METHOD AND PRECODER INFORMATION FEEDBACK IN MULTI-ANTENNA
`WIRELESS COMMUNICATION SYSTEMS
`
`Description
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`CROSS REFERENCE TO RELATED APPLICATIONS
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`[0001]
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`The present application is a non-provisional application of U.S. provisional
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`Application No. 61/331,818 filed on May 5, 2010, the contents of which are incorporated herein
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`by reference and from which benefits are claimed under 35 U.S.C. 119.
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`FIELD OF THE DISCLOSURE
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`[0001][0002] The present disclosure relates generally to wireless communications and, more
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`particularly, to a feedback framework in wireless communication systems.
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`BACKGROUND
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`[0002][0003] In wireless communication systems, channel state information at a transmitter, for
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`example, at a base station, is important for beam-forming transmissions (also referred to as
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`precoding) that deliver more power to a targeted user while minimizing interference on other
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`users. Precoding operations can be in the context of single-user multiple input multiple output
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`(SU-MIMO) or multi-user MIMO (MU-MIMO), where two or more users are served by a single
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`base station. An eNB needs accurate spatial channel information in order to perform a high rank
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`transmission to a single UE or to perform precoding to two or more UEs simultaneously so that
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`the mutual interference among multiple transmissions can be minimized at each UE.
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`[0003][0004] Precoding operations may also be in the context of SU/MU-MIMO users served
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`by coordinated multi-point (CoMP) transmissions where antennas belonging to different eNBs,
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`rather than to the same eNB, can coordinate their precoding to serve multiple users
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`LG Elecs. Ex. 1019
`LG Elecs. v. Pantech Corp.
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`simultaneously. Further support for up to eight transmit antennas is enabled in the next
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`generation cellular standards like 3GPP LTE Release-10. Due to such a relatively large number
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`of antennas (4-Tx or 8-Tx) involved in such transmissions, it is desirable that the UE feedback be
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`designed efficiently with good performance overhead trade-off, so that feedback does not scale
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`linearly with the increasing number of antennas.
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`[0004][0005] The antenna configurations which support a large number of antennas in practice
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`must allow large beamforming gains and also larger spatial multiplexing gains achieved from
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`higher rank transmission. Beamforming allows efficient support for low geometry users and also
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`for multi-user transmission thereby improving cell-edge and cell-average throughput with larger
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`number of users in the system, while spatial multiplexing allows higher peak spectral efficiency.
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`A typical antenna configuration to achieve this would be to have groups of antennas where each
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`group is a set of correlated antennas and each group is uncorrelated with the other groups. A
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`cross-polarized antenna configuration is one such setup. The correlated antenna elements provide
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`the required beamforming gains and the uncorrelated antenna elements enable high rank
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`transmissions.
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`[0005][0006] The above structure in the antennas has some unique spatial characteristics that
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`can be exploited. For example, the correlation among correlated antennas changes slowly and is
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`confined to a smaller vector space on an average. This can be used to feedback the correlated and
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`uncorrelated channel characteristics, i.e., two components, at different rates and/or with different
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`levels of quantization/overhead in time and frequency to reduce feedback overhead. One of the
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`components representing the correlated channel characteristics can be fed back on a wideband
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`basis and/or slowly in time, while the other component is fed back on a subband basis and/or
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`more frequently in time.
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`[0006][0007] However, one of the key challenges in designing such a two component feedback
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`system is identifying the parameters used in the two components and the construction of the final
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`precoder matrix as a function of the two components.
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`[0007][0008] The various aspects, features and advantages of the invention will become more
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`fully apparent to those having ordinary skill in the art upon a careful consideration of the
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`following Detailed Description thereof with the accompanying drawings described below. The
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`drawings may have been simplified for clarity and are not necessarily drawn to scale.
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`BRIEF DESCRIPTION OF THE DRAWINGS
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`[0008][0009] FIG. 1 illustrates a wireless communication system.
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`[0009][0010] FIG. 2 illustrates an embodiment with a base station transmitting to a device.
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`[0010][0011] FIG. 3 illustrates an example of a frame structure used in the 3GPP LTE Release-
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`8 (Rel-8) specification and different reference symbols.
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`[0011][0012] FIG. 4 illustrates exemplary antenna configurations at a base unit.
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`[0012][0013] FIG. 5 illustrates a first subset of antennas and a second subset of antennas
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`transmitting two spatial layers to a device.
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`[0013][0014] FIG. 6 illustrates a wideband and subbands, each of which is further composed of
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`contiguous subcarriers.
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`DETAILED DESCRIPTION
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`[0014][0015] In FIG. 1, a wireless communication system 100 comprises one or more fixed
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`base infrastructure units 110 and 120 forming a network distributed over a geographical region
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`for serving remote units in the time and/or frequency domain. The base infrastructure unit may
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`also be referred to as the transmitter, access point (AP), access terminal (AT), base, base station
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`(BS), base unit (BU), Node-B (NB), enhanced Node-B (eNB), Home Node-B (HNB), Home
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`eNB (HeNB) or by other terminology used in the art. The base units are generally part of a radio
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`access network that includes one or more controllers communicably coupled to one or more
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`corresponding base units. The access network is generally communicably coupled to one or more
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`core networks, which may be coupled to other packet or data networks, like the Internet, and to
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`public switched telephone networks (PSTN), among other networks. These and other elements of
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`access and core networks are not illustrated but they are well known generally by those having
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`ordinary skill in the art.
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`[0015][0016] The one or more base units each comprise one or more transmitters for downlink
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`transmissions and one or more receivers for receiving uplink transmissions from the remote units
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`as described further below. The one or more base units serve a number of remote units, for
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`example, remote unit 102 and 104 in FIG. 1, within a corresponding serving area, for example, a
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`cell or a cell sector of the base unit, via a wireless communication link. The remote units may be
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`fixed units or wireless communication devices. The remote unit may also be referred to as a
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`receiver, subscriber station (SS), mobile, mobile station (MS), mobile terminal, user, terminals,
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`user equipment (UE), user terminal (UT) or by other terminology used in the art. The remote
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`units also comprise one or more transmitters and one or more receivers. In FIG. 1, the base
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`unit 110 transmits downlink communication signals to serve remote unit 102 in the time and/or
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`frequency domain. The remote unit 102 communicates directly with base unit 110 via uplink
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`communication signals.
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`[0016][0017] The term “transmitter” is used herein to refer to a source of a transmission
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`intended for receipt by a user or receiver. A transmitter may have multiple co-located antennas
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`each of which emits, possibly different, waveforms based on the same information source.
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`In FIG. 1, for example, antennas 112 and 114 are co-located. A transmitter is typically associated
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`with a cell or a cell sector in the case of a base unit having or serving multiple sectors. Also, if a
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`base unit has geographically separated antennas (i.e., distributed antennas with remote radio
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`heads), the scenario is also referred to as “a transmitter”. Thus generally one or more base units
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`transmit information from multiple antennas for reception by a remote unit.
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`[0017][0018] In the diagram 200 of FIG. 2, at 210, a base unit transmits from a plurality of
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`antennas. Also in FIG. 2, a remote unit receives transmissions from a plurality of antennas,
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`which may or may not be co-located. In a typical embodiment, a base unit may be associated
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`with a cell-ID, by which it identifies itself to a remote unit. As a conventional mode of operation,
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`also sometimes referred to as a single-point transmission scheme, a remote unit 240 receives
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`transmissions from a plurality of antennas of a single base unit 210. Such a base unit is also
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`referred to as a serving cell (or serving base unit) to the user device/remote unit.
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`[0018][0019] In one implementation, the wireless communication system is compliant with the
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`Third Generation Partnership Project (3GPP) Universal Mobile Telecommunications System
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`(UMTS) Long Term Evolution protocol, also referred to as Evolved Universal Terrestrial Radio
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`Access (EUTRA), or some future generation thereof, wherein the base unit transmits using an
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`orthogonal frequency division multiplexing (OFDM) modulation scheme on the downlink and
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`the user terminals transmit on the uplink using a single carrier frequency division multiple access
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`(SC-FDMA) scheme. In another implementation, the wireless communication system is
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`compliant with the IEEE 802.16 protocol or a future generation thereof. More generally,
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`however, the wireless communication system may implement some other open or proprietary
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`communication protocol where channel feedback is useful or desired. Thus the disclosure is not
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`intended to be limited to or by the implementation of any particular wireless communication
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`system architecture or protocol. The teachings herein are more generally applicable to any
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`system or operation that utilizes multiple antennas in a transmission, whether the multiple
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`antennas belong to a single base unit or to multiple base units or whether the multiple antennas
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`are geographically co-located (e.g., belong to a single base unit) or distributed (belong to either
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`remote radio heads or multiple cells).
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`[0019][0020] In a general embodiment, pilots or reference symbols are sent from each antenna
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`in a transmitter. These pilots occupy the operational bandwidth to allow users to estimate the
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`channel state information (CSI) of the entire bandwidth. Typically the pilots from different
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`antennas are orthogonal so the pilots do not interfere with each other. Such orthogonality can be
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`ensured if the pilots are sent using different time and/or frequency resources or code resources.
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`For example, in systems based on OFDM technology, the pilots can occupy different subcarriers
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`in frequency or different OFDM symbols in time or share the same set of resources, but different
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`code sequences.
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`[0020][0021] In FIG. 3 illustrates a frame structure used in the 3GPP LTE Release-8 (Rel-8)
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`protocol to illustrate a possible reference symbol (RS) pattern in an OFDM system. A
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`subframe 310 in a radio frame 302 spans 14 OFDM symbols in time. Further a
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`subframe 310 contains multiple resource blocks 312, each spanning 12 consecutive subcarriers in
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`frequency. In typical OFDM based systems like 3GPP LTE, a block of consecutive OFDM
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`symbols are referred to as a subframe. Each sub-carrier location in each of the OFDM symbols is
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`referred to as a resource element (RE), since a single data modulation symbol can be mapped to
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`such a resource element. A resource block (RB) is defined as a block of REs comprising a set of
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`consecutive sub-carrier locations in frequency and a set of symbols. In LTE Rel-8, a slot is
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`defined to span 7 symbols and each subframe is made of two slots, and hence 14 symbols. A
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`minimum resource unit allocated to a user is the two RBs corresponding to two slots in a
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`subframe for a total of 2×12×7 REs. A resource block may be more generally defined as a set of
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`resource elements/OFDM subcarrier resources in time and frequency domain.
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`[0021][0022] Some of the REs in a RB are reserved for reference symbols (also referred to as
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`pilots) to help in the demodulation and other measurements at the UE. These reference symbols,
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`as defined in Release 8 specification of LTE can be further divided into two types. The first type
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`is cell-specific reference symbols, which are cell-specific and “common” to all users, and are
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`transmitted in all the RBs. A common reference symbol (CRS) may or may not correspond to
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`actual physical antennas of the transmitter, but CRSs are associated with one or more antenna
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`“ports”, either physical or virtual. In FIG. 3, as an example only,
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`RE 304, 305, 306, 307, 308 and 309 may be a CRS. The second type is user-specific or a
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`dedicated reference symbol (DRS), which are user-specific and hence applicable only to that
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`user, and allocated in the RB's allocated to that user's data. Furthermore, DRS typically
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`correspond to “precoded” or beam-formed RSs, which can be directly used by a user for the
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`demodulation of the data streams. The precoding operation is explained later. In FIG. 4, as an
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`example only, RE 320, 325, 330, 335, 340, 345, 350 and 355 may be a DRS. In LTE Release-10,
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`a new spare RS, namely CSI-RS are defined to enable channel measurements, while DRSs are
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`primarily relied upon for demodulation. These can be used similar to CRSs in LTE Release-8 to
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`derive channel feedback information.
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`[0022][0023] The location of the reference symbols is known to the UE from higher layer
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`configurations. For example, depending on the number of antenna ports as configured by a
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`transmission unit, UE knows the location of all the reference symbols corresponding to all
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`configured antenna ports. As another example, when a UE is instructed to use a DRS, the UE
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`also knows the DRS locations, which may depend on the user identification.
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`[0023][0024] In typical FDD operation of a LTE Rel-8 system, CRSs are used for both channel
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`related measurements at the UE and also for demodulation. If eNB employs a precoder at the
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`transmitter, such information is made available to the UE, which allows it to construct the
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`channel for demodulation based on the CRSs. In a FDD operation of a future LTE Rel-10
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`system, CSI-RS (and possibly CRSs that may still be available) may be used for channel related
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`measurements, while DRSs are used for demodulation. Hence an eNB may apply precoder which
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`are not exactly the same as the UE feedback, and does not have to signal the precoder explicitly.
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`This is further described in detail later.
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`[0024][0025] The “precoding” operation is explained in the following. The base station
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`transmits a signal via weighting each antenna signal with a complex value, an operation referred
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`to as precoding, which may be mathematically represented by the matrix equation:
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`[0025]
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`
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`Y=HVs+n
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`[0026][0026] in which, when transmitting one spatial layer of data, or rank-1, may be
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`represented as:
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`[0027]
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`
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`[0028][0027] in which, when transmitting two spatial layers of data, or rank-2, may be
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`represented as:
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`[0029]
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`
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`
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`[0030][0028] where y1 . . . yN R may be the received data at the UE receive antenna #1 to #NR,
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`respectively. In the example with a rank-1 transmission, or a transmission with one data stream
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`denoted as “s”, the Matrix V may be a precoding vector with weights v1,1 . . . vN r ,1 for base
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`station transmit antenna #1 to #NT respectively. In an embodiment with a rank-2 transmission, or
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`a transmission with two data streams s1 and s2 on the same subcarrier, V may be a precoding
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`matrix. Precoding vector and precoding matrix can be referred to as precoding matrix given
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`vector is a degenerated case of matrix.
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`[0031][0029] Matrix H may be the propagation channel matrix between transmit antennas and
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`receive antennas with entry hij representing a channel between the jth transmit and ith receive
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`antennas. Value n may represent noise and interference. The precoding weights V, either a vector
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`or matrix, may be determined by the base station, typically based on the channel particular to the
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`UE or can be UE-specific and may also take into account a preference indicated by feedback
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`from the UE. Further the matrix HV can be referred to as the effective channel between a user's
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`data streams and its receivers. The effective channel, instead of the propagation channel H, is all
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`a UE needs for demodulation purposes. The precoding weights may or may not be constrained to
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`a predefined codebook that consists of a set of pre-defined vectors or matrices. In an embodiment
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`with constrained precoding, the precoding matrix may be signaled by the base unit efficiently
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`with a precoding matrix index (PMI) or with an index to a precoding matrix within a predefined
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`codebook. The term “matrix” in this context may include the degenerated special case of vector,
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`which applies to single stream transmission. In the most generic sense, the term “precoding”
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`refers to any possible transmission scheme that may be deemed as mapping a set of data streams
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`to an antenna set using a matrix V.
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`[0032][0030] The applied precoding could be based on corresponding feedback from the UE or
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`channel measurements at a base station. In a simple single-user single base unit scheme, one set
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`of DRSs could be defined corresponding to the effective precoded channel (i.e., “HV” in the
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`above equation). If two streams are transmitted to a user in a rank-2 transmission, then only 2
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`DRS ports (i.e., 2 subsets of DRS each corresponding to a precoded antenna port) are sufficient,
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`even though the actual signal transmission may come from all the NT antennas at the base unit
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`where NT can be greater than 2. In FIG. 3, as an example only, RE 320, 340, 330 and 350 may
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`correspond to one DRS port while RE 325, 345, 335 and 355 may correspond to another DRS
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`port.
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`[0033][0031] In a future migration of a system, for example in 3GPP LTE Release 10 and
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`beyond, user-specific RS (or DRS) are expected to be used widely with advanced Multiple-Input
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`Multiple-Output (MIMO) modes like Coordinated Multipoint transmission (CoMP) and multi-
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`user (MU) MIMO modes described earlier. As described earlier, DRSs are sufficient to enable
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`demodulation. This is also helpful since an eNB is not required to signal exact transmission
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`parameters like precoders, co-ordinating points, etc. However, an estimate of the actual (un-
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`precoded or explicit) channel is required at the eNB to derive such transmission parameters. So
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`as mentioned before, feedback measurements for this purpose are enabled in LTE Release-10 by
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`defining lower density reference signals specifically for the purpose of feedback measurements
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`(CSI-RS). Since they do not need to support demodulation, like CRS in LTE Release 8, a lower
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`density is sufficient. Further, with CoMP, CSI-RS may be setup to enable measurements at the
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`user device on a plurality of antennas from multiple base units. In FIG. 3, as an example only,
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`RE 304, 305, 306, 307, 308 and 309 may also be CSI-RS.
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`[0034][0032] From either CRS or CSI-RS, the remote unit receiver can estimate the CSI. For
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`the OFDM example, the receiver estimates CSI at each subcarrier between each receiver antenna
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`and each transmitter antenna. The CSI may be denoted as a channel matrix on a sub-carrier k
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`represented by
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`[0035]
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`
`
`
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`[0036][0033] where hij is the channel matrix from j th transmit antenna to the ith receive
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`antenna.
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`[0037][0034] A correlation between antenna port i and antenna port j may be computed as
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`follows
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`[0038]
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`[0039][0035] where hki is the channel measured corresponding to antenna port i on subcarrier k,
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`S is a set of subcarriers, typically corresponding to the whole operational bandwidth (denoted as
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`RWB) or a sub-band/narrowband (denoted as RNB).
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`[0040][0036] More generally, an antenna correlation matrix that represents the spatial
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`covariance among a plurality of transmit antennas can be computed as follows
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`[0041]
`
`
`
`
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`[0042][0037] The Eigen Decomposition of R may be expressed in a well-defined format as
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`(1)
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`where V is a unitary matrix of Eigen vectors, where the first column is the most dominant vector,
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`the second column the second dominant vector and so on. D is a diagonal matrix with diagonal
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`entries as Eigen values of R. The full knowledge of R at the transmitter will enable advanced
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`beamforming/precoding techniques that will improve spectral efficiency and system throughput.
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`However, the overhead may be large and approximations suitable to the transmission mode are
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`applied.
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`[0043][0038] For SU-MIMO precoding, the Eigen space information as represented by V above
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`can be viewed as optimal precoding transmission weights in a capacity maximizing sense.
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`[0044][0039] Existing 4th Generation (4G) air interfaces (i.e., 3GPP LTE and IEEE 802.16e)
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`already support beamforming operation via the precoding operation as described earlier. To
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`support precoding operation from the base station, a user terminal will be reporting back to the
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`base station a preferred Precoding Matrix Index (PMI) which is an index to a set of
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`predetermined precoding matrices. The recommended precoding matrix is obtained at the user
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`terminal based on a certain metric such as maximizing the post-precoding link quality or
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`throughput and is selected from one of the quantized codebook entries, wherein the codebook is
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`known to the transmitter and the receiver. Specifically, the standard requires the UE to feedback
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`the PMI that supports a MCS (modulation and coding scheme) with the highest rate, while
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`satisfying a probability if block error target. In future releases, different or more explicit
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`definitions of PMI may be defined. However, in general, the preferred PMI approximately
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`represents a vector quantization of the dominant Eigenspace of R. Further PMI is feedback with
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`an associated rank and as such PMI is an quantized approximation of V(1:r), where ‘r’ is the
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`rank.
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`[0045][0040] FIG. 4 illustrates some exemplary antenna configurations at a base unit. A closely
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`spaced ULA, with a typical spacing of 0.5 to 1 wavelengths, is illustrated in 410. A large spaced
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`ULA with typical spacing of 4 to 10 wavelengths is illustrated in 420. A cross-polarized
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`configuration with two sets of cross-poles each with two antennas at +/−45 polarizations is
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`illustrated in 440. Depending on the configuration, the correlation between different antenna
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`elements may have a certain structure. Some exemplary cases are described herein.
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`[0046][0041] We now illustrate how the structure of the antenna configuration can be used to
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`develop efficient precoder structures.
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`[0047][0042] One of the structures that can be exploited is a Kronecker based approximation of
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`the channel covariance. For example, an 8×8 long term covariance matrix corresponding to 8
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`antennas, as in FIG. 4 at 460, for the transmitter can be approximated as a Kronecker product of
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`a 4×4 correlation matrix corresponding to the ULA and a 2×2 correlation matrix, corresponding
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`to the cross-polarized component i.e.,
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`[0048]
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`
`
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`[0049][0043] Conceptually, the ULA Kronecker component RULA captures the correlation
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`submatrix between two non-overlapping subsets of antennas with similar ULA configuration,
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`which in FIG. 4 at 460 are antenna sets (461-464) and (465-468). The polarization Kronecker
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`component RPol captures the correlation submatrix between subsets with similar cross-polarized
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`configuration, namely antenna subsets (461,465), (462,466), (463,467) and (464,468) in FIG. 4.
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`More generally, the spacing/location and polarization of antenna elements introduce some
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`redundant structure in the antenna correlation, which lead to good Kronecker approximations and
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`can be used as effective compression schemes for feedback overhead reduction. The above
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`representation in the covariance matrix also translates to similar structure for the precoder.
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`[0050][0044] Even for ULA, the transmit antennas can also be divided into two non-
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`overlapping subsets of antennas. An example is shown in FIG. 4 for subset 431 and 432.
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`[0051][0045] The final precoder for SU-MIMO rank-r may be computed as
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`
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`[0052][0046] The principal Eigen vectors and Eigen values of the constructed matrix are related
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`to that of the Kronecker components as
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`
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`(0.2)
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`D = permute(DXP ® DuLA)
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`V = permute(V XP ® VuLA)
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`(0.3)
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`
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`where the “permute” operation performs re-ordering of Eigen values.
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`[0053][0047] We can further illustrate how the reordering influences the structure of the
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`precoder for a 4 Tx cross-pole as an example, where both the ULA and cross-pole sub-matrices
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`are of size 2×2, i.e.,
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`and
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`
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`(0.4)
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`(0.5)
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`
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`
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`Let us consider a rank-2 SU-MIMO transmission as a further example. Typically the cross-pole
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`covariance matrix is highly rank-2 and ULA covariance can be approximated as rank 1. To
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`express it quantitatively, if the two Eigen values ratios satisfy
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`then the rank-2 SU-MIMO precoder, after corresponding re-ordering, can be approximated as
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`
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`(0.6)
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`
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`On the other hand, in case of
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`
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`(which is less likely but could occur on short-term basis, like a subband of contiguous
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`subcarriers), then the rank-2 precoder may be approximated as
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`(0.7)
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`
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`
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`[0054][0048] As can be seen, two structures are shown which allow expressing the overall
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`precoder as a Kronecker product of two precoders. Further, the ULA component of the precoder
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`may be feedback at a different time/frequency granularity than the cross-pole component of the
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`precoder, and allows two component feedback schemes.
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`[0055][0049] Though the Kronecker representation leads to an elegant separation to two
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`component precoders and is one way to achieve two-component feedback, it also imposes some
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`limitations, where either the ULA or the cross-pol component is assumed to be rank 1 for
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`deriving an overall rank-2 precoder. In general, however a more general two-component
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`precoder structure is useful for higher ranks, which will be further discussed below.
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`[0056][0050] For the purpose of discussion, we will assume the long-term/correlated
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`component corresponds to a wide frequency band such as the whole system bandwidth and the
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`short-term component corresponds to a subband/narrowband that is composed of a set of
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`contiguous subcarriers and is a part of the wideband.
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`[0057][0051] The optimal precoding vector V (optimal in an information theoretic capacity
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`maximizing sense) can be obtained from the Eigen decomposition of the narrowband covariance
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`matrix for band indexed ‘b’ as follows.
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`
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`(0.8)
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`
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`For the rank-2 or 2-layer precoder, the ideal precoder is simply the first two columns of VNB,b.
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`Let us denote the rank-2 Eigen decomposition based precoder as follows (a partition based
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`representation of VNB,b)
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`
`
`
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`(0.9)
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`where vij is a 4×1 (assuming 8-Tx eNB) vector. Clearly, each block corresponds to a vector of
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`weights applied on a subset of antennas (e.g., ULA subset) corresponding to one spatial layer of
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`data stream.
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`[0058][0052] In a preferred embodiment, we approximate or otherwise represent VNB,b as
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`(0.10)
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`
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`and then we can impose the constraint ∥v11∥=∥v12∥=∥v21∥=∥v22∥=1 and γij are real values and θ1,
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`
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`θ2 ε[0, 2π].
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`[0059][0053] Clearly, the above precoder representation is based on a matrix with a block of
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`sub-matrices, where each sub-matrix is represented with a vector multiplied with a scalar. More
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`importantly, each sub-matrix corresponds to transmission from a subgroup of antennas, and as
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`one special case, where they all have the same polarization.
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`[0060][0054] FIG. 5 further describes the above precoding operation from two subsets of
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`antennas. Two non-overlapping subsets of antennas 510, 520 are weighted by a first and a
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`second sub-precoder matrix, respectively. Each sub-precoder matrix corresponds to one or more
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`spatial layers of data transmission, for example in FIG. 5, the first sub-precoder is for spatial
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`layer 1 (530) and layer-2 (540). Similarly for the second-precoder, it corresponds to two spatial
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`layers. Mathematically, as an example with eight antennas composed of two groups of 4
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`antennas, where the first subgroup is number 1-4, and second subgroup numbered 5-8, a rank r
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`precoder may be expressed as follows
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`(11)
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`
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`
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`In the above the first sub-precoder is the top 4 rows (1-4) and the second sub-precoder is the
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`bottom 4 rows (5-8)
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`[0061][0055] A precoder matrix of one or more vectors associated with one or more spatial
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`layers consists of a first sub-precoder matrix, which comprises of a first set of weights on a first
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`subsets of transmit antennas of the base station, and a second sub-precoder matrix which
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`comprises of a second set of weights on a second subset of transmit antennas of the base station
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`as illustrated above. The set of weights here can be for one or more spatial layers of
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`transmission.
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`[0062][0056] In the final precoder matrix, the first sub-precoder matrix is one or more column
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`vectors, which are of length equal to the number of antennas in the first subgroup, multiplied by
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`one or more scalars. Similarly for the second sub-precoder.
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`[0063][0057] For practical reasons, it is often preferred to have the precoder satisfy two
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`constraints, namely i) Full power utilization on each transmit antenna, for maximum Power
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`Amplifier (PA) use and ii) Equal power on each transmitted stream. These constraints can be
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`imposed on the precoder structure above [00058][00059]. To satisfy equal power constraint on
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`each transmit stream, we can impose additional constraint of γ11+γ21=γ12+γ22. To satisfy full
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`power utilization on each individual transmit antenna, we could impose as a sufficient condition,
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`that γ11+γ12=γ21+γ22 and that vij are constant modulus vectors. With these constraints, we have
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`another preferred embodiment of the precoder structure as follows,
`
`[0064]
`
`
`
`
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`[0065][0058] The above discussion on the precoder structure is tied to feedback method in this
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`invention. In the feedback scheme for a wireless communication device to send a precoder
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`matrix information to a base station, the wireless communication device sends a first
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`representation of a first matrix chosen from a first codebook, wherein the first matrix has at least
`
`two column vectors. The wireless communication device sends a second representation of a
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`
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`second matrix chosen from a second codebook, wherein the first representation and the second
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`representation together convey a precoder matrix of one or more vectors associated with one or
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`more spatial layers. The precoder matrix comprises a first sub-precoder matrix including a first
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`set of weights on a first subsets of transmit antennas of the base station and a second sub-
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`precoder matrix including a second set of weights on a second subset of transmit antennas of the
`
`base station. The first sub-precoder matrix is one or more column vectors of the first matrix
`
`corresponding to the first representation, multiplied by one or more entries of the second matrix
`
`corresponding to the second representation, and the second sub-precoder matrix is one or more
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`column vectors of the first matrix corresponding to the first representation, multiplied by one or
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`more entries of the second matrix corresponding to the second representation.
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`[0066][0059] The two-component feedback conveys the information of a precoder matrix
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`recommended by the user to the base station. The actual precoder used by the base station may
`
`be different from the suggested precoder, but the actual precoder is derived from the
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`recommended feedback.
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`[0067][0060] We can use the embodiment above to describe a particular example here. A user
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`feeds back a representation of a first chosen matrix that has a set of vectors v11, v12, v21, v22,
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`wherein the representation can be just the index of the chosen matrix within a codebook. Then,
`
`the user feeds back a represen