WO2014204544A2 - Combination of multiple precoding techniques for multicarrier modulation systems - Google Patents

Abstract

Systems, methods, and instrumentalities are disclosed to utilize a combined precoding technique in a multicarrier modulation system to reduce out-of-band power leakage. A combined precoder may be used to precede a symbol stream using a matrix-based precoding component to generate a first precoded symbol stream. The combined precoder may then be used to apply a perturbation to the first precoded symbol stream to generate a second precoded symbol stream.

Description

COMBINATION OF MULTIPLE PRECODING TECHNIQUES FOR MULTiCARRiER

MODULATION SYSTEMS

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of United States Provisional Patent Application No. 61 /806,614, filed March 29, 2013, the contents of which are hereby incorporated by reference in their entirety.

BACKGROUND

[0002] Multicarrier modulation (MCM) may enable transmission of a set of data over multiple narrow band subcarriers simultaneously. With an advanced wideband modulation and coding scheme, a system with MCM may achieve higher spectral efficiency in frequency selective channels compared to those using single carrier modulation techniques. Orthogonal frequency division multiplexing (OFDM) technology , which divides the total bandwidth into several orthogonal sub-bands overlapping in frequency, is an example MCM scheme.

[0003] OFDM may have several favorable properties like high spectral efficiency, robustness to channel fading, multipath delay spread tolerance, efficient fast Fourier transform

(FFT) implementation, etc. However, one problem is the high sidelobes of its subcarriers. As a result, OFDM signals may create relatively large out-of-band (OOB) radiation and/or out-of- band emissions (OOBE), and may not be ideal for certain wireless communication systems and applications. For example. Cognitive Radio (CR), as a promising solution to the spectrum congestion problem brought by the rapid increasing number of wireless communication techniques and devices, has drawn significant attention recently. A CR system may operate in the bands assigned to licensed users (LUs) by utilizing vacant parts of LU bands and may reduce or minimize its interference to LUs. OFDM has been considered as a candidate for CR in the first cognitive radio based standard, IEEE 802.22. OFDM-based CR systems may suffer from large OOB radiation that interferes with other bands occupied by LUs.

SUMMARY

[0004] Systems, methods, and instrumentalities are disclosed to utilize a combmed preceding technique in a multiearrier modulation system. A combined precoder may be used to precede a symbol stream using a matrix-based preceding component to generate a first preceded symbol stream. The combined precoder may then be used to apply a perturbation to the first preceded symbol stream to generate a second preceded symbol stream. As a result, OOBEs associated with transmission of the second preceded symbol stream may be less than the OOBEs associated with transmissions of a uncoded transmission of the data stream.

[0005] For example, the matrix-based preceding scheme may include one or more of a singular value decomposition (SVD) precoder scheme, an N-continuous precoder scheme, a spectral preceding scheme, and/or the like. A perturbation may be added to the first preceded symbol stream when generating the second preceded symbol stream. The perturbation may be transmitted on a first set of subcaniers and data symbols may be transmitted on a second set of subcaniers. The first preceding scheme may reduce OOBEs by exploiting a first preceding matrix property, and the second preceding scheme may reduce ihe OOBEs by exploiting a different preceding matrix property. For example, the first preceding property may be the null space property and the second preceding property may be the continuous derivative property.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] A more detailed understanding may be had from the following description, given by way of example in conjunction with the accompanying drawings wherein:

[0007] FIG. 1A is a system diagram of an example communications system in which one or more disclosed embodiments may be implemented;

[0008] FIG. IB is a system diagram of an example wireless transmit/receive unit (WTRU) that may be used within the communications system illustrated in FIG. lA;

[0009] FIG. 1C is 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. 1 A; [0030] FIG. ID is a system diagram of an another example radio access network and another example core network that may be used within the communications system illustrated in FIG. 1 A;

[003 3] FIG. IE is a system diagram of an another example radio access network and another example core network that may he used within the communications system illustrated in F G . 1A;

[0012] FIG. 2 is a block diagram illustrating an exemplary combined precoder;

[0013] FIG. 3 is a block diagram illustrating an example transmitter of a preceded Orthogonal Frequency Division Multiplexing (P-OFDM) system;

[0034] FIG. 4 is a block diagram illustrating an example receiver of the P-OFDM system:

[0015] FIG. 5 is a block diagram illustrating an example OFDM system adopting a precoding technique;

[0016] FIG. 6 is a graph illustrating the PSD after applying a spectral precoding method to an example OFDM system;

[0037] FIG. 7 is a graph illustrating the PSD after applying SVD precoding method to an example OFDM system;

[0038] FIG. 8 is a graph illustrating the comparison of SVD-based and combined NG-OFDM for close-notched frequencies;

[0019] FIG. 9 is a graph illustrating the comparison of SVD-based and combined NG-OFDM for close-notched frequencies;

[0020] FIG. 10 is a graph illustrating the comparison of SVD-based and combined ZP-OFDM for close-notched frequencies;

[0023] FIG. 1 3 is a graph illustrating the comparison of SVD-based and combined ZP-OFDM for close-notched frequencies;

[0022] FIG. 12 is a graph illustrating the comparison of SVD-based and combined CP-OFDM for close-notched frequencies;

[0023] FIG. 13 is a graph illustrating the comparison of SVD-based and combined CP-OFDM for close-notched frequencies:

[0024] FIG. 14 is a graph illustrating the bit error rate (BER.) of IFFT outputs in an example NG-OFDM system;

[0025] FIG. 35 illustrates an example where a combined precoder may be used with a perturbation vector;

- ^ - [0026] FIG. 16 illustrates an example PSD comparison of a SVD precoder, an N- continuous precoder, and a combined precoder in a system without a CP;

[0027] FIG. 17 illustrates an example PSD comparison of a SVD precoder, an N- continuous precoder, and a combined precoder in a system with a CP;

[0028] FIG. 18 illustrates the CCDFs for an uncoded system, an SVD precoder, a N- continuous precoder, and a combined precoder; and

[0029] FIG. 19 illustrates a comparison of the BERs for a SVD precoder, an N- continuous precoder, and a combined precoder.

DETAILED DESCRIPTION

[0030] 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.

[0031 ] FIG. 1 A is a diagram of an example communications s stem 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.

[0032] As shown in FIG. 1 A, 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 1 10, and other networks 1 12, 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, 102d may be any type of device configured to operate and/or communicate in a wireless environment. By way of example, the WTRU s 102a, 102b, 102c, 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.

[0033] The communications systems 100 may also include a base station 1 14a and a base station 1 14b. Each of the base stations 1 14a, 1 14b may be any type of device configured to wirelessiy interface with at least one of the WTRUs 102a, 102b, 102c, 102d to facilitate access to one or more communication networks, such as the core network 1 06/107/109, the Internet 110, and/or the networks 1 12. By way of example, the base stations 1 14a, 1 14b 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 1 14a, 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.

[0034] The base station 1 14a 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. Tints, in one embodiment, the base station 1 14a may include three transceivers, e.g., one for each sector of the cell, in another embodiment, the base station 1 14a may employ multiple-input multiple output (MIMO) technology and, therefore, may utilize multiple transceivers for each sector of the cell

[0035] The base stations 1 14a, 1 14b may communicate with one or more of the WTRUs 102a, 102b, 102c, 102d over an air interface 115/1 16/1 17, 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 15/1 16/1 17 may be established using any suitable radio access technology (RAT).

[0036] 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 1 14a in the RAN 103/104/105 and the WTRUs 102a, 102b, 102c may implement a radio technology such as Universal Mobile Telecommunications System (UMTS) Terrestrial Radio Access (UTRA), which may establish the air interface 1 15/1 16/1 17 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).

[0037] In another embodiment, the base station 1 14a and the WTRUs 102a, 102b, 102c may implement a radio technology such as Evolved UMTS Terrestrial Radio Access (E- UTRA), which may establish the air interface 1 15/116/1 17 using Long Term Evolution (LTE) and/or LTE-Advanced (LTE-A).

[0038] In other embodiments, the base station 1 14a and the WTRUs 102a, 102b, 102c may implement radio technologies such as IEEE 802.16 (e.g.. 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.

[0039] The base station 1 14b 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 802.11 to establish a wireless local area network (WEAN). 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 femtoceli. As shown in FIG. 1A, the base station 1 14b may have a direct connection to the Internet 1 10. Thus, the base station 1 14b may not be required to access the Internet 110 via the core network 106/107/109.

[0040] 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, I02d. 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. 1 A, 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/ 09 may also be in communication with another RAN (not shown) employing a GSM radio technology.

[0041] The core network 106/107/109 may also serve as a gateway for the WTRUs 102a, 102b, 102c, 102d to access the PSTN 108, the Internet 1 10, and/or other networks 1 12. The PSTN 108 may include circuit-switched telephone networks that provide plain old telephone sendee (POTS). The Internet 1 10 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 ihe Internet protocol (IP) in the TCP/IP Internet protocol suite. The networks 1 12 may include wired or wireless communications networks owned and/or operated by other service providers. For example, the networks 1 12 may include another core network connected to one or more RANs, which may employ ihe same RAT as the RAN 103/104/105 or a different RAT.

[0042] Some or all of the WTRUs 102a, 102b, 102c, 102d in the communications system 100 may include multi-mode capabilities, e.g., the WTRUs 102a, 102b, 102c, 102d may include multiple iransceivers for communicating with different wireless networks over difierent wireless links. For example, the WTRU 102c shown in FIG. 1 A may be configured to communicate with the base station 1 14a, which may employ a cellular-based radio technology, and with the base station 1 14b, which may employ an IEEE 802 radio technology.

[0043] FIG. IB is 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.

[0044] 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 will be appreciated that the processor 1 18 and the transceiver 120 may be integrated together in an electronic package or chip.

[0045] The transmit/receive element 122 may be configured to transmit signals to, or receive signals from, a base station (e.g., the base station 1 14a) over the air interface

1 15/1 16/1 17. 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, ^"U V, 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.

[0046] In addition, although the transmit/receive element 12.2. 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 15/1 16/1 17.

[0047] 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 12.2. 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.

[0048] The processor 1 18 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 dispiay/touchpad 128 (e.g., a liquid crystal display (LCD) display unit, or organic light-emitting diode (OLED) display unit). The processor 1 18 may also output user data to the speaker/microphone 124, the keypad 126, and'Or the dispiay/touchpad 128. In addition, the processor 1 1 8 may access information from, and store data in, any type of suitable memory, such as the non-removable memory 130 and'or the removable memor 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 1 18 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).

[0049] 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 (NiCd), nickel- zinc (NiZn), nickel metal hydride (NiMH), lithium-ion (Li-ion), etc.), solar cells, fuel cells, and the like.

[0050] 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 1 15/1 16/1 17 from a base station (e.g., base stations 1 14a, 1 14b) 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,

[0051 ] 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.

[0052] FIG. 1 C is 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, 102c over the air interface 1 15. The RAN 103 may also be in communication with the core network 106, As shown in FIG. IC, the RAN 103 may include Node-Bs 140a, 140b, 140c, which may each include one or more transceivers for communicating with the WTRUs 102a, 102b, 102c over the air interface 1 15, The Node-Bs 140a, 140b, 140c may each be associated with a particular cell (not shown) within the RAN 103. The RAN 103 may also include RNCs 142a, 142b. It will be appreciated that the RAN 103 may include any number of Node-Bs and RNCs while remaining consistent with an embodiment. [0053] As shown in FIG. 1C, the Node-Bs 140a, 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, 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 lur interface. Each of the RNCs 142a, 142b may be configured to control the respective Node-Bs 140a, 140b, 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.

[0054] 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.

[0055] The RNC 142a in the RAN 103 may be connected to the MSC 146 in the core network 106 via an luCS interface. The MSC 146 may be connected to the MGW 144. The MSC 146 and the MGW 144 may provide the WTRUs 102a, 102b, 102c with access to circuit- switched networks, such as the PSTN 108, to facilitate communications between the WTRUs 102a, 102b, 102c and traditional land- line communications devices.

[0056] The RNC 142a in the RAN 103 may also be connected to the SGSN 148 in the core network 106 via an luPS interface. The SGSN 148 may be connected to the GGSN 150. The SGSN 148 and the GGSN 150 may provide the WTRUs 102a, 102b, 102c with access to packet-switched networks, such as the Internet 1 10, to facilitate communications between and the WTRUs 102a, 102b, 102c and IP-enabled devices.

[0057] As noted above, the core network 106 may also be connected to the networks 1 12, which may include other wired or wireless networks that are owned and/or operated by- other sendee providers.

[0058] FIG. ID is 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, 102c over the air interface 1 16. The RAN 104 may also be in communication with the core network 107.

[0059] The RAN 104 may include eNode-Bs 160a, 160b, 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, 160c may each include one or more transceivers for communicating with the WTRUs 102a, 102b, 102c over the air interface 1 16, In one embodiment, the eNode-Bs 160a, 160b, 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.

[0060] Each of the eNode-Bs 160a, 160b, 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, 160e may communicate with one another over an X2 interface.

[0061] 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.

[0062] The MME 162 may be connected to each of the eNode-Bs 160a, 160b, 160e 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 WTRU s 102a, 102b, 102c, bearer activation/deactivation, selecting a particular serving gateway during an initial attach of the WTRUs 102a, 102b, 102c, and the like. The MME 162. may also pro vide 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.

[0063] The serving gateway 164 may be connected to each of the eNode-Bs 160a, 160b, 160c in the RAN 104 via the S I interface. The serving gateway 164 may generally route and forward user data packets to/from the WTRUs 102a, 102b, 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, 102c, managing and storing contexts of the WTR Us 102a, 102b, 102c, and the like.

[0064] The serving gateway 164 may also be connected to the PDN gateway 166, which may provide the WTRUs 102a, 102b, 102c with access to packet-switched networks, such as the Internet 1 10, to facilitate communications between the WTRUs 102a, 102b, 102c and IP- enabled devices.

[0065] The core network 107 may facilitate communications with other networks. For example, the core network 107 may provide the WTRUs 102a, 102b, 102c with access to circuit-switched networks, such as the PSTN 108, to facilitate communications between the WTRUs 102a, 102b, 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, 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.

[0066] FIG. IE is 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, 102c over the air interface 1 17. As will be further discussed below, the communication links between the different functional entities of the WTRUs 102a, 102b, 102c, the RAN 105, and the core network 109 may be defined as reference points.

[0067] As shown in FIG, IE, the RAN 105 may include base stations 180a, 180b, 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, 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, 102c over the air interface 1 17. In one embodiment, the base stations 180a, 180b, 180c may implement MJMO 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, 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 A SN 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.

[0068] The air interface 1 17 between the WTRUs 102a, 102b, 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, 102c may establish a logical interface (not shown) with the core network 109. The logical interface between the WTRUs 102a, 102b, 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.

[0069] The communication link between each of the base stations 180a, 180b, 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, 1 80c and the ASN gateway 1 82. 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 102 a, i 02b, 102c.

[0070] 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 mcludes 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.

[0071 ] The MIP-HA may be responsible for IP address management, and may enable the WTRUs 102a, 102b, 102c to roam between different ASNs and/or different core networks. The MIP-HA 184 may provide the WTRUs 102a, 102b, 102c with access to packet-switched networks, such as the Internet 110, to facilitate communications between the WTRUs 102a, 102b, 102c and IP-enabled devices. The AAA server 1 86 may be responsible for user authentication and for supporting user sendees. The gateway 188 may facilitate interworking with other networks. For example, the gateway 188 may provide the WTRUs 102a, 102b, 102c with access to circuit-switched networks, such as the PSTN 108, to facilitate communications between the WTRUs 102a, 102b, 102c and traditional land-line communications devices. In addition, the gateway 188 may provide the WTRUs 102a, 102b, 102c with access to the networks 1 12, which may include other wired or wireless networks that are owned and/or operated by other sendee providers,

[0072] Although not shown in FIG. 1 E, it will be appreciated that the RA 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, 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.

[0073] At a multicarrier modulation based transmitter, a combined preceding technique may achieve one or multiple multicarrier modulation waveform design goals including reducing or minimizing out-of-band power leakage. For example, a combined preceding technique may combine multiple component preceding techniques in a sequential way with matched coding rates to achieve one or multiple of the multicarrier modulation design goals, such as reducing or minimizing out-of-band power leakage, reducing PAPR, reducing or minimizing BER, and/or the like. Each component precoding technique may contribute to one or multiple design goals and the combination of the component precoders may be designed such that applying the components in series may not disable sought-after functionality of individual component precoding techniques. Examples of different precoding techniques that may be used as the individual preceding components of the combined preceding technique are described below.

[0074] An example combined precoder may utilize Singular Value Decomposition (SVD) preceding as a first preceding component and spectral preceding as a second precoding component in an OFDM system to reduce or minimize OOB power leakage, in the transmitter, before IFFT operation, each block of complex symbols may be preceded twice. The first precoder may utilize the SVD precoder to notch down the power at certain frequencies located out of passband to reduce or minimize out-of-band power emission. Then, the second component, which may be a spectral precoder, may be used to replace the rectangular pulse shaping in OFDM with spectral precoding across subcarriers to achieve faster roll off in power spectral density located out of passband. At the receiver, after FFT operation, the receiver may decode the block of the signal in the reverse order as the transmitting precoding process.

[0075] Other types of component precoders may be utilized. For example, matrix based preceding techniques may be utilized in a first precoding component and may be combined with precoding techniques utilizing a perturbation vector that may be implemented in a second precoding component. For example, SVD precoding may be implemented by a first precoding component, which may be combined with a second precoding component that implements an N-continuous precoding technique to minimize OOB power leakage. For example, at the transmitter, SVD precoding may be applied to the data vector, and then a perturbation vector may be calculated and added to the preceded signal to make the l^s; to J^"' derivatives on the left edge of each CP-OFDM symbol equal to those on the right edge of its previous symbol. At the receiver, the perturbation vector may be estimated and subtracted from the received signal, and the data may be recovered by using a decoding matrix. The method of adding the perturbation vector may be achieved by expanding the data vector to a space with larger dimensions and creating a perturbation vector that is orthogonal to the original data vector within this expanded space. In this manner, the receiver may operate without estimating the perturbation vector, but instead may project the estimated data in expanded space to the original one.

[0076] Rather than or in addition to using one or more preceding components, several others types of transmission schemes may be utilized to reduce the OOB radiation of Orthogonal Frequency Division Multiplexing (OFDM) based Cognitive Radio (CR) systems. For example, filtering and/or windowing techniques may be utilized. However, for example, filtering and/or windowing techniques may introduce long delays and/or degradation of bit error rate (BER).

[0077] Another example method that may be used to reduce leakage involves disabling or refraining from utilizing some of the CR subcarriers to create one or more guard bands between CR bands and LU bands. However, purposefully creating guard band(s) alone by refraining from using one or more subcarriers may be insufficient to reduce the interference to a practically acceptable level, and such techniques may cause the loss of some spectral efficiency. In an example, Cancellation Carriers (CC) may be used in order to generate an effect guard band and reduce spurious emissions. For example, instead of disabling or refraining from using subcarriers, the inputs to the specified CCs may be such that the radiation at certain frequencies, which are usually assigned to LUs, is reduced or minimized. The contents of the inputs to the CC may depend on the inputs of the remaining data subcarriers, which may be computationally complex, making the use of CCs difficult to implement in practice,

[0078] In an example, another method, referred to as Subcarrier Weighting (SW), may be utilized as a preceding component, SW may be viewed as a preceding method with a real diagonal matrix that does not decrease the spectral efficiency. Subcarrier Weighting may involve configuration of inputs of subcarriers to reduce or minimize the radiation at certain frequencies, and may also be computationally complex.

[0079] Another example preceding method that may be used as a preceding component is singular value decomposition (SVD) preceding. For example, although SVD preceding may decrease the spectral efficiency somewhat, SVD may utilize a preceding matrix with a less-than-one code rate to reduce the OOB radiation. Unlike Subcarrier Weighting, the matrix used in this preceding method may not be a square matrix. This matrix design, however, does not depend on the input data. Thus, the complexity of implementing such a precoder may be decreased as compared to techniques that require knowledge of each of the inputs.

[0080] Another preceding component scheme, e.g., spectral preceding, is also independent of the input data. Instead of SVD preceding that reduces or minimizes the system's energy at certain frequencies, spectral preceding uses new orthogonal basis sets to replace the rectangular pulse for each conventional OFDM symbol so that the new sidelobes fall off faster than those of the sine functions. The spectral efficiency may be reduced due to the limited number of available basis sets when the in-band range is fixed. Significant OOB power suppression improvement may occur when the spectral efficiency is reduced from 1 to (N-I) N and from (N-l)/N to (N-2) N, where N may be the number of subcarriers. As the spectral efficiency continues to decrease, the improvement may become less significant.

Accordingly, if part of the total spectral efficiency loss is redistributed from Spectral preceding to some other preceding schemes such as SVD preceding, the resulting combined schemes may be better than either of the schemes used separately.

[0081 ] Another example precoding component scheme may be referred to as N- continuous precoding. -continuous preceding may have approximately the same OOBE suppression effect irrespective of whether a cyclic prefix (CP) is utilized or not. For example, instead of designing a precoding matrix, N-eontiivuous precoding may design a perturbation vector depending on the current and the previous symbols so that the corresponding time-domain symbols may have continuous values and derivatives everywhere. Since the perturbation vector may not be correctly estimated in the receiver when the maximum derivative order is large, some errors may occur even in situations where the channel is ideal and an iterative decoder is used. By increasing the maximum derivative order, larger OOBE suppression may be achieved.

[0082] Orthogonal Frequency Division Multiplexing (OFDM) may have a high peak-to-average power ratio (PAPR) that may lead to low power efficiency of the system. Many MCM systems suffer from the high PAPR. problem. PAPR may be reduced using signal scrambling techniques, which may use scramble codes to decrease the PAPR, such as Selective Level Mapping (SLM) and Partial Transmit Sequences (PTS). Side information is usually utilized for signal scrambling techniques, by which redundancy is introduced and the effective throughput may be reduced. The precoding technique may also be an efficient way of reducing PAPR while maintaining decent error performance by introducing some redundancy. PAPR may be reduced by signal distortion, which may reduce high peaks by directly distorting the signal using, for example, companding techniques and clipping and filtering techniques.

Though such techniques may be efficient in reducing PAPR, they may degrade error performance significantly.

[0083] Precoding techniques may provide remedies to the drawbacks of MCM systems, such as OFDM systems. Different precoding techniques may achieve different goals it] MCM waveform design. Integrating different aspects of various types of preceding techniques may achieve various design goals in a MCM waveform system while avoiding undesirable effects of the individual techniques. For example, a preceding systsm may be designed to reduce or minimize OOB power leakage, reduce PAPR, minimize BER, etc.

[0084] A combined preceding technique may be used to combine multiple individual preceding techniques as illustrated in FIG. 2, e.g., ih th

where G_N may be the N component precoder (e.g., the i precoder the data streams essentially go through) and may represent the preceding matrix of one preceding technique.

[0085] FIG. 2 conceptually illustrates each component precoder of a combined precoder 200 as a precoder block 202. Utilizing multiple component precoders may be referred to herein as utilizing combined preceding. Combined preceding techniques may utilize a series of component precoders to satisfy a number of design goals. For example, each individual component precoder may be designed to contribute to one or multiple design goals, such as reducing or minimizing OOB power leakage, reducing or minimizing ih

PAPR, reducing or minimizing BER, and/or the like. In an example, the i preceding matrix G_i of dimension Α'_έ X K_j may satisfy the matched coding rate (dimension) constraint such that

[0086] Further, the combination of preceding techniques may be designed such that the total combination of precoders does not disable the functionality of one or more of the component precoding techniques (e.g., ensure that applying each of the precoders in combination does not overly weaken the effect that an individual precoder was designed to achieve).

[0087] FIG. 3 illustrates a transmitter 300 of an example Orthogonal Frequency Division Multiplexing (OFDM) system. FIG. 4 illustrates a receiver 400 of the OFDM system. FIGS. 3 and 4 may be used to illustrate the general case of a preceded OFDM (P-OFDM) system with an arbitrary contiguous or non-contiguous available spectrum.

[0088] When the available spectrum is non-contiguous, in order to reduce out-of- band (OOB) power leakage, one of the component precoding matrices may be designed to notch down the out-of-band frequencies.

[0089] In an example, in addition to utilizing a plurality of component precoders to process a signal prior to transmission (e.g., for various design purposes), a perturbation vector may be added to the transmit signal. For example, FIG. 15 illustrates an example where a combined precoder 1500 may be used with a perturbation vector,

[0090] For example, let d_} ~ d_2ii ... d._K ,\^T denote the /* data vector, where

/ may be the index in the time domain and K may be the length of each vector. A vector may be left-multiplied by an N X K preceding matrix G and added by a perturbation vector w¾ =

I ^wi,i ^W2,i ^■-^{■ W}N,I]⁷ , For example, the resulting signal may be such that:

where b> = [b_{l l} b_2>l ... b_{N l}]^T may denote the f preceded vector. The coding rate may be defined as K/N, which may be no larger than 1. may be the inverse fast Fourier transform (IFFT) operation output corresponding to an input of b_j . A CP may be insetted before χ_{ί ;} for example, in order to counteract channel effects. At the receiver, the CP may be removed from the received vector r . Then, the received vector may be processed with a fast Fourier transform (FFT) block and decoded by being left-multiplied by a K X N decoding matrix G after the perturbation vector is estimated and removed, e.g.,

d, = G( , - Wj) (4) where w_; may be the estimated perturbation vector and d_{ may be the estimated data signal. If the channel is ideal, then the data may be correctly decoded if Wj = w> and GG = I. In this combined preceding technique, G may be defined similarly as was represented in Equation (1 ).

[0091] As an example of a combined precoding technique, component precoders may be used to reduce OOB power leakage in an OFDM system. For example, an example SVD precoding method may be utilized as a first component precoder to notch down the power at certain frequencies located outside the passband, for example, in order to reduce out-of-band power emission. A spectral precoding method may be designed to replace the rectangular pulse shaping in OFDM with spectral precoding across subcarriers to achieve faster roll off in power spectral density located outside the passband and may be utilized as another component precoder. These precoding methods can be used as component precoders in a combined precoder, for example, as shown generally in FIG. 2. and/or FIG. 15. By properly adjusting the precoding matrices' dimensions (e.g. , by properly assigning the matched code rates) the combined precoder may have a better OOB power suppression effect than either of the two component precoders individually.

[0092] FIG. 5 illustrates an example OFDM system 500 that may adopt a precoding technique. As shown in FIG. 5, the source bit stream may be mapped into a symbol stream by a PSK/QAM modulation block 502. The symbol stream may be applied to a serial-to-parallel (S/P) lh

conversion block 504. If d_t — [d _l d₂ ... d_Kil)^T denotes the data vector, where / may be the index in the time domain and K may be the length of each vector, then a vector may be left- multiplied by an N X A^" precodmg matrix G, such that:

th _c

where b_t = b_N>l]^T may denote the / preceded vector, at a precodmg block 506.

The code rate may be defined as K/N, which may be no larger than 1. x> may be the IFFT output for b_j at an IFFT block 508. Cyclic Prefix (CP) and/or Zero Padding (ZP) may be added to x_{ at a block 510 to counteract the channel effects. The symbol stream may be transmitted via a channel at a block 512. At the receiver, CP and/or ZP may be removed from the received vector r^'J.at a block 514. The symbol siream may be processed by FFT block 516 and may be decoded being left-multiplied by a K X N decoding matrix G, such that:

If the channel is ideal, then the data may be correctly decoded if

GG = I (7)

[0093] The decoded symbol stream may be processed by a parallel-to-serial (P/S) conversion block 52.0 and may be mapped to a bit stream by a PSK/QAM demodulation block 522,

[0094] In SVD preceding, the continuous time-domain transmit signal x^t) for a given j may be expressed as:

(i ) =∑ , />/ ,P,( (8) where p_t(_t) may be the windowed subcarrier waveform expressed as:

P_.(0 = ³²^g_c t) (9) with the pulse shape function

QA t ί = 1 . . 10 ) ^ac ' ( 0, otherwise.

where T_d may be the effective symbol duration and T_CP may be the cyclic prefix duration. In the frequency domain, x<(t) may be expressed as:

where p ₍ ) ₌ ^{e ·} " ^' sin (_π ( - ή τ)

f \T_d )

where = T_CP + T_d , which may be ihe entire symbol duration. In an example, the precoder

V alues for a precodmg matrix G may be designed such that the system reduces or minimizes the radiation power at the frequencies f , fz, ... ,†^'M - For example, denote

Xi = l^xi ( i ) Xi ( ^τ, which may result in

[0095] To reduce or minimize j|X_; jj regardless of d., a SVD of P may be performed, for example to factorize P as:

P = u∑V^H (14) where U may be an M X M unitary matrix,∑ may be a diagonal M X N matrix that may contain the singular values of P in non-increasing order, and V may be an N X N unitary matrix whose columns may be v_t, v₂, · · · , v_N. The preceding matrix may be selected as:

G - h'v K M %-K + 2 ■· ] (15) If R is defined as the coding redundancy such that R = N^■- ft^", if R≥ M, then jjX; |j = 0 for any arbitrary dj because b> may be in the null space of P,

[0096] Rectangularly pulsed OFDM may possess discontinuous pulse edges and may exhibit relatively large power spectral sidelobes that may fall off as f ^'"2. Continuous-phase OFDM signals may exhibit relatively small power spectral sidelobes that fall off as f ^"4, and may provide much higher spectral efficiency than a rectangularly pulsed OFDM signal . In an example spectral preceding method, two families of basis sets that satisfy the continuous-phase condition may be used, e.g., family and family V, respectively.

[0097] A corresponding precoded OFDM structure may be used to construct OFDM signals using the basis sets along with input data. The entries of the family W_L -based preceding matrix G ^VVL may be defined as:

W l

9N( ")+η +v 2^~(-l) ¹⁺*^«-^», n e 0, : and v e [0, 2^U - 1] (16) for u— 1,2, ... , L. In Equation (16), ip_UM may be the sum of the most and least significant bits in the binary representation (e.g., in bits) of the modulo-2" value of v when u >. 2 and ψι,ν ^~ 1 by default. Other entries may equal 0.

[0098] The entries of the family F^-based preceding matrix G^VL may be defined as:

9 ί i,\ 0, : and v e [0, 2^U - 1] ( 17)

)V l - 2^{1 ~}") +n,n +~^v 2 ² >u,v. n ^e for u ~ 1,2, ... , L. In Equation (17), φ_η>ν = 1 if u = log₂ N and <p_u>v = (— otherwise, where ζ_ν may represent the least significant bit in the binary representation of v. Other entries may equal 0. L in Equations (16) and/or (17) may be a parameter that may determine the code rate. For example, the code rate may be expressed as 1 — 2^~L, L £ [1, log₂ N] , Since G⁵, G^WL and G^VL may be left unitary matrices containing orthonormal columns, then the decoding matrices may be their conjugate transposes,

[0099] The SVD preceding matrix and Spectral precoding matrix (using G ^{'A L} as example) may be combmed, for example, by defining either G = G^ G^or G = G^M'^LG^S.

Defining G as G = G^SG^WL may result in the failure of G^WLh, to have a continuous-phase property once the matrix is left- mul iplied by G⁵, which may introduce errors. On the other hand, by selecting G = G ^G , the continuous-phase property may be maintained, and the advantage of being able to utilize SVD precoding may be achieved.

[0100] In an example, the combined precoder may be designed as follows, G^WL may be defined using Equation (16) without considering G'\ SVD may be performed for PG^Wi {e.g. , replace P in Equation ( 14) by VG^WL), for example to determine G" (e.g. , utilize Equation (15) to determine G⁵). By doing so, the combined precoding matrix G and the decoding matrix G may^¬ be expressed as:

G - G'^G⁵ and G - {G^WL G^S)^H (18)

[0.101] The transmitted signal x< for spectral preceding may be the real part of the IFFT output, while the complex part of the IFFT output may be used for SVD precoding. In an example, as shown in FIG. 5, the complex part of the IFFT output may be used.

[0102] In an example, the matched dimensions of G'^¾ and G^{Vi i} for a given dimension of G may be distributed such that a high degree of OOB po wer suppression may be achieved. For example, FIG. 6 may be a graph 600 that illustrates the PSD after applying the spectral precoding to a 64-subcarrier OFDM system without any CP or ZP (e.g. , No Guard (NG)) using QPSK modulation and an FFT size of 256. Simulation results illustrate that the PSD of f'Fr-based systems may outperform that of the r-based systems for the same L for the given scenario (e.g. , NG, ZP, and CP). The code rate may be 1— 2 ^"L . The five curves 602, 604, 606, 608, and 610 in FIG. 6 may show that the largest OOB power decrement appears when the code rate drops from 1 (uncoded) to 63/64 (L=6). The curve 602 illustrates the PSD for an imcoded system. The curves 604, 606, 608, and 610 illustrate the PSD for values oi^'L of 6, 5, 4, and 3, respectively. As L further decreases linearly, the cumulative suppression impact may become less effective as the code rate drops exponentially.

[0103] FIG. 7 is a graph 700 that illustrates the PSD after applying an SVD precoding method. A curve 702 illustrates the PSD for an uncoded system. Two groups of notched frequencies are used in this simulation, namely, group I comprising close-notched frequencies of [-14.5 - 13.5 - 12.5 - 11.5 74.5 75.5 76.5 77.5 j and group 2 comprising distant-notched frequencies of [-35.5 - 34.5 - 33.5 - 32.5 95.5 96.5 97.5 98.5] , Curves 704 arid 706 illustrate the PSD for groups 1 and 2, respectively, when R=2. Curves 708 and 7.10 illustrate the PSD for groups 1 and 2, respectively, when RH-. Curves 712 and 714 illustrate the PSD for groups 1 and 2, respectively, when R=6. Curves 716 and 718 illustrate the PSD for groups 1 and 2, respectively, when R=8.

[0104] With an active subcarrier index of 0-63 and an FFT size of 256 in this simulation, group 1 may be close to the in-band and group 2 may be distant. FIG. 7 shows that the allocation of the chosen notched frequencies may provide a tradeoff between the OOB power and the decaying rate. The po wer decrement per 1/64 coding decrement does not change substantially and may be much larger than that of spectral preceding when the code rate is less than 62/64. Based on this observation, when the overall rate is fixed as k/n, an acceptable level of OOB power suppression to decay rate may be achieved by adopting the [K/(N— 1), (N— 1 /N] code rate pair, which may result in assigning K/ (N— 1) as the SVD precede rate and (N— 1)/N as the spectral precode rate.

[0105] FIGS. 8 and 9 are graphs 800 and 900 that illustrate the comparison of SVD- based precoding method and a combined NG-OFDM preceding method for group 1 (close-notched) and group 2 (distant-notched) notched frequencies, respectively. FIG. 8 is based on the notched frequencies in group 1 in SVD precoding and a combined NG-OFDM precoding. FIG. 9 is based on the notched frequencies in group 2 in SVD precoding and a combined NG-OFDM precoding. In FTGS. 8 and 9, curves 802 and 902 show the PSD for an uncoded system. Curves 804 and 904 show the PSD for a code rate for R=4 using SVD precoding. Curves 806 and 906 show the PSD for a code rate for R=3, L=6 for a combined NG-OFDM precoding technique. Curves 808 and 908 show the PSD for a code rate for R=6 using SVD precoding. Curves 810 and 910 show a PSD for a code rate for R^;;;5, L=6 for a combined NG-OFDM precoding technique. Curves 812 and 912 show a PSD for a code rate for R=8 using SVD precoding. Curves 814 and 914 show a PSD for a code rate for R=7, L=6 for a combined NG-OFDM precoding technique. FIG. 8 shows that, each of the three code rates, the combined NG-OFDM precoding scheme provides about 15 dB lower total OOB po wer than SVD precoding scheme at a cost of a slightly wider transition band, which may be hardly observable in FIG. 8. The transition band difference between SVD precoding method and the combined NG-OFDM precoding scheme disclosed herein may be larger in FIG. 9, but a relatively significant OOB power decrement is seen using the combined NG-OFDM precoding scheme.

[0106] FIGS. 10 and 1 1 are graphs 1000 and 1 100 that illustrate a comparison of SVD-based precoding and a combined ZP-OFDM precoding method for group 1 (close- notched) and group 2 (distant-notched) notched frequencies, respectively. FIG. 10 is based on the notched frequencies in group 1 in SVD precoding and a combined ZP-OFDM preceding scheme. FIG. 1 1 is based on the notched frequencies in group 2 in SVD precoding and a combined ZP-OFDM precoding scheme. In FIGS. 10 and 1 1, curves 1002 and 1 102 show the PSD for an uncoded system. Curves 1004 and 1 104 show the PSD for a code rate for R=4 using SVD precoding. Curves 1006 and 1 106 show the PSD for a code rate for R=3, L=6 using the combined ZP-OFDM precoding scheme. Curves 1008 and 1 108 show the PSD for a code rate for R=6 using SVD precoding. Curves 1010 and 1 110 show a PSD for a code rate for R=5, L=6 using the combined ZP-OFDM precoding scheme. Curves 1012 and 1 1 12 show a PSD for a code rate for R=8 using SVD precoding. Curves 1014 and 1 1 14 show a PSD for a code rate for R=7, L=6 using the combined ZP-OFDM precoding scheme. In FIGS. 10 and 1 1, the length of ZP may be T_d/ 16 (e.g., 1/16 of the data block's length). FIGS. 10 and 1 1 may appear similar to FIGS. 8 and 9, for example due in part to the fact that the continuous-phase property of Spectral precoding is maintained because the value on both edges of each data block before ZP may also be zero and because the P and V values in Equation (14) may be almost unchanged after the ZP is added.

[0107] FIGS. 12. and 13 are graphs 1200 and 1300 that show the comparison of SVD- based and a combined CP-OFDM precoding technique for group 1 (close-notched) and group 2 (distant-notched) notched frequencies, respectively. FIG. 12 is based on the notched frequencies in group 1 in SVD precoding method and the combined CP-OFDM precoding scheme. FIG. 13 is based on the notched frequencies in group 2 in SVD precoding and the combined CP-OFDM precoding scheme. In this example, the length of CP is also ^d/

Since the CP is added and the starting edge of CP is usually not zero, then the spectral precoding scheme may be unable construct a continuous signal with a CP. Therefore, assigning 1/K of the total spectral efficiency loss to spectral precoding and the remaining (K— 1)/K to SVD precoding may not be much better (if at all) than assigning all the spectral efficiency loss to SVD precoding alone.

[0108] In FIGS. 12 and 13, curves 1202 and 1302 illustrate the PSD for an uncoded system. Curves 1204 and 1304 sho the PSD for a code rate for R=4 using SVD precoding. Curves 1206 and 1306 show the PSD for a code rate for R 3. L=6 for a combined CP-OFDM precoding method. Curves 1208 and 1308 show the PSD for a code rate for R^:;;:6 using SVD precoding. Curves 1210 and 1310 show a PSD for a code rate for R=5, L=6 for a combined CP- OFDM precoding method. Curves 1212 and 1312 show a PSD for a code rate for R=8 using

- t _ SVD precoding. Curves 1214 and 1314 show a PSD for a code rate for R-7, L=6 for a combined CP-OFDM precoding method.

[0109] By comparing FIGS. 1 1 and 12 to FIGS. 7- 10, it can be seen that the OOB power suppression effects of all three code rates for CP-OFDM may be worse than for NG- OFDM and ZP-OFDM. This may be because in NG-OFDM and ZP-OFDM, the width of the sidelobes may be equal to the frequency spacing of adjacent subcarners. This may result in each sideiobe of a subcarrier completely overlapping with some or sidelobes from all of the other subcarners. As a result, the singular values of P in the Equation (14) may drop quickly.

However, when CP is added and symbol duration is increased, the width of the sideiobe may become narrower. Therefore, the singular values of P may drop more slowly. If fy is the average power leakage after precoding at the chosen notched frequencies fi, the average power leakage after precoding may be expressed as:

where fy may be the average power of &i and σ'(Ρ) may be the i^th largest singular value of P. In this sense, for the same value of R, the power leakage fy of a combined CP -OFDM precoding method may be larger than the fy for either the combined NG-OFDM precoding method and/or the combined ZP-OFDM precoding method.

[01 10] FIG. 14 illustrates the bit error rate (BER) of the three schemes' IFFT outputs in an example NG-OFDM system using QPSK modulation. The number of subcarriers may be 64 and the FFT size may be 256. In this example, the channel may be an Additive White Gaussian Noise (AWGN) channel, e.g., r( = xj + n_¾, where n_¾ may denote the noise

[01 1 1 j A curve 1402 shows the BER for an uncoded system. A curve 1404 shows the ER for a code rate for R=4 for a system utilizing SVD precoding. A curve 1406 shows the BER for a code rate for L=4 for a system utilizing spectral precoding. A curve 1408 shows the BER for a code rate for R=3, 1.^~6 for a system utilizing combined NG-OFDM precoding. A curve 1410 shows the BER for a code rate for R=6 for a system utilizing SVD precoding. A curve 1412 shows the BER for a code rate for L=3 for a system utilizing spectral precoding. A curve 1414 shows the BER for a code rate for R=7, L-6 for a system utilizing combined NG- OFDM precoding. In the example illustrated in FIG. 14, Curves 1404, 1406, and 1408 may represent systems utilizing essentially the same coding rate. Similarly, curves 1410, 1412, and 1414 may represent systems utilizing essentially the same coding rate.

[01 12] As shown in FIG. 14, the combined scheme, which uses distant notched frequencies, may have almost the same BER curves as SVD preceding or spectral preceding when they have the same code rates. Further, as the code rate decreases, the BER may become slightly better, {e.g., smaller) because the length of d,, which may be estimated at the receiver, may be reduced while the row size of the preceding matrix may be unchanged. Accordingly, a lower code rate may provide a slightly higher diversity gain.

[01 13] Other examples of combined precoders may be utilized in OFDM systems in order to reduce or minimize OOB power leakage. For example, a SVD precoder design may notch down the power at certain frequencies located out of passband to reduce or minimize out-of-band power emission. After SVD preceding, an N-continuous preceding method may be performed. The N-continuous preceding method may utilize a perturbation vector thai may depend on the current and the previous symbols. As a result, the N-continous preceding may be performed such that the corresponding time-domain symbols may have continuous values and derivatives, e.g., everywhere. Since the maximum derivative order may be increased to achieve larger OOBE suppression, if other techniques or methods may be specifsed in order to achieve similar goal(s) {e.g., a scheme that may suppress the OOBE by achieving the continuous derivative property and/or a scheme that may suppress the OOBE by utilizing the null space property), then a large order may not have to be utilized. For example, considering that the N-continuous preceding scheme may suppress the OOBE by achieving the continuous derivative property and the SVD preceding scheme may suppress the OOBE by utilizing the null space property, a different preceding scheme may be specified that utilizes both properties.

[01 14] For example, a combined preceding scheme may be specified that utilizes Beck's preceding for a first component precoder and that utilizes N-continuous preceding for a second component precoder. Such a technique may utilize a preceding matrix and a perturbation vector and may provide better OOBE suppression than either the Beck's preceding technique or the N-continuous preceding technique may provide individually.

[01 15] For example, one of the causes of high OOBE may be the discontinuity of time-domain signals. Since the signal may be continuous everywhere within a CP-OFDM symbol, the problem of discontinuous signal derivatives may be addressed by ensuring the value and its l^s: to . "^" derivatives on the left edge of a CP-OFDM symbol may be equal to the value and the 1^st to J^"' derivatives on the right edge of the previous symbol. For exampl e, such

[01 16] In an example, a perturbation vector wf may be used to ensure Equation (21) is satisfied (e.g. , ensuring the value and its I^st to derivatives on the left edge of a CP- OFDM symbol may be equal to the value and the I^s'' to J^'LL derivatives on the right edge of the previous symbol). An additional precoder component may be used with a perturbation vector to satisfy Equation (21), for example, while further decreasing OOBE.

[01 17] As an example, let bj = d; + wf. Ensuring that the left edge value and the r to J^h derivatives on the left edge of each CP-OFDM symbol is equivalent to the right edge value and the 1^st to ./^'"^' derivatives on the right edge of the previous CP-OFDM symbol may be achieved by finding a wf such that:

ΑΦ^ = Α¾$_Ϊ„, , (22) where

and

[oi is; Since A may be a (J + 1) X N matrix and /V may be larger than (/ + 1), the solution of wf may not be unique. Among the possible values wf that satisfy Equations (21)- (24), a value of wf with the smallest magnitude may be found by introducing the Moore - Penrose pseudoinverse of ΑΦ, denoted as (ΑΦ) ^"1" . If so, then wf may be expressed as:

f(A )⁺Ab,_i ^■- (ΑΦ)⁺ΑΦΰ_ι, Ζ > 1

(25)

), Z = 1

[01 19] At the receiver, if it is assumed that there is no channel effect or noise, bj = b_{ may be correctly recovered after the FFT process, w may be correctly estimated so that wf can be removed from b_£ to recover dj . Based on Equation (25), wf may depend on d_j. An iterative decoder may be utilized. In the Γ¹ (i > 1) iteration, the estimated perturbation vector may be expressed as:

,-Λ( _ /' Λ Λ + Λ ΛΪ. . — f Λ Α ίϊί^{1"" 1}·* (26) where d}'"' (i > 1) may be chosen from the possible frequency-domain symbol vectors to reduce or minimize The iteration decision vector d ' may be expressed d|^'° = (I ·^■■■ (ΑΦ)⁺ΑΦ)ί>_ί + (ΑΦ) ⁺ ΑΦίί ^{ί 1}} (27) with d;^{0 ~} 0. Since w may depend on bj..-, and d_;, such a scheme that utilizes a perturbation vector to reduce OOBE may be data-dependent. If such a scheme is implemented by the structure shown in FIG. 15, then in Equation (4), G = I and \v₍ = wf .

[0120] A combined precoder may be designed to utilize SVD precoder as a first component precoder and N-continuous preceding a second component precoder. For example, such a combined preceding scheme may be functionally illustrated in FIG. 15. To ensure that the combined scheme may take advantage of the null space property from the SVD preceding method and the continuous derivative property from the N-continuous precoding method, the perturbation vector may be expressed as w_; = Gvj. Based on this relationship. Equation (3) may be expressed as:

hi = G(d, + V;) (28)

[0121 ] In order to design the combined precoder, G may be configured such that

G = G⁵ regardless of v,. Equation (28) may be substituted into Equation (22), and the Moore-

Penrose pseudoinverse method may be utilized. The least magnitude value for v_t may be expressed as:

f (A G ⁺Ab,_i - (ΑΦΟ)⁺ ΑΦΟί},, I > 1

V' = l ^' 0, 1 = 1 ^{' (29)}

[0122] At the receiver, j may be the recovered FFT output, which may correspond to the l^lh precoded frequency-domain symbol. The precoded frequency-domain signal may be processed by the SVD decoder G. Let G = (G⁵)^H and bj = Gb_{. After processing by the SVD decoder, b; may be processed through the iterative N-continuous decoder. The estimated perturbation vector of the i^t (t > 1) iteration vj^ may be expressed as:

v ^;) = (ΑΦ6)⁺ΑΦ6Β_¾ - (ΑΦ6)⁺ΑΦ6«ϊ'ί^{έ " 5 )} (30) and the i^lh iteration decision vector <! ^ may be expressed as:

<¾° = (I — (ΑΦ6)⁺ΑΦ6)Β,_: + (A G)⁺A Gd{^i"1 (31)

[0123] In an example, the N-continuous precodmg component precoder may operate utilizing selected subcarriers. For example, in N-continuous precoding a perturbation may be added to the data on each subcarrier. At the receiver, an iterative algorithm may be utilized to estimate the transmitted data. In an example, a subset of the subcarriers may be used to carry perturbation while the remaining subcarriers may be used to cany data, for example without any perturbation. At the receiver, the subcarriers with perturbation may be discarded while the remaining subcarriers may be processed as in regular OFDM data transmission.

[0124] As an example, based on Equation (22), the N- continuity condition may be expressed as:

A*l>b Ab 0>z) wher

In Equation (33), W_j may be the vector of perturbation without data, and d_t may be the vector of data without perturbation. The vector b< may be formed in many different ways using d_t and W_j. For example, as long as any element of b_{ is either an element of d_t or an element of Wi, but not the sum of the two, the vector b₍ may be expressed in multiple ways as a function of άι and Wj. The dimension of Wj may be ( X 1), where M may be the number of subcarriers used to carry perturbation. The dimension of ά, may be ((iV— M) X 1). Thus, a given subcarrier may carry either perturbation or data. By substituting Equation (33) into Equ

[0125] To solve Equation (34), the following method may be utilized. For the first block, I = 1, it may be assumed that u>{_i = w_Q ~ 0. w_t may then be determined, for example, by determining that W_j = w based on Equation (34) since the data may be known. For the second block, I = 2, the determined value of w from the previous step may be utilized to compute ₂ based on Equation (34). This process may be repeated for each block based the determined value of Wi-i from the previous step. Thus, For the /^th block, wj may be determined based on the determined value of W_|__t that was determined from the previous iteration and the data to be transmitted based on Equation (34).

[0126] At the receiver, the subcarriers carrying the perturbation may be discarded, while the subcamers carrying data may be processed in an OFDM decoder. In an example, the subcarriers carrying the perturbation may be distributed rather than contiguous. If the subcarriers carrying the perturbation are non-contiguous, then Equation (33) may be expressed accordingly.

[0127] A numerical analysis may be performed to evaluate the performance of a combined precoder that utilizes a fsrst component precoder implementing SVD preceding and a second component precoder that implements an N-continuous precoder. For example, the performance of the combined precoder may be evaluated relative to the performance of a SVD precoder alone and/or a N-continuous precoder alone,

[0128] For example, consider a 300-subcarrier OFDM system (e.g., let N= 300). For example, the subcarriers indexes for subcarrier frequencies j f_z ... f₃₀₀] may be expressed as [-150 -149 ... -2 - 1 1 2 ... 149 150]. In the following example, 16QAM modulation may be used, and the FFT size may be 102.4.

[0129] FIG. 16 illustrates an example PSD comparison of a SVD precoder, an Ν- continuous precoder, and a combined precoder with a SVD precoder component and a Ν- continuGus precoder component in a system without a cyclic prefix (CP). For example, curve 1602 illustrates an example of the PSD of an uncoded system. Curve 1604 illustrates an example of the PSD of a system utilizing N-continuous preceding. The term J^~\ may represent that the N-continuous precoder system may have a maximum derivative order of J=\. Curve 1606 illustrates an example of the PSD of a system utilizing SVD preceding. The term R=8 may represent that the SVD precoder may perform the preceding with a redundancy of R=8. The number of notched frequencies (M) may be selected to be =8. For example, the indices of the notched frequencies may be selected to be [-184,5 -183.5 - 182.5 - 181.5 181.5 182,5 1 83.5 184.5], Curve 1608 illustrates an example of the PSD of the combined precoder that utilizes an SVD preceding component with i?=8 and a N-continuous preceding component w ith ./ i .

[0130] In FIG. 16, a CP may not be inserted (e.g., T _P = 0). Compared with the uncoded- OFDM (e.g., curve 1602), both the N-continuous precoder (e.g., curve 1604) and the SVD scheme (e.g., curve 1606) show around 40 dB more OOBE suppression in the stopband. However, the two schemes have quite different roll-off behaviors. For example, the N- continuous scheme may have a very slow roll-off and a relatively large transition band, while the SVD scheme may have a much smaller transition band. Compared to the SVD scheme and the N-continuous scheme, the combined scheme may have a relatively small transition band similar to the SVD scheme while providing approximately the sum of the OOBE suppression of the two schemes individually. This may be because the two component schemes may suppress the OOBE by using two properties that may be substantially independent of each other (e.g., the null space property and the continuous derivative property). Thus, each component may add to the total OOBE suppression by taking advantage of a different property in order to avoid one of the component schemes affecting the operation of the other.

[0131] FIG. 17 illustrates an example PSD comparison of a SVD precoder, an N- continuous precoder, and a combined precoder with a SVD precoder component and a N- continuous precoder component in a syste that utilizes a cyclic prefix (CP). For example, curve 1702 illustrates an example of the PSD of an uncoded system that utilizes a CP. Curve 1704 illustrates an example of the PSD of a system utilizing N-continuous preceding with a maximum derivative order of J=l . Curve 1706 illustrates an example of the PSD of a system utilizing SVD preceding with a redundancy of R=8. The number of notched frequencies ( i) may be selected to be Λ =8. For example, the indices of the notched frequencies may be selected to be [- 184.5 - 183.5 - 1 82.5 - 181 .5 181.5 182.5 183.5 184.5]. Curve 1708 illustrates an example of the PSD of the combined precoder that utilizes an S VD preceding component with Λ=8 and a N-continuous preceding component with J=\ in a system with CP.

[0132] In FIG. 17, a CP may be inserted with T_CP = 9/128T_d. Comparing FIG. 1 7 with FIG. 16, it may be noted that for the SVD scheme, the OOBE suppression may be reduced by 20 dB after CP insertion. The N-continuous scheme may have approximately the same OOBE suppression irrespective of whether a CP is utilized or not. Furthermore, as illustrated in both FIG. 1 6 and FIG. 17, the combined preceding scheme may show a significant improvement over either of the SVD scheme or the N-continuous scheme. The OOBE suppression of the combined scheme may be even greater if CP insertion is utilized (e.g. , FIG. 17) than if it is not (e.g., FIG. 16).

[0133] In an example, the average transmit power of x! (/ = 1 , 2, 500) of the four schemes illustrated in FIG. 16 and FIG. 17 may be compared. Table 1 illustrates the transmission power comparison between the SVD precoder, the N-continuous precoder, and the combined precoder with a SVD precoder component and a N-continuous precoder component. In the example illustrated in Table 1 , the expectation of the source data symbol power may be normalized so that the power of the uncoded-OFDM is equal to 1 in both cases (e.g. , with CP and without CP).

Table 1

[0134] Since the SVD preceding matrix may be a semi-unitary matrix with coding rate less than one, the average transmit power of the SVD scheme may also be reduced.

Comparing the uncoded systems with the N-continuous precoder system, the power increment brought by the perturbation vector w in the N-continuous scheme may be negligible. Similarly, the power increment brought by the perturbation vector Vj in the combined scheme may be negligible with a small value of J (e.g., J = 1).

[0135] In order to compare the peak-to-average power ratio fPAPR) performance of the various preceding systems, the complementary cumulative distribution function (CC-DF) of the transmit signal Xj (/ = 1 , 2, , .., 500) of the different schemes may be considered. For example, FIG. 1 8 illustrates the CCDFs for an uncoded system, an example SVD precoder, a N-continuous precoder, and a combined precoder with a SVD component and a N-continuous component for the case where T_CP— 0. For example, curve 1802 may represent the CCDF for an uncoded system. Curve 1804 may represent the CCDF for a N-continuous precoder with J=] . Curve 1806 may represent the CCDF for a SVD precoder with i?=8. Curve 1808 may represent the CCDF of a combined precoder with a S VD precoder component with R=S and an N-continuous precoder component with J=l .

[0136] In an example, the lower the SVD coding rate is, the higher PAPR. becomes. As the coding rate of the SVD scheme and the combined scheme may be 292/300 « 0,97 in this example, the difference between the SVD curve {e.g., curve 1806), N-continuous curve {e.g., curve 1804), and the combined precoder curve (e.g., curve 1808) may be subtle.

[0137] The bit error rate (BER) performance of the different preceding systems may be evaluated. For example, FIG. 19 illustrates a comparison of the BERs for an example SVD precoder, an example N-continuous preocoder, and a combined precoder with a SVD component and a N-continuous precoder component. For example, curve 1902 may represent the BER for an uncoded system. Curve 1904 may represent the BER for a N-continuous precoder with j=l. Curve 1906 may represent the BER for a SVD precoder with R-8. Curve 1908 may represent the BER of a combined precoder with a S VD precoder component with R=8 and an N-continuous precoder component with J=\ .

[0138] The channel may be assumed as an AWGN channel, which means that r_l' = x'i + n_t, where n_{ denotes the noise vector. SNR (dB) may be expressed as:

An iterative decoder may be utilized for the N-continuous scheme and/or the combined scheme with a N-continuous precoder component. For example, the number of the iterations may be set to be three, although other values may be used. The lower the SVD coding rate, the lower the BER may become. Since the coding rate here may be close to 1 , the difference maybe subtle. For the N-continuous schemes, the perturbation vector may not be correctly es timated in the iterative procedure and may no t be removed for each symbol. When J is small enough (e.g., J- 1) so that the magnitude of w is much smaller than the minimum distance of the constellation plots (e.g., 16QAM in this case), then the error brought by the incorrect estimation of wf may be negligible. For at least these reasons, each of the four curves in FIG. 19 may nearly overlap.

[0139] The simulation results show that a combined precoder scheme with a plurality of independent precoding components may provide increased OOBE suppression than either an SVD precoding scheme alone or an N-continuous preceding scheme alone, irrespective of whether there is a CP or not. The PAPR performance may be almost the same as the uncoded-OFDM because significant OOBE suppression effects may be achieved at the cost of very little loss of coding rate (e.g., 8/300 may be the loss in the above simulations). A small number of iterations and a proper setting of the maximum derivative order may reduce the BER influence from the perturbation vector to a negligible level.

[0140] A WTR.U may refer to an identity of the physical device, or to the user's identity such as subscription related identities, e.g., MS1SDN, SIP URI, etc. WTRU may refer to application-based identities, e.g., user names that may be used per application. The precoding methods (e.g., combined precoding methods) described herein may be implemented by various transmitters (e.g., a WTRU, a base station such as an e B, an NB, an access point, etc.). The precoding methods described herein may be used in the uplink and/or downlink. Example wireless communication systems that may utilize the described precoding techniques include 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/or the like.

[0141] 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, sofiware, 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.

Claims

CLAIMS What is Claimed:

1. A combined precoder for reducing out-of-band emissions (OOBEs) in a multicarrier modulation system, the combined precoder comprising:

a first precodmg component configured to apply a matrix-based preceding scheme to a data stream to generate a first preceded symbol stream; and

a second preceding component configured to apply a perturbation to the first preceded symbol stream to generate a second preceded symbol stream.

2. The combined precoder of claim 1, wherem OOBEs associated with transmission of the second preceded symbol stream are less than the OOBEs associated with transmissions of a uncoded transmission of the data stream.

3. The combined precoder of claim 1, wherein the first preceding scheme comprises one of a singular value decomposition (SVD) precoder scheme, an N-continuous preceding scheme, or a spectral precodmg scheme.

4. The combined precoder of claim 1, wherein the perturbation is transmitted on a first set of subcarners and data symbols are transmitted on a second set of subcarners.

5. The combined precoder of claim 4, wherem the data symbols are transmitted on the second set of subcarriers without perturbation,

6. The combined precoder of claim 1, wherein the matrix-based preceding scheme reduces OOBEs by exploiting a first preceding property and the second precodmg component reduces OOBEs by exploiting a different preceding property.

7. The combined precoder of claim 6, wherem the first preceding property comprises a null space property and the second preceding property comprises a continuous derivative property.

8. A method to reduce out-of-band emissions (OOBE) in a multicarrier modulation system, the method comprising: preceding a symbol stream using a matrix-based preceding scheme to generate a precoded symbol stream; and

applying a perturbation to the precoded symbol stream.

9. The method of clai 8, wherein OOBEs associated with transmission of the second precoded symbol stream are less than the OOBEs associated with transmissions of a uncoded transmission of the data stream.

10. The method of claim 8, wherein the first preceding scheme comprises one of a singular value decomposition (SVD) precoder scheme, an N-continuous preceding scheme, or a spectral preceding scheme.

1 1. The method of claim 8, further comprising:

transmitting the perturbation on a first set of subcarriers; and

transmitting data symbols on a second sei of subcarriers.

12. The method of claim 1 1, wherein the data symbols are transmitted on the second set of subcarriers without perturbation.

13. The method of claim 8, wherein the matrix-based preceding scheme reduces OOBEs by exploiting a first preceding property and the second precodmg component reduces OOBEs by exploiting a different precoding property.

14. The method of claim 13, wherein the first precoding property comprises a null space property and the second precoding property comprises a continuous derivative property.

15. A device comprising:

a processor; and

a memory comprising instructions that, when executed by the processor, cause the device to

precede a symbol stream using a matrix-based precoding scheme to generate a precoded symbol stream; and

apply a perturbation to the precoded symbol stream.

16. The device of claim 15, wherein OOBEs associated with transmission of the second precoded symbol stream are less than the OOBEs associated with transmissions of a uncoded transmission of the data stream.

17. The device of claim 15, wherein the first precodmg scheme comprises one of a singular value decomposition (SVD) precoder scheme, an N-continuous precoding scheme, or a spectral precoding scheme.

18. The device of claim 15, wherein the memory comprises further instructions for: transmitting the perturbation on a first set of subcarriers; and

transmitting data symbols on a second set of subcarriers.

19. The device of claim 15, wherein the matrix-based precoding scheme reduces OOBEs by exploiting a first precoding property and the second precodmg component reduces OOBEs by exploiting a different precoding property.

20. The device of claim 19, wherein the first precoding property comprises a null space property and the second precoding property comprises a continuous derivative property.