DISTRIBUTED COMPRESSION

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Patent Application No.

61/659,846, filed June 14, 2012, titled "SYSTEMS AND METHODS FOR PROVIDING A ROBUST UPLINK TRANSMISSION VIA DISTRIBUTED CODING AND COMPRESSION", and U.S. Provisional Patent Application No. 61/659,856, filed June 14, 2012, titled "SYSTEMS AND METHODS FOR PROVIDING JOINT BASE STATION SCHEDULING AND DISTRIBUTED COMPRESSION", the disclosures of both applications hereby incorporated by reference herein in their respective entirety, for all purposes.

BACKGROUND

[0002] Current wireless communication system deployments and networks are facing a

"bandwidth crunch" that may be caused by an increasing demand for devices and high data rate applications (e.g. executed thereon). Bandwidth may be defined by the net bit rate of a logical or physical communication path in a digital communication system. Bandwidth in bit/s may also refer to consumed bandwidth, corresponding to achieved throughput, for example the average rate of successful data transfer through a communication path.

SUMMARY

[0003] Systems, methods, and/or techniques for providing an uplink with compression are contemplated. Such systems, methods, and/or techniques may include performing joint base station scheduling and distributed compression. The joint base station scheduling and distribution compression may include a two-phase joint selection and compression algorithm. Additionally, the joint base station scheduling and distribution compression may be configured to be performed jointly using sparsity-inducing optimization. A covariance matrix, channel information, a correlation matrix, a linear transformation matrix, a sum-rate metric, a compression strategy, a determined codebook, a sparsity inducing term, a block-coordinate ascent algorithm, one or more test channels, convergence criterion, and the like may also be used to perform the joint base station scheduling and distribution compression. For example, according to an embodiment, performing the joint base station scheduling and distribution compression may include one or more of the following: receiving at least one of the following: channel information, test channels computed for base stations selected using the two phase-joint selection and compression algorithm, and a signal; determining a compression strategy;

compressing the received signal based on the compression strategy; and sending an index associated with the compressed signal; and the like.

[0004] Systems, methods, and/or techniques for providing an uplink with compression are contemplated. Such systems, methods, and/or techniques may include performing distributed source coding and compression. The distributed source coding and compression may be configured to be performed via sequential source coding with side information. Additionally, a covariance matrix (e.g. that may depend on channel realizations of one or more base stations), channel information, a correlation matrix, a linear transformation matrix, a sum-rate metric, a compression strategy, a determined codebook, and the like may be used to perform the distributed source coding and compression. For example, according to an embodiment, performing the distributed source coding and compression may include one or more of the following: receiving channel information, a determined ordering for compression, a correlation matrix, and/or a signal; providing information derived from the received signal; applying a linear transformation matrix to the received signal; adjusting a resolution of the predefined quantization codebook based on the linear transformation matrix; performing component-wise quantization to an output of the linear transformation to obtain a point in a predefined quantization codebook; sending an index associated with the point in the predefined quantization codebook; computing a sum-rate metric based on one or more system parameters; determining a compression strategy; compressing the received signal based on the compression strategy; and the like.

[0005] Embodiments contemplate techniques for performing the distributed coding and compression that may comprise receiving at least one of the following: channel information, a determined ordering for compression, a correlation matrix, and a signal. The techniques may also comprise providing information derived from the received signal. Further, techniques may comprise applying a linear transformation matrix to the received signal. Techniques may also comprise adjusting a resolution of the predefined quantization codebook based on the linear transformation matrix. Also, techniques may also comprise performing component-wise quantization to an output of the linear transformation to obtain a point in a predefined quantization codebook. Techniques may also include sending an index associated with the point in the predefined quantization codebook. And techniques may include computing a sum-rate metric based on one or more system parameters. Also, techniques may include determining a compression strategy and/or compressing the received signal based on the compression strategy.

[0006] Embodiments contemplate techniques for performing joint base station scheduling and distribution compression. One or more techniques may include receiving channel information by a device. The device may be in communication with one or more base stations. Techniques may include selecting the one or more base stations by the device. Techniques may also include determining one or more compression strategies by the device. Techniques may also include reporting one or more test channels by the device to the one or more base stations. Techniques may include performing rate control by the device and/or performing decoding on compressed information received by the device.

[0007] Embodiments contemplate techniques for performing uplink with compression. One or more techniques may include receiving channel information by a device. The device may be in communication with one or more base stations. Techniques may also include determining by the device an order of the one or more base stations for compression. Techniques may also include reporting by the device one or more correlation matrices to the one or more base stations.

Techniques may also include determining one or more compression strategies by the device. Techniques also include reporting one or more test channels by the device to the one or more base stations. Also, techniques may include performing rate control by the device and/or performing decoding on compressed information received by the device.

[0008] Embodiments contemplate a device, where the device may be in communication with a cloud communication network. The device may comprise a processor. The processor may be configured to at least receive channel information by a device. The device may be in communication with one or more base stations. The processor may be configured to select the one or more base stations by the device. The processor may also be configured to determine one or more compression strategies by the device. The processor may be configured to report one or more test channels by the device to the one or more base stations. In addition, the processor may be configured to perform rate control by the device and/or to perform decoding on compressed information received by the device. [0009] The Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, not is it intended to be used to limit the scope of the claimed subject matter. Furthermore, the claimed subject matter is not limited to any limitations that solve any or all disadvantages noted in any part of this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] A more detailed understanding of the embodiments disclosed herein may be had from the following description, given by way of example in conjunction with the accompanying drawings.

[001 1] FIG. 1A depicts a diagram of an example communications system in which one or more disclosed embodiments may be implemented.

[0012] FIG. IB depicts a system diagram of an example wireless transmit/receive unit (WTRU) that may be used within the communications system illustrated in FIG. 1A.

[0013] FIG. 1C depicts a system diagram of an example radio access network and an example core network that may be used within the communications system illustrated in FIG. 1A.

[0014] FIG. ID depicts a system diagram of another example radio access network and an example core network that may be used within the communications system illustrated in FIG.

1A.

[0015] FIG. IE depicts a system diagram of another example radio access network and an example core network that may be used within the communications system illustrated in FIG. 1A.

[0016] FIG. 2 depicts an example embodiment of an uplink of a cloud radio access network with one or more base stations (BSs) such Home BSs (HBSs) and Macro BSs (MBSs) consistent with embodiments.

[0017] FIG. 3 depicts an example embodiment of a cell of a cloud radio access network consistent with embodiments.

[0018] FIG. 4 depicts an example technique for base station (BS) selection and compression consistent with embodiments.

[0019] FIG. 5 depicts an example technique for providing an uplink system with compression at a base station (BS) consistent with embodiments. DETAILED DESCRIPTION

[0020] A detailed description of illustrative embodiments will now be described with reference to the various Figures. Although this description provides a detailed example of possible implementations, it should be noted that the details are intended to be exemplary and in no way limit the scope of the application.

[0021] Systems and methods for providing and/or employing joint base station scheduling and distributed source compression schemes at remote radio heads connected to a central processor in an uplink transmission scenario may be provided.

[0022] Systems and methods for providing and/or employing distributed source compression schemes at remote radio heads connected to a central processor in an uplink transmission scenario may be provided. The proposed distributed compression schemes may be used when the remote radio heads may have imperfect channel state information in the network

[0023] FIG. 1A depicts a diagram of an example communications system 100 in which one or more disclosed embodiments may be implemented. The communications system 100 may be a multiple access system that provides content, such as voice, data, video, messaging, broadcast, etc., to multiple wireless users. The communications system 100 may enable multiple wireless users to access such content through the sharing of system resources, including wireless bandwidth. For example, the communications systems 100 may employ one or more channel access methods, such as code division multiple access (CDMA), time division multiple access (TDMA), frequency division multiple access (FDMA), orthogonal FDMA (OFDMA), single- carrier FDMA (SC-FDMA), and the like.

[0024] As shown in FIG. 1A, the communications system 100 may include wireless

transmit/receive units (WTRUs) 102a, 102b, 102c, and/or 102d (which generally or collectively may be referred to as WTRU 102), a radio access network (RAN) 103/104/105, a core network 106/107/109, a public switched telephone network (PSTN) 108, the Internet 110, and other networks 112, though it will be appreciated that the disclosed embodiments contemplate any number of WTRUs, base stations, networks, and/or network elements. Each of the WTRUs 102a, 102b, 102c, and/or 102d may be any type of device configured to operate and/or communicate in a wireless environment. By way of example, the WTRUs 102a, 102b, 102c, and/or 102d may be configured to transmit and/or receive wireless signals and may include user equipment (UE), a mobile station, a fixed or mobile subscriber unit, a pager, a cellular telephone, a personal digital assistant (PDA), a smartphone, a laptop, a netbook, a personal computer, a wireless sensor, consumer electronics, and the like. [0025] The communications systems 100 may also include a base station 1 14a and a base station 1 14b. Each of the base stations 114a, 114b may be any type of device configured to wirelessly interface with at least one of the WTRUs 102a, 102b, 102c, and/or 102d to facilitate access to one or more communication networks, such as the core network 106/107/109, the Internet 1 10, and/or the networks 1 12. By way of example, the base stations 1 14a and/or 114b may be a base transceiver station (BTS), a Node-B, an eNode B, a Home Node B, a Home eNode B, a site controller, an access point (AP), a wireless router, and the like. While the base stations 114a, 1 14b are each depicted as a single element, it will be appreciated that the base stations 1 14a, 1 14b may include any number of interconnected base stations and/or network elements.

[0026] The base station 114a may be part of the RAN 103/104/105, which may also include other base stations and/or network elements (not shown), such as a base station controller (BSC), a radio network controller (RNC), relay nodes, etc. The base station 1 14a and/or the base station 1 14b may be configured to transmit and/or receive wireless signals within a particular geographic region, which may be referred to as a cell (not shown). The cell may further be divided into cell sectors. For example, the cell associated with the base station 1 14a may be divided into three sectors. Thus, in one embodiment, the base station 1 14a may include three transceivers, i.e., one for each sector of the cell. In another embodiment, the base station 114a may employ multiple-input multiple output (MIMO) technology and, therefore, may utilize multiple transceivers for each sector of the cell.

[0027] The base stations 1 14a and/or 1 14b may communicate with one or more of the WTRUs 102a, 102b, 102c, and/or 102d over an air interface 1 15/116/117, which may be any suitable wireless communication link (e.g., radio frequency (RF), microwave, infrared (IR), ultraviolet (UV), visible light, etc.). The air interface 1 15/116/117 may be established using any suitable radio access technology (RAT).

[0028] More specifically, as noted above, the communications system 100 may be a multiple access system and may employ one or more channel access schemes, such as CDMA, TDMA, FDMA, OFDMA, SC-FDMA, and the like. For example, the base station 114a in the RAN 103/104/105 and the WTRUs 102a, 102b, and/or 102c may implement a radio technology such as Universal Mobile Telecommunications System (UMTS) Terrestrial Radio Access (UTRA), which may establish the air interface 115/1 16/117 using wideband CDMA (WCDMA).

WCDMA may include communication protocols such as High-Speed Packet Access (HSPA) and/or Evolved HSPA (HSPA+). HSPA may include High-Speed Downlink Packet Access (HSDPA) and/or High-Speed Uplink Packet Access (HSUPA). [0029] In another embodiment, the base station 1 14a and the WTRUs 102a, 102b, and/or 102c may implement a radio technology such as Evolved UMTS Terrestrial Radio Access (E-UTRA), which may establish the air interface 1 15/1 16/117 using Long Term Evolution (LTE) and/or LTE-Advanced (LTE-A).

[0030] In other embodiments, the base station 114a and the WTRUs 102a, 102b, and/or 102c may implement radio technologies such as IEEE 802.16 (i.e., Worldwide Interoperability for Microwave Access (WiMAX)), CDMA2000, CDMA2000 IX, CDMA2000 EV-DO, Interim Standard 2000 (IS-2000), Interim Standard 95 (IS-95), Interim Standard 856 (IS-856), Global System for Mobile communications (GSM), Enhanced Data rates for GSM Evolution (EDGE), GSM EDGE (GERAN), and the like.

[0031] The base station 114b in FIG. 1A may be a wireless router, Home Node B, Home eNode B, or access point, for example, and may utilize any suitable RAT for facilitating wireless connectivity in a localized area, such as a place of business, a home, a vehicle, a campus, and the like. In one embodiment, the base station 1 14b and the WTRUs 102c, 102d may implement a radio technology such as IEEE 802.1 1 to establish a wireless local area network (WLAN). In another embodiment, the base station 1 14b and the WTRUs 102c, 102d may implement a radio technology such as IEEE 802.15 to establish a wireless personal area network (WPAN). In yet another embodiment, the base station 1 14b and the WTRUs 102c, 102d may utilize a cellular- based RAT (e.g., WCDMA, CDMA2000, GSM, LTE, LTE-A, etc.) to establish a picocell or femtocell. As shown in FIG. 1A, the base station 114b may have a direct connection to the Internet 110. Thus, the base station 1 14b may not be required to access the Internet 110 via the core network 106/107/109.

[0032] The RAN 103/104/105 may be in communication with the core network 106/107/109, which may be any type of network configured to provide voice, data, applications, and/or voice over internet protocol (VoIP) services to one or more of the WTRUs 102a, 102b, 102c, and/or 102d. For example, the core network 106/107/109 may provide call control, billing services, mobile location-based services, pre-paid calling, Internet connectivity, video distribution, etc., and/or perform high-level security functions, such as user authentication. Although not shown in FIG. 1A, it will be appreciated that the RAN 103/104/105 and/or the core network 106/107/109 may be in direct or indirect communication with other RANs that employ the same RAT as the RAN 103/104/105 or a different RAT. For example, in addition to being connected to the RAN 103/104/105, which may be utilizing an E-UTRA radio technology, the core network

106/107/109 may also be in communication with another RAN (not shown) employing a GSM radio technology. [0033] The core network 106/107/109 may also serve as a gateway for the WTRUs 102a, 102b, 102c, and/or 102d to access the PSTN 108, the Internet 1 10, and/or other networks 112. The PSTN 108 may include circuit-switched telephone networks that provide plain old telephone service (POTS). The Internet 110 may include a global system of interconnected computer networks and devices that use common communication protocols, such as the transmission control protocol (TCP), user datagram protocol (UDP) and the internet protocol (IP) in the TCP/IP internet protocol suite. The networks 112 may include wired or wireless

communications networks owned and/or operated by other service providers. For example, the networks 112 may include another core network connected to one or more RANs, which may employ the same RAT as the RAN 103/104/105 or a different RAT.

[0034] Some or all of the WTRUs 102a, 102b, 102c, and/or 102d in the communications system 100 may include multi-mode capabilities, i.e., the WTRUs 102a, 102b, 102c, and/or 102d may include multiple transceivers for communicating with different wireless networks over different wireless links. For example, the WTRU 102c shown in FIG. 1A may be configured to communicate with the base station 1 14a, which may employ a cellular-based radio technology, and with the base station 114b, which may employ an IEEE 802 radio technology.

[0035] FIG. IB depicts a system diagram of an example WTRU 102. As shown in FIG. IB, the WTRU 102 may include a processor 118, a transceiver 120, a transmit/receive element 122, a speaker/microphone 124, a keypad 126, a display/touchpad 128, non-removable memory 130, removable memory 132, a power source 134, a global positioning system (GPS) chipset 136, and other peripherals 138. It will be appreciated that the WTRU 102 may include any subcombination of the foregoing elements while remaining consistent with an embodiment. Also, embodiments contemplate that the base stations 1 14a and 1 14b, and/or the nodes that base stations 1 14a and 1 14b may represent, such as but not limited to transceiver station (BTS), a Node-B, a site controller, an access point (AP), a home node-B, an evolved home node-B (eNodeB), a home evolved node-B (HeNB), a home evolved node-B gateway, and proxy nodes, among others, may include some or all of the elements depicted in FIG. IB and described herein.

[0036] The processor 1 18 may be a general purpose processor, a special purpose processor, a conventional processor, a digital signal processor (DSP), a plurality of microprocessors, one or more microprocessors in association with a DSP core, a controller, a microcontroller,

Application Specific Integrated Circuits (ASICs), Field Programmable Gate Array (FPGAs) circuits, any other type of integrated circuit (IC), a state machine, and the like. The processor 1 18 may perform signal coding, data processing, power control, input/output processing, and/or any other functionality that enables the WTRU 102 to operate in a wireless environment. The processor 1 18 may be coupled to the transceiver 120, which may be coupled to the

transmit/receive element 122. While FIG. IB depicts the processor 1 18 and the transceiver 120 as separate components, it may be appreciated that the processor 1 18 and the transceiver 120 may be integrated together in an electronic package or chip.

[0037] The transmit/receive element 122 may be configured to transmit signals to, or receive signals from, a base station (e.g., the base station 114a) over the air interface 1 15/1 16/117. For example, in one embodiment, the transmit/receive element 122 may be an antenna configured to transmit and/or receive RF signals. In another embodiment, the transmit/receive element 122 may be an emitter/detector configured to transmit and/or receive IR, UV, or visible light signals, for example. In yet another embodiment, the transmit/receive element 122 may be configured to transmit and receive both RF and light signals. It will be appreciated that the transmit/receive element 122 may be configured to transmit and/or receive any combination of wireless signals.

[0038] In addition, although the transmit/receive element 122 is depicted in FIG. IB as a single element, the WTRU 102 may include any number of transmit/receive elements 122. More specifically, the WTRU 102 may employ MIMO technology. Thus, in one embodiment, the

WTRU 102 may include two or more transmit/receive elements 122 (e.g., multiple antennas) for transmitting and receiving wireless signals over the air interface 1 15/116/117.

[0039] The transceiver 120 may be configured to modulate the signals that are to be transmitted by the transmit/receive element 122 and to demodulate the signals that are received by the transmit/receive element 122. As noted above, the WTRU 102 may have multi-mode capabilities. Thus, the transceiver 120 may include multiple transceivers for enabling the WTRU

102 to communicate via multiple RATs, such as UTRA and IEEE 802.1 1, for example.

[0040] The processor 118 of the WTRU 102 may be coupled to, and may receive user input data from, the speaker/microphone 124, the keypad 126, and/or the display/touchpad 128 (e.g., a liquid crystal display (LCD) display unit or organic light-emitting diode (OLED) display unit).

The processor 118 may also output user data to the speaker/microphone 124, the keypad 126, and/or the display/touchpad 128. In addition, the processor 1 18 may access information from, and store data in, any type of suitable memory, such as the non-removable memory 130 and/or the removable memory 132. The non-removable memory 130 may include random-access memory (RAM), read-only memory (ROM), a hard disk, or any other type of memory storage device. The removable memory 132 may include a subscriber identity module (SIM) card, a memory stick, a secure digital (SD) memory card, and the like. In other embodiments, the processor 118 may access information from, and store data in, memory that is not physically located on the WTRU 102, such as on a server or a home computer (not shown). [0041] The processor 1 18 may receive power from the power source 134, and may be configured to distribute and/or control the power to the other components in the WTRU 102. The power source 134 may be any suitable device for powering the WTRU 102. For example, the power source 134 may include one or more dry cell batteries (e.g., nickel-cadmium ( iCd), nickel-zinc (NiZn), nickel metal hydride (NiMH), lithium-ion (Li-ion), etc.), solar cells, fuel cells, and the like.

[0042] The processor 1 18 may also be coupled to the GPS chipset 136, which may be configured to provide location information (e.g., longitude and latitude) regarding the current location of the WTRU 102. In addition to, or in lieu of, the information from the GPS chipset 136, the WTRU

102 may receive location information over the air interface 115/1 16/1 17 from a base station (e.g., base stations 1 14a, 114b) and/or determine its location based on the timing of the signals being received from two or more nearby base stations. It will be appreciated that the WTRU 102 may acquire location information by way of any suitable location-determination method while remaining consistent with an embodiment.

[0043] The processor 1 18 may further be coupled to other peripherals 138, which may include one or more software and/or hardware modules that provide additional features, functionality and/or wired or wireless connectivity. For example, the peripherals 138 may include an accelerometer, an e-compass, a satellite transceiver, a digital camera (for photographs or video), a universal serial bus (USB) port, a vibration device, a television transceiver, a hands free headset, a Bluetooth® module, a frequency modulated (FM) radio unit, a digital music player, a media player, a video game player module, an Internet browser, and the like.

[0044] FIG. 1C depicts a system diagram of the RAN 103 and the core network 106 according to an embodiment. As noted above, the RAN 103 may employ a UTRA radio technology to communicate with the WTRUs 102a, 102b, and/or 102c over the air interface 1 15. The RAN

103 may also be in communication with the core network 106. As shown in FIG. 1C, the RAN 103 may include Node-Bs 140a, 140b, and/or 140c, which may each include one or more transceivers for communicating with the WTRUs 102a, 102b, and/or 102c over the air interface 1 15. The Node-Bs 140a, 140b, and/or 140c may each be associated with a particular cell (not shown) within the RAN 103. The RAN 103 may also include RNCs 142a and/or 142b. It will be appreciated that the RAN 103 may include any number of Node-Bs and RNCs while remaining consistent with an embodiment.

[0045] As shown in FIG. 1C, the Node-Bs 140a and/or 140b may be in communication with the

RNC 142a. Additionally, the Node-B 140c may be in communication with the RNC142b. The

Node-Bs 140a, 140b, and/or 140c may communicate with the respective RNCs 142a, 142b via an Iub interface. The RNCs 142a, 142b may be in communication with one another via an Iur interface. Each of the RNCs 142a, 142b may be configured to control the respective Node-Bs 140a, 140b, and/or 140c to which it is connected. In addition, each of the RNCs 142a, 142b may be configured to carry out or support other functionality, such as outer loop power control, load control, admission control, packet scheduling, handover control, macrodiversity, security functions, data encryption, and the like.

[0046] The core network 106 shown in FIG. 1C may include a media gateway (MGW) 144, a mobile switching center (MSC) 146, a serving GPRS support node (SGSN) 148, and/or a gateway GPRS support node (GGSN) 150. While each of the foregoing elements are depicted as part of the core network 106, it will be appreciated that any one of these elements may be owned and/or operated by an entity other than the core network operator.

[0047] The RNC 142a in the RAN 103 may be connected to the MSC 146 in the core network 106 via an IuCS interface. The MSC 146 may be connected to the MGW 144. The MSC 146 and the MGW 144 may provide the WTRUs 102a, 102b, and/or 102c with access to circuit- switched networks, such as the PSTN 108, to facilitate communications between the WTRUs 102a, 102b, and/or 102c and traditional land-line communications devices.

[0048] The RNC 142a in the RAN 103 may also be connected to the SGSN 148 in the core network 106 via an IuPS interface. The SGSN 148 may be connected to the GGSN 150. The SGSN 148 and the GGSN 150 may provide the WTRUs 102a, 102b, and/or 102c with access to packet-switched networks, such as the Internet 110, to facilitate communications between and the WTRUs 102a, 102b, and/or 102c and IP-enabled devices.

[0049] As noted above, the core network 106 may also be connected to the networks 112, which may include other wired or wireless networks that are owned and/or operated by other service providers.

[0050] FIG. ID depicts a system diagram of the RAN 104 and the core network 107 according to an embodiment. As noted above, the RAN 104 may employ an E-UTRA radio technology to communicate with the WTRUs 102a, 102b, and/or 102c over the air interface 1 16. The RAN 104 may also be in communication with the core network 107.

[0051] The RAN 104 may include eNode-Bs 160a, 160b, and/or 160c, though it will be appreciated that the RAN 104 may include any number of eNode-Bs while remaining consistent with an embodiment. The eNode-Bs 160a, 160b, and/or 160c may each include one or more transceivers for communicating with the WTRUs 102a, 102b, and/or 102c over the air interface 1 16. In one embodiment, the eNode-Bs 160a, 160b, and/or 160c may implement MIMO technology. Thus, the eNode-B 160a, for example, may use multiple antennas to transmit wireless signals to, and receive wireless signals from, the WTRU 102a.

[0052] Each of the eNode-Bs 160a, 160b, and/or 160c may be associated with a particular cell (not shown) and may be configured to handle radio resource management decisions, handover decisions, scheduling of users in the uplink and/or downlink, and the like. As shown in FIG. ID, the eNode-Bs 160a, 160b, and/or 160c may communicate with one another over an X2 interface.

[0053] The core network 107 shown in FIG. ID may include a mobility management gateway (MME) 162, a serving gateway 164, and a packet data network (PDN) gateway 166. While each of the foregoing elements are depicted as part of the core network 107, it will be appreciated that any one of these elements may be owned and/or operated by an entity other than the core network operator.

[0054] The MME 162 may be connected to each of the eNode-Bs 160a, 160b, and/or 160c in the RAN 104 via an S I interface and may serve as a control node. For example, the MME 162 may be responsible for authenticating users of the WTRUs 102a, 102b, and/or 102c, bearer activation/deactivation, selecting a particular serving gateway during an initial attach of the WTRUs 102a, 102b, and/or 102c, and the like. The MME 162 may also provide a control plane function for switching between the RAN 104 and other RANs (not shown) that employ other radio technologies, such as GSM or WCDMA.

[0055] The serving gateway 164 may be connected to each of the eNode-Bs 160a, 160b, and/or 160c in the RAN 104 via the SI interface. The serving gateway 164 may generally route and forward user data packets to/from the WTRUs 102a, 102b, and/or 102c. The serving gateway 164 may also perform other functions, such as anchoring user planes during inter-eNode B handovers, triggering paging when downlink data is available for the WTRUs 102a, 102b, and/or 102c, managing and storing contexts of the WTRUs 102a, 102b, and/or 102c, and the like.

[0056] The serving gateway 164 may also be connected to the PDN gateway 166, which may provide the WTRUs 102a, 102b, and/or 102c with access to packet-switched networks, such as the Internet 110, to facilitate communications between the WTRUs 102a, 102b, and/or 102c and IP-enabled devices.

[0057] The core network 107 may facilitate communications with other networks. For example, the core network 107 may provide the WTRUs 102a, 102b, and/or 102c with access to circuit- switched networks, such as the PSTN 108, to facilitate communications between the WTRUs 102a, 102b, and/or 102c and traditional land-line communications devices. For example, the core network 107 may include, or may communicate with, an IP gateway (e.g., an IP multimedia subsystem (IMS) server) that serves as an interface between the core network 107 and the PSTN 108. In addition, the core network 107 may provide the WTRUs 102a, 102b, and/or 102c with access to the networks 1 12, which may include other wired or wireless networks that are owned and/or operated by other service providers.

[0058] FIG. IE depicts a system diagram of the RAN 105 and the core network 109 according to an embodiment. The RAN 105 may be an access service network (ASN) that employs IEEE 802.16 radio technology to communicate with the WTRUs 102a, 102b, and/or 102c over the air interface 117. As will be further discussed below, the communication links between the different functional entities of the WTRUs 102a, 102b, and/or 102c, the RAN 105, and the core network 109 may be defined as reference points.

[0059] As shown in FIG. IE, the RAN 105 may include base stations 180a, 180b, and/or 180c, and an ASN gateway 182, though it will be appreciated that the RAN 105 may include any number of base stations and ASN gateways while remaining consistent with an embodiment. The base stations 180a, 180b, and/or 180c may each be associated with a particular cell (not shown) in the RAN 105 and may each include one or more transceivers for communicating with the WTRUs 102a, 102b, and/or 102c over the air interface 117. In one embodiment, the base stations 180a, 180b, and/or 180c may implement MIMO technology. Thus, the base station 180a, for example, may use multiple antennas to transmit wireless signals to, and receive wireless signals from, the WTRU 102a. The base stations 180a, 180b, and/or 180c may also provide mobility management functions, such as handoff triggering, tunnel establishment, radio resource management, traffic classification, quality of service (QoS) policy enforcement, and the like. The ASN gateway 182 may serve as a traffic aggregation point and may be responsible for paging, caching of subscriber profiles, routing to the core network 109, and the like.

[0060] The air interface 1 17 between the WTRUs 102a, 102b, and/or 102c and the RAN 105 may be defined as an Rl reference point that implements the IEEE 802.16 specification. In addition, each of the WTRUs 102a, 102b, and/or 102c may establish a logical interface (not shown) with the core network 109. The logical interface between the WTRUs 102a, 102b, and/or 102c and the core network 109 may be defined as an R2 reference point, which may be used for authentication, authorization, IP host configuration management, and/or mobility management.

[0061] The communication link between each of the base stations 180a, 180b, and/or 180c may be defined as an R8 reference point that includes protocols for facilitating WTRU handovers and the transfer of data between base stations. The communication link between the base stations 180a, 180b, and/or 180c and the ASN gateway 182 may be defined as an R6 reference point. The R6 reference point may include protocols for facilitating mobility management based on mobility events associated with each of the WTRUs 102a, 102b, and/or 102c.

[0062] As shown in FIG. IE, the RAN 105 may be connected to the core network 109. The communication link between the RAN 105 and the core network 109 may defined as an R3 reference point that includes protocols for facilitating data transfer and mobility management capabilities, for example. The core network 109 may include a mobile IP home agent (MIP-HA) 184, an authentication, authorization, accounting (AAA) server 186, and a gateway 188. While each of the foregoing elements are depicted as part of the core network 109, it will be appreciated that any one of these elements may be owned and/or operated by an entity other than the core network operator.

[0063] The MIP-HA may be responsible for IP address management, and may enable the WTRUs 102a, 102b, and/or 102c to roam between different ASNs and/or different core networks. The MIP-HA 184 may provide the WTRUs 102a, 102b, and/or 102c with access to packet-switched networks, such as the Internet 110, to facilitate communications between the WTRUs 102a, 102b, and/or 102c and IP-enabled devices. The AAA server 186 may be responsible for user authentication and for supporting user services. The gateway 188 may facilitate interworking with other networks. For example, the gateway 188 may provide the WTRUs 102a, 102b, and/or 102c with access to circuit-switched networks, such as the PSTN 108, to facilitate communications between the WTRUs 102a, 102b, and/or 102c and traditional land-line communications devices. In addition, the gateway 188 may provide the WTRUs 102a, 102b, and/or 102c with access to the networks 112, which may include other wired or wireless networks that are owned and/or operated by other service providers.

[0064] Although not shown in FIG. IE, it should, may, and/or will be appreciated that the RAN 105 may be connected to other ASNs and the core network 109 may be connected to other core networks. The communication link between the RAN 105 the other ASNs may be defined as an R4 reference point, which may include protocols for coordinating the mobility of the WTRUs 102a, 102b, and/or 102c between the RAN 105 and the other ASNs. The communication link between the core network 109 and the other core networks may be defined as an R5 reference, which may include protocols for facilitating interworking between home core networks and visited core networks.

[0065] Embodiments recognize that current deployments of cellular systems may be facing the

"bandwidth crunch" caused by the increasing demand for high data rate applications. To alleviate the "bandwidth crunch," cloud radio access networks may be used where a baseband processing of base stations (BSs) may be migrated to or integrated into a central unit in a "cloud" or the Internet to which the BSs may be connected via backhaul links such that an effective implementation of network MIMO that may simplifying the deployment and management of BSs and may reduce BS energy consumption may be enabled. On the uplink of a cloud radio access network, the BSs may operate as terminals that may relay "soft" information to a cloud decoder regarding received baseband signals. Perhaps since the signals received at different BSs may be correlated, among other reasons, distributed source coding strategies may be used.

Embodiments recognize that the performance of distributed source coding may be sensitive to imperfections in received signals that may be compressed. Embodiments also recognize an efficient operation of the cloud that may include portions of radio access networks may include a parsimonious use of base stations whose energy consumption tends to be among relevant contributions to the overall energy expenditure for the networks.

[0066] To alleviate the "bandwidth crunch," cloud radio access networks may be used where a baseband processing of base stations (BSs) may be migrated to or integrated into a central unit in a "cloud" or the Internet to which the BSs may be connected via backhaul links such that an effective implementation of network MIMO that may simplify the deployment and management of BSs and may reduce BS energy consumption may be enabled.

[0067] On the uplink of a cloud radio access network, the BSs may operate as terminals that may relay "soft" information to a cloud decoder regarding received baseband signals. Since the signals received at different BSs may be correlated, distributed source coding strategies may be used. Unfortunately, the performance of distributed source coding tends to be sensitive to imperfections in received signals that may be compressed. Additionally, an efficient operation of the cloud that may include portions of radio access networks tends to include a parsimonious use of base stations whose energy consumption tends to be among relevant contributions to the overall energy expenditure for the networks.

[0068] As described herein, systems and/or methods for distributed source coding and compression schemes (e.g. that may use correlation between received signals at different base stations (BSs)) for an uplink of a cloud radio access network where multiple multi-antenna base stations (BSs) may be connected to a central unit (e.g. a cloud de-coder as shown in FIG. 2) via capacity -constrained backhaul links may be extended to include scheduling (e.g. BS scheduling). In such scenarios, for example, a number of active base stations (BSs) may be reduced and, thus, may improve or enhance the energy efficiency of the mobile network. Such systems and/or methods may include an optimization problem that may be formulated where compression and scheduling may be performed jointly by introducing a sparsity-inducing term into an objective function. Additionally or alternatively, such systems and/or methods may provide an iterative method or algorithm that may be used to converge to a locally optimal point.

[0069] As described herein, distributed compression (e.g. compression with distributed source coding in the presence of multi-antenna BSs by focusing on robustness and efficiency) for an uplink of a cloud radio access network where multiple multi-antenna base stations (BSs) may be connected to a central unit (e.g. a cloud de-coder as shown in FIG. 2) via capacity-constrained backhaul links may be provided. Since the signals that may be received at different BSs may be correlated, distributed source coding strategies may be potentially beneficial and may be implemented via sequential source coding with side information. For compression with side information, available compression strategies based on the criteria of maximizing an achievable rate or minimizing a mean square error may be used. In either case, one or more, or each BS may use information about a specific covariance matrix to realize an advantage of distributed source coding. Since such a covariance matrix may depend on channel realizations

corresponding to other BSs, among other reasons, a robust compression method may be provided and/or used in which the information about the covariance available at each BS may be imperfect, for example. In some embodiments, such a method may be formulated using a deterministic worst-case approach and scheme may be provided and/or used that may achieve a stationary point.

[0070] According to an example embodiment, the systems and/or methods disclosed herein may be applicable to and used with a UE, an eNB, a Het-Nets, Remote Radio Heads, across L1-L2, and the like. Additionally, the same notation for probability mass functions (pmfs) and probability density functions (pdfs), namely p(x) represents the distribution, pmf or pdf, of random variable X may be used. Similar notations may also be used for joint and conditional distributions. In an example embodiment, the schemes, equations, and/or algorithms disclosed herein may be in base two (e.g. unless specified). Additionally, given a vector x = [x _\ , x ₂ .., x _n ] ^T , xs for a subset S G {I, 2, n} may be defined as the vector including, in arbitrary order, entries Xi with i S. Notation∑ _x may also be used for the correlation matrix of random vector x, i.e.,∑ _x = and∑ _x | _y may represent the "conditional" correlation matrix of x given y, namely∑ _x | _y =∑ _x - ΣηΣ^'Σ^. In an embodiment, notation H" may represent the set of n n Hermitian matrices. [0071] A system model may be provided and/or used as described herein. For example, a cluster of cells that may include a total number B of BSs, one or more, or each, being either a MBS or a HBS, may be provided and/or used (e.g. as shown in FIG. 2). M active MSs may also be provided and/or used. FIG. 2 depicts an example embodiment of an uplink of a cloud radio access network with one or more base stations (BSs) such Home BSs (HBSs) and Macro BSs (MBSs). In one or more embodiments, the set of BSs may be denoted as N _B = {1, NB}. Additionally, one or more, or each, z ^' th BS may be connected to the cloud decoder via a finite- capacity link of capacity Q and may have ΠΒ _, Ι antennas, while one or more, or each MS may have w¾i antennas. Embodiments disclosed herein may be illustrated or shown with respect to the uplink as an example.

[0072] Defining ¾ as the ΠΒ _, Ι ^X « J channel matrix between the y ^' th MS and the z ^' th BS, the overall channel matrix toward BS i may be given as the ΠΒ, _Ϊ ^X « matrix

H, = [H ₍₁ - H _iM ]. (1)

[0073] If the NM MSS in a cluster may be synchronous, at a discrete-time channel use (c.u.) of a given time-slot, the signal received by the z ^' th BS may be given by y _« = Η,·χ + ζ _ί . (2)

In (2), the vector x ··· XNM'V may be the « ^x 1, and may be a vector of symbols transmitted by the MSs in the cluster (e.g. the particular cluster). The noise vectors z _z - may be independent over i and may be distributed as z _z - ~ CN (0, I), for i€ {I, NB}. In one or more embodiments, the noise covariance matrix may be selected as an identity without loss of generality, as the received signal may be whitened by the BSs. Additionally or

alternatively, the channel matrix ¾ may be constant in each time-slot.

[0074] Using standard random coding arguments, the coding strategies that may be employed by the MSs in each time-slot may entail and/or use a distribution p(x) on the transmitted signals that may factorize as

(3) since the signals that may be sent by different MSs may be independent.

[0075] According to an example embodiment, the distribution /?(x _; ) may represent (e.g. in a compact way) parameters of the modulation and channel coding scheme adopted such as constellation, transmission power, beamforming vs. space-time coding, distance between the codewords, and the like. The signals x may be discrete (e.g. taken from a discrete constellation). For example, if -QAM signals may be transmitted, signal x _; may take discrete values from a

M -QAM constellation that may be denoted by 6 _M . When particular (e.g. good) channel codes may be used such as a turbo code or low-density parity check (LDPC) codes, the distribution p( i ) may be approximated by a Gaussian distribution if communication may take place over a

Gaussian channels. In an embodiment, the distribution ρ(χΐ) of the signal that may be transmitted by the ith MS may be given as x _z - ~ CN (0,∑ _Xi - ) for a given covariance matrix∑ _xi .

[0076] The BSs may communicate with the cloud by providing, for example, the cloud with soft information derived from the received signal. In one or more embodiments, compression strategies that may not involve the BSs knowing one or more codebooks such as a constellation set, MCS level, and the like may be provided, used, and/or employed by the MSs. Using conventional rate-distortion theory, a compression strategy for the ith BS may be provided and/or defined by a test channel p(yi \y{) that may describe the relationship between the signal to be compressed, namely y _i; and its description y _t to be communicated to the cloud.

[0077] As described herein (e.g.in Lemma 2), each BS i may apply linear transformation A _; to the received signal y _; (e.g. first) and may then perform component-wise quantization to the linear transformation output A _l y _l to obtain a point in the predefined quantization codebook ^ .

BS i may then send the index associated with the resulting point in the codebook ^ to the cloud decoder via the backhaul link of capacity C _t . The quantization effect may be equivalently modeled by adding Gaussian noise q _; according to an embodiment. Moreover, the correlation matrix of such noise may be an identity matrix since component-wise quantization may be provided and/or used. The resolution of the quantization codebook may be controlled by adjusting the linear transform matrix A _; . According to example embodiments, matrix A _; may include A _; . = diag(« ₁ ,· · ·, α )U ^† where unitary matrix U may play a role of producing conditionally uncorrected output elements (e.g. also called conditional KLT) and the resolution of each compression output element may be controlled via diagonal matrix diag(« _j , · · · , « ) , which may mean that if a, > a _m (I≠ m e {1, ... , n _{B i} } ) , the / th element may be compressed with resolution better than the m th element. According to an embodiment, such compression may be limited to Q bits per received symbol. As such, the size of quantization codebook may satisfy \&\.≤ C _; . The cloud may decode jointly the signals x of the MSs based on the descriptions y _t for i E N _B . From standard information-theoretic considerations, the achievable sum-rate may be given by

(4) I? _s¾rfi = i(x; y _A¾ ).

[0078] Once the linear transform matrices A _; for i e V _M may be determined, the sum-rate metric (e.g. mutual information Ι(χ;γ^ ) ) may then be computed as a function of system parameters such as SNR, input distribution p(x) and/or channel matrices H _; together (perhaps in some embodiments) with the linear transformer A _; for i e V _M . From the resulting sum-rate, the size of codebooks adopted by the MSs may be determined (e.g. perhaps assuming successive decoding at the cloud decoder in one or more embodiments).

[0079] Since the signals y _z - that may be measured by different BSs may be correlated, distributed source coding schemes or techniques may have the potential to improve the quality of the descriptions y _t . Specifically, given compression test channels p(y ^~ i the descriptions y _t may be recovered at the cloud if or when the capacities d may satisfy the following conditions

(5)

where <S = J\f _B — S, According to example embodiments, s may include each ; with i £ S and similarly for Ys and $¾ ·

[0080] FIG. 5 depicts an example of a technique (e.g. that may provide and/or use Algorithm 1) for providing an uplink with compression at a base station (BS). As shown in FIG. 5, at 8002, channel information may be received and/or acquired. An order for one or more BSs may be determine for compression at 8004. At 8006, correlation matrices may be reported or provided and, at 8008, compression strategies or schemes may be determined (e.g. a test channel may be computed). Rate control may be performed at 8010 (e.g. a sum-rate may be computed, a codebook may be determined, and/or a codebook index may be provided or reported). At 8012, uplink

communications may be provided (e.g. a signal may be generated from the codebook and a signal correlated may be provided and/or received). At 8014, a compression may be performed (e.g. a signal such as received signal may be compressed based on a test channel). At 8016, decoding may be performed (e.g. a signal that may be generated based on the codebook may be decoded (e.g. jointly) based on, for example, the descriptor or the compressed signal).

[0081] In one or more embodiments, the sum-rate may be maximized as described herein. For example, a greedy approach may be used for maximizing the sum-rate (4). Such a greedy approach may be part of a compression method such as, at 8004 (e.g. for BS ordering for compression) and, at 8008 (for compression strategies), in FIG. 5.

[0082] The sum-rate (4) may be maximized under the constraints (5). For example, if a search may be restricted to the vertices of the rate region (5), a solution (e.g. a suboptimal solution) may be obtained by solving the problem maximize i ^' (x: ^' ,¾ ;. }

(V)

J oralis

(6) where the optimization may be subject to the constraints (6) and the optimization space may include the BS permutation π.

[0083] In some embodiments, the problem (7) may still be complex. As such scenarios, a greedy approach in Algorithm 1 may be used on or applied to the selection of the permutation π while optimizing the test channels p(y _£ \y _t ) at one or more, or each, phase of the greedy approach or algorithm. The greedy algorithm may be based on the chain rule for the mutual information that may enable or allow the sum-rate (4) to be written as

(8)

for a permutation π of the set {I, NB} . AS a result of the algorithm, a permutation π* may be obtained and may be feasible (e.g. in the sense of satisfying constraint (5)) test channels V ^* (yAyd- In one or more embodiments, the compression based on (9) in Algorithm 1 may be referred to as Max-Rate compression, for example.

[0084] The implementation of the greedy algorithm in Algorithm 1 may solve the problem (9) for one or more, or each, z ^' th BS for a given order π. Additionally, problem (9) may be solved at the cloud decoder, which may then communicate the result to the z ^' th BS. As described herein, in such embodiments, the cloud center may know the channel matrices Hi, Ϊ=1 ,...,Ν _Β . Alternatively or additionally, once the order π may be fixed by the cloud, problem (9) may be solved at one or more, or each, z ^' th BS. In such embodiments, the cloud may communicate some information to one or more, or each, BS, for example, as described herein.

[0085] In one or more embodiments, the max-rate or maximized sum-rate may be compressed as described herein. The solution to problem (9) of optimizing the compression test channel p( ; |y;) at the z ^' th BS under the assumption that the cloud decoder has side information y _s with S = (π(\), . . . , π(ί - I)} may be provided. The random vectors involved in problem (9) may satisfy the Markov chain y _s <→ x <→ y _z - <→ y _i

[0086] Algorithm 1 or the greedy approach to the selection of the ordering π and the test channels P(9i \yd ^ma Y be provided or defined as follows. First, a set S may be initialized to be an empty set, i.e., 5^ ⁰⁾ = 0 . Then, for / = 1, . . . , Ng, the following may be performed.

[0087] One or more, or each ith BS with i G ΝΒ - S may evaluate a test channel <Pl< ^' * 13 ^{' ¾} ) by solving the problem maximize J(x;

(9)

[0088] In one or more embodiments, an optimal value of such a problem may be denoted as φ*ι and an optimal test channel as P $> |y*)* Then, the BS i G ΝΒ - S with the largest optimal value may be chosen and may be added to the set S such as S^ = S^ ^_1) U fij and set n*(j) = i.

[0089] In one or more embodiments, compression techniques and/or schemes based on MMSE compression may be provided and/or used. For example, based on a Gaussian input vector x, the optimal test channel p(y _t \y ) for problem (9) may be given by a Gaussian distribution as stated in the following lemma (e.g. Lemma 2). For a Gaussian distributed x, the optimal test channel

PCji lJi) ^ma Y be characterized as where A _z - may be a matrix to be calculated and q _; - — CN (0, I) may be the compression noise, which may be independent of x and z,. Moreover, defining Ω _; - = problem (9) may be restated as maximize £· ( Hi )— loedet (I ÷ Ω. _; ) s.t. _, / _; (f _t ) < .

(1 1) where the function^ (Ω _; ) may be defined as fi (O, $ = 1ο¾ ^· det. f I ÷ O, fH,-∑ _ii ,.H ÷ i )

\ v ^■ · " ' ^■ / ./· ( 1 2 ) and

∑ _x ^ _; , =s∑ _x. -∑ _x ¾ (¾∑ _x i¾ 4- H _ts ) ^' ¾∑ _z .

(13)

In one or more embodiments, H _; = A _; H _; and∑ _t = A _; A† + 1 .

[0090] With compression model (10), at the it stage in the greedy algorithm, the side information y _s available to the cloud decoder may be given as

where ί _π{]) = _{π(] π{])} + fory = 1, - , i - 1.

[0091] In one or more embodiments, minimum mean squared error (MMSE) compression may be provided and/or used. For example, MSE based approaches for problem (9) may be provided and/or used. Specifically, techniques that may aim at minimizing the MSE or minimum MSE (MMSE) techniques may be provided. In some embodiments, the MMSE techniques may differ from the Max-rate compression in the criterion of optimizing test channels (and perhaps in some embodiments only so). As a result, the greedy algorithm in Algorithm 1 may be operated with the MMSE compressions and the difference from the Max-Rate may lie on the fact that problem (9) may be replaced with a problem with MMSE criterion as described herein.

[0092] In one or more embodiments, direct MMSE with no side information (NSI) may be provided and/or used. For example, in some scenarios, compression may be done or performed with the aim of minimizing the MSE on the received signal y _z - and neglecting the fact that the cloud decoder may have side information y _s . This may lead to the following compression criterion: minimize Β|||< — V; j j ~ i

(17)

where g(-) may be a function such as a MMSE estimate that may be affected at the decoder's side. In one or more embodiemnts, the constraint in problem (17) may involve mutual information that may not be conditioned on y _s as the side information at the cloud may not be leveraged.

[0093] In one or more embodiments, indirect MMSE with no side information (NSI) may be provided and/or used. For example, a compression (e.g. a potentially better compression) may be obtained by accounting for the fact that the cloud may be interested in recovering x and not y _; -, and thus using the MMSE criterion miiiiiiiize X

(18)

si. / ί v · ^■ ν · 5

where function g(-) may have the same interpretation as previously described. This strategy may be "indirect" MMSE since it may compress yi but with the goal of providing a description of x, which may not be directly measured at the BSs.

[0094] By leveraging the side information y _s , which for example may be available at the cloud decoder, improved versions of the direct and/or indirect MMSE strategies discussed above may be obtained. The side information y _s may be used for various purposes such as to reduce the compression rate from I(y , y _t ) to I(y , yt \y _s ) and/or to obtain the final estimate at the cloud decoder as a function (y;, ) of both the description y _t and the side information y _s .

[0095] In one or more embodiments, direct MMSE with side information (SI) may be provided and/or used. For example, the direct MMSE method that may leverage side information may lead to the criterion minimize

(19)

[0096] Alternatively or additionally, indirect MMSE with side information (SI) may be provided and/or used. For example, the indirect MMSE method may lead to the criterion minimize Ej

[0097] For example, in a proposition (e.g. proposition 2) , the optimal compression for the MMSE criteria listed above may be given as (10) with Aj such that . _i = AjAi and n _t = P ^f _i Udiag(a ₁ , ... , ^ϋ^Ρι

(21)

where P; = I for direct methods and P; =∑ _xyj ∑ _y ^~ for indirect methods (where∑ _xy . =∑ _X H. ) and ∑ _y . = Hi∑ _x H^ + 1. The columns of matrix U may be the eigenvectors of covariance matrices ∑ . = + I)P for the NSI and SI case, respectively, corresponding to the ordered eigenvalues λ _χ ≥...≥ _ng ., and

1 1 -+

a,

where μ may be such that the condition log(l + = C _t may be satisfied.

[0098] In an embodiment, the proof of the proposition (e.g. proposition 2) and/or the support for the proposition may follow by conditional KLT results.

[0099] In one or more embodiments as described herein, robust optimal compression may be provided and/or used. For example, as described above, the optimal compression resulting from the solution of problem (9) at the z ^' th BS may depend on the covariance matrix∑ _x \y _s in (13) of the vector of transmitted signals that may be conditioned on the compressed version y _s of the signals received by the BSs in set 5 ^* . The y _s may be available at the cloud decoder. In general, it may not be realistic to assume that matrix∑ _x \y _s may be known (e.g. perfectly known) at the z ^' th BS as it may depend on the channel matrices of all BSs in the set S (e.g. as shown in (13)). As such, a robust version of the optimization problem (9) may be provided and/or used by assuming that the z ^' th BS may have an estimate of matrix∑ _x \y _s that may be related to the actual matrix∑ _x \y _s as v — Y: , . - A -

(23) where £ Ή" ^{Μ ma} y be a deterministic Hermitian matrix that may model the estimation error. According to an embodiment, the error matrix Δ ₅ may belong (e.g. may be known to belong to) a set ¾i ^: ίΞ H. ^I,M , which may model the uncertainty at the z ^' th BS regarding matrix∑ _x \ _ys .

[0100] In some embodiments, perhaps to define the uncertainty set U _A , among other reasons, one or more bounds may be imposed on given measures of the eigenvalues and/or eigenvectors of matrix Δ ₅ . Based on the observation that the mutual information / ( ;yj|ys) in (1 1) may be written as i = fi(«i.2 _X| ¾) - io _g det(i + n _; ) ,

(24)

where f^, A _x]ys ) = log det (i + Ω,(Η, Ϊ^Η; ^† + A _x]ys + /)) ,

and Δ ₅ = Η,-ύ^Η, ^† , the uncertainty may be bounded on the eigenvalues of A _x y _s ■ [0101] This may be equivalent to bounding, within some constant, a norm of matrix A _x \y _s . Specifically, in an embodiment, the uncertainty set UA may be defined as the set of Hermitian matrices l _{x 9s} such that conditions _min (2 _¾|¾ )≥ _LB and A _max (¾ _|¾ ) < λ _υΒ of Δ _χ ^ ₅ may hold for given lower and upper bounds ( _LB , λ _υΒ ) on the eigenvalues of matrix A _x $ _s .

[0102] In such embodiments (e.g. under this model), the problem of deriving the optimal robust compression strategy may be formulated as

max _{n >} o min _{2 eH} nM f^, Δ ) - log det(I + Ω _; ) , (26) such that

fifoi _> A _x \y _s )≤ C;, λ,ηΐη Δχβ _ς ≥ _LB , and h _max (A _x \ ^) < λ _υΒ .

[0103] In some embodiments, problem (26) may not be convex and a closed-form solution may be prohibitive. The next theorem derives a solution to the KKT conditions for problem (26), which may be referred to as a stationary point.

[0104] For example, in a theorem (e.g. Theorem 1), a stationary point for problem (26) may be found as (10) with matrix Ai such that Ω _; = A^A, may be given as (15), where matrix U may be obtained from the eigenvalue decomposition Η, Χ,^Η, ^† + / = Udiag^ ^ ... , a _{nB i} )t/ ^† and the diagonal elements a _x , ... , a _{nB i} may be calculated by solving the following mixed integer- continuous problem

ηΒ,ί

i r \

max. a i> , a nB, - ^ log detOL + a

i=i s.t. 0 < μ < 1, a; G Ρι (μ), 1 = 1, ... , ηΒ, ί,

may be defined as ηΒ,ί

i ,

and

ηΒ,ί

i ,

with C; ^L = A; + X _LB and C; ^y = A _; + λ _υΒ ; and the discrete set Ρ _; (μ) may be defined as

with Qi and Si given as

and

[0105] One or more embodiments contemplate joint base station selection and compression (e.g., distributed compression) via sparsity-inducing optimization, which may be provided and/or used as described herein. For example, to operate the network efficiently, a subset S ^NB of the Ng available BSs may communicate to the cloud decoder in a given time-slot. Such embodiments may be used, for example, when different BSs may share the same backhaul resources or energy consumption and green networking may be important. As such (e.g. under such an assumption), the system design may provide and/or entail a choice of the subset S, along with that of the

compression test channels p(y _t \y _t ) for i £ S. In one or more embodiments, such a BS selection may use an exhaustive search of exponential complexity in the number Ng of BSs. As such, in some embodiments, an efficient approach based on the addition of a sparsity-inducing term to an objective function may be provided and/or used.

[0106] For example, a cost q _t per spectral unit resource (e.g. per discrete-time channel use) may be associated to the z ^' th BS. This may measure the relative cost per spectral resource of activating the z ^' th BS over the revenue per bit. To fix the ideas, a single cell with one MBS and Ns - 1 HBSs as shown FIG. 3 may be provided and/or used. The HBSs (e.g. shown) may share the same total backhaul capacity CR to the cloud decoder, as may be the embodiment if the HBSs may communicate to the cloud decoder via a shared wireless link. If or when the MBS may be active, a subset of the HBSs may be scheduled, for example, to provide additional information y _sH * to the cloud decoder under the given total backhaul constraint CR- In one or more embodiments, the solution proposed herein may also be generalized to more complex systems with multiple cells.

[0107] In one or more embodiments, SM = and ¾ = {2, . . . , NB} may denote the set that may include the MBS and the HBSs, respectively. If or when the Gaussian test channel (10) may be employed at each z ^' th BS with a given covariance matrix Ω _; 0, the joint problem of HBS selection and compression via sparsity -inducing optimization may be formulated as —· - >· (34) maximize / (xi ys^ j i)— ¾s / . > 0) s.t. I (ysu -. fsn lfx )≤ i, where 1(·) may be the indicator function that may take a 1 if the argument state may be true and 0 otherwise, and ¾¾ = . . . = qm = qn for simplicity. In (34), y _t may be conditioned, for example, to account for the fact that the MBS may be active. According to an embodiment, the second term in the objective of problem (34) may be the -norm of vector [ tr(0 ₂ ) ··· ti Av _® ) ]· If the cost qii may be large enough, this term may force the solution to set some of the matrices Ω; to zero, thus keeping the corresponding z ^' th HBS inactive. To avoid the non-smoothness induced by the -norm, problem (34) may be modified by replacing the ^ ₀ -norm with the l _\ - norm of the same vector. Problem (34) may, thus, be reformulated as follows: maxmux i ^' n.... {35)

where f Q _{2 L} ... , Ω _ΝΒ = I .x; % _H - [0108] Based on such a formulation, a two-phase approach to the problem of joint HBS selection and compression may be provided and/or used (e.g. as shown in Algorithm 2). For example, in a first phase, a block-coordinate ascent algorithm may be executed to address problem (35). As a result, a subset ¾* of HBSs with nonzero Ω _; - may be obtained. In the second phase, the block-coordinate ascent algorithm may be run on the subset ¾* by setting Ω _; - = 0 for all i€/ ¾* and qn = 0. In some embodiments, the second phase may be used to refine the test channels obtained in the first phase. This two-phase algorithm for joint HBS selection and compression may be used with an overall communications flow, for example, as shown in FIG. 4 (e.g. at 6004 for HBS selection and at 6006 for compression strategies).

[0109] For example, the two-phase joint HBS selection and compression algorithm (e.g. Algorithm 2) may include or perform the following. In phase 1, problem (35) may be solved or computed via the block-coordinate ascent algorithm. For example, n = 0 and Ω ₂ ⁽ - ^Η ... , ΩΝΒ^ ⁼ 0 may be initialized. For i = 2,.. . , B, may be updated as a solution of the following problem.

[0110] In one or more embodiments, the foregoing (e.g. updating Ω^ ^Η ') may be repeated if convergence criterion may not be satisfied and otherwise may be stopped (e.g. the algorithm may be terminated). Once the algorithm may be terminated, the obtained Ω _; may be denoted as Ω; ^* for i=2,... ,NB, and ¾ = {i £ S _H : ₂ *≠ 0} may be set.

[011 1] In a phase 2, the block-coordinate ascent algorithm may be applied to problem (35) with qn = 0 and with the HBSs in set S _H ^* .

[0112] FIG. 4 depicts an example technique (e.g. that may provide and/or use Algorithm 2) for base station (BS) selection and compression consistent with embodiments. As shown in FIG. 4, at 6002, channel information may be received and/or acquired. One or more HBSs may be selected at 6004. At 6006, compression strategies or schemes may be determined (e.g. a test channel may be computed) and, at 6008, compression test channels may be reported or sent. Rate control may then be performed at 6010 (e.g. a sum-rate may be computed, a codebook may be determined, and/or a codebook index may be provided or reported). At 6012, uplink communications may be provided (e.g. a signal may be generated from the codebook and a signal correlated may be provided and/or received). At 6014, a compression may be performed (e.g. a signal such as a received signal may be compressed based on a test channel). Then, at 6016, decoding may be performed (e.g. a signal that may be generated based on the codebook may be decoded (e.g. jointly) based, for example, descriptions or the compressed signal).

[0113] In one or more embodiments, problem (36) of a proposed algorithm (e.g. Algorithm 2) may be solved as described herein. Such a solution or embodiment may correspond to the update of Ω _; when the other variables may be fixed to the values obtained from previous iterations. The global maximum of problem (36) may be obtained as shown below (e.g. in Theorem 2).

[0114] For example (e.g. according to Theorem 2), a solution to problem (36) may be given by (10), with matrix Ai such that Ω; = A^A _j , where∑ _y = Udiag^a^ ... , a _{nB i} )t/ ^† and matrix∑, may be given as

i ^y '\ NB\{i] with R _t = I +∑x _| y ₁ ∑jeSH\{i} H _j (I + flj) ¹ nj Hj. The diagonal element a _{1 ;} ....,a _n B,i, may be obtained as ¾ = αι( *), with

for 1 = 1,...,n _B, i with q _H ' = log _e 2 . q _H . The Lagrange multiplier μ* may be obtained as follows. If hi(0) < Cj, where C _t may be given by,

(\ ... ] ₀ g R _; ... lag < (I + Π _; ) . (39) then μ* = 0; otherwise, μ* may be unique value μ > 0 such that ¾(μ) =C where ¾(μ)

=∑?f ₁ ⁱ log(l + A _i a _i ( i)) .

[0115] Although features and elements are described above in particular combinations, one of ordinary skill in the art will appreciate that each feature or element can be used alone or in any combination with the other features and elements. In addition, the methods described herein may be implemented in a computer program, software, or firmware incorporated in a computer- readable medium for execution by a computer or processor. Examples of computer-readable media include electronic signals (transmitted over wired or wireless connections) and computer- readable storage media. Examples of computer-readable storage media include, but are not limited to, a read only memory (ROM), a random access memory (RAM), a register, cache memory, semiconductor memory devices, magnetic media such as internal hard disks and removable disks, magneto-optical media, and optical media such as CD-ROM disks, and digital versatile disks (DVDs). A processor in association with software may be used to implement a radio frequency transceiver for use in a WTRU, UE, terminal, base station, RNC, or any host computer.