Classifications

• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/0413—MIMO systems
  • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
  • H04B7/046—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking physical layer constraints into account
  • H04B7/0469—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking physical layer constraints into account taking special antenna structures, e.g. cross polarized antennas into account
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/0413—MIMO systems
  • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
  • H04B7/0478—Special codebook structures directed to feedback optimisation
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/0413—MIMO systems
  • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/0413—MIMO systems
  • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
  • H04B7/0486—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking channel rank into account
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
  • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
  • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
  • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
  • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
  • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
  • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
  • H04B7/0621—Feedback content
  • H04B7/0626—Channel coefficients, e.g. channel state information [CSI]
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
  • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
  • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
  • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
  • H04B7/0636—Feedback format
  • H04B7/0639—Using selective indices, e.g. of a codebook, e.g. pre-distortion matrix index [PMI] or for beam selection
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
  • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
  • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
  • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
  • H04B7/0636—Feedback format
  • H04B7/0641—Differential feedback
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04B—TRANSMISSION
  • H04B7/00—Radio transmission systems, i.e. using radiation field
  • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
  • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
  • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
  • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
  • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
  • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
  • H04B7/0636—Feedback format
  • H04B7/0645—Variable feedback
  • H04B7/065—Variable contents, e.g. long-term or short-short
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
  • H04L1/0023—Systems modifying transmission characteristics according to link quality, e.g. power backoff characterised by the signalling
  • H04L1/0026—Transmission of channel quality indication
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
  • H04L1/0023—Systems modifying transmission characteristics according to link quality, e.g. power backoff characterised by the signalling
  • H04L1/0027—Scheduling of signalling, e.g. occurrence thereof
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L1/00—Arrangements for detecting or preventing errors in the information received
  • H04L1/02—Arrangements for detecting or preventing errors in the information received by diversity reception
  • H04L1/06—Arrangements for detecting or preventing errors in the information received by diversity reception using space diversity
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L25/00—Baseband systems
  • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
  • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
  • H04L25/03891—Spatial equalizers
  • H04L25/03898—Spatial equalizers codebook-based design
  • H04L25/0391—Spatial equalizers codebook-based design construction details of matrices
• • H—ELECTRICITY
  • H04—ELECTRIC COMMUNICATION TECHNIQUE
  • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
  • H04L27/00—Modulated-carrier systems
  • H04L27/18—Phase-modulated carrier systems, i.e. using phase-shift keying
  • H04L27/20—Modulator circuits; Transmitter circuits

Definitions

• the present invention relates to precoding matrix design and, more particularly, to precoding matrix design to derive a precoding matrix as a product of two matrices.
• MIMO multiple antenna or multiple-input and multiple-output
• closed loop transmission technologies such as beamforming and precoding
• the data to be transmitted is divided into one or more streams, the streams are mapped onto one or more transmission layers, and the data in the layers are precoded with a precoder or precoding matrix before transmission.
• the number of transmission layers is called transmission rank.
• the transmission rank can be optimally chosen for a given channel realization by considering, for example, the transmit power and the overall channel statistics.
• a predetermined codebook is made available to the transmitter, i.e., base station (BS), and all receivers, i.e., mobile stations (MSs) or user equipments (UEs).
• the receiver chooses a precoder from the codebook which maximizes its performance (e.g. its data rate) and feeds back the precoder index.
• the selection of precoder rank may also be included in the precoder selection algorithm.
• the feedback rate may vary from a short-term feedback once every coherent time interval to a long-term feedback once every several coherent time intervals.
• the optimal precoders from the codebook for two adjacent transmission blocks are close with respect to a proper distance measure in the set of all possible precoders.
• the adjacent blocks may be considered in time or in frequency, e.g., over the set of tones in orthogonal frequency-division multiplexing (OFDM) systems since in practical systems the channel does not change abruptly from one transmission block to the adjacent one.
• OFDM orthogonal frequency-division multiplexing
• the precoder used in those blocks can be equal if the channel is pretty steady and the codebook resolution is not too high.
• the precoders of the adjacent blocks are not equal anymore, yet, they might be close.
• the closeness between two precoders can be measured based on a proper distance metric in the space of all such precoders.
• precoding codebook design for the 4 transmit antenna (TX) MIMO downlink channel and detail a codebook structure that is suitable for both the uniform linear array (ULA) and the cross-pole antenna configurations, in order to obtain a codebook that is efficient, i.e., has a low feedback overhead and is easy to store and search over, and effective over both uniform linear array (ULA) and the cross-pole configurations.
• the fundamental properties of the spatial correlation matrices that we use have not been exploited in the prior art.
• the codebook structure herein is derived using fundamental properties of the spatial correlation matrices under the ULA and cross-pole antenna configurations.
• Each precoding codeword is derived as the product of two matrices which makes them efficient and achieves lower feedback overhead for a given performance level and better performance for a given feedback overhead.
• E-UTRA Physical layer procedures (Release 10), htt ://www.3 gpp.org/.
• NEC Group "MU-MIMO: CQI Computation and PMI Selection," 3GPP TSG RAN WG1 Rl-103832.
• NEC Group "DL MU-MIMO enhancement via Residual Error Norm feedback," 3GPP TSG RAN WG1 Rl-113874.
• An objective of the present invention is to provide a codebook of efficient precoding codewords which require lower feedback overhead for a given performance level and achieve better performance for a given feedback overhead.
• An aspect of the present invention includes a method implemented in a base station used in a wireless communications system.
• the method comprises having 1 -layer, 2-layer, 3 -layer, and 4-layer codebooks for 4 transmit antenna (4TX) transmission, each codebook including a plurality of precoding matrices, precoding data with one of the plurality of precoding matrices, and transmitting, to a user equipment, the precoded data, wherein each of the 1 -layer and 2 layer codebooks comprises a first codebook and a second codebook, and wherein each precoding matrix in the first codebook comprises a first index and a second index.
• 4TX transmit antenna
• Another aspect of the present invention includes a method implemented in a user equipment used in a wireless communications system.
• the method comprises receiving, from a base station, precoded data, wherein each of 1 -layer, 2-layer, 3 -layer, and 4-layer codebooks for 4 transmit antenna (4TX) transmission includes a plurality of precoding matrices, wherein each of the 1 -layer and 2-layer codebooks comprises a first codebook and a second codebook, and wherein each precoding matrix in the first codebook comprises a first index and a second index.
• Still another aspect of the present invention includes a base station used in a wireless communications system.
• the base station comprises a transmitter to transmit, to a user equipment, precoded data, wherein each of 1 -layer, 2-layer, 3-layer, and 4-layer codebooks for 4 transmit antenna (4TX) transmission includes a plurality of precoding matrices, wherein each of the 1 -layer and 2 layer codebooks comprises a first codebook and a second codebook, and wherein each precoding matrix in the first codebook comprises a first index and a second index.
• Still another aspect of the present invention includes a user equipment used in a wireless communications system.
• the user equipment comprises a receiver to receive, from a base station, precoded data, wherein each of 1 -layer, 2-layer, 3-layer, and 4-layer codebooks for 4 transmit antenna (4TX) transmission includes a plurality of precoding matrices, wherein each of the 1 -layer and 2 layer codebooks comprises a first codebook and a second codebook, and wherein each precoding matrix in the first codebook comprises a first index and a second index.
• Still another aspect of the present invention includes a wireless communications system comprising a base station having 1 -layer, 2-layer, 3 -layer, and 4-layer codebooks for 4 transmit antenna (4TX) transmission, each codebook including a plurality of precoding matrices and precoding data with one of the plurality of precoding matrices, a user equipment receiving, from the base station, the precoded data, wherein each of the 1 -layer and 2 layer codebooks comprises a first codebook and a second codebook, and wherein each precoding matrix in the first codebook comprises a first index and a second index.
• 4TX transmit antenna
• Still another aspect of the present invention includes a method implemented in a wireless communications system.
• the method comprises precoding data; and transmitting, from a base station to a user equipment, the precoded data, wherein each of 1 -layer, 2-layer, 3 -layer, and 4-layer codebooks for 4 transmit antenna (4TX) transmission includes a plurality of precoding matrices, wherein each of the 1 -layer and 2 layer codebooks comprises a first codebook and a second codebook, and wherein each precoding matrix in the first codebook comprises a first index and a second index.
• the first index may be for a plurality of subbands and the second index may be for each subband.
• the second codebook may comprise a legacy codebook or a householder codebook.
• Each of the 3 -layer and 4-layer codebooks may compris a legacy codebook or a householder codebook.
• Still another aspect of the present invention includes a method implemented in a base station used in a wireless communications system.
• Still another aspect of the present invention includes a method implemented in a user equipment used in a wireless communications system.
• Still another aspect of the present invention includes a base station used in a wireless communications system.
• Still another aspect of the present invention includes a user equipment used in a wireless communications system.
• Still another aspect of the present invention includes a method implemented in a wireless communications system.
• Fig. 1 depicts a downlink multiuser MIMO system with N T transmit-antennas at the transmitter and N R receive antennas at the receiver.
• Fig. 3 depicts co-phasing terms in 8-PSK alphabet for Rank-1.
• Fig. 4A depicts co-phasing terms in 16-PSK alphabet for Rank-2.
• Fig. 4B depicts other co-phasing terms in 16-PSK alphabet for Rank-2.
• Fig. 5 depicts co-phasing terms in 8-PSK alphabet for Rank-2.
• Fig. 6A depicts co-phasing terms in 8-PSK alphabet for Rank-1.
• Fig. 6B depicts other co-phasing terms in 8-PSK alphabet for Rank-1.
• Fig. 7 depicts co-phasing terms in 24-PSK alphabet for Rank-2.
• Fig. 8A depicts co-phasing terms in 24-PSK alphabet for Rank-2.
• Fig. 8B depicts co-phasing terms in 12-PSK alphabet for Rank-2.
• Fig. 9 depicts co-phasing terms in 16-PSK alphabet for Rank-2.
• Fig. 10 depicts co-phasing terms in 16-PSK alphabet for Rank-2.
• FIG. 1 shows a downlink multiuser MIMO system with N T transmit-antennas at the BS and N R receive antennas at the UE.
• Multiple-antenna communication system 100 with a multi-level precoding codebook is schematically shown in FIG. 1.
• Transmitter 110 transmits from t transmitting antennas 111.1-111. t over fading channel 130 to r receiving antennas 121.1-121. r coupled to receiver 120.
• Channel estimator 125 provides an estimate of channel 130 to receiver 120. The channel estimate is also quantized and provided to transmitter 110 via quantized rate control feedback channel 135.
• the beamforming matrix (referred to also as a precoding matrix, a precoder, a codeword, or a precoding codeword) generated in response to perceived channel conditions is computed and quantized at the receiver first, and then is provided to the source transmitter (e.g., via feedback).
• a conventional approach to reduce the overhead associated with this feedback is to provide matrix codebook(s) at each of the transmitter and the receiver, each of the codebook(s) comprising a plurality, or set, of potential beamforming matrices that may be used depending on the channel conditions perceived at the receiver.
• the receiver will feed back one or more indices (instead of the actual matrix entries) that points to the appropriate codeword in the codebook(s) stored at the transmitter.
• x denotes the conjugate of x.
• the matrix C is a Hermitian Toeplitz matrix, i.e., C satisfies
• a simplified model for the correlation matrix is the exponential correlation model [3], which is discussed further in the Appendix, and is given by
• ⁇ 2 - ⁇ 3 ⁇ + y 2 - y 3
• the transmitter has 2N cross-polarized antennas comprising of a pair of N co-polarized antennas each.
• the correlation matrix of each one of these two co-polarized sets is denoted by C which is Hermitian and Toeplitz.
• the overall 2N x 2N correlation matrix C can be written as
• the matrix also models the correlation matrix of the 2 transmit ULA.
• the codebook which is suitable for closely spaced 4TX ULA and cross-pole antenna configurations as well as other configurations.
• rank-1 codebook which comprises of a set of 4 x 1 vectors. Without loss of generality, we first consider a generic structure
• the gain vectors corresponding to indices 0,1,2 follow the constraint in (8) and hence are suitable to the 4 TX closely spaced ULA case.
• the gain vector corresponding to index 0 is suitable to the 4 TX cross-pole case, whereas the ones corresponding to indices 3,4 address a scenario referred to here as the power imbalance case (cf. Appendix 8).
• the index 7 indicates re-use of an existing default codebook while indices 5,6 are included to simply offer more choices.
• rank-2 codebook which comprises of a set of semi-unitary 4 x 2 matrices. From the observations made in Section 1 we can define a subset of such matrices having the structure
• the ra -1 outer codebook is defined as
• rank-2 outer codebook is defined as
• rank-3 and rank-4 codebooks can be fixed to the legacy (Householder) rank-3 and rank-4 codebooks.
• the entire legacy codebook can be included as a subset.
• the first embodiment has a desirable property which is missing in the second one.
• This property is that for each rank k, for each choice of inner precoder W ⁇ , assuming that each precoder matrix in the codebook C[(W ⁇ ) corresponding to that rank can be selected equi-probably, the expected value of each row norm square (i.e., sum of the magnitude squares of elements in that row) of the selected precoder matrix is identical. This property is beneficial for operating (i.e., controlling the backoff of) the power amplifiers and utilizing the available transmit power.
• the channel matrix realization depends on both the spatial correlation matrix as well as the short-term (a.k.a. fast) fading.
• the short-term (a.k.a. fast) fading In some scenarios there can be significant variations in the observed channel matrix on account of fast-fading, such as the case where the co-polarized antennas are widely spaced.
• a good codebook needs to accommodate such significant variations in the observed channel matrix on account of fast-fading as well, which makes it necessary to include codewords that are designed using other criteria such as minimum chordal distance [4].
• a useful way to address such cases would be to embed the codebook obtained using the aforementioned principles as a subset in a larger codebook.
• the matrix J for this case can be written as,
• C EAE ⁇ (25) denote its eigen-decomposition
• (. ) ⁇ denotes the conjugate transpose operation
• ⁇ diag ⁇ , ⁇ 2 , ⁇ 3 , ⁇ 4 ⁇ with ⁇ 1 ⁇ ⁇ 2 ⁇ ⁇ 3 ⁇ ⁇ 4 denoting the four real-valued eigenvalues.
• ⁇ ⁇ 2 ⁇ h 4 . 1 h 4 . 2
• h 21 h 22 ⁇ h 31 h 32
• hnh- 14 ⁇ h 4 . 1 h 4 . 4 .
• h 21 h 24 . —h 31 h 34 .
• a more general model for the spatial correlation of the cross-pole antenna configuration is the following.
• a transmitter with 2N cross-polarized antennas comprising of a pair of N co-polarized antennas each.
• the correlation matrix of each one of these two co-polarized sets is denoted by C which is Hermitian and Toeplitz.
• the overall 2N x 2N correlation matrix C can be written as
• rank-1 outer codebook is now defined as
• the rank-1 outer codebook is defined as
• D(q>2) diag ⁇ l,l, exp(j2nY q2 ), exp(j2nY q2 ) ⁇ , i.e., D(q>2) is a diagonal matrix whose main diagonal contains the vector
• the rank-1 outer codebook is defined as
• a rank-1 final codeword is formed by selecting an inner codeword s) from to obtain the final codeword for that subband as s)
• V/ ⁇ (r, s, q2 exp(j2nr q2 )e s -exp(j2nr q2 )e s Jexp(j2nY q2 )e s ⁇ jexp(j2nY q2 )e s
• the outer codebook can be made dependent on the choice of the inner codeword.
• the feasible combinations (r, s) in (2-4) or (r, s, q2) in (2-5) can themselves be functions, respectively, of the choice of the inner codeword.
• two different inner codewords can have different feasible combinations to select codewords from the outer codebook.
• the set of feasible combinations for each choice of the inner codeword is pre-determined and known to all users and the base-stations.
• (. ) is an pre-defined operator such that for any unit-norm vector x, (x) is a unit norm vector in the sub-space I— xx ⁇ .
• an operator may have the property that if the vector x possesses the constant magnitude property, which is that all its elements have the same magnitude, then even (x) has that property.
• An example of such an operator is HH(x, t), which for t E ⁇ 2,3,4 ⁇ and any unit norm vector x whose first element is real and strictly less than one, yields the t th column of the 4 x 4 unitary matrix obtained via the
• MU-MIMO transmission will be served using a rank lower than what it reported. In this case a better resolution will ensure that the column subsets extracted from the user's reported precoders are also effective, i.e., have enough accuracy and thus allow for MU-MIMO gains.
• codebook subset restriction can also be applied on a per-CSI process basis given the choice of component codebooks for those processes.
• codebook subset restriction can also be applied on a per-CSI process basis given the choice of component codebooks for those processes.
• the rank-1 outer (subband) codebook is then defined as where denotes the i / x 1 column selection vector (i.e., the i column of the / x / identity matrix) and exp(/6> s i) is a co-phasing term.
• the (maximum) size of the Rank-1 codebook is thus JS.
• a smaller size can be obtained by selecting only a subset of all possible such vectors.
• the co-phasing terms can be obtained by optimizing a suitable metric such as the average Chordal distance after restricting them to lie in an M-PSK alphabet where the positive integer M > 1 is a design parameter. The optimization can be constrained to ensure that a minimum angular separation is maintained between the co-phasing terms.
• the outer (subband) codebook is defined as
• the co-phasing terms can be obtained by optimizing a suitable metric such as the average Chordal distance after restricting them to lie in an M' -PSK alphabet where the positive integer M' > 1 is a design parameter and can be different from M.
• the optimization can be constrained to ensure that a minimum angular separation is maintained between the co-phasing terms.
• each inner codeword is a 4 x 8 matrix.
• the corresponding sub-band codebook is of size 4-bits for both ranks 1 and 2.
• the co-phasing terms in the rank-1 codebook lie in the 8-PSK alphabet and are given in Fig. 6A or Fig. 6B.
• For the rank-2 codebook we choose
• the rank-3 and rank-4 codebooks can be fixed to the legacy (Householder) rank-3 and rank-4 codebooks.
• legacy Heuseholder
• all codeword matrices in the aforementioned codebook satisfy the constant magnitude property.
• the sub-sampled rank-3 codebook is obtained by removing one or more codewords from the rank-3 legacy codebook whereas by removing one or more codewords from the rank-4 legacy codebook the sub-sampled rank-4 codebook is obtained.
• These sub-sampled codebooks are defined by the network and conveyed in advance to all users. Another approach which offers more flexibility is to leverage codebook subset restriction. Here, suppose that the size
• the network can determine a subset (in a semi-static and possibly user-specific manner) containing no more than M codewords from the legacy rank-3 codebook and convey this subset to the user. The user then restricts its search (for rank-3 codewords) to this subset on each subband.
• the user adopts lexicographic ordering (labelling), i.e., the codeword in the indicated subset having the smallest index (as in the original rank-3 legacy codebook) is assigned a new index of one, the codeword in the indicated subset having the second smallest index (as in the original rank-3 legacy codebook) is assigned a new index of two.
• This process continues till all codewords in the subset have been assigned new indices.
• the new indices will span from 1 to M' where M' ⁇ M.
• the set of new indices is also common across all subbands and hence must be determined by the user once.
• the user then reports the new index of its selected precoder on each subband. The same procedure can be applied for rank-4 as well where we note that the value of M can be different for rank 4 and rank 3.
• CSI process or equivalently the mode defined for that CSI process.
• the user can also report MU-CQI(s) along with its Single-user (SU) channel state information (CSI) report.
• This SU-CSI (comprising of wideband or per-subband PMI, and per-subband CQI) is computed using the pilots and resource elements for interference measurement that are configured for that CSI process.
• MU-CQI(s) Several ways to compute these MU-CQI(s) were detailed in our previous work [9], one of which involved the user using the PMI(s) determined in its SU-CSI report or determined using SU-MIMO rules (referred to below as base-PMI(s)) to compute MU-CQI(s), after assuming (or emulating) a set of co-scheduled interferers (on a subband basis if so configured).
• base-PMI(s) SU-MIMO rules
• Each set of co-scheduled interfering PMIs that the user must assume can be configured by the network in a semi-static (and possibly user-specific) manner.
• the size of the set interfering PMIs can be greater than one.
• the resulting MU-CQI(s) computed on a subband basis can be combined into one or (or at-most two) wideband MU-CQI(s) (as detailed in our work [10] on wideband residual error norm feedback) which are then reported.
• multiple such sets of interfering PMIs for each base-PMI can be configured.
• the user reports one (or at-most two) wideband MU-CQI(s) for each configured set of interfering PMIs and differential feedback can be leveraged to reduce the feedback overhead.
• the process described above can be repeated for several choices of base-PMIs and the user can choose one particular base-PMI (using an appropriate selection rule such as the one maximing an expected MU gain) and report it along with the associated MU-CQI(s).
• N which is referred to as granularity
• / which is equal to the number of beam vectors per inner codeword
• a larger angular span (which can be achieved by having a smaller N (i.e., lower granularity or a larger 2 ⁇ / ⁇ ) for a given /, or a larger / for a given N) would allow us to make the codebook suitable even for less correlated fading scenarios and would also provide robustness against timing alignment errors.
• N i.e., lower granularity or a larger 2 ⁇ / ⁇
• the cost of increasing / is a larger size of each outer sub-band codebook whereas choosing a smaller N can degrade performance in closely spaced cross-pole configuration since it hinders localization of beam vectors in a given inner codeword.
• the scalars ⁇ d q ⁇ (referred to as staggering factors) help control the separation between the phase terms in any two beam vectors that belong with two inner codewords A(q>)W ⁇ 1 ⁇ (/c) and A(q f )V/W (k) for some q, q E ⁇ 1, ⁇ , Q ⁇ .
• staggering factors help control the separation between the phase terms in any two beam vectors that belong with two inner codewords A(q>)W ⁇ 1 ⁇ (/c) and A(q f )V/W (k) for some q, q E ⁇ 1, ⁇ , Q ⁇ .
• staggering factors help control the separation between the phase terms in any two beam vectors that belong with two inner codewords A(q>)W ⁇ 1 ⁇ (/c) and A(q f )V/W (k) for some q, q E ⁇ 1, ⁇ , Q ⁇ .
• a small such separation would be beneficial for exploiting correlation in time and frequency.
• K t and Q are sets of indices associated with the i th granularity N ⁇ . Note that / remains fixed across different granularities. In certain scenarios (with very low correlation) it might be advantageous to choose at-least one of the granularities such that two or more of the beamvectors in many of its associated inner codewords are mutually orthogonal.
• Rank-1 codebook is thus JS.
• a smaller size can be obtained by selecting only a subset of all possible such vectors.
• the co-phasing terms can be obtained by optimizing a suitable metric such as the average Chordal distance after restricting them to lie in an M-PSK alphabet where the positive integer M > 1 is a design parameter. The optimization can be constrained to ensure that a minimum angular separation is maintained between the co-phasing terms.
• the outer (subband) codebook is defined as
• the co-phasing terms can be obtained by optimizing a suitable metric such as the average Chordal distance after restricting them to lie in an M' -PSK alphabet where the positive integer M' > 1 is a design parameter and can be different from M.
• the optimization can be constrained to ensure that a minimum angular separation is maintained between the co-phasing terms.

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