Transmission modes and signaling for uplink MIMO support or single TB dual-layer transmission in LTE uplink

Abstract

An apparatus for mapping data in a wireless communication system. The apparatus includes circuitry for generating a precoding matrix for multi-antenna transmission based on a precoding matrix indicator (PMI) feedback from at least one remote receiver where the PMI indicates a choice of precoding matrix derived from a matrix multiplication of two matrices from a first code book and a second codebook. The apparatus further includes circuitry for precoding one or more layers of a data stream with the precoding matrix and transmitting the precoded layers of data stream to the remote receiver.

Claims

1. A method comprising: determining a first precoding matrix indicator (PMI) value and a second PMI value, the first and second PMI values being indicative of a precoding matrix W derived from a matrix multiplication of a W1 matrix and a W2 matrix, the W1 matrix corresponding to a matrix from a first codebook C1, the W2 matrix corresponding to a matrix from a second codebook C2, the first PMI value corresponding to the W1 matrix and the second PMI value corresponding to the W2 matrix, wherein the second codebook C2 includes the following matrices: $\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ \mathrm{jY}\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -\mathrm{jY}\end{array}\right]\right\},$ $\text{where:}$ $Y\in \left\{\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]\right\};$ transmitting the first PMI value at a first periodicity; transmitting the second PMI value at a second periodicity different than the first periodicity; and transmitting a rank indicator (RI) value at the first periodicity.

2. The method of claim 1, wherein: the first codebook C1 includes at least the following matrices: $B=\left[\begin{array}{cccc}{b}_0& b_1& \mathrm{.Math.}& b_{15}\end{array}\right],{\left[B\right]}_{1+m,1+n}=e^{j\frac{2\pi \mathrm{mn}}{16}},m=0,1,2,3n=0,1,\mathrm{.Math.},15$ $X^{\left(k\right)}\in \left\{\left[\begin{array}{cccc}{b}_{\left(2k\right)\mathrm{mod}16}& b_{\left(2k+1\right)\mathrm{mod}16}& b_{\left(2k+2\right)\mathrm{mod}16}& b_{\left(2k+3\right)\mathrm{mod}16}\end{array}\right]\text{:}k=0,1,\mathrm{.Math.},7\right\}$ $W_1^{\left(k\right)}=\left[\begin{array}{cc}{X}^{\left(k\right)}& 0\\ 0& X^{\left(k\right)}\end{array}\right],C_1=\left\{W_1^{\left(0\right)},W_1^{\left(1\right)},W_1^{\left(2\right)},\mathrm{.Math.},W_1^{\left(7\right)}\right\}.$

3. The method of claim 1, wherein: the first PMI value is periodically transmitted within a same set of subframes as a rank indicator, and the second PMI value is periodically transmitted within a different set of subframes from the first PMI value.

4. The method of claim 1, wherein determining the first PMI value and the second PMI value includes: selecting the first PMI value from a first set of PMI values, each of the PMI values in the first set of PMI values corresponding to a respective one of a plurality of first matrices in the first codebook C1; and selecting the second PMI value from a second set of PMI values, each of the PMI values in the second set of PMI values corresponding to a respective one of a plurality of second matrices in the second codebook C2.

5. The method of claim 4, wherein: the first PMI value is periodically transmitted within a same set of subframes as a rank indicator, and the second PMI value is periodically transmitted within a different set of subframes from the first PMI value.

6. A method comprising: determining a first precoding matrix indicator (PMI) value and a second PMI value, the first and second PMI values being indicative of a precoding matrix W, the precoding matrix W being equal to a matrix multiplication of a W1 matrix and a W2 matrix, the W1 matrix corresponding to a matrix from a first codebook C1, the W2 matrix corresponding to a matrix from a second codebook C2, the first PMI value corresponding to the W1 matrix and the second PMI value corresponding to the W2 matrix, wherein the second codebook C2 includes the following matrices: $\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ \mathrm{jY}\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -\mathrm{jY}\end{array}\right]\right\},$ $\text{where:}$ $Y\in \left\{\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]\right\};$ transmitting the first PMI value at a first periodicity; transmitting the second PMI value at a second periodicity different than the first periodicity; and transmitting a rank indicator (RI) value at the first periodicity.

7. The method of claim 6, wherein: the first codebook C1 includes at least the following matrices: $B=\left[\begin{array}{cccc}{b}_0& b_1& \mathrm{.Math.}& b_{15}\end{array}\right],{\left[B\right]}_{1+m,1+n}=e^{j\frac{2\pi \mathrm{mn}}{16}},m=0,1,2,3n=0,1,\mathrm{.Math.},15$ $X^{\left(k\right)}\in \left\{\left[\begin{array}{cccc}{b}_{\left(2k\right)\mathrm{mod}16}& b_{\left(2k+1\right)\mathrm{mod}16}& b_{\left(2k+2\right)\mathrm{mod}16}& b_{\left(2k+3\right)\mathrm{mod}16}\end{array}\right]\text{:}k,0,1,\mathrm{.Math.},7\right\}$ $W_1^{\left(k\right)}=\left[\begin{array}{cc}{X}^{\left(k\right)}& 0\\ 0& X^{\left(k\right)}\end{array}\right],C_1=\left\{W_1^{\left(0\right)},W_1^{\left(1\right)},W_1^{\left(2\right)},\mathrm{.Math.},W_1^{\left(7\right)}\right\}.$

8. The method of claim 6, wherein: the first PMI value is periodically transmitted within a same set of subframes as a rank indicator, and the second PMI value is periodically transmitted within a different set of subframes from the first PMI value.

9. The method of claim 6, wherein determining the first PMI value and the second PMI value includes: selecting the first PMI value from a first set of PMI values, each of the PMI values in the first set of PMI values corresponding to a respective one of a plurality of first matrices in the first codebook C1; and selecting the second PMI value from a second set of PMI values, each of the PMI values in the second set of PMI values corresponding to a respective one of a plurality of second matrices in the second codebook C2.

10. The method of claim 9, wherein: the first PMI value is periodically transmitted within a same set of subframes as a rank indicator, and the second PMI value is periodically transmitted within a different set of subframes from the first PMI value.

11. A user equipment (UE) comprising: a processor configured to determine a first precoding matrix indicator (PMI) value and a second PMI value, the first and second PMI values being indicative of a precoding matrix W derived from a matrix multiplication of a W1 matrix and a W2 matrix, the W1 matrix corresponding to a matrix from a first codebook C1, the W2 matrix corresponding to a matrix from a second codebook C2, the first PMI value corresponding to the W1 matrix and the second PMI value corresponding to the W2 matrix, wherein the second codebook C2 includes the following matrices: $\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ \mathrm{jY}\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -\mathrm{jY}\end{array}\right]\right\},$ $\text{where:}$ $Y\in \left\{\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]\right\};$ and a transceiver configured to transmit the first PMI value at a first periodicity, transmit the second PMI value at a second periodicity different than the first periodicity, and to transmit a rank indicator (RI) value at the first periodicity.

12. The UE of claim 11, wherein: the first codebook C1 includes at least the following matrices: $B=\left[\begin{array}{cccc}{b}_0& b_1& \mathrm{.Math.}& b_{15}\end{array}\right],{\left[B\right]}_{1+m,1+n}=e^{j\frac{2\pi \mathrm{mn}}{16}},m=0,1,2,3n=0,1,\mathrm{.Math.},15$ $X^{\left(k\right)}\in \left\{\left[\begin{array}{cccc}{b}_{\left(2k\right)\mathrm{mod}16}& b_{\left(2k+1\right)\mathrm{mod}16}& b_{\left(2k+2\right)\mathrm{mod}16}& b_{\left(2k+3\right)\mathrm{mod}16}\end{array}\right]\text{:}k,0,1,\mathrm{.Math.},7\right\}$ $W_1^{\left(k\right)}=\left[\begin{array}{cc}{X}^{\left(k\right)}& 0\\ 0& X^{\left(k\right)}\end{array}\right],C_1=\left\{W_1^{\left(0\right)},W_1^{\left(1\right)},W_1^{\left(2\right)},\mathrm{.Math.},W_1^{\left(7\right)}\right\}.$

13. The UE of claim 11, wherein: the first PMI value is periodically transmitted within a same set of subframes as a rank indicator, and the second PMI value is periodically transmitted within a different set of subframes from the first PMI value.

14. The UE of claim 11, wherein the processor is further configured to: select the first PMI value from a first set of PMI values, each of the PMI values in the first set of PMI values corresponding to a respective one of a plurality of first matrices in the first codebook C1; and select the second PMI value from a second set of PMI values, each of the PMI values in the second set of PMI values corresponding to a respective one of a plurality of second matrices in the second codebook C2.

15. The UE of claim 14, wherein: the first PMI value is periodically transmitted within a same set of subframes as a rank indicator, and the second PMI value is periodically transmitted within a different set of subframes from the first PMI value.

16. A user equipment (UE) comprising: a processor configured to determine a first precoding matrix indicator (PMI) value and a second PMI value, the first and second PMI values being indicative of a precoding matrix W, the precoding matrix W being equal to a matrix multiplication of a W1 matrix and a W2 matrix, the W1 matrix corresponding to a matrix from a first codebook C1, the W2 matrix corresponding to a matrix from a second codebook C2, the first PMI value corresponding to the W1 matrix and the second PMI value corresponding to the W2 matrix, wherein the second codebook C2 includes the following matrices: $\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ \mathrm{jY}\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -\mathrm{jY}\end{array}\right]\right\},$ $\text{where:}$ $Y\in \left\{\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]\right\};$ and a transceiver configured to transmit the first PMI value at a first periodicity, transmit the second PMI value at a second periodicity different than the first periodicity, and to transmit a rank indicator (RI) value at the first periodicity.

17. The UE of claim 16, wherein: the first codebook C1 includes at least the following matrices: $B=\left[\begin{array}{cccc}{b}_0& b_1& \mathrm{.Math.}& b_{15}\end{array}\right],{\left[B\right]}_{1+m,1+n}=e^{j\frac{2\pi \mathrm{mn}}{16}},m=0,1,2,3n=0,1,\mathrm{.Math.},15$ $X^{\left(k\right)}\in \left\{\left[\begin{array}{cccc}{b}_{\left(2k\right)\mathrm{mod}16}& b_{\left(2k+1\right)\mathrm{mod}16}& b_{\left(2k+2\right)\mathrm{mod}16}& b_{\left(2k+3\right)\mathrm{mod}16}\end{array}\right]\text{:}k,0,1,\mathrm{.Math.},7\right\}$ $W_1^{\left(k\right)}=\left[\begin{array}{cc}{X}^{\left(k\right)}& 0\\ 0& X^{\left(k\right)}\end{array}\right],C_1=\left\{W_1^{\left(0\right)},W_1^{\left(1\right)},W_1^{\left(2\right)},\mathrm{.Math.},W_1^{\left(7\right)}\right\}.$

18. The UE of claim 16, wherein: the first PMI value is periodically transmitted within a same set of subframes as a rank indicator, and the second PMI value is periodically transmitted within a different set of subframes from the first PMI value.

19. The UE of claim 16, wherein the processor is further configured to: select the first PMI value from a first set of PMI values, each of the PMI values in the first set of PMI values corresponding to a respective one of a plurality of first matrices in the first codebook C1; and select the second PMI value from a second set of PMI values, each of the PMI values in the second set of PMI values corresponding to a respective one of a plurality of second matrices in the second codebook C2.

20. The UE of claim 19, wherein: the first PMI value is periodically transmitted within a same set of subframes as a rank indicator, and the second PMI value is periodically transmitted within a different set of subframes from the first PMI value.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) These and other aspects of this invention are illustrated in the drawings, in which:

(2) FIG. 1 illustrates an exemplary prior art wireless communication system to which this application is applicable;

(3) FIG. 2 shows the Evolved Universal Terrestrial Radio Access (E-UTRA) Time Division Duplex (TDD) frame structure of the prior art;

(4) FIG. 3 is a simplified block diagram describing a precoder selection mechanism at the receiver (UE) based on the dual-stage codebook;

(5) FIG. 4 shows some examples of configuration for 8-antenna array (a) array of ULA pairs (b) dual-polarized array;

(6) FIG. 5 is an example of reporting configuration where the first PMI (PMI.sub.1) is reported together with RI and separately from the second PMI (PMI.sub.2);

(7) FIG. 6 is an example of reporting configuration where the first PMI (PMI.sub.1) is reported together with the second PMI (PMI.sub.2) and separately from RI;

(8) FIG. 7 is an example of reporting configuration where the first PMI (PMI.sub.1) and the second PMI (PMI.sub.2) are reported separately from each other and from RI; and

(9) FIG. 8 is a block diagram illustrating internal details of a base station and a mobile user equipment in the network system of FIG. 1 suitable for implementing this invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

(10) FIG. 1 shows an exemplary wireless telecommunications network 100. The illustrative telecommunications network includes base stations 101, 102 and 103, though in operation, a telecommunications network necessarily includes many more base stations. Each of base stations 101, 102 and 103 (eNB) are operable over corresponding coverage areas 104, 105 and 106. Each base station's coverage area is further divided into cells. In the illustrated network, each base station's coverage area is divided into three cells. Handset or other user equipment (UE) 109 is shown in Cell A 108. Cell A 108 is within coverage area 104 of base station 101. Base station 101 transmits to and receives transmissions from UE 109. As UE 109 moves out of Cell A 108 and into Cell B 107, UE 109 may be handed over to base station 102. Because UE 109 is synchronized with base station 101, UE 109 can employ non-synchronized random access to initiate handover to base station 102.

(11) Non-synchronized UE 109 also employs non-synchronous random access to request allocation of up-link 111 time or frequency or code resources. If UE 109 has data ready for transmission, which may be traffic data, measurements report, tracking area update, UE 109 can transmit a random access signal on up-link 111. The random access signal notifies base station 101 that UE 109 requires up-link resources to transmit the UEs data. Base station 101 responds by transmitting to UE 109 via down-link 110, a message containing the parameters of the resources allocated for UE 109 up-link transmission along with a possible timing error correction. After receiving the resource allocation and a possible timing advance message transmitted on down-link 110 by base station 101, UE 109 optionally adjusts its transmit timing and transmits the data on up-link 111 employing the allotted resources during the prescribed time interval.

(12) Base station 101 configures UE 109 for periodic uplink sounding reference signal (SRS) transmission. Base station 101 estimates uplink channel quality information (CSI) from the SRS transmission.

(13) FIG. 2 shows the Evolved Universal Terrestrial Radio Access (E-UTRA) time division duplex (TDD) Frame Structure. Different subframes are allocated for downlink (DL) or uplink (UL) transmissions. Table 1 shows applicable DL/UL subframe allocations.

(14) TABLE-US-00001 TABLE 1 Con- Switch-point Sub-frame number figuration periodicity 0 1 2 3 4 5 6 7 8 9 0  5 ms D S U U U D S U U U 1  5 ms D S U U D D S U U D 2  5 ms D S U D D D S U D D 3 10 ms D S U U U D D D D D 4 10 ms D S U U D D D D D D 5 10 ms D S U D D D D D D D 6 10 ms D S U U U D S U U D

(15) The preferred embodiments of the present invention provide improved communication through precoded multi-antenna transmission with codebook-based feedback. In a cellular communication system a user equipment (UE) is uniquely connected to and served by a single cellular base station (eNB) at a given time. An example of such system is the 3GPP Long-Term Evolution (LTE) which includes the LTE-Advanced (LTE-A) system. With increasing number of transmit antennas at the eNB, the task of designing an efficient codebook with desirable properties is challenging. This set of properties includes the following for 8-antenna-port (termed 8 Tx) system.

(16) (1) Applicability for several relevant antenna setups and spatial channel conditions. Relevant 8 Tx antenna setups typically result in a structured spatial covariance matrix which is a long-term channel statistics. Some relevant antenna setups for 8 Tx include: Uniform linear array (ULA) with L/2 (half wavelength) spacing; 4 dual-polarized elements with L/2 spacing between two elements; and 4 dual-polarized elements with 4L (larger) spacing between two elements

(17) (2) Applicability for both Single User Multiple Input, Multiple Output (SU-MIMO) and Multiple User Multiple Input, Multiple Output (MU-MIMO).

(18) (3) Finite alphabet whereby each matrix element belongs to a finite set of values or constellation such as Quadrature Phase Shift Keying (QPSK) or Phase Shift Keying (8PSK) alphabet.

(19) (4) Constant modulus where all elements in a precoding matrix have the same magnitude. This ensures power amplifier (PA) balance property in all scenarios.

(20) (5) Nested property where every matrix/vector of rank-n is a sub-matrix of a rank-(n+1) precoding matrix, n=1, 2, . . . N−1 where N is the maximum number of layers.

(21) (6) The associated signaling overhead should be minimized especially UE feedback.

(22) A precoding structure that fulfills properties 1 and 2 separates the long-term and short-term components of the precoder. Long-term and short-term refer to the need for feedback interval or time granularity which may be associated with frequency granularity as well. The long-term component does not need high frequency granularity while the short-term component may need higher frequency granularity. A particular structure of interest known as a dual-stage precoder is as follows:
W=ƒ(W.sub.1,W.sub.2)  (1)
where: W.sub.1 is the long-term component; and W.sub.2 is the short-term component. Each component is assigned a codebook. Thus two distinct codebooks CB.sub.1 and CB.sub.2 are needed. W.sub.1 adapts to the long-term channel statistics such as the spatial covariance matrix. W.sub.2 adapts to the short-term channel properties such as phase adjustment needed to counteract short-term fading. For this structure the feedback overhead can be potentially reduced as compared to a one-stage counterpart since W.sub.1 does not need to be updated as often as W.sub.2. An example of the matrix function f(.,.) includes a product (matrix multiplication) function f(x,y)=xy or the Kronecker product function ƒ(x,y)=x.Math.y. The dual-stage representation in (1) can be thought as a multiple-codebook design where:

(23) (1) A set of N codebooks {W.sub.1.sup.(0), W.sub.1.sup.(1), . . . , W.sub.1.sup.(N-1)} are defined where one codebook is selected out of the N codebooks in a long-term basis. This (first) codebook is represented by W.sub.1 in equation (1). The choice of W.sub.1 is enumerated by a precoding matrix indicator PMI.sub.1 where PMI.sub.1∈{0, 1, . . . , N−1}.

(24) (2) The short-term precoding matrix/vector is then derived from the chosen codebook via a short-term operation. The short-term operation is represented by W.sub.2 in (1). Note that W.sub.2 can be as simple as selecting a sub-matrix of W.sub.1 or performing linear combining across a subset of column vectors of W.sub.1. In this case, all possible W.sub.2 matrices/vectors (for a given W.sub.1) formed a second codebook CB.sub.2. For an efficient design, the second codebook CB.sub.2 is made dependent on the choice of the first codebook W.sub.1. The choice of W.sub.2 is enumerated by a precoding matrix indicator PMI.sub.2 where PMI.sub.2∈{0, 1, . . . , M.sub.2−1} where M.sub.2=|CB.sub.2(PMI.sub.1)|. Notice the dependence of CB.sub.2 on PMI.sub.1.

(25) FIG. 3 illustrates the precoding matrix/vector selection process. The final precoding matrix/vector is a function of two PMIs:
W=ƒ(PMI.sub.1,PMI.sub.2)  (2)
where: PMI.sub.1 is updated at a significantly less frequent rate than PMI.sub.2. PMI.sub.1 is intended for the entire system bandwidth while PMI.sub.2 can be frequency-selective.

(26) FIG. 3 illustrates the technique used in downlink LTE-Advanced (LTE-A). The UE selects PMI.sub.1 and PMI.sub.2 and hence W.sub.1 and W.sub.2 in a manner similar to the LTE feedback paradigm.

(27) The UE first selects the first precoder codebook W.sub.1 (block 311) based on the long-term channel properties such as spatial covariance matrix such as in a spatial correlation domain from an input of PMI.sub.1. This is done in a long-term basis consistent with the fact that spatial covariance matrix needs to be estimated over a long period of time and in a wideband manner.

(28) Conditioned upon W.sub.1, the UE selects W.sub.2 based on the short-term (instantaneous) channel. This is a two stage process. Block 312 selects one of a set of codebooks CB.sub.2.sup.(0) to CB.sub.2.sup.(N-1) based upon the PMI.sub.1 input. Block 313 selects one precoder corresponding to the selected codebook CB.sub.2.sup.(PMI.sup.1.sup.) and PMI.sub.2. This selection may be conditioned upon the selected rank indicator (RI). Alternatively, RI can be selected jointly with W.sub.2. Block 314 takes the selected W.sub.1 and W.sub.2 and forms the function ƒ(W.sub.1, W.sub.2).

(29) PMI.sub.1 and PMI.sub.2 are reported to the base station (eNodeB or eNB) at different rates and/or different frequency resolutions.

(30) Based on this design framework, several types of codebook design are described. While each type can stand alone, it is also possible to use different types in a single codebook design especially if the design is intended for different scenarios. A simple yet versatile design can be devised as follows:

(31) PMI.sub.1 selects one of the N codebooks W.sub.1 as indicated above.

(32) PMI.sub.2 selects at least one of the column vectors of W.sub.1. The number of selected column vectors is essentially the recommended transmission rank (RI).

(33) This design allows construction of N different scenarios where the codebook W.sub.1 for each scenario is chosen to contain a set of basis vectors for a particular spatial channel characteristic W.sub.2. While any two-dimensional function can be used in equation (2), the patent application assumes a product (matrix multiplication) function f(x,y)=xy. Thus the final short-term precoding matrix/vector is computed as a matrix product of W.sub.1 and W.sub.2: W=W.sub.1W.sub.2.

(34) Consider an embodiment of a dual-codebook design for 8 Tx ULA with L/2 spacing at the transmitter (eNB). For this particular antenna setup, a set of discrete Fourier transform (DFT) vectors forms a complete basis and hence serves as a good codebook. The following construction for rank-1 transmission can be used:

(35) $\begin{array}{cc}{W}_1=\frac{1}{2\sqrt{2}}\left[\begin{array}{cccc}1& 1& \mathrm{.Math.}& 1\\ 1& e^{j\frac{2\pi }{8}}& \mathrm{.Math.}& e^{j\left(7\right)\frac{2\pi }{8}}\\ \mathrm{.Math.}& \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ 1& e^{j\left(7\right)\frac{2\pi }{8}}& \mathrm{.Math.}& e^{j\left(7\right)\left(7\right)\frac{2\pi }{8}}\end{array}\right],{\mathrm{CB}}_2=\left\{\left[\begin{array}{c}1\\ 0\\ \mathrm{.Math.}\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ \mathrm{.Math.}\\ 0\end{array}\right],\mathrm{.Math.},\left[\begin{array}{c}0\\ 0\\ \mathrm{.Math.}\\ 1\end{array}\right]\right\}& \left(3\right)\end{array}$
Here N=1 thus having no need for PMI.sub.1. CB.sub.2 consists of 8 selection vectors which imply at least 3 bits of signaling for PMI.sub.2. For higher ranks, CB.sub.2 represents group selection. For example CB.sub.2 for rank-2 may include all or a subset of the twenty eight possible 8×2 group selection matrices which selects 2 out of 8 beams.

(36) This represents the critically-sampled DFT vectors. Generally it is beneficial to use oversampled DFT vectors especially for MU-MIMO or space-division multiple access (SDMA) applications. While a design with N=1 with 8×8n matrix W.sub.1, where n is the oversampling factor, is possible, overhead reduction for updating W.sub.2 can be obtained by partitioning the 8n DFT vectors into multiple W.sub.1 matrices. Such partitioning uses the fact that the direction of arrival (DoA) varies quite slowly for each UE. With n=4 resulting in a total of 32 DFT vectors and keeping the size of W.sub.1 as 8×8, the following construction can be used:

(37) $\begin{array}{cc}{W}_1^{\left(n\right)}=\frac{1}{2\sqrt{2}}\hspace{1em}\times \hspace{1em}\hspace{1em}\hspace{1em}\left[\begin{array}{cccc}1& 1& \mathrm{.Math.}& 0\\ 0& e^{j\left(8\right)\frac{2\pi }{\left(8\right)\left(4\right)}n}& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ 0& 0& \mathrm{.Math.}& e^{j\left(7\right)\left(8\right)\frac{2\pi }{\left(8\right)\left(4\right)}n}\end{array}\right][\begin{array}{cccc}1& 1& \mathrm{.Math.}& 1\\ 1& e^{j\frac{2\pi }{\left(8\right)\left(4\right)}}& \mathrm{.Math.}& e^{j\left(7\right)\frac{2\pi }{\left(8\right)\left(4\right)}}\\ \mathrm{.Math.}& \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ 1& e^{j\left(7\right)\frac{2\pi }{\left(8\right)\left(4\right)}}& \mathrm{.Math.}& e^{j\left(7\right)\left(7\right)\frac{2\pi }{\left(8\right)\left(4\right)}}\end{array}],n=0,1,2,3{\mathrm{CB}}_2=\left\{\left[\begin{array}{c}1\\ 0\\ \mathrm{.Math.}\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ \mathrm{.Math.}\\ 0\end{array}\right],\mathrm{.Math.},\left[\begin{array}{c}0\\ 0\\ \mathrm{.Math.}\\ 1\end{array}\right]\right\}& \left(4\right)\end{array}$
Here CB.sub.2 (size-8) is the same for different W.sub.1 matrices. In this case N=4. The selection of W.sub.1 is indicated by PMI.sub.1 which requires a 2-bit signaling. This divides the DoA space into 4 partitions.

(38) Partition 1 (n=0): DoA={0, 22.5, 45, 67.5} in degrees,

(39) Partition 2 (n=1): DoA={90, 112.5, 135, 157} in degrees,

(40) Partition 3 (n=2): DoA={180, 202.5, 225, 247.5} in degrees, and

(41) Partition 4 (n=3): DoA={270, 292.5, 315, 337.5} in degrees.

(42) A total of 32 length-8 vectors are obtained from {W.sub.1.sup.(0), W.sub.1.sup.(1), W.sub.1.sup.(2), W.sub.1.sup.(3)} which amounts to oversampling the 8-dimensional angle space by a factor of 4. It is possible to synthesize each of the 32 vectors from the 8-DFT matrix used in equation (3) as the 8 orthonormal column vectors in the 8-DFT matrix form a complete basis for 8-dimensional complex-valued space. This is be achieved by choosing W.sub.2 accordingly. This minimizes the number of W.sub.1, but it increases the required number W.sub.2 vectors. This increase goes against the purpose of saving the short-term feedback overhead incurred by W.sub.2.

(43) This construction divides the DoA space into 4 partitions. Each UE may update PMI.sub.1 and thus W.sub.1 at a lower rate as the DoA region in which each UE resides changes slowly. The precise DoA may change at a faster rate. This is adapted with the change of W.sub.2.

(44) This construction can be generalized to any oversampling factor n and any number of partitions. A design with n=2 resulting in a total of 16 DFT vectors is shown in equation (4b). In this case N=2. The selection of W.sub.1 is indicated by PMI.sub.1 which requires 1-bit signaling. This divides the DoA space into 2 partitions.

(45) Partition 1 (n=0): DoA={0, 22.5, 45, 67.5, 90, 112.5, 135, 157.5} in degrees, and

(46) Partition 2 (n=1): DoA={180, 202.5, 225, 247.5, 270, 292.5, 315, 337.5} in degrees.

(47) $\begin{array}{cc}{W}_1^{\left(n\right)}=\frac{1}{2\sqrt{2}}\times \left[\begin{array}{cccc}1& 0& \mathrm{.Math.}& 0\\ 0& e^{j\left(8\right)\frac{2\pi }{\left(8\right)\left(2\right)}n}& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ 0& 0& \mathrm{.Math.}& e^{j\left(7\right)\left(8\right)\frac{2\pi }{\left(8\right)\left(2\right)}n}\end{array}\right]\hspace{1em}\left[\begin{array}{cccc}1& 1& \mathrm{.Math.}& 1\\ 1& e^{j\frac{2\pi }{\left(8\right)\left(2\right)}}& \mathrm{.Math.}& e^{j\left(7\right)\frac{2\pi }{\left(8\right)\left(2\right)}}\\ \mathrm{.Math.}& \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ 1& e^{j\left(7\right)\frac{2\pi }{\left(8\right)\left(2\right)}}& \mathrm{.Math.}& e^{j\left(7\right)\left(7\right)\frac{2\pi }{\left(8\right)\left(2\right)}}\end{array}\right],n=0,1{\mathrm{CB}}_2=\left\{\left[\begin{array}{c}1\\ 0\\ \mathrm{.Math.}\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ \mathrm{.Math.}\\ 0\end{array}\right],\mathrm{.Math.},\left[\begin{array}{c}0\\ 0\\ \mathrm{.Math.}\\ 1\end{array}\right]\right\}& \left(4b\right)\end{array}$
Instead of dividing the DoA space into several DoA-contiguous partitions, it is possible to divide the DoA space into N comb-like partitions as shown in equation (5).

(48) $\begin{array}{cc}{W}_1^{\left(n\right)}=\frac{1}{2\sqrt{2}}\times \left[\begin{array}{cccc}1& 0& \mathrm{.Math.}& 0\\ 0& e^{j\frac{\pi n}{4N}}& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ 0& 0& \mathrm{.Math.}& e^{j7\frac{\pi n}{4N}}\end{array}\right]\hspace{1em}\left[\begin{array}{cccc}1& 1& \mathrm{.Math.}& 1\\ 1& e^{j\frac{2\pi }{8}}& \mathrm{.Math.}& e^{j\left(7\right)\frac{2\pi }{8}}\\ \mathrm{.Math.}& \mathrm{.Math.}& \ddots & \mathrm{.Math.}\\ 1& e^{j\left(7\right)\frac{2\pi }{8}}& \mathrm{.Math.}& e^{j\left(7\right)\left(7\right)\frac{2\pi }{8}}\end{array}\right],n=0,1,\mathrm{.Math.},N-1& \left(5\right)\end{array}$
With N=2 this results in the following 2 partitions:

(49) Partition 1: DoA={0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4} in radians, and

(50) Partition 1: DoA=π/8+{0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4} in radians.

(51) One of the drawbacks of this design is the need for higher update rate of PMI.sub.1 because a slight change of DoA over time requires updating W.sub.1. Unless W.sub.1 is updated at the same rate as W.sub.2 the short-term adaptation, this design may not be preferred from overhead perspective.

(52) When using this design for higher ranks, the same set or different sets of W.sub.1 matrices can be used as codebook CB.sub.1 for different ranks. Regardless, there are several possible schemes that can be used to construct higher-rank precoding matrices from these W.sub.1 constructions. Some schemes include construction based on group selection of the columns of W.sub.1. For W.sub.1 of size 8×M, CB.sub.2 for rank-2 consists of all or a subset of the M*(M−1)/2 possible M×2 group selection matrices which selects 2 out of M beams. This is possible, but the composite precoding matrix W is preferably unitary to ensure constant output power. This cannot be guaranteed for any W.sub.1 matrix unless W.sub.1 is also unitary. A precoding matrix for higher rank can be constructed only from orthogonal column vectors of W.sub.1. For example take the rank-1 construction in equation (4b) where M=8. For a given W.sub.1 and one of its column vectors v, there are 3 other column vectors that are orthogonal to v. Table 2 shows this in terms of beam angle θ where the corresponding length-8 vector is:

(53) $\begin{array}{cc}v\left(\theta \right)=\frac{1}{2\sqrt{2}}\times {\left[\begin{array}{cccccccc}1& e^{j\theta }& e^{j2\theta }& e^{j3\theta }& e^{j4\theta }& e^{j5\theta }& e^{j6\theta }& e^{j7\theta }\end{array}\right]}^T& \left(5\right)\end{array}$
It is possible to may construct the higher rank codebooks up to rank-4 while ensuring the composite precoding matrix is unitary. A nested property can also be enforced. The following rank-2 design can be used. The vector v(θ) corresponding to the beam angle θ in second column of Table 2 represents the first column of the composite precoding matrix W. If the column ordering of W which represents ordering across layers is considered a redundancy and hence not considered in generating distinct precoding matrices and not incorporated into the codebook design, than a given W.sub.1 allows 3+3+2+2+1+1+0+0 or 12 distinct rank-2 precoding matrix W. The size-12 codebook resulting from a given W.sub.1 or n is given by:

(54) $\hspace{1em}\left\{\begin{array}{c}\left[\begin{array}{cc}v\left(0\right)& v\left(\frac{\pi }{4}\right)\end{array}\right],\left[\begin{array}{cc}v\left(0\right)& v\left(\frac{\pi }{2}\right)\end{array}\right],\left[\begin{array}{cc}v\left(0\right)& v\left(\frac{3\pi }{4}\right)\end{array}\right],\left[\begin{array}{cc}v\left(\frac{\pi }{8}\right)& v\left(\frac{3\pi }{8}\right)\end{array}\right],\\ \left[\begin{array}{cc}v\left(\frac{\pi }{8}\right)& v\left(\frac{5\pi }{8}\right)\end{array}\right],\left[\begin{array}{cc}v\left(\frac{\pi }{8}\right)& v\left(\frac{7\pi }{8}\right)\end{array}\right],\left[\begin{array}{cc}v\left(\frac{\pi }{4}\right)& v\left(\frac{\pi }{2}\right)\end{array}\right],\left[\begin{array}{cc}v\left(\frac{\pi }{4}\right)& v\left(\frac{3\pi }{4}\right)\end{array}\right],\\ \left[\begin{array}{cc}v\left(\frac{3\pi }{8}\right)& v\left(\frac{5\pi }{8}\right)\end{array}\right],\left[\begin{array}{cc}v\left(\frac{3\pi }{8}\right)& v\left(\frac{7\pi }{8}\right)\end{array}\right],\left[\begin{array}{cc}v\left(\frac{\pi }{2}\right)& v\left(\frac{3\pi }{4}\right)\end{array}\right],\left[\begin{array}{cc}v\left(\frac{5\pi }{8}\right)& v\left(\frac{7\pi }{8}\right)\end{array}\right]\end{array}\right\}$

(55) For W.sub.1 given in equation (4b), the corresponding CB.sub.2 is given below where e.sub.n denotes a length-8 column vector with 1 in the n-th row and zero elements elsewhere:
{[e.sub.1e.sub.3],[e.sub.1e.sub.5],[e.sub.1e.sub.7],[e.sub.2e.sub.4],[e.sub.2e.sub.6],[e.sub.2e.sub.8],[e.sub.3e.sub.5],[e.sub.3e.sub.7],[e.sub.4e.sub.6],[e.sub.4e.sub.8],[e.sub.5e.sub.7],[e.sub.6e.sub.8]}
The composite rank-2 codebook is then computed as W=W.sub.1W.sub.2.

(56) Table 2 is a beam angle table of the resulting orthogonal vectors based on equation (4b).

(57) TABLE-US-00002 TABLE 2 θ Set of θ's resulting in orthogonal n (beam angle) vectors within the same W.sub.1 0 0 {π/4, π/2, 3π/4} π/8 π/8 + {π/4, π/2, 3π/4} π/4 {0, π/2, 3π/4} 3π/8 π/8 + {0, π/2, 3π/4} π/2 {0, π/4, 3π/4} 5π/8 π/8 + {0, π/4, 3π/4} 3π/4 {0, π/4, π/2} 7π/8 π/8 + {0, π/4, π/2} 1 π π + {π/4, π/2, 3π/4} 9π/8 9π/8 + {π/4, π/2, 3π/4} 5π/4 π + {0, π/2, 3π/4} 11π/8 9π/8 + {0, π/2, 3π/4} 4π/3 π + {0, π/4, 3π/4} 13π/8 9π/8 + {0, π/4, 3π/4} 7π/4 π + {0, π/4, π/2} 15π/8 9π/8 + {0, π/4, π/2}
Rank-3 and rank-4 codebooks can be designed similarly. Following the above design methodology:

(58) A size-8 rank-3 codebook (and hence CB.sub.2) can be constructed for a given W.sub.1 (or n). Here, CB.sub.2 is:
{[e.sub.1e.sub.3e.sub.5],[e.sub.1e.sub.3e.sub.7],[e.sub.1e.sub.5e.sub.7],[e.sub.3e.sub.5e.sub.7],[e.sub.2e.sub.4e.sub.6],[e.sub.2e.sub.4e.sub.8],[e.sub.2e.sub.6e.sub.8],[e.sub.4e.sub.6e.sub.8]}
A size-2 rank-4 codebook (and hence CB.sub.2) can be constructed for a given W.sub.1 or n.
{[e.sub.1e.sub.3e.sub.5e.sub.7],[e.sub.2e.sub.4e.sub.6e.sub.8]}

(59) In the second part of this invention, a dual-codebook design exploits a certain product structure of the spatial channel. This is suitable for pairs of ULA as well as pairs of dual-polarized array setup as illustrated in FIG. 4. Using the 8 Tx dual-polarized setup illustrated in FIG. 4(b) and assuming the spacing of L/2 between two dual-polarized antenna elements, the spatial channel covariance matrix can be approximated as follows:

(60) $C\approx \left[\begin{array}{cc}{C}_H& 0\\ 0& C_V\end{array}\right]=\left[\begin{array}{cc}{C}_{\mathrm{ULA}\text{-}4}& 0\\ 0& C_{\mathrm{ULA}\text{-}4}\end{array}\right]$
The 4×4 covariance matrices C.sub.H and C.sub.V follow that of the 4 Tx ULA. The spatial covariance matrix is block diagonal since the spatial channel coefficients associated with different polarizations are uncorrelated. Thus even with L/2 spacing, a rank-2 transmission can occur quite often. Two different structures are possible. In the first structure the elements associated with different polarization groups are combined via the second stage precoding where Y collapses the two polarization groups into one.

(61) $\begin{array}{cc}\begin{array}{c}W=\left[\begin{array}{c}{\alpha }_H\mathrm{XY}\\ {\alpha }_V\mathrm{XY}\end{array}\right]\\ =\left[\begin{array}{c}{\alpha }_H\\ {\alpha }_V\end{array}\right].Math.\left(\mathrm{XY}\right)\\ =\alpha .Math.\left(\mathrm{XY}\right)\\ =\left[\begin{array}{cc}X& 0\\ 0& X\end{array}\right]\left(\alpha .Math.Y\right)\\ \equiv W_1{W}_2\end{array}& \left(6\right)\end{array}$
This scheme does not allow transmission higher than rank-4. In fact a rank>1 will not occur frequently with L/2 spacing. Thus equation (6) is more suitable for rank-1 transmission in this particular antenna setup. While this scheme may increase precoding diversity gain, the two different polarization groups should also be used spatial multiplexing due to the uncorrelated nature of the different polarization groups. To take advantage of such property, equation (6) can be expanded as follows:

(62) $\begin{array}{cc}W=\left[\begin{array}{cc}X& 0\\ 0& X\end{array}\right]\left[\begin{array}{cc}{\alpha }_{\mathrm{HH}}{Y}_1& {\alpha }_{\mathrm{HV}}{Y}_2\\ {\alpha }_{\mathrm{VH}}{Y}_1& {\alpha }_{\mathrm{VV}}{Y}_2\end{array}\right]\equiv W_1{W}_2& \left(7\right)\end{array}$
Equation (7) is reduced to equation (6) when α.sub.HV and α.sub.VV are set to zero. Y.sub.1 and Y.sub.2 can be the same or different. For this particular antenna setup, the matrix X can be constructed based on the oversampled 4 Tx DFT vectors. Analogous to the first embodiment, any oversampling factor can be used such as 4× oversampling or 8× oversampling. For the short-term and/or frequency selective component W.sub.2 typical co-phasing coefficients can be used for {α.sub.H, α.sub.V} or {α.sub.HH, α.sub.VHα.sub.HV, α.sub.VV}. The coefficients belong to QPSK or 8PSK alphabet. Thus α.sub.H=1 and

(63) 0${\alpha }_V=e^{j*2\pi \frac{k}{N}}$
where k=0, 1 . . . N−1 with an appropriate normalization. The matrix Y or Y.sub.1/Y.sub.2 represent selection or group selection of the columns of X.

(64) The design in the second invention can also be used for 8 Tx ULA array since the block-diagonal design constructed from two 4 Tx DFT matrices can be used to generate all the 8 Tx DFT beam angles with appropriate co-phasing operation in W.sub.2. This property holds due to the so-called butterfly property of DFT operations.

(65) An exemplary first embodiment uses the 4× oversampled 4 Tx DFT vectors at generate 4 beam angles per polarization group. The beam angle space is partitioned into 4 non-overlapping groups resulting in W.sub.1 of size 8×8 block diagonal matrix since X is a 4×4 matrix:

(66) $\begin{array}{cc}{X}^{\left(n\right)}=\frac{1}{2}\times \left[\begin{array}{cccc}1& 0& 0& 0\\ 0& {\left(j\right)}^n& 0& 0\\ 0& 0& {\left(-1\right)}^n& 0\\ 0& 0& 0& {\left(-j\right)}^n\end{array}\right]\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& e^{j\frac{\pi }{8}}& e^{j\left(2\right)\frac{\pi }{8}}& e^{j\left(3\right)\frac{\pi }{8}}\\ 1& e^{j\left(2\right)\frac{\pi }{8}}& e^{j\left(2\right)\left(2\right)\frac{\pi }{8}}& e^{j\left(3\right)\left(2\right)\frac{\pi }{8}}\\ 1& e^{j\left(3\right)\frac{\pi }{8}}& e^{j\left(2\right)\left(3\right)\frac{\pi }{8}}& e^{j\left(3\right)\left(3\right)\frac{\pi }{8}}\end{array}\right],n=0,1,2,3W_1^{\left(n\right)}=\left[\begin{array}{cc}{X}^{\left(n\right)}& 0\\ 0& X^{\left(n\right)}\end{array}\right],{\mathrm{CB}}_1=\left\{W_1^{\left(0\right)},W_1^{\left(1\right)},W_1^{\left(2\right)},W_1^{\left(3\right)}\right\}& \left(8\right)\end{array}$
With the above choice of X, the following size-16 W.sub.2 codebook design can be used for rank-1 transmission. Here QPSK co-phasing is used.

(67) $\begin{array}{cc}{W}_2\in {\mathrm{CB}}_2=\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ \mathrm{jY}\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -\mathrm{jY}\end{array}\right]\right\}Y\in \left\{\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]\right\}& \left(9\right)\end{array}$
For rank-2 transmission, the following W.sub.2 codebook design can be used. This is also based on the QPSK alphabet and Y.sub.1=Y.sub.2=Y. In general Y.sub.1 and Y.sub.2 can be different.

(68) $\begin{array}{cc}{W}_2\in {\mathrm{CB}}_2=\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{cc}Y& Y\\ Y& -Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{cc}Y& Y\\ \mathrm{jY}& -\mathrm{jY}\end{array}\right]\right\}Y\in \left\{\left[\begin{array}{c}1\\ 0\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\\ 0\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 0\\ 0\\ 1\end{array}\right]\right\}& \left(10\right)\end{array}$
The first exemplary embodiment uses 16 4 Tx oversampled DFT beam angles for constructing X and partitions them into 4 non-overlapping groups. This results in 4 W.sub.1 matrices. Alternatively, each X may be constructed with the same size 4×4 matrix which represents more than 4 overlapping groups of beam angles. Thus for each X two adjacent X matrices will overlap in 2 beam angles. This is motivated to reduce the so-called edge effect in the precoder selection since W.sub.1 is typically chosen before W.sub.2. This is relevant only for frequency-selective precoding where different precoders W=W.sub.1*W.sub.2 can be used for different parts of the transmission bandwidth such as sub-bands.

(69) Based this design philosophy, a second exemplary embodiment is described in equation (11) with appropriate scalar normalization.

(70) $\begin{array}{cc}B=\left[\begin{array}{cccc}{b}_0& b_1& \mathrm{.Math.}& b_{N-1}\end{array}\right],{\left[B\right]}_{1+m,1+n}=e^{j\frac{2\pi \mathrm{mn}}{16}},m=0,1,2,3n=0,1,\mathrm{.Math.},N-1X^{\left(k\right)}\in \left\{\left[\begin{array}{cccc}{b}_{\left(N_{b}k/2\right)\mathrm{mod}N}& b_{\left(N_{b}k/2+1\right)\mathrm{mod}N}& \mathrm{.Math.}& b_{\left(N_{b}k/2+N_b-1\right)\mathrm{mod}N}\end{array}\right]\text{:}k=0,1,\mathrm{.Math.},\frac{2N}{N_b}-1\right\}{W}_1^{\left(k\right)}=\left[\begin{array}{cc}{X}^{\left(k\right)}& 0\\ 0& X^{\left(k\right)}\end{array}\right],C_1=\left\{W_1^{\left(0\right)},W_1^{\left(1\right)},W_1^{\left(2\right)},\mathrm{.Math.},W_1^{\left(2N/N_b\right)-1}\right\}& \left(11\right)\end{array}$
where: W.sub.1 is a block diagonal matrix of X; X is a 4×Nb matrix; and Nb denotes the number of adjacent 4 Tx DFT beams contained in X. Such a design is able to synthesize N 4 Tx DFT beams within each polarization group. For a given N, the spatial oversampling factor is essentially N/4. The overall 4 Tx DFT beam collections are captured in the 4×N matrix B. Using co-phasing in W.sub.2 the composite precoder W can synthesize up to N 8 Tx DFT beams. Allowing an overlapping of Nb/2 beam angles between two consecutively-indexed W.sub.1 matrices, the set of W.sub.1 matrices represents (2N/Nb)-level partitioning of the N 4 Tx beam angles in X, each polarization group. This design results in a codebook size of 2N/Nb for W.sub.1. The construction of W.sub.2 codebook can be performed accordingly.

(71) Based on the overlapping design given in equation (11), some exemplary constructions for W.sub.2 codebook are given below. To construct at least 16 8 Tx DFT beam angles, N=16 is chosen. As the choice of W.sub.1 codebook can be different for different transmission ranks, one W.sub.1 codebook design is chosen for ranks 1 and 2, and another W.sub.1 codebook design chosen for ranks 3 and 4. For ranks 1 and 2, Nb=4 allows good trade-off between frequency-selective precoding gain and feedback overhead. For ranks 3 and 4, Nb=8 accommodates higher-rank transmission which tends to undergo channels with richer scattering. The complete design for ranks 1, 2, 3, and 4 are given below. For rank-5 to 8, 8 Tx precoding tends to be limited for practical antenna setups. Thus the design for rank-5 to 8 is not given thus fixed precoding can be used. The examples below use the following notations: (1) {tilde over (e)}.sub.n is a 4×1 selection vector with all zeros except for the n-th element with value 1; (2) e.sub.n is a 8×1 selection vector with all zeros except for the n-th element with value 1. The W.sub.2 matrix chooses a column vector or a group of column vectors from the W.sub.1 matrix for each polarization group where each group is represented by one of the two block diagonal components while performing some co-phasing operation across the two polarization groups.

(72) Rank-1:

(73) $B=\left[\begin{array}{cccc}{b}_0& b_1& \mathrm{.Math.}& b_{15}\end{array}\right],{\left[B\right]}_{1+m,1+n}=e^{j\frac{2\pi \mathrm{mn}}{16}},m=0,1,2,3$$n=0,1,\mathrm{.Math.},15$$X^{\left(k\right)}\in \left\{\left[\begin{array}{cccc}{b}_{\left(2k\right)\mathrm{mod}16}& b_{\left(2k+1\right)\mathrm{mod}16}& b_{\left(2k+2\right)\mathrm{mod}16}& b_{\left(2k+3\right)\mathrm{mod}16}\end{array}\right]\text{:}k=0,1,\mathrm{.Math.},7\right\}$$W_1^{\left(k\right)}=\left[\begin{array}{cc}{X}^{\left(k\right)}& 0\\ 0& X^{\left(k\right)}\end{array}\right],C_1=\left\{W_1^{\left(0\right)},W_1^{\left(1\right)},W_1^{\left(2\right)},\mathrm{.Math.},W_1^{\left(7\right)}\right\}$$W_2\in {\mathrm{CB}}_2=\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ \mathrm{jY}\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -\mathrm{jY}\end{array}\right]\right\},Y\in \left\{{\tilde{e}}_1,{\tilde{e}}_2,{\tilde{e}}_3,{\tilde{e}}_4\right\}$
Rank-2:
The W.sub.1 codebook design is the same as rank-1.

(74) $W_2\in {\mathrm{CB}}_2=\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{Y}_1& Y_2\\ Y_1& -Y_2\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{Y}_1& Y_2\\ {\mathrm{jY}}_1& -{\mathrm{jY}}_2\end{array}\right]\right\}$$\left(Y_1,Y_2\right)\in \left\{\left({\tilde{e}}_1,{\tilde{e}}_1\right),\left({\tilde{e}}_2,{\tilde{e}}_2\right),\left({\tilde{e}}_3,{\tilde{e}}_3\right),\left({\tilde{e}}_4,{\tilde{e}}_4\right),\left({\tilde{e}}_1,{\tilde{e}}_2\right),\left({\tilde{e}}_2,{\tilde{e}}_3\right),\left({\tilde{e}}_1,{\tilde{e}}_4\right),\left({\tilde{e}}_2,{\tilde{e}}_4\right)\right\}$
Rank-3:

(75) $B=\left[\begin{array}{cccc}{b}_0& b_1& \mathrm{.Math.}& b_{15}\end{array}\right],{\left[B\right]}_{1+m,1+n}=e^{j\frac{2\pi \mathrm{mn}}{16}},m=0,1,2,3$$n=0,1,\mathrm{.Math.},15$$X^{\left(k\right)}\in \left\{\left[\begin{array}{cccc}{b}_{\left(4k\right)\mathrm{mod}16}& b_{\left(4k+1\right)\mathrm{mod}16}& \mathrm{.Math.}& b_{\left(4k+7\right)\mathrm{mod}16}\end{array}\right]\text{:}k=0,1,2,3\right\}$$W_1^{\left(k\right)}=\left[\begin{array}{cc}{X}^{\left(k\right)}& 0\\ 0& X^{\left(k\right)}\end{array}\right],C_1=\left\{W_1^{\left(0\right)},W_1^{\left(1\right)},W_1^{\left(2\right)},W_1^{\left(3\right)}\right\}$$W_2\in {\mathrm{CB}}_2=\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{cc}{Y}_1& Y_2\\ Y_1& -Y_2\end{array}\right]\right\}$$\left(Y_1,Y_2\right)\in \left\{\begin{array}{c}\begin{array}{c}\begin{array}{c}\left(e_1,\left[\begin{array}{cc}{e}_1& e_5\end{array}\right]\right),\left(e_2,\left[\begin{array}{cc}{e}_2& e_6\end{array}\right]\right),\left(e_3,\left[\begin{array}{cc}{e}_3& e_7\end{array}\right]\right),\left(e_4,\left[\begin{array}{cc}{e}_4& e_8\end{array}\right]\right),\\ \left(e_5,\left[\begin{array}{cc}{e}_1& e_5\end{array}\right]\right),\left(e_6,\left[\begin{array}{cc}{e}_2& e_6\end{array}\right]\right),\left(e_7,\left[\begin{array}{cc}{e}_3& e_7\end{array}\right]\right),\left(e_8,\left[\begin{array}{cc}{e}_4& e_8\end{array}\right]\right),\end{array}\\ \left(\left[\begin{array}{cc}{e}_1& e_5\end{array}\right],e_5\right),\left(\left[\begin{array}{cc}{e}_2& e_6\end{array}\right],e_6\right),\left(\left[\begin{array}{cc}{e}_3& e_7\end{array}\right],e_7\right),\left(\left[\begin{array}{cc}{e}_4& e_8\end{array}\right],e_8\right),\end{array}\\ \left(\left[\begin{array}{cc}{e}_5& e_1\end{array}\right],e_1\right),\left(\left[\begin{array}{cc}{e}_6& e_2\end{array}\right],e_2\right),\left(\left[\begin{array}{cc}{e}_7& e_3\end{array}\right],e_3\right),\left(\left[\begin{array}{cc}{e}_8& e_4\end{array}\right],e_4\right)\end{array}\right\}$
Rank-4:
The W.sub.1 codebook design is the same as rank-3.

(76) $W_2\in {\mathrm{CB}}_2=\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{cc}Y& Y\\ Y& -Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{cc}Y& Y\\ jY& -jY\end{array}\right]\right\}$$Y\in \left\{\left[e_1{e}_5\right],[e_6],\left[e_3{e}_7\right],\left[e_4{e}_8\right]\right\}$

(77) Other exemplary constructions, variations, and embodiments can be designed based on these principles. These two designs are not exclusive of each other. It is possible to combine designs 1 and 2 into one codebook framework as depicted in FIG. 3. The different W.sub.1 matrices corresponding to different designs are enumerated with PMI.sub.1 while the codebook CB.sub.2 for W.sub.2 is dependent on the choice of W.sub.1. Such a setup allows the 8 Tx design to accommodate for several scenarios including 8 Tx ULA and pairs of dual-polarized elements. It is also possible to include other designs for W.sub.1 such as a Grassmanian codebook or virtual antenna selection components which are suitable for low spatial correlation. The W.sub.2 codebook can be different for different W.sub.1 matrices. While the codebook example is presented covering a multi-rank format of rank-1 to rank-4, any multi-rank design constructed from taking at least one rank-specific codebook(s) from one example and some other rank-specific codebook(s) from other example(s) is not precluded. A multi-rank codebook may be constructed from a subset of a design. It is possible to construct a multi-rank codebook which uses the rank-1 and rank-2 designs from any of the examples below but which uses a fixed matrix precoding “size-1 codebook” for rank-3 and above.

(78) Some UE feedback signaling mechanisms to support the dual-codebook designs given above in the context of 3GPP LTE-Advanced systems. In LTE Rel. 8 and 9, there are currently two UE feedback mechanisms for PMI reporting: (1) Periodic reporting on Physical Uplink Control CHannel (PUCCH) with the content possibly piggybacked onto Physical Uplink Shared CHannel (PUSCH) in the presence of uplink (UL) grant with wideband frequency non-selective PMI; and (2) Aperiodic reporting on PUSCH which allows frequency-selective PMI reporting. For LTE-A, some new reporting schemes may be introduced such as periodic PUSCH and new formats on PUCCH and PUSCH based reports. A UE may transmit on both PUCCH and PUSCH at the same time. This patent application focuses on how the two-stage PMI is periodically reported on PUCCH. Reporting PMI.sub.1 long-term PMI can be treated analogous to rank indicator (RI) where the reporting interval for RI can be configured larger than channel quality indicator/precoding matrix indicator (CQI/PMI) for PUCCH based reporting. Thus the reporting mechanism for the long-term PMI.sub.1 can be designed as follows:

(79) (1) The reporting instances subframes of PMI.sub.1 are aligned (identical) with those of RI. PMI.sub.1 is reported in the same subframes as RI. This is a reasonable solution to avoid complication due to inter-dependence among reports. The following possibilities exist: PMI.sub.1 is reported at the same periodicity as RI; and PMI.sub.1 is reported at larger periodicity than RI where the periodicity of PMI.sub.1 is an integer Q multiple of that of RI (Q=1, 2, 3 . . . ). The first possibility is a special case of the second where the integer multiple is 1.

(80) (2) While it is possible to reserve a different PUCCH resource for reporting PMI.sub.1, this seems unnecessary since the PUCCH resource used for reporting RI which is at most 3 bits for 8 Tx can still accommodate a few more bits as long as the payload size of PMI.sub.1 is not excessive. Thus PMI.sub.1 is not only reported at the same subframes as RI, but also shares the same PUCCH resource as RI. PMI.sub.2 is then treated as the Rel. 8/9 LTE PMI which is reported together with CQI.

(81) FIG. 5 illustrates an example where the reporting periodicity of RI/PMI.sub.1 is 4× as that of wideband CQI/PMI.sub.2 with reporting offset of zero where PMI.sub.1 has the same periodicity as the RI. Subframes 501 and 505 report both RI and PMI.sub.1. Subframes 502, 503, 504, 506, 507 and 508 report wideband CQI and PMI.sub.2. Thus the periodicity of RI/PMI.sub.1 is 4× as that of wideband CQI/PMI.sub.2.

(82) As an alternative, the reporting periodicity subframes of PMI.sub.1 can be smaller than that of RI. There are several possibilities. In one embodiment, PMI.sub.1 is reported with the same periodicity as PMI.sub.2. In this case PMI.sub.1 and PMI.sub.2 possess the same time-domain granularity are always reported together. The RI reporting periodicity is O times that of the PMI.sub.1/PMI.sub.2 reporting periodicity where O is a positive integer. The frequency-domain granularity of PMI.sub.1 and PMI.sub.2 may be different. PMI.sub.1 may be a wideband precoder while PMI.sub.2 may be either wideband or subband. FIG. 6 illustrates an example of this periodicity. Subframes 601 and 604 report RI. Subframes 602, 603, 605 and 606 report PMI.sub.1, PMI.sub.2 and CQI.

(83) In another embodiment, PMI.sub.1 is reported at larger periodicity than PMI.sub.2 and RI is reported at larger periodicity than PMI.sub.1. For example, RI reporting periodicity is O1 times that of reporting periodicity of PMI.sub.1 and PMI.sub.1 periodicity is O2 times that of PMI.sub.2. This is illustrated in FIG. 7. Subframes 701 and 708 report RI. Subframes 702, 705, 709 and 712 report PMI.sub.1. Subframes 703, 704, 706, 707, 710, 711, 713 and 714 report PMI.sub.2 and CQI. This is perhaps the least desirable mode of operation despite its apparent flexibility.

(84) The description of this invention has focused on the design of codebooks and its associated signaling for 8-antenna (8 Tx) systems. Those familiar with the art would understand that this invention can be extended to different number of transmit antennas at the eNodeB. An extension for 4 Tx systems in the context of 3GPP LTE is as follows. 3GPP LTE Release 8 (Rel. 8) supports a codebook-based precoding and feedback for 4 Tx systems. Using the dual-codebook product design W=W.sub.1W.sub.2, it is possible to augment the Release 8 design for performance improvement with lower rank transmissions such as rank-1 and/or rank-2. This can benefit MU-MIMO operation. One possible embodiment uses the Rel. 8 4 Tx codebook for the short-term precoding component W.sub.2. W.sub.1 is then defined to achieve the design goal. This permits the designer to add more W.sub.1 matrices to cater for spatial channel scenarios such as antenna setup, angular spread, etc.

(85) One embodiment improves rank-1 transmission MU-MIMO performance for the 4 Tx ULA setup with L/2 spacing. The Rel. 8 4 Tx codebook includes 8 4 Tx and hence 2× oversampling DFT vectors, additional DFT vectors allow higher spatial resolution using 16 4 Tx DFT vectors including those from the Rel. 8 codebook. If the DFT vectors from the Rel. 8 codebook are used, a possible embodiment is:

(86) (1) For a given value of n spatial/angular oversampling factor, n contiguous groups are defined.

(87) (2) The size of each contiguous group is 4. Each contiguous group is associated with one W.sub.1 matrix. For the i-th group (i=0, 1, . . . , n−1):

(88) $\begin{array}{cc}{W}_1^{\left(i\right)}={\frac{1}{2}\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right]}^H(\frac{1}{2}\times \left[\begin{array}{cccc}1& 0& 0& 0\\ 0& e^{j\left(4\right)\frac{\pi }{2n}i}& 0& 0\\ 0& 0& e^{j\left(2\right)\left(4\right)\frac{\pi }{2n}i}& 0\\ 0& 0& 0& e^{j\left(3\right)\left(4\right)\frac{\pi }{2n}i}\end{array}\right]\hspace{1em}\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& e^{j\frac{\pi }{2n}}& e^{j\left(2\right)\frac{\pi }{2n}}& e^{j\left(3\right)\frac{\pi }{2n}}\\ 1& e^{j\left(2\right)\frac{\pi }{2n}}& e^{j\left(2\right)\left(2\right)\frac{\pi }{2n}}& e^{j\left(2\right)\left(3\right)\frac{\pi }{2n}}\\ 1& e^{j\left(3\right)\frac{\pi }{2n}}& e^{j\left(2\right)\left(3\right)\frac{\pi }{2n}}& e^{j\left(3\right)\left(3\right)\frac{\pi }{2n}}\end{array}\right])=\frac{1}{4}\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& -j& -1& j\\ 1& -1& 1& -1\\ 1& j& -1& -j\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& e^{j\left(4\right)\frac{\pi }{2n}i}& 0& 0\\ 0& 0& e^{j\left(2\right)\left(4\right)\frac{\pi }{2n}i}& 0\\ 0& 0& 0& e^{j\left(3\right)\left(4\right)\frac{\pi }{2n}i}\end{array}\right]\hspace{1em}\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& e^{j\frac{\pi }{2n}}& e^{j\left(2\right)\frac{\pi }{2n}}& e^{j\left(3\right)\frac{\pi }{2n}}\\ 1& e^{j\left(2\right)\frac{\pi }{2n}}& e^{j\left(2\right)\left(2\right)\frac{\pi }{2n}}& e^{j\left(2\right)\left(3\right)\frac{\pi }{2n}}\\ 1& e^{j\left(3\right)\frac{\pi }{2n}}& e^{j\left(2\right)\left(3\right)\frac{\pi }{2n}}& e^{j\left(3\right)\left(3\right)\frac{\pi }{2n}}\end{array}\right]& \left(12\right)\end{array}$
Only the first 4 DFT vectors in equation (12) are used for CB.sub.2 for v=1 codebook. That is:

(89) 0$\begin{array}{cc}{\mathrm{CB}}_2=\frac{1}{2}\left[\begin{array}{cccc}1& 1& 1& 1\\ 1& j& -1& -j\\ 1& -1& 1& -1\\ 1& -j& -1& j\end{array}\right]\left(\mathrm{in}\mathrm{the}\mathrm{form}\mathrm{of}4\times 4\mathrm{matrix}\right)& \left(13\right)\end{array}$
Note that in equation (12) the 4-DFT matrix forms a complete orthonormal basis for 4-dimensional complex vector space. For n=4, this design results in 4 contiguous groups (which results in a 2-bit PMI.sub.1 per PMI report) and 2-bit PMI.sub.2 for rank-1 for v=1.

(90) To allow a natural dynamic switching with SU-MIMO applications where the other 8 vectors in the v=1 codebook may be more useful, this codebook can augment the Rel. 8 4 Tx codebook. For the original Rel. 8 codebook, W.sub.1 is chosen to be an identity matrix where CB.sub.2 is simply the Rel. 8 codebook. This allows dynamic switching between the two W.sub.1 matrices via an update of PMI.sub.1. When PMI.sub.1 indicates that W.sub.1 identity is chosen, CB.sub.2 is chosen as the original Rel. 8 codebook. When PMI.sub.1 indicates some other W.sub.1, W.sub.1 and CB.sub.2 are chosen as the enhanced component given above.

(91) Another embodiment is applicable for rank-1 or rank-2 transmissions aimed at improving MU-MIMO performance for the 4 Tx dual-polarized antenna setup. The enhanced component can be designed independently of the Rel. 8 codebook. The enhanced component can be combined with the Rel. 8 codebook via the same augmentation procedure of choosing W.sub.1. That is:

(92) (1) When PMI.sub.1 indicates that W.sub.1 identity is chosen, CB.sub.2 is chosen as the original Rel. 8 codebook.

(93) (2) When PMI.sub.1 indicates some other W.sub.1, W.sub.1 and CB.sub.2 are chosen as the enhanced component.

(94) For the enhanced components not including when W.sub.1 is the identity matrix and CB.sub.2 is the Rel. 8 codebook, a design similar to the 8 Tx counterpart can be used. For example, a Nb/2 overlapping beam design is used for W.sub.1. This can be written as follows.

(95) $\begin{array}{cc}B=\left[\begin{array}{cccc}{b}_0& b_1& \mathrm{.Math.}& b_{N-1}\end{array}\right],{\left[B\right]}_{1+m,1+n}=\frac{1}{\sqrt{2}}{e}^{j\frac{2\pi \mathrm{mn}}{N}},m=0,1n=0,1,\mathrm{.Math.},N-1X^{\left(k\right)}\in \left\{\left[\begin{array}{cccc}{b}_{\left(N,k/2\right)\mathrm{modN}}& b_{\left(N,k/2+1\right)\mathrm{modN}}& \mathrm{.Math.}& b_{\left(N,k/2+N_b-1\right)\mathrm{modN}}\end{array}\right]\text{:}k=0,1,\mathrm{.Math.},\frac{2N}{N_b}-1\right\}{W}_1^{\left(k\right)}=\left[\begin{array}{cc}{X}^{\left(k\right)}& 0\\ 0& X^{\left(k\right)}\end{array}\right],C_1=\left\{W_1^{\left(0\right)},W_1^{\left(1\right)},W_1^{\left(2\right)},\mathrm{.Math.},W_1^{\left(2N/N_b\right)-1}\right\}& \left(14\right)\end{array}$
The same W.sub.2 design as that for the 8 Tx case can be applied for a given value of N and Nb. The following design concept for W.sub.2 can be used for the enhanced components.

(96) (1) The first part of W.sub.2 utilizes beam selection or beam group selection within each polarization group. The same or different beam(s) can be used for different polarization groups.

(97) (2) The second part of W.sub.2 utilizes co-phasing between two different polarization groups. The co-phasing can be done with a unitary vector or matrix assuming a certain alphabet size such as QPSK or 8PSK.

(98) The combination of beam selection and co-phasing in W.sub.2 combined with W.sub.1 should result in a unitary precoder W=W.sub.1*W.sub.2.

(99) Assuming the same beam (group) selection for different polarization groups and QPSK-based co-phasing, the following W.sub.2 design can be used for:

(100) Nb=2:

(101) Rank-1:

(102) $W_2\in {\mathrm{CB}}_2=\left\{\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ jY\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -Y\end{array}\right],\frac{1}{\sqrt{2}}\left[\begin{array}{c}Y\\ -jY\end{array}\right]\right\},Y\in \left\{\left[\begin{array}{c}1\\ 0\end{array}\right],\left[\begin{array}{c}0\\ 1\end{array}\right]\right\}$
Rank-2: