Transmit diversity techniques provide attractive solutions for increasing downlink capacity in 3G (Third Generation) communication systems within low-mobility environments. The complexity to implement transmit diversity mainly burdens the base station making the technique more suitable for low-cost handsets than, e.g., receive diversity. Open-loop and closed-loop transmit diversity techniques have been already standardized and improvements are being developed constantly with 3GPP (Third Generation Partnership) WCDMA (Wideband Code Division Multiple Access) FDD (Frequency Division Duplex) and TDD (Time Division Duplex) modes, and transmit diversity is considered with EDGE (Enhanced Data rates for GSM Evolution) standardization as well.
In closed-loop transmit diversity techniques two of the critical phenomena that may change the performance of the closed-loop schemes are the temporal correlation corresponding to each antenna separately and the spatial correlation between the antennas. The first one of these phenomena is critical when mobile is moving and/or a feedback word is long. The second phenomenon is affecting usually slower or there might even be static correlations between antennas. However, it is not realistic to assume that the spatial correlation properties remain the same in all environments. Therefore it is of great interest to search schemes that are able to adapt to the characteristics of the fading channel.
When there are several antenna elements in a transmitter antenna array, it is useful to design feedback modes (as mode 1 and mode 2 in FDD WCDMA) by which the downlink capacity can be increased. The conventional design criteria for these modes is based on the channel covariance matrix R given byR=HHH, H=(h1,h2, . . . , hM), hm=(hm.1,hm.2, . . . , hm.1.)t,where M is the number of transmit antennas, L is the number of channel paths and hmj is the complex channel coefficient corresponding to /th path of the channel between antenna m and mobile. The problem is to find antenna weight vector w=(w1, w2, . . . , wM)T such that
            w      H        ⁢    Rw    =                            Hw                    2        =                                                ∑                          m              =              1                        M                    ⁢                                          ⁢                                    h              m                        ⁢                          w              m                                                  2      is maximized. Another common approach is to choose w such that
            w      H        ⁢    Rw              w      H        ⁢    Kw  where K refers to the covariance of the noise and interference, is maximized. Alternatively, the generalized eigenvalue problem can be expressed to maximizewHHHK−1Hwwhere K−1 is inverse or pseudo inverse of K. Furthermore, a channel covariance matrix can be calculated using a subset of channel paths.
Since the feedback capacity is limited, we must choose a quantized set of feedback vectors w and design algorithms that provide best possible choice of w among all quantized weights. The standard describes two feedback modes where the first mode adjusts phases only and the second one adjusts transmit power as well [1]. Moreover, selection and/or phase adjustment algorithms have been proposed in [2]. The algorithms are based only on the fast feedback and they do not take into account the spatio-temporal properties of the channel. Furthermore, the quantization sets have been fixed in all previous concepts and specific values of weights have been chosen beforehand to be the same in all environments.
Recently, Siemens proposed an “eigenbeamformer” approach [3] where MS (Mobile Station) measures R and signals a subset of eigenvectors to the BS (Base Station), which are subsequently used for transmission. The idea is to reduce dimension so that, for example, in the case of 4 Tx (Transmit) antennas the MS needs to monitor only two beams and consequently feedback signaling works with higher mobile speeds than in the case when the mobile station continuously updates weights of the 4 transmit antennas. However, if there is no spatial correlation between the antennas the SNR (Signal to Noise Ratio) improvement becomes the same as with 2 Tx antennas. Furthermore, Siemens remarks that it is not necessary to calibrate the antennas when beamforming is based on the feedback from mobile to base.
For a moment it is assumed that we have a single path Rayleigh fading channel, M uncorrelated transmit antennas and relative phases of signals from different antennas have been adjusted by applying an algorithm given in [4]. That is, some or all signals from the different antennas are ranked and each phase is independently adjusted against the phase of the reference channel or antenna. Moreover, assume that the channel coefficients have been ordered with respect to their amplitudes αm=|hm| into a descending order. Using the brackets in subindices denotes the given order. Then the expected SNR is given by:
                                          E            ⁢                          {                                                                                                            ∑                                              m                        =                        1                                            M                                        ⁢                                                                                  ⁢                                                                  h                                                  (                          m                          )                                                                    ⁢                                              w                        m                                                                                                              2                            }                                =                                    u              T                        ⁢                          C              ·              u                                      ,                                  ⁢                  u          =                      (                                                                          w                  1                                ⁢                                                    ,                                                  ⁢                                  w                  2                                ⁢                                                                        ,                    …                    ⁢                                                                                  ,                                                                    ⁢                                  w                  M                                                                    )                          ,                            (        1        )            where components of the weight vector u are now real and non-negative. Here C is the ordered covariance matrix that takes into account the correlation between amplitudes and phases. (Note that C and R are different.) C is an example of an ordered and phase adjusted channel matrix. It is found that the elements of C are the following
                                          c                          m              ,              m                                =                      E            ⁢                          {                              α                                  (                  m                  )                                2                            }                                      ,                                  ⁢                              c                          m              ,              1                                =                                    c              N                        ⁢            E            ⁢                          {                                                α                                      (                    m                    )                                                  ⁢                                  α                                      (                    1                    )                                                              }                                      ,                              c                          m              ,              k                                =                                    c              N              2                        ⁢            E            ⁢                          {                                                α                                      (                    m                    )                                                  ⁢                                  α                                      k                    )                                                              }                                      ,                                  ⁢                  m          ≠          k                ,                                  ⁢                              c            N                    =                                                    2                N                            π                        ⁢                                          sin                ⁡                                  (                                      π                                          2                      N                                                        )                                            .                                                          (        2        )            
Here N is the number of phase adjustment feedback bits per antenna. If there is no spatial correlation between antennas, then the above expectations can be computed analytically and thus, weight vector u can be chosen beforehand since it is the eigenvector corresponding to the largest eigenvalue of C. The adjustment algorithm is then such that the mobile station estimates the channel from M antennas and orders the samples according to magnitude. The mobile station can either store the whole order information or only part of it. Relative phases of the signals (not necessarily all phases; this depends on the specific algorithm) are then adjusted, i.e. the mobile station searches through possible adjustment combinations applying some algorithm and then chooses the best combination. Both the order and phase adjustment information is then sent to the transmitter in the base station. The transmitter selects antenna weights w based on the feedback information. The phases are obtained directly from the FB (Feed Back) information and magnitudes of weights are selected using quantization based on (1) and (2) when order information is known. This requires in total log2 (M!)+(M−1)N FB bits (M! is the number of permutations of {αm}m=1M, and N is the number of phase bits/antenna), and the SNR improvement is very close to the theoretical maximum, for example SNR=3.8 in the case of M=4 Tx antennas and N=3 phase adjustment bits/antenna. Suboptimal FB weights requiring less FB bits can be determined using similar procedure as proposed in [4]. For example, if all antennas but the strongest one have the same Tx amplitude weight then only log2 (M)+(M−1)N FB bits are required.
However, there are some basic restrictions in the above procedure. Channels can attain multipath structure, fading statistics can be due to Rice, Rayleigh, Nagakami statistics or something else, and antennas can be spatially correlated. Moreover, the nature of all these phenomena can change when mobile is moving. Therefore, it is not always practical to fix the same weight magnitude quantization beforehand as it has been done in the above theoretical consideration, and as has been specified in Tx diversity mode 2 of FDD WCDMA.