (RF) chain, are impractical. 
     SUMMARY 
     The present disclosure relates to wireless communication systems and, more specifically, the present disclosure relates to a system and method for time-delay based hybrid beamforming. 
     In one embodiment, a method includes determining one or more delay values and one or more phase shift values for generation of multiple desired frequency-dependent analog beams. The method also includes configuring one or more true-time delay (TTD) elements and one or more phase shifters of a transceiver based on the one or more delay values and the one or more phase shift values, the transceiver having one or more radio-frequency (RF) chains connected to multiple antennas via the one or more TTD elements and the one or more phase shifters. The method also includes operating the transceiver to generate the multiple desired frequency-dependent analog beams. 
     In another embodiment, a device includes a transceiver that includes multiple antennas, one or more TTD elements, one or more phase shifters, and one or more RF chains connected to the multiple antennas via the one or more TTD elements and the one or more phase shifters. The device also includes a processor operably connected to the transceiver. The processor is configured to: determine one or more delay values and one or more phase shift values for generation of multiple desired frequency-dependent analog beams; configure the one or more TTD elements and the one or more phase shifters based on the one or more delay values and the one or more phase shift values; and control the transceiver to generate the multiple desired frequency-dependent analog beams. 
     In yet another embodiment, a non-transitory computer readable medium includes program code that, when executed by a processor of a device, causes the device to: determine one or more delay values and one or more phase shift values for generation of multiple desired frequency-dependent analog beams; configure one or more TTD elements and one or more phase shifters of a transceiver based on the one or more delay values and the one or more phase shift values, the transceiver having one or more RF chains connected to multiple antennas via the one or more TTD elements and the one or more phase shifters; and operate the transceiver to generate the multiple desired frequency-dependent analog beams. 
     Other technical features may be readily apparent to one skilled in the art from the following figures, descriptions, and claims. 
     Before undertaking the DETAILED DESCRIPTION below, it may be advantageous to set forth definitions of certain words and phrases used throughout this patent document. The term “couple” and its derivatives refer to any direct or indirect communication between two or more elements, whether or not those elements are in physical contact with one another. The terms “transmit,” “receive,” and “communicate,” as well as derivatives thereof, encompass both direct and indirect communication. The terms “include” and “comprise,” as well as derivatives thereof, mean inclusion without limitation. The term “or” is inclusive, meaning and/or. The phrase “associated with,” as well as derivatives thereof, means to include, be included within, interconnect with, contain, be contained within, connect to or with, couple to or with, be communicable with, cooperate with, interleave, juxtapose, be proximate to, be bound to or with, have, have a property of, have a relationship to or with, or the like. The term “controller” means any device, system, or part thereof that controls at least one operation. Such a controller may be implemented in hardware or a combination of hardware and software and/or firmware. The functionality associated with any particular controller may be centralized or distributed, whether locally or remotely. The phrase “at least one of,” when used with a list of items, means that different combinations of one or more of the listed items may be used, and only one item in the list may be needed. For example, “at least one of: A, B, and C” includes any of the following combinations: A, B, C, A and B, A and C, B and C, and A and B and C. 
     Moreover, various functions described below can be implemented or supported by one or more computer programs, each of which is formed from computer readable program code and embodied in a computer readable medium. The terms “application” and “program” refer to one or more computer programs, software components, sets of instructions, procedures, functions, objects, classes, instances, related data, or a portion thereof adapted for implementation in a suitable computer readable program code. The phrase “computer readable program code” includes any type of computer code, including source code, object code, and executable code. The phrase “computer readable medium” includes any type of medium capable of being accessed by a computer, such as read only memory (ROM), random access memory (RAM), a hard disk drive, a compact disc (CD), a digital video disc (DVD), or any other type of memory. A “non-transitory” computer readable medium excludes wired, wireless, optical, or other communication links that transport transitory electrical or other signals. A non-transitory computer readable medium includes media where data can be permanently stored and media where data can be stored and later overwritten, such as a rewritable optical disc or an erasable memory device. 
     Definitions for other certain words and phrases are provided throughout this patent document. Those of ordinary skill in the art should understand that in many if not most instances, such definitions apply to prior as well as future uses of such defined words and phrases. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure and its advantages, reference is now made to the following description taken in conjunction with the accompanying drawings, in which like reference numerals represent like parts: 
         FIG.  1    illustrates an example wireless network according to embodiments of the present disclosure; 
         FIG.  2    illustrates an example gNB according to embodiments of the present disclosure; 
         FIG.  3    illustrates an example UE according to embodiments of the present disclosure; 
         FIG.  4 A  illustrates a high-level diagram of an orthogonal frequency division multiple access transmit path according to embodiments of the present disclosure; 
         FIG.  4 B  illustrates a high-level diagram of an orthogonal frequency division multiple access receive path according to embodiments of the present disclosure; 
         FIG.  5    illustrates an example beamforming architecture according to embodiments of the present disclosure; 
         FIG.  6    illustrates a system that performs phase-shifter based hybrid beamforming with a single RF chain; 
         FIGS.  7  through  10    illustrate several desirable frequency-dependent beam behaviors according to embodiments of the present disclosure; 
         FIG.  11    illustrates an example transceiver for performing TTD-based hybrid beamforming according to embodiments of the present disclosure; 
         FIG.  12    illustrates an example transceiver for performing TTD-based hybrid beamforming for Beam Behavior 1 according to embodiments of the present disclosure; 
         FIG.  13    illustrates an example algorithm to achieve Beam Behavior 1 according to embodiments of the present disclosure; 
         FIG.  14    illustrates charts showing the beamforming gains that can be achieved in Beam Behavior 1; 
         FIG.  15    illustrates another example transceiver for performing TTD-based hybrid beamforming for Behavior 1 according to embodiments of the present disclosure; 
         FIG.  16    illustrates another example algorithm to achieve Beam Behavior 1 according to embodiments of the present disclosure; 
         FIG.  17    illustrates charts showing the beamforming gains that can be achieved in Beam Behavior 1; 
         FIG.  18    illustrates yet another example transceiver for performing TTD-based hybrid beamforming for Behavior 1 according to embodiments of the present disclosure; 
         FIG.  19    illustrates another example algorithm to achieve Beam Behavior 1 according to embodiments of the present disclosure; 
         FIG.  20    illustrates charts showing the beamforming gains that can be achieved in Beam Behavior 1; 
         FIG.  21    illustrates an example transceiver for performing TTD-based hybrid beamforming for Beam Behavior 2 according to embodiments of the present disclosure; 
         FIG.  22    illustrates an example algorithm to achieve Beam Behavior 2 according to embodiments of the present disclosure; 
         FIG.  23    illustrates charts showing the beamforming gains that can be achieved in Beam Behavior 2; 
         FIG.  24    illustrates another example algorithm to achieve Beam Behavior 2 according to embodiments of the present disclosure; 
         FIG.  25    illustrates charts showing the beamforming gains that can be achieved in Beam Behavior 2; 
         FIG.  26    illustrates another example transceiver for performing TTD-based hybrid beamforming for Behavior 2 according to embodiments of the present disclosure; 
         FIG.  27    illustrates another example algorithm to achieve Beam Behavior 2 according to embodiments of the present disclosure; 
         FIG.  28    illustrates charts showing the beamforming gains that can be achieved in Beam Behavior 2; 
         FIG.  29    illustrates an example transceiver for performing TTD-based hybrid beamforming for Beam Behavior 3 according to embodiments of the present disclosure; 
         FIG.  30    illustrates an example algorithm to achieve Beam Behavior 3 according to embodiments of the present disclosure; 
         FIG.  31    illustrates charts showing the beamforming gains that can be achieved in Beam Behavior 3; 
         FIG.  32    illustrates another example transceiver for performing TTD-based hybrid beamforming for Behavior 3 according to embodiments of the present disclosure; 
         FIG.  33    illustrates another example algorithm to achieve Beam Behavior 3 according to embodiments of the present disclosure; 
         FIG.  34    illustrates charts showing the beamforming gains that can be achieved in Beam Behavior 3; 
         FIG.  35    illustrates another example algorithm to achieve Beam Behavior 3 according to embodiments of the present disclosure; 
         FIG.  36    illustrates charts showing the beamforming gains that can be achieved in Beam Behavior 3; 
         FIG.  37    illustrates a flow diagram of an example process for configuring hardware to achieve the desired beam behaviors according to embodiments of the present disclosure; 
         FIG.  38    illustrates a flow diagram of an example process for configuring hardware to achieve desired beam behaviors using offline computation according to embodiments of the present disclosure; 
         FIG.  39    illustrates an example iterative optimization algorithm according to embodiments of the present disclosure; and 
         FIG.  40    illustrates an example process for determining delay values and phase shift values according to embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
       FIGS.  1  through  40   , discussed below, and the various embodiments used to describe the principles of the present disclosure in this patent document are by way of illustration only and should not be construed in any way to limit the scope of the disclosure. Those skilled in the art will understand that the principles of the present disclosure may be implemented in any suitably arranged system or device. 
     Aspects, features, and advantages of the disclosure are readily apparent from the following detailed description, simply by illustrating a number of particular embodiments and implementations, including the best mode contemplated for carrying out the disclosure. The disclosure is also capable of other and different embodiments, and its several details can be modified in various obvious respects, all without departing from the spirit and scope of the disclosure. Accordingly, the drawings and description are to be regarded as illustrative in nature, and not as restrictive. The disclosure is illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings. 
     The present disclosure covers several components which can be used in conjunction or in combination with one another, or can operate as standalone schemes. Certain embodiments of the disclosure may be derived by utilizing a combination of several of the embodiments listed below. Also, it should be noted that further embodiments may be derived by utilizing a particular subset of operational steps as disclosed in each of these embodiments. This disclosure should be understood to cover all such embodiments. 
     To meet the demand for wireless data traffic having increased since deployment of 4G communication systems and to enable various vertical applications, efforts have been made to develop and deploy an improved 5G/NR or pre-5G/NR communication system. Therefore, the 5G/NR or pre-5G/NR communication system is also called a “beyond 4G network” or a “post LTE system.” The 5G/NR communication system is considered to be implemented in higher frequency (mmWave) bands, e.g., 28 GHz or 60 GHz bands, so as to accomplish higher data rates or in lower frequency bands, such as 6 GHz, to enable robust coverage and mobility support. To decrease propagation loss of the radio waves and increase the transmission distance, the beamforming, massive multiple-input multiple-output (MIMO), full dimensional MIMO (FD-MIMO), array antenna, analog beam forming, large scale antenna techniques are discussed in 5G/NR communication systems. 
     In addition, in 5G/NR communication systems, development for system network improvement is under way based on advanced small cells, cloud radio access networks (RANs), ultra-dense networks, device-to-device (D2D) communication, wireless backhaul, moving network, cooperative communication, coordinated multi-points (CoMP), reception-end interference cancelation and the like. 
     The discussion of 5G systems and frequency bands associated therewith is for reference as certain embodiments of the present disclosure may be implemented in 5G systems. However, the present disclosure is not limited to 5G systems or the frequency bands associated therewith, and embodiments of the present disclosure may be utilized in connection with any frequency band. For example, aspects of the present disclosure may also be applied to deployment of 5G communication systems, 6G or even later releases which may use terahertz (THz) bands. 
       FIGS.  1 - 4 B  below describe various embodiments implemented in wireless communications systems and with the use of orthogonal frequency division multiplexing (OFDM) or orthogonal frequency division multiple access (OFDMA) communication techniques. The descriptions of  FIGS.  1 - 4 B  are not meant to imply physical or architectural limitations to the manner in which different embodiments may be implemented. Different embodiments of the present disclosure may be implemented in any suitably-arranged communications system. 
       FIG.  1    illustrates an example wireless network according to embodiments of the present disclosure. The embodiment of the wireless network shown in  FIG.  1    is for illustration only. Other embodiments of the wireless network  100  could be used without departing from the scope of this disclosure. 
     As shown in  FIG.  1   , the wireless network includes a gNB  101  (e.g., base station, BS), a gNB  102 , and a gNB  103 . The gNB  101  communicates with the gNB  102  and the gNB  103 . The gNB  101  also communicates with at least one network  130 , such as the Internet, a proprietary Internet Protocol (IP) network, or other data network. 
     The gNB  102  provides wireless broadband access to the network  130  for a first plurality of UEs within a coverage (or broadcast) area  120  of the gNB  102 . The first plurality of UEs includes a UE  111 , which may be located in a small business; a UE  112 , which may be located in an enterprise (E); a UE  113 , which may be located in a WiFi hotspot (HS); a UE  114 , which may be located in a first residence (R); a UE  115 , which may be located in a second residence (R); and a UE  116 , which may be a mobile device (M), such as a cell phone, a wireless laptop, a wireless PDA, or the like. The gNB  103  provides wireless broadband access to the network  130  for a second plurality of UEs within a coverage area  125  of the gNB  103 . The second plurality of UEs includes the UE  115  and the UE  116 . In some embodiments, one or more of the gNBs  101 - 103  may communicate with each other and with the UEs  111 - 116  using 5G/NR, LTE, LTE-A, WiMAX, WiFi, or other wireless communication techniques. 
     Depending on the network type, the term “base station” or “BS” can refer to any component (or collection of components) configured to provide wireless access to a network, such as transmit point (TP), transmit-receive point (TRP), an enhanced base station (eNodeB or eNB), a 5G/NR base station (gNB), a macrocell, a femtocell, a WiFi access point (AP), or other wirelessly enabled devices. Base stations may provide wireless access in accordance with one or more wireless communication protocols, e.g., 5G/NR 3GPP new radio interface/access (NR), LTE, LTE advanced (LTE-A), high speed packet access (HSPA), Wi-Fi 802.11a/b/g/n/ac, etc. For the sake of convenience, the terms “BS” and “TRP” are used interchangeably in this patent document to refer to network infrastructure components that provide wireless access to remote terminals. Also, depending on the network type, the term “user equipment” or “UE” can refer to any component such as “mobile station,” “subscriber station,” “remote terminal,” “wireless terminal,” “receive point,” or “user device.” For the sake of convenience, the terms “user equipment” and “UE” are used in this patent document to refer to remote wireless equipment that wirelessly accesses a BS, whether the UE is a mobile device (such as a mobile telephone or smartphone) or is normally considered a stationary device (such as a desktop computer or vending machine). 
     Dotted lines show the approximate extents of the coverage areas  120  and  125 , which are shown as approximately circular for the purposes of illustration and explanation only. It should be clearly understood that the coverage areas associated with gNBs, such as the coverage areas  120  and  125 , may have other shapes, including irregular shapes, depending upon the configuration of the gNBs and variations in the radio environment associated with natural and man-made obstructions. 
     As described in more detail below, one or more of the UEs  111 - 116  include circuitry, programming, or a combination thereof for time-delay based hybrid beamforming. In certain embodiments, and one or more of the gNBs  101 - 103  includes circuitry, programming, or a combination thereof for time-delay based hybrid beamforming. 
     Although  FIG.  1    illustrates one example of a wireless network, various changes may be made to  FIG.  1   . For example, the wireless network could include any number of gNBs and any number of UEs in any suitable arrangement. Also, the gNB  101  could communicate directly with any number of UEs and provide those UEs with wireless broadband access to the network  130 . Similarly, each gNB  102 - 103  could communicate directly with the network  130  and provide UEs with direct wireless broadband access to the network  130 . Further, the gNBs  101 ,  102 , and/or  103  could provide access to other or additional external networks, such as external telephone networks or other types of data networks. 
       FIG.  2    illustrates an example gNB  102  according to embodiments of the present disclosure. The embodiment of the gNB  102  illustrated in  FIG.  2    is for illustration only, and the gNBs  101  and  103  of  FIG.  1    could have the same or similar configuration. However, gNBs come in a wide variety of configurations, and  FIG.  2    does not limit the scope of this disclosure to any particular implementation of a gNB. 
     As shown in  FIG.  2   , the gNB  102  includes multiple antennas  205   a - 205   n , multiple RF transceivers  210   a - 210   n , transmit (TX) processing circuitry  215 , and receive (RX) processing circuitry  220 . The gNB  102  also includes a controller/processor  225 , a memory  230 , and a backhaul or network interface  235 . 
     The RF transceivers  210   a - 210   n  receive, from the antennas  205   a - 205   n , incoming RF signals, such as signals transmitted by UEs in the network  100 . The RF transceivers  210   a - 210   n  down-convert the incoming RF signals to generate IF or baseband signals. The IF or baseband signals are sent to the RX processing circuitry  220 , which generates processed baseband signals by filtering, decoding, and/or digitizing the baseband or IF signals. The RX processing circuitry  220  transmits the processed baseband signals to the controller/processor  225  for further processing. 
     The TX processing circuitry  215  receives analog or digital data (such as voice data, web data, e-mail, or interactive video game data) from the controller/processor  225 . The TX processing circuitry  215  encodes, multiplexes, and/or digitizes the outgoing baseband data to generate processed baseband or IF signals. The RF transceivers  210   a - 210   n  receive the outgoing processed baseband or IF signals from the TX processing circuitry  215  and up-converts the baseband or IF signals to RF signals that are transmitted via the antennas  205   a - 205   n.    
     The controller/processor  225  can include one or more processors or other processing devices that control the overall operation of the gNB  102 . For example, the controller/processor  225  could control the reception of forward channel signals and the transmission of reverse channel signals by the RF transceivers  210   a - 210   n , the RX processing circuitry  220 , and the TX processing circuitry  215  in accordance with well-known principles. The controller/processor  225  could support additional functions as well, such as more advanced wireless communication functions. For instance, the controller/processor  225  could support methods for time-delay based hybrid beamforming. Any of a wide variety of other functions could be supported in the gNB  102  by the controller/processor  225 . 
     The controller/processor  225  is also capable of executing programs and other processes resident in the memory  230 , such as an OS. The controller/processor  225  can move data into or out of the memory  230  as required by an executing process. 
     The controller/processor  225  is also coupled to the backhaul or network interface  235 . The backhaul or network interface  235  allows the gNB  102  to communicate with other devices or systems over a backhaul connection or over a network. The interface  235  could support communications over any suitable wired or wireless connection(s). For example, when the gNB  102  is implemented as part of a cellular communication system (such as one supporting 5G/NR, LTE, or LTE-A), the interface  235  could allow the gNB  102  to communicate with other gNBs over a wired or wireless backhaul connection. When the gNB  102  is implemented as an access point, the interface  235  could allow the gNB  102  to communicate over a wired or wireless local area network or over a wired or wireless connection to a larger network (such as the Internet). The interface  235  includes any suitable structure supporting communications over a wired or wireless connection, such as an Ethernet or RF transceiver. 
     The memory  230  is coupled to the controller/processor  225 . Part of the memory  230  could include a RAM, and another part of the memory  230  could include a Flash memory or other ROM. 
     Although  FIG.  2    illustrates one example of gNB  102 , various changes may be made to  FIG.  2   . For example, the gNB  102  could include any number of each component shown in  FIG.  2   . As a particular example, an access point could include a number of interfaces  235 , and the controller/processor  225  could support routing functions to route data between different network addresses. As another particular example, while shown as including a single instance of TX processing circuitry  215  and a single instance of RX processing circuitry  220 , the gNB  102  could include multiple instances of each (such as one per RF transceiver). Also, various components in  FIG.  2    could be combined, further subdivided, or omitted and additional components could be added according to particular needs. 
       FIG.  3    illustrates an example UE  116  according to embodiments of the present disclosure. The embodiment of the UE  116  illustrated in  FIG.  3    is for illustration only, and the UEs  111 - 115  of  FIG.  1    could have the same or similar configuration. However, UEs come in a wide variety of configurations, and  FIG.  3    does not limit the scope of this disclosure to any particular implementation of a UE. 
     As shown in  FIG.  3   , the UE  116  includes an antenna  305 , a radio frequency (RF) transceiver  310 , TX processing circuitry  315 , a microphone  320 , and RX processing circuitry  325 . The UE  116  also includes a speaker  330 , a processor  340 , an input/output (I/O) interface (IF)  345 , a touchscreen  350 , a display  355 , and a memory  360 . The memory  360  includes an operating system (OS)  361  and one or more applications  362 . 
     The RF transceiver  310  receives, from the antenna  305 , an incoming RF signal transmitted by a gNB of the network  100 . The RF transceiver  310  down-converts the incoming RF signal to generate an intermediate frequency (IF) or baseband signal. The IF or baseband signal is sent to the RX processing circuitry  325 , which generates a processed baseband signal by filtering, decoding, and/or digitizing the baseband or IF signal. The RX processing circuitry  325  transmits the processed baseband signal to the speaker  330  (such as for voice data) or to the processor  340  for further processing (such as for web browsing data). 
     The TX processing circuitry  315  receives analog or digital voice data from the microphone  320  or other outgoing baseband data (such as web data, e-mail, or interactive video game data) from the processor  340 . The TX processing circuitry  315  encodes, multiplexes, and/or digitizes the outgoing baseband data to generate a processed baseband or IF signal. The RF transceiver  310  receives the outgoing processed baseband or IF signal from the TX processing circuitry  315  and up-converts the baseband or IF signal to an RF signal that is transmitted via the antenna  305 . 
     The processor  340  can include one or more processors or other processing devices and execute the OS  361  stored in the memory  360  in order to control the overall operation of the UE  116 . For example, the processor  340  could control the reception of forward channel signals and the transmission of reverse channel signals by the RF transceiver  310 , the RX processing circuitry  325 , and the TX processing circuitry  315  in accordance with well-known principles. In some embodiments, the processor  340  includes at least one microprocessor or microcontroller. 
     The processor  340  is also capable of executing other processes and programs resident in the memory  360 , such as processes for time-delay based hybrid beamforming. The processor  340  can move data into or out of the memory  360  as required by an executing process. In some embodiments, the processor  340  is configured to execute the applications  362  based on the OS  361  or in response to signals received from gNBs or an operator. The processor  340  is also coupled to the I/O interface  345 , which provides the UE  116  with the ability to connect to other devices, such as laptop computers and handheld computers. The I/O interface  345  is the communication path between these accessories and the processor  340 . 
     The processor  340  is also coupled to the touchscreen  350  and the display  355 . The operator of the UE  116  can use the touchscreen  350  to enter data into the UE  116 . The display  355  may be a liquid crystal display, light emitting diode display, or other display capable of rendering text and/or at least limited graphics, such as from web sites. 
     The memory  360  is coupled to the processor  340 . Part of the memory  360  could include a random access memory (RAM), and another part of the memory  360  could include a Flash memory or other read-only memory (ROM). 
     Although  FIG.  3    illustrates one example of UE  116 , various changes may be made to  FIG.  3   . For example, various components in  FIG.  3    could be combined, further subdivided, or omitted and additional components could be added according to particular needs. As a particular example, the processor  340  could be divided into multiple processors, such as one or more central processing units (CPUs) and one or more graphics processing units (GPUs). Also, while  FIG.  3    illustrates the UE  116  configured as a mobile telephone or smartphone, UEs could be configured to operate as other types of mobile or stationary devices. 
       FIG.  4 A  illustrates a high-level diagram of an orthogonal frequency division multiple access (OFDMA) transmit path  400  according to embodiments of the present disclosure.  FIG.  4 B  illustrates a high-level diagram of an OFDMA receive path  450  according to embodiments of the present disclosure. In  FIGS.  4 A and  4 B , for downlink communication, the transmit path  400  may be implemented in a base station (gNB)  102  or a relay station, and the receive path  450  may be implemented in a user equipment (e.g., user equipment  116  of FIG.  1 ). In other examples, for uplink communication, the receive path  450  may be implemented in a base station (e.g., gNB  102  of  FIG.  1   ) or a relay station, and the transmit path  400  may be implemented in a user equipment (e.g., user equipment  116  of  FIG.  1   ). 
     The transmit path  400  comprises channel coding and modulation block  405 , serial-to-parallel (S-to-P) block  410 , Size N Inverse Fast Fourier Transform (IFFT) block  415 , parallel-to-serial (P-to-S) block  420 , add cyclic prefix block  425 , and up-converter (UC)  430 . The receive path  450  comprises down-converter (DC)  455 , remove cyclic prefix block  460 , serial-to-parallel (S-to-P) block  465 , Size N Fast Fourier Transform (FFT) block  470 , parallel-to-serial (P-to-S) block  475 , and channel decoding and demodulation block  480 . 
     At least some of the components in  FIGS.  4 A and  4 B  may be implemented in software, while other components may be implemented by configurable hardware or a mixture of software and configurable hardware. In particular, it is noted that the FFT blocks and the IFFT blocks described in this disclosure document may be implemented as configurable software algorithms, where the value of Size N may be modified according to the implementation. 
     Furthermore, although this disclosure is directed to an embodiment that implements the Fast Fourier Transform and the Inverse Fast Fourier Transform, this is by way of illustration only and may not be construed to limit the scope of the disclosure. It may be appreciated that in an alternate embodiment of the present disclosure, the Fast Fourier Transform functions and the Inverse Fast Fourier Transform functions may easily be replaced by discrete Fourier transform (DFT) functions and inverse discrete Fourier transform (IDFT) functions, respectively. It may be appreciated that for DFT and IDFT functions, the value of the N variable may be any integer number (i.e., 1, 4, 3, 4, etc.), while for FFT and IFFT functions, the value of the N variable may be any integer number that is a power of two (i.e., 1, 2, 4, 8, 16, etc.). 
     In the transmit path  400 , the channel coding and modulation block  405  receives a set of information bits, applies coding (e.g., LDPC coding) and modulates (e.g., quadrature phase shift keying (QPSK) or quadrature amplitude modulation (QAM)) the input bits to produce a sequence of frequency-domain modulation symbols. The serial-to-parallel block  410  converts (i.e., de-multiplexes) the serial modulated symbols to parallel data to produce N parallel symbol streams where N is the IFFT/FFT size used in the gNB  102  and the UE  116 . The Size N IFFT block  415  then performs an IFFT operation on the N parallel symbol streams to produce time-domain output signals. The parallel-to-serial block  420  converts (i.e., multiplexes) the parallel time-domain output symbols from the Size N IFFT block  415  to produce a serial time-domain signal. The add cyclic prefix block  425  then inserts a cyclic prefix to the time-domain signal. Finally, the up-converter  430  modulates (i.e., up-converts) the output of the add cyclic prefix block  425  to RF frequency for transmission via a wireless channel. The signal may also be filtered at baseband before conversion to RF frequency. 
     The transmitted RF signal arrives at the UE  116  after passing through the wireless channel, and reverse operations to those at the gNB  102  are performed. The down-converter  455  down-converts the received signal to baseband frequency, and the remove cyclic prefix block  460  removes the cyclic prefix to produce the serial time-domain baseband signal. The serial-to-parallel block  465  converts the time-domain baseband signal to parallel time-domain signals. The Size N FFT block  470  then performs an FFT algorithm to produce N parallel frequency-domain signals. The parallel-to-serial block  475  converts the parallel frequency-domain signals to a sequence of modulated data symbols. The channel decoding and demodulation block  480  demodulates and then decodes the modulated symbols to recover the original input data stream. 
     Each of gNB s  101 - 103  may implement a transmit path that is analogous to transmitting in the downlink to the UEs  111 - 116  and may implement a receive path that is analogous to receiving in the uplink from the UEs  111 - 116 . Similarly, each one of the UEs  111 - 116  may implement a transmit path corresponding to the architecture for transmitting in the uplink to the gNBs  101 - 103  and may implement a receive path corresponding to the architecture for receiving in the downlink from the gNBs  101 - 103 . 
       FIG.  5    illustrates an example beamforming architecture  500  according to embodiments of the present disclosure. The embodiment of the beamforming architecture  500  illustrated in  FIG.  5    is for illustration only.  FIG.  5    does not limit the scope of this disclosure to any particular implementation of the beamforming architecture  500 . In certain embodiments, one or more of gNB  102  or UE  116  can include the beamforming architecture  500 . For example, one or more of antenna  205  and its associated systems or antenna  305  and its associated systems can be configured the same as or similar to the beamforming architecture  500 . 
     Rel.14 LTE and Rel.15 NR support up to 32 CSI-RS antenna ports which enable an eNB to be equipped with a large number of antenna elements (such as 64 or 128). In this case, a plurality of antenna elements is mapped onto one CSI-RS port. For mmWave bands, although the number of antenna elements can be larger for a given form factor, the number of CSI-RS ports—which can correspond to the number of digitally precoded ports—tends to be limited due to hardware constraints (such as the feasibility to install a large number of analog-to-digital converts/digital-to-analog converts (ADCs/DACs at mmWave frequencies)). 
     In the example shown in  FIG.  5   , the beamforming architecture  500  includes analog phase shifters  505 , an analog beamformer (BF)  510 , a hybrid BF  515 , a digital BF  520 , and one or more antenna arrays  525 . In this case, one CSI-RS port is mapped onto a large number of antenna elements in antenna arrays  525 , which can be controlled by the bank of analog phase shifters  505 . One CSI-RS port can then correspond to one sub-array which produces a narrow analog beam through analog beamforming by analogy BF  510 . The analog beam can be configured to sweep  530  across a wider range of angles by varying the phase shifter bank  505  across symbols or subframes. The number of sub-arrays (equal to the number of RF chains) is the same as the number of CSI-RS ports NCSI-PORT. A digital BF  515  performs a linear combination across NCSI-PORT analog beams to further increase precoding gain. While analog beams are wideband (hence not frequency-selective), digital precoding can be varied across frequency sub-bands or resource blocks. 
     Since the above system utilizes multiple analog beams for transmission and reception (wherein one or a small number of analog beams are selected out of a large number, for instance, after a training duration—to be performed from time to time), the term “multi-beam operation” is used to refer to the overall system aspect. This includes, for the purpose of illustration, indicating the assigned DL or UL transmit (TX) beam (also termed “beam indication”), measuring at least one reference signal for calculating and performing beam reporting (also termed “beam measurement” and “beam reporting”, respectively), and receiving a DL or UL transmission via a selection of a corresponding receive (RX) beam. 
     Additionally, the beamforming architecture  500  is also applicable to higher frequency bands such as &gt;52.6 GHz (also termed the FR4). In this case, the beamforming architecture  500  can employ only analog beams. Due to the O2 absorption loss around 60 GHz frequency (˜10 decibels (dB) additional loss @ 100 m distance), larger numbers of and sharper analog beams (hence larger number of radiators in the array) will be needed to compensate for the additional path loss. 
     As previously discussed, fully digital transceiver implementations, where each antenna element is fed by a dedicated radio-frequency (RF) chain, are impractical. To keep the hardware cost and power consumption of such large antenna arrays manageable, typically an analog beamforming or hybrid beamforming architecture is adopted where the large antenna array is fed with a much smaller number of RF chains via the use of analog hardware such as phase shifters. This reduces the number of mixed-signal components, which significantly reduces the cost, size and power consumption of the transceivers. When transmitting a signal at the transmitter, a combination of digital beamforming before DAC and analog beamforming using the phase shifters is used to create the overall beam shape in the desired direction. Similarly, when receiving a signal at the receiver, a combination of analog beamforming using phase shifters and digital beamforming after ADC is used to create the overall beam shape in the desired direction. 
     Conventional forms of analog beamforming or hybrid beamforming rely on the analog hardware components (e.g., phase shifters and switches) to create the beam shapes. However, these analog hardware components create a frequency-flat response, i.e., all components of the input signal frequency undergo a similar transformation after passing through them. This reduces the flexibility of the beamforming that is possible in such analog or hybrid beamforming systems, as compared to fully digital architectures where each antenna array is fed with a dedicated RF chain. This limitation of frequency-flat beamforming is further exacerbated at the mm-wave and THz frequencies, where beam-alignment, beam-tracking, link blockage and initial access are difficult problems to solve and usually involve significant overhead. There also exist several scenarios where the frequency flat-beamforming can limit the number of users that can be served simultaneously with the full beamforming gain. 
       FIG.  6    illustrates a system  600  that performs phase shifter based hybrid beamforming with a single RF chain, i.e., R=1. Note that with M antennas, the maximum possible beamforming gain in any direction is M. In that case, with frequency-flat beamforming, two spatially separated users cannot be simultaneously (at the same time) served on half the bandwidth with the maximum beamforming gain of M. Similarly, in a scenario that includes many internet-of-things (IoT) users (each requiring a low bandwidth) that are spread uniformly in the angular space, they cannot all be served simultaneously (at the same time) with the full beamforming gain of M. Note that here, angular space refers to the angle subtended by the receiver&#39;s line-of-sight path at the transmitter. Furthermore, the beams that can achieve the full beamforming gain of M are often pencil thin and are highly prone to blockage, or misalignment caused by user mobility/rotation. The overhead for tracking these beam directions (in case of misalignment) and also to perform the initial alignment can be very high in large antenna systems with very few RF chains. This limits the performance gains achievable using frequency-flat hybrid beamforming. 
     To address these and other issues, this disclosure provides a system and method for time-delay based hybrid beamforming. As described in more detail below, the disclosed embodiments utilize a type of analog hardware called true-time delay (TTD). Unlike switches and phase shifters, TTDs have a frequency-dependent behavior, i.e., different components of the input signal frequency undergo different transformations after passing through the TTD. Thus, the disclosed embodiments feature hybrid transceiver architectures where a small number of RF chains are connected to a large antenna array using TTDs. Using such architectures, the disclosed embodiments can achieve frequency-dependent beamforming that is more versatile than conventional, frequency-flat beamforming methods. Note that, here, frequency-dependent beamforming refers to a technique where different components of the input signal may encounter a differently shaped analog beam based on their frequency. The disclosed embodiments feature any of several transceiver architectures that use a combination of phase shifters, switches, and TTDs as analog components that connect the large antenna array to a small number of RF chains. The disclosed embodiments also feature several key frequency-dependent beamforming behaviors that can be realized, and also feature multiple algorithms for realizing the frequency-dependent beamforming behaviors. 
     Note that while some of the embodiments discussed below are described in the context of hybrid beamforming systems, these are merely examples. It will be understood that the principles of this disclosure may be implemented in any number of other suitable contexts or systems. 
       FIGS.  7  through  10    illustrate several desirable frequency-dependent beam behaviors that can be useful in different scenarios. 
     Beam Behavior 1: As shown in  FIG.  7   , in frequency-dependent beam forming scenarios that exhibit this behavior, the maximum gain region of the beam sweeps over an angle range as the signal frequency varies. This behavior can be useful at a BS in scenarios where many users are uniformly distributed in an angular region and require simultaneous service in downlink and uplink (PDSCH and PUSCH). For such uniformly spread users, the physical uplink control channel (PUCCH) overhead can also be reduced with this beam behavior, since it enables all users to send small uplink control packets (e.g. HARQ-ACK packets) simultaneously. This behavior is also desirable in scenarios where the users are moving at a high velocity, and good link reliability and fast beam re-alignment are needed. In addition, such a beam behavior is also beneficial in scenarios where the BS wishes to obtain initial beam alignment with one or more users at a very low overhead. Finally, this behavior is also useful for increasing the uplink cell coverage range, by allowing each user device on cell edge to accumulate more power by transmitting longer. 
     Beam Behavior 2: As shown in  FIG.  8   , in frequency-dependent beam forming scenarios that exhibit this behavior, the maximum gain region points in one angular direction over the lower half of the signal bandwidth and it points in another angular direction over the upper half bandwidth. This behavior is useful in scenarios where the users are sparsely distributed in the angular domain, and the BS wishes to provide service to multiple users simultaneously on different portions of the large available system bandwidth. Such service on portions of the bandwidth is helpful, for example, if each user is incapable of utilizing the full system bandwidth or if each user only has very low traffic to send. Extensions of such behavior that cover more than two angular directions can also be considered, such as shown in the bottom of  FIG.  8   . 
     Beam Behavior 3: As shown in the examples of  FIG.  9   , the maximum gain region spans region  1  of the angular space at one subset of frequencies (subset  1 ) and region  2  of the angular space at a disjoint set of frequencies (subset  2 ). Within each of subset  1  and subset  2  frequencies, the maximum gain region sweeps across angular space region  1  and angular space region  2 , respectively. This behavior is useful when the users are clustered in several different localized regions and require simultaneous service or require fast beam realignment. 
     Beam Behavior 4: As shown in  FIG.  10   , in this behavior, a wide beam is constructed that provides coverage for a certain angular region for most of the bandwidth. However, for a sub-band of the bandwidth, the width of the wide beam may be adapted to reduce co-channel interference to some incumbent users using that sub-band. 
     Similar behaviors of the frequency-dependent beam can also be useful at a user device in several scenarios, e.g. for initial beam alignment and tracking. Note that this kind of frequency-dependent beamforming is not possible using conventional hybrid beamforming techniques that use only phase shifters or switches. In the present disclosure, several different embodiments of transceiver architectures are described that utilize a combination of phase shifters, TTDs, and switches that can realize the aforementioned beam behaviors. In addition, multiple design algorithms are provided for choosing the values of the phase-shifts and the TTDs that can achieve these beam-behaviors. 
       FIG.  11    illustrates an example transceiver  1100  for performing TTD-based hybrid beamforming according to embodiments of the present disclosure. As shown in  FIG.  11   , the transceiver  1100  is a BS transceiver that is equipped with M antennas  1105  and one RF chain  1110 . Each antenna  1105  (represented as m) is connected to L different phase shifters  1115  via one or more power amplifiers  1120 . In the figure, the corresponding frequency-independent phase-shifts are identified as {φ m,1 , φ m,1 , . . . , φ m,L }. For each l∈{1, . . . , L} the phase shifts {φ 1,l , φ 2,l , . . . , φ M,l } are connected to N dedicated TTDs  1125  having delay values {τ 1,l , τ 2,l , . . . , τ N,l }, where N≤M, via a mapping matrix  1130  (represented as P l ). The mapping matrix  1130  P l  essentially determines how the N TTDs  1125  connect to the corresponding M phase shifters  1115 . In some embodiments, each mapping matrix  1130  may be simply a set of fixed connections. In some embodiments, the mapping can be performed using one or more RF switches, which create re-configurable mappings. 
     The inputs to the TTDs  1125  are all directly fed by the output of the RF chain  1110  of the transceiver  1100 . Thus in total, the transceiver  1100  has ML phase shifters  1115 , L mapping matrices  1130  and NL TTD elements  1125  (where N≤L). Here the TTD elements  1125  can be implemented using electronic components or using photonic components. Moreover, the TTD elements  1125  can have either fixed or reconfigurable delay values. Additionally, some of the TTD elements  1125  can also be implemented in the digital domain by including more RF chains. 
     It is noted that the architecture of the transceiver  1100  shown in  FIG.  11    is only one example and should not be interpreted as a limitation of the present disclosure. For example, the same architecture can also be extended to a multiple-RF chain scenario by incorporating several such arrays in parallel, each having their own separate RF chain. It is noted that for this architecture at the transmitter, assuming orthogonal frequency division multiplexing (OFDM), the transmit signal on subcarrier k∈  can be expressed as: 
     
       
         
           
             
               
                 
                   
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     where ⊙ is the Hadamard product (i.e., the element-wise matrix product), T l  is the l-th phase-shifter vector, and D k,l  is the TTD vector at subcarrier k∈ , respectively. 
     The desired frequency-dependent beam-behaviors described above (i.e., Behavior 1, Behavior 2, Behavior 3, and Behavior 4) can all be interpreted as wanting the maximum beamforming (of M) in some desired angular regions Θ=U i=1   l [θ i −Δθ i , θ i +Δθ i ] as the transceiver  1100  sweeps across the frequencies within the system bandwidth. For example, in Behavior 1, I=1, θ 1  is the center angle of the angular region over which the BS intends to sweep the beam, and 2Δθ 1  is the overall angle of sweep. Similarly in Behavior 2, I=2, θ 1  and θ 2  are the angles corresponding to user  1  and user  2 , respectively, and Δθ 1 =Δθ 2 =0 (i.e., no beam sweeping). Since in many scenarios, it does not matter which frequency region is assigned to each of the angular regions of interest, in some embodiments, the phase shifter and TTD design problem can be formulated as: 
     
       
         
           
             
               
                 
                   
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     where β can be a system design parameter, † represents the transpose operation, and α tx (θ) is the array response vector of the antenna array in direction θ. For example, for a uniform linear antenna array with half-wave inter-element spacing, the array response vector α tx (θ) can be expressed as: 
     
       
         
           
             
               
                 
                   
                     
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     It is noted the problem formulation in Equation (2) is not limited to uniform linear arrays, and one can use the proper α tx (θ) that matches the array structure. Other array structures may include planner uniform arrays and non-uniform arrays. 
     Next, some embodiments for realizing the desired beam behaviors will be described. 
     Beam Behavior 1: 
     Beam Behavior 1 can be useful in scenarios where simultaneous service is required for several users in a localized region with the full beamforming gain, or in scenarios where link reliability and easy beam-tracking are desired, or where fast initial beam-alignment is desired. In this scenario, it is assumed without loss of generality that the desired coverage region is Θ=[θ 1 −Δθ 1 θ 1 +Δθ 1 ]. 
       FIG.  12    illustrates an example transceiver  1200  for performing TTD-based hybrid beamforming for Beam Behavior 1 according to embodiments of the present disclosure. As shown in  FIG.  12   , the transceiver  1200  includes multiple antennas  1205 , a RF chain  1210 , multiple phase shifters  1215 , multiple amplifiers  1220 , and multiple TTDs  1225 . The transceiver  1200  is a special case of the transceiver  1100  shown in  FIG.  11   , with L=1, N=M, P l =   M . Thus in the transceiver  1200 , the number of phase shifters  1215  and the number of TTDs  1225  are both set to M, and each mapping matrix is just a straight wire connection. In some embodiments, the TTDs  1225  are reconfigurable, and the TTD  1225  corresponding to antenna m is configured to have a delay variation between τ m,1 ∈[0, (m−1) sin (Δθ max )/W], where W is the system bandwidth and Δθ max  is the maximum desired beam-sway in one direction of the center angle. In some embodiments, to achieve the desired behavior over Θ, the TTD delays and phase shifts can be set based on the example algorithm  1300  shown in  FIG.  13   . 
     As an example, the achievable antenna gain for a TX with a half-wavelength spaced uniform linear array with M=N=64, θ 1 =0 and Δθ 1 =π/8 is illustrated in  FIG.  14   . As can be seen from  FIG.  14   , this design can achieve the desired Beam Behavior 1. 
     In the architecture represented by the transceiver  1200 , for each angle in the vicinity of θ 1 , there is a unique frequency region where the peak beamforming gain is obtained. Thus in fast user mobility scenarios, by observing the frequency or sub-carrier where the highest signal power is obtained, the receiver can estimate the best beam direction or the required beam correction to be used at the transmitter. Thus fast beam-alignment can be achieved using this architecture. Furthermore, as the user moves away by more than a 3 dB beam-width on one frequency, the SNR doesn&#39;t completely fall to zero on the whole band. Rather the maximum beamforming gain shifts to a different frequency. This can beneficial since it can provide a graceful degradation of service with user mobility and does not cause sudden outage as in the case of frequency-flat beamforming. 
     In some scenarios, it might be costly to implement finely tunable TTDs. And so, in a related embodiment, the transceiver  1200  may support only discrete beam-sway values 2Δθ 1 . In this case, selectable fixed delay TTDs can be used. For example, to support three beam-sway options 
     
       
         
           
             
               
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     the algorithm  1300  can be used to compute three sets of TTDs  1225 , then switches can be implemented to select one on the three fixed TTD options per antenna  1205 . The transceiver  1200  may be designed such that the maximum beam-sway value 2Δθ max  is less than or equal to the beam-width of the individual antenna elements in the array. 
     In the aforementioned embodiment, the required delay values for larger antenna indices m≈M can be quite large: [0, (m−1) sin (Δθ max )/πW]. Correspondingly, in another embodiment (referred to as Embodiment 2 for clarity), the antenna array can be divided into [M/ M ] sub-arrays, each containing  M  adjacent antenna elements. For example,  FIG.  15    illustrates another example transceiver  1500  for performing TTD-based hybrid beamforming for Behavior 1 (Embodiment 2) according to embodiments of the present disclosure. As shown in  FIG.  15   , the transceiver  1500  includes multiple antennas  1505 , a RF chain  1510 , multiple phase shifters  1515 , multiple amplifiers  1520 , and multiple TTDs  1525 - 1526 . Each sub-array has a dedicated TTD  1525  for providing a large delay value, while each antenna within the sub-array may also have a TTD  1526  providing small intra-sub-array delays that require a much smaller max delay range. 
     The transceiver  1500  is a special case of the transceiver  1100  shown in  FIG.  11   , with L=1, N=M, P l =   M , and τ n,1 = τ   [n/ M ] +{circumflex over (τ)} n . In the transceiver  1500 , the number of phase shifters  1515  is M and number of TTDs  1525 - 1526  is M+[M/ M ], where  M  is a design parameter and each mapping matrix is just a straight wire connection. However for the TTDs  1525 - 1526 , the required tunable delay range is: {circumflex over (τ)} m ∈[0, (mod(m−1,  M )) sin (Δθ max )/W] and  τ   u ∈[0, (u−1) M sin (Δθ max )/W]. Thus in other words, out of the total TTDs, M TTDs  1526  only require a small max-delay while the [M/ M ] TTDs  1525  require a larger delay value. Since the number of TTDs  1525  with large delay is reduced, the hardware cost can be lower than Embodiment 1 described with respect to  FIG.  12   . In some embodiments, to achieve the desired behavior over Θ, the TTD delays and phase-shifts can be set based on the example algorithm  1600  shown in  FIG.  16   . 
     As an example, the achievable antenna gain for a TX with a half-wavelength spaced uniform linear array with M=N=64, θ 1 =0 and Δθ 1 =π/8 is illustrated in  FIG.  17   . As can be seen from  FIG.  17   , this design can achieve the desired Beam Behavior 1. By comparing  FIG.  14    and  FIG.  17   , it can be seen that this architecture can achieve identical performance as Embodiment 1 described with respect to  FIG.  12   . 
     In some embodiments, in the transceiver  1500 , instead of one RF chain  1510 , U RF chains can be used to allow for a digital implementation of the TTDs  τ   u  while keeping the analog implementation of {circumflex over (τ)} m . 
     In both the aforementioned two embodiments, the number of TTDs  1525 - 1526  is equal to or larger than the number of antenna elements  1505 , M, which could be difficult to fabricate in some scenarios. Therefore, in another embodiment (referred to as Embodiment 3 for clarity), the antenna array can be divided into [M/ M ] sub-arrays, each containing  M  adjacent antenna elements. For example,  FIG.  18    illustrates another example transceiver  1800  for performing TTD-based hybrid beamforming for Behavior 1 (Embodiment 3) according to embodiments of the present disclosure. As shown in  FIG.  18   , the transceiver  1800  includes multiple antennas  1805 , a RF chain  1810 , multiple phase shifters  1815 , multiple amplifiers  1820 , and multiple TTDs  1825 . Unlike Embodiment 2 ( FIG.  15   ), the transceiver  1800  does not include any intra-sub-array TTD elements. 
     The transceiver  1800  is a special case of the transceiver  1100  shown in  FIG.  11   , with L=1, N=[M/ M ], P 1 =   N ⊗     M × 1   . In the transceiver  1800 , the number of phase shifters  1815  is M and number of TTDs  1825  is only [M/ M ], where  M  is a design parameter and each mapping matrix is just a splitter that connects each delay output to all the  M  phase shifters in the corresponding sub-array. The desired tunable delay range is: τ n,1 ∈[0, n M  sin (Δθ max )/W]. In some embodiments, to achieve the desired behavior over Θ, the TTD delays and phase shifts can be set based on the example algorithm  1900  shown in  FIG.  19   . 
     As an example, the achievable antenna gain for a TX with a half-wavelength spaced uniform linear array with M=N=64,  M =8, θ 1 =0 and Δθ 1 =π/8 is illustrated in  FIG.  20   . As can be seen from  FIG.  20   , this design can approximately achieve the desired Beam Behavior 1. Due to the limited number of TTDs  1825 , the beamforming gain is less then M as the beam sweeps away from the center angle. Thus the transceiver  1800  can be a good choice when the desired sweep angle Δθ 1  is small, which can limit the loss due to reduction in the beamforming gain. For larger values of Δθ 1 , the loss in beamforming gain can be significant with this low-complexity architecture. To avoid such loss,  M  can be chosen such that  M ≤π/2Δθ 1 . In some embodiments, in the transceiver  1800 , instead of one RF chain, N RF chains can be used to allow for a digital implementation of the TTDs τ u . 
     Beam Behavior 2: 
     Beam Behavior 2 can be useful in scenarios where simultaneous service is required for users that are spatially far apart with the full beamforming gain. In this scenario, it is assumed without loss of generality that the desired coverage region is Θ={θ 1 ,θ 2 }. In Beam Behavior 2, it is possible to create good beamforming gain in two discontinuous angular regions, albeit on different portions of the bandwidth. 
       FIG.  21    illustrates an example transceiver  2100  for performing TTD-based hybrid beamforming for Beam Behavior 2 according to embodiments of the present disclosure. As shown in  FIG.  21   , the transceiver  2100  includes multiple antennas  2105 , a RF chain  2110 , multiple phase shifters  2115 , multiple amplifiers  2120 , and multiple TTDs  2125 . 
     The transceiver  2100  is a special case of the transceiver  1100  shown in  FIG.  11   , with N=1, P l =   M×1 . For clarity and ease of discussion, this embodiment is referred to as Embodiment 4. Each antenna  2105  is connected to L different phase shifters  2115  with the frequency-independent phase-shifts being {φ m,1 , φ m,1 , . . . , φ m,L }. The l-th phase shifters  2115  from all the antennas  2105  are connected together and fed by a common TTD  2125  with delay τ 1,l . Thus in the transceiver  2100 , the number of phase shifters  2115  is ML and number of TTDs  2125  is L, and each mapping matrix is a splitter that connects the l-th TTD  2125  to each of the l-th phase shifters  2115  corresponding to the M antennas  2105 . In some embodiments, the TTDs  2125  are reconfigurable, and the TTD l is designed to have a delay variation between τ 1,l ∈[0, (l−1)/W], where W is the system bandwidth. In one embodiment where L=2, to achieve the desired behavior over Θ, the TTD delays and phase shifts can be set based on the example algorithm  2200  shown in  FIG.  22   . 
     As an example, the achievable antenna gain for a TX with a half-wavelength spaced uniform linear array with M=64, L=2, θ 1 =π/4 and θ 2 =−π/4 is illustrated in  FIG.  23   . As can be seen from  FIG.  23   , the transceiver  2100  can achieve the desired Beam Behavior 2, where a nearly-full beamforming gain (of  52 ) is achievable in the two directions on two halves of the system bandwidth. In a related embodiment, in the transceiver  2100 , instead of one RF chain  2110 , L RF chains  2110  can be used to allow for a digital implementation of the TTDs τ 1,l . 
     In the transceiver  2100  (Embodiment 4), although the number of required TTDs  2125  is very few, the architecture may require many phase shifters  2115  (ML) and the corresponding routing of the phase shifters  2115  to the TTDs  2125  can be complex. Therefore, the TTD-based architecture of the transceiver  1200  (Embodiment 1) can be used in conjunction with another algorithm to achieve the desired Beam Behavior 2. Note that this is a special case of the transceiver  1100  shown in  FIG.  11   , with L=1, N=M, P l =   M . The number of phase shifters  1215  and number of TTDs  1225  are both set to M, and each mapping matrix is just a straight wire connection. In one embodiment, the TTDs  1225  are reconfigurable and the TTD  1225  corresponding to antenna m is designed to have a delay variation between τ m,1 ∈[0, 3/(4W)], where W is the system bandwidth. This delay range can be much smaller than what is required to achieve Beam Behavior 1 using Embodiment 1. In some embodiments, to achieve the desired behavior over Θ, the TTD delays and phase-shifts can be set based on the example algorithm  2400  shown in  FIG.  24   . 
     As an example, the achievable antenna gain for a TX with a half-wavelength spaced uniform linear array with M=N=64, L=1, θ 1 =π/4 and θ 2 =−π/4 is illustrated in  FIG.  25   . As can be seen from  FIG.  25   , this design can achieve the desired Beam Behavior 2, where a nearly-full beamforming gain (of 64) is achievable in the two directions on two halves of the system bandwidth. In comparison to Embodiment 4, the main difference is there can be a small side-lobe of the beam in the vicinity of θ=0. 
     As shown above, both the transceiver  1200  (Embodiment 1) and the transceiver  2100  (Embodiment 4) can generate the desired Beam Behavior 2. However, the transceiver  1200  may need many TTDs (albeit with small maximum required delay), and the transceiver  2100  may require many phase shifters and complex signal routing. Therefore, in another embodiment (referred to as Embodiment 5 for clarity), the number of phase shifters and TTDs is kept to a low number. 
     For example,  FIG.  26    illustrates another example transceiver  2600  for performing TTD-based hybrid beamforming for Behavior 2 (Embodiment 5) according to embodiments of the present disclosure. As shown in  FIG.  26   , the transceiver  2600  includes multiple antennas  2605 , a RF chain  2610 , multiple phase shifters  2615 , multiple amplifiers  2620 , multiple TTDs  2625 , and multiple switches  2630 . 
     The transceiver  2600  is a special case of the transceiver  1100  shown in  FIG.  11   , with L=1, and P 1  being realized using the bank of switches  2630 . In the transceiver  2600 , the RF chain  2610  can be connected to N TTDs  2625  each having a distinct and fixed delay value: τ n,1 =3 (n−1)/[4(N−1)W]. Each antenna  2605  also has one dedicated phase shifter  2615  and the phase shifter  2615  can be connected to any of the N fixed TTDs  2625  using the bank of switches  2630 . Thus for any desired beam behavior, each antenna  2605  can be connected to one of the N fixed TTDs  2625 . In some embodiments, to achieve the desired behavior over Θ, the TTD delays and phase shifts can be set based on the example algorithm  2700  shown in  FIG.  27   . 
     As an example, the achievable antenna gain for a TX with a half-wavelength spaced uniform linear array with M=64, N=4, θ 1 =π/4 and θ 2 =−π/4 is illustrated in  FIG.  28   . As can be seen from  FIG.  28   , the transceiver  2600  can achieve the desired Beam Behavior 2, where a nearly-full beamforming gain (of 64) is achievable in the two directions on two halves of the system bandwidth, with just four TTDs  2625 . However, as with Embodiment 4, it can be seen that there can be a small side-lobe outside of the angles of interest in Θ. In some embodiments, in the transceiver  2600 , instead of one RF chain, N RF chains can be used to allow for a digital implementation of the TTDs τ n,1 . 
     Beam Behavior 3: 
     Beam Behavior 3 can be useful in scenarios where simultaneous service is required for several users that are distributed in two disjoint localized regions with the full beamforming gain, or in scenarios where link reliability and easy beam-tracking are desired. In this scenario, it is assumed without loss of generality that the desired coverage region is Θ=[θ 1 −Δθ 1 , θ 1 +Δθ 1 ]U[θ 2 −Δθ 2 , θ 2 +Δθ 2 ]. In some respects, Beam Behavior 3 can be considered as a modified combination of Beam Behavior 1 and Beam Behavior 2. 
       FIG.  29    illustrates an example transceiver  2900  for performing TTD-based hybrid beamforming for Beam Behavior 3 (Embodiment 6) according to embodiments of the present disclosure. As shown in  FIG.  29   , the transceiver  2900  includes multiple antennas  2905 , a RF chain  2910 , multiple phase shifters  2915 - 2916 , multiple amplifiers  2920 , and multiple TTDs  2925 - 2926 . 
     The architecture of the transceiver  2900  is different from the generic transceiver  1100  shown in  FIG.  11   , since the transceiver  2900  includes two different phase shifter arrays  2915 - 2916  separated by intermediary TTDs  2925 . Here the signal from the RF chain  2910  is split and fed to L TTDs  2926  that can implement large delays { τ   1 , . . . ,  τ   L }. The outputs of the TTDs  2926  are fed to an L×L array of phase shifters  2916 , with phase shifts { φ   1,2 , . . . ,  φ   L,L }, to generate L transformed signals. Similarly, each antenna  2905  (m={1, . . . M}) is connected to L different phase shifters  2915 , with the frequency-independent phase-shifts being {φ m,1 , φ m,1 , . . . , φ m,L }. Each of these phase shifters  2915  also has a dedicated TTD  2925  with delay {circumflex over (τ)} m,l  that can achieve a small delay range. In turn, the l-th TTDs from all the antennas  2905  are connected together and fed by the l-th transformed signal. Thus in the transceiver  2900 , the number of phase shifters  2915 - 2916  is ML+L 2 , and the number of TTDs  2925 - 2926  is ML+L, and each mapping matrix P l  is a straight wire connection for each phase shifter. 
     In some embodiments, the TTDs  2925 - 2926  are reconfigurable and are designed to have a delay variation between  τ   l ∈[0, 25(1−1)/W] and {circumflex over (τ)} m,L ∈[0, (m−1) sin (Δθ max )/W] for l∈{1, . . . , L}, m∈{1, . . . , M}, where W is the system bandwidth and Δθ max  is the maximum desired beam-sway in one direction of the center angle. In one embodiment where L=2, to achieve the desired behavior over Θ, the TTD delays and phase shifts can be set based on the example algorithm  3000  shown in  FIG.  30   . 
     As an example, the achievable antenna gain for a TX with a half-wavelength spaced uniform linear array with M=64, L=2, θ 1 =π/4, Δθ 1 =π/16, θ 2 =−π/4 and Δθ 2 =0 is illustrated in  FIG.  31   . As can be seen from  FIG.  31   , the transceiver  2900  can generate the desired Beam Behavior 3, while also providing a nearly-full beamforming gain (of 64). In a related embodiment, in the transceiver  2900 , instead of one RF chain  2910 , L RF chains can be used to allow for a digital implementation of the TTDs  τ   l . 
     Although the transceiver  2900  can generate the Beam Behavior 3, it may involve a large hardware cost of implementation. Therefore, in another embodiment (referred to as Embodiment 7 for clarity), to reduce the complexity, a slight relaxation of Beam Behavior 3 can be considered, where the desired coverage region is Θ=[θ 1 −Δθ, θ 1 +Δθ]U[θ 2 −Δθ, θ 2 +Δθ]. In other words, the same squint of the beams is desired in the two angular directions: Δθ 1 =Δθ 2 =Δθ. 
     For example,  FIG.  32    illustrates another example transceiver  3200  for performing TTD-based hybrid beamforming for Behavior 3 (Embodiment 7) according to embodiments of the present disclosure. As shown in  FIG.  32   , the transceiver  3200  includes multiple antennas  3205 , a RF chain  3210 , multiple phase shifters  3215 , multiple amplifiers  3220 , and multiple TTDs  3225 - 3226 . 
     The transceiver  3200  is a special case of the transceiver  1100  shown in  FIG.  11   , with N=M, P l =   M . Each antenna  3205  is connected to L different phase shifters  3215  with the frequency-independent phase-shifts being {φ m,1 , φ m,1 , . . . , φ m,L }. Each phase shifter  3215  also has a dedicated TTD  3225  with delay {circumflex over (τ)} m,l  that can achieve a small delay variation. In addition, the l-th TTDs  3225  from all the antennas  3205  are connected together and fed by a common TTD  3226  with larger delay rate  τ   l . Thus in the transceiver  3200 , the number of phase shifters  3215  is ML and number of TTDs  3225 - 3226  is ML+L, and each mapping matrix P l  is a straight wire connection for each phase shifter  3215 . 
     In a variant of this embodiment, the L large common TTDs  3226  can be merged with the smaller per-antenna TTDs  3225  (τ m,l = τ   l +{circumflex over (τ)} m,l ) to create an architecture having only M TTDs. In some embodiments, the TTDs  3225 - 3226  are reconfigurable and are designed to have a delay variation between  τ   l ∈[0, 25(l−1)/W] and {circumflex over (τ)} m,L ∈[0, (m−1)sin(Δθ max )/W] for l∈{1, . . . , L}, m∈{1, . . . , M}, where W is the system bandwidth and Δθ max  is the maximum desired beam-sway in one direction of the center angle. In one embodiment where L=2, to achieve the desired behavior over Θ, the TTD delays and phase shifts can be set based on the example algorithm  3300  shown in  FIG.  33   . 
     As an example, the achievable antenna gain for a TX with a half-wavelength spaced uniform linear array with M=64, L=2, θ 1 =π/4, Δθ=π/16 and θ 2 =−π/4 is illustrated in  FIG.  34   . As can be seen from  FIG.  34   , the transceiver  3200  generate the desired relaxed Beam Behavior 3, while also providing a nearly-full beamforming gain (of 64). In a related embodiment, in the transceiver  3200 , instead of one RF chain  3210 , L RF chains can be used to allow for a digital implementation of the TTDs  τ   l    
     Although the transceiver  3200  (Embodiment 7) is able to generate the relaxed Beam Behavior 3, the transceiver  3200  may still require many phase shifters  3215  (ML) and TTDs  3225 - 3226  (ML+L), and the corresponding routing of the phase shifters  3215  to the TTDs  3225 - 3226  can be complex. Therefore, the TTD-based architecture of the transceiver  1200  (Embodiment 1) can be used in conjunction with another algorithm to achieve the desired Beam Behavior 3. Note that this is a special case of the transceiver  1100  shown in  FIG.  11   , with L=1, N=M, P l =   M . The number of phase shifters  3215  and the number of TTDs  3225 - 3226  are both set to M, and each mapping matrix is just a straight wire connection. In one embodiment, the TTDs  3225 - 3226  are reconfigurable and the TTD  3225 - 3226  corresponding to antenna m is designed to have a delay variation between τ m,1 ∈[0, (m−1)sin(Δθ max )/W], where W is the system bandwidth. In some embodiments, to achieve the desired behavior over Θ, the TTD delays and phase-shifts can be set based on the example algorithm  3500  shown in  FIG.  35   . 
     As an example, the achievable antenna gain for a TX with a half-wavelength spaced uniform linear array with M=N=64, L=1, θ 1 =π/4, Δθ=π/16 and θ 2 =−π/4 is illustrated in  FIG.  36   . As can be seen from  FIG.  36   , this design can achieve the desired relaxed Beam Behavior 3, however the achievable beamforming gain can be half the maximum (≤32). 
     In some scenarios, there are benefits to using fully digital chains with low resolution data converters. In such fully-digital architecture, the previously mentioned behaviors can be synthesized by applying the algorithms described herein and using digital TTDs and digital phase shifters. Also, in this fully-digital architecture, these behaviors can be implemented using only phase shifters, e.g., by applying different phase-shifts to different sub-carriers. Moreover, the previously mentioned architectures can be implemented in a hybrid digital and analog beamforming architectures. For example, in the transceiver  3200  in  FIG.  32   , L digital and RF chains can be used instead, then the  τ   l  can be implemented as digital TTDs. 
       FIG.  37    illustrates a flow diagram of an example process  3700  for configuring hardware to achieve the desired beam behaviors according to embodiments of the present disclosure. Here the determination of desired beam behavior can be based on an external trigger such as a scheduler, etc. 
     In some embodiments, the algorithm to generate the hardware parameters can be pre-computed offline and the values stored in a dictionary. The dictionary can be based on a discretization of the acceptable parameters for the BS and the desired beam behaviors. Based on the desired behavior and the BS parameters, the corresponding hardware parameters can then be fetched from the dictionary. For example,  FIG.  38    illustrates a flow diagram of an example process  3800  for configuring hardware to achieve desired beam behaviors using offline computation according to embodiments of the present disclosure. 
     Generic beamformer design to achieve desired beam behavior: 
     In some embodiments, an algorithm can be performed to design the beamformer to achieve any arbitrary desired beam behavior. For an OFDM system with subcarriers in set  , the desired beam behavior can be defined as the set of desired beamforming vectors {b k |k∈ }. Here b k  is the desired beamforming vector on OFDM subcarrier k. For example, for Beam Behavior 1, b k =α tx (θ 1 +kΔθ 1 / |) where it is assumed that the sub-carrier index is centered. For the TTD architecture, a special case of the transceiver  1100  shown in  FIG.  11    is considered, with L=1. In other words, each antenna m is connected to only one phase shifter, a power amplifier, and the corresponding frequency-independent phase-shift is {φ m }. These phase shifters are connected to N TTDs with delay values {τ 1 , τ 2 , . . . , τ N } where N≤M via a mapping matrix P. The mapping matrix P essentially determines how the N TTDs connect to the corresponding M phase shifters. Thus in total, the transceiver has M phase shifters, one mapping matrix and N TTD elements. Note that for this architecture at the transmitter, assuming orthogonal frequency division multiplexing (OFDM), the transmit signal on subcarrier k∈  can be expressed as: 
     
       
         
           
             
               
                 
                   
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     where  b   k =b k /∥b k ∥, and auxiliary variable set ψ={ψ k |k∈ }. In some embodiments, the solution to Equation (5) can be obtained using an iterative optimization algorithm, such as the example algorithm  3900  shown in  FIG.  39   . 
     In a variant of the algorithm  3900 , the computation of τ n  inside the for loop of i can be obtained as a solution of the weighted least squares problem: 
     
       
         
           
             
               
                 
                   
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     where  (.) is the phase unwrapping function that for each k adds phase-shifts of integer multiples of 2π to the argument to make the argument to ensure that the phase-difference between adjacent sub-carriers satisfies: 
       | (ψ k +∠[   b     k ] m )− (ψ k−1 +∠[   b     k−1 ] m )|≤π  (7)
 
       FIG.  40    illustrates an example process  4000  for determining delay values and phase shift values according to embodiments of the present disclosure. As shown in  FIG.  40   , the process  4000  includes obtaining various inputs  4005 . At operation  4010 , one or more delay values and one or more phase shift values for fixed digital precoding are updated. At operation  4015 , clipping and/or rounding are performed to ensure a maximum delay or ensure one or more phase constraints are satisfied. At operation  4020 , digital precoding is updated for fixed delay values and fixed phase shift values. The operations  4010 - 4020  can be repeated in an iterative fashion until convergence or a maximum number of iterations is performed. 
     Although  FIGS.  7  through  40    illustrates examples of beamforming behaviors, multiple example transceivers for performing TTD-based hybrid beamforming, and related details, various changes may be made to  FIGS.  7  through  40   . For example, various components in  FIGS.  7  through  40    could be combined, further subdivided, or omitted and additional components could be added according to particular needs. In addition, various operations in  FIGS.  7  through  40    could overlap, occur in parallel, occur in a different order, or occur any number of times. The embodiments shown in  FIGS.  7  through  40    are for illustration only. Other embodiments could be used without departing from the scope of this disclosure. 
     The frequency-dependent hybrid beamforming architectures described herein can significantly improve the capabilities of beamforming in high frequency systems like mm-wave and THz systems. The additional capabilities can be quite useful at a base station in a wide variety use cases, and can also help make the beam alignment and tracking easier. For example, the architectures can be used to serve multiple users in disconnected regions with full beamforming gain with just one ADC at the base station. 
     Although the present disclosure has been described with exemplary embodiments, various changes and modifications may be suggested to one skilled in the art. It is intended that the present disclosure encompass such changes and modifications as fall within the scope of the appended claims. None of the description in this application should be read as implying that any particular element, step, or function is an essential element that must be included in the claims scope. The scope of patented subject matter is defined by the claims.