# Patent

## Title
Method for transmitting information in a mimo radio communication system and radio communication system

## Abstract

A method is provided for transmitting information in a radio communication system provided with at least one transmitting station (AP) and at least two receiver stations (MT). The transmitting station (AP) and the receiver stations (MT) are connected together via a radio communication interface. The transmitting stations (AP) includes a transmitting antenna with K<SB>B</SB>31 antenna elements, whereby K<SB>B</SB>≧1, and the receiving stations (MT) respectively include a transmitting antenna with K<SB>M</SB> antenna elements, whereby K<SB>M</SB>≧1, and which communicate via a MIMO-transmission. The transmitting signals transmitted from the antenna elements of the transmitting antenna of the transmitting station (AP) are produced in a common process and are adapted in relation to the transmitting energy to be used during radiation. Receiving signals received by the antenna elements of the receiver antenna of the receiver stations (MT) are detected in a linear signal process.

## Background
BACKGROUND OF THE INVENTION
In a radio communication systems, information (for example speech, image information, video information, SMS (Short Message Service) or other data) is transmitted using electromagnetic waves over a radio interface between transmitting and receiver stations (base station or subscriber station). In such cases, the electromagnetic waves are propagated using carrier frequencies lying within the frequency band provided for the relevant system. For the GSM (Global System for Mobile Communication) mobile radio system which has been introduced, frequencies at 900, 1800 und 1900 MHz were used. For future mobile radio systems with CDMA or TD/CDMA procedures, such as UMTS (Universal Mobile Telecommunication System) or other third-generation systems, there is provision for frequencies in the frequency band of around 2000 MHz.
The access from stations to the shared transmission medium is regulated in these radio communication systems by Multiple Access (MA). With these multiple accesses, the transmission medium can be subdivided between the stations in the time area (Time Division Multiple Access, TDMA), in the frequency area (Frequency Division Multiple Access, FDMA), in the code area (Code Division Multiple Access, CDMA) or in the space area (Space Division Multiple Access, SDMA). In this case, the transmission medium (with GSM (Global System for Mobile Communications), TETRA (Terrestrial Trunked Radio), DECT (Digital Enhanced Cordless Telecommunication), UMTS (Universal Mobile Telecommunication System) for example) is frequently subdivided in the frequency and/or time channels in accordance with the radio interface. These channels are generally referred to as transmission channels or radio channels. For systems where coordination is decentralized, measurements are used to decide on the usability of these transmission channels. In accordance with the radio radiation (i.e., depending on the radio field attenuation), re-use of these transmission channels at an appropriate spacing is possible.
For radio transmission between a transmit station and at least one receiver station of a radio transmission system, interference occurrences now arise as a result of the frequency selectivity of the transmission channels, such interference being known as intersymbol interference and Multiple Access interference. The greater the transmission bandwidth of the transmission channel, the more these interferences distort the transmit signals.
Conventionally, the transmit signals are generated at the transmit station without taking account of the effective radio channels. The interference occurrences then arising are rectified in a second step, at least approximately by the appropriate matched and generally very expensive methods for detecting the transmitted data at the receiver stations.
Radio communication systems with at least one transmit station (Transmit station AP or base station) and at least two receiver stations (Receiver station MT) are known, with the transmit station (AP) and the receiver stations (MT) being connected to one another over a radio communications interface. Here, the transmit station features a transmit antenna with KB antenna elements (with KB≧1) and the receiver stations each feature a transmit antenna with KM antenna elements (with KM≧1). They communicate by MIMO (Multiple Input-Multiple Output) transmission.
Radio transmission devices with at least one transmit station having a number of transmit elements and with at least one receiver station having a number of receive elements are referred to in this document as MIMO systems. Radio transmission between at least one transmit station and at least one receiver station of a MIMO system is subject, as a result of the frequency selectivity of the transmission channels, to interference occurrences which are known as intersymbol interferences and Multiple Access interference. For the purposes of radio transmission from at least one transmit station to the receiver stations in a MIMO there are basically two requirements which need to be fulfilled:

    
    
        suitable transmit signals are to be generated and propagated by the relevant transmit station for each of the transmit antennas; and
        the data which is of interest in each case is to be detected by each of the receiver stations by suitable processing of the receive signals of all receive antennas.
    
    


In recent years, alternative concepts, such as Joint Transmission or Joint Predistortion have been investigated, which, by taking account of the effective transmission channels, eliminate the interference occurrences completely, to a large extent or at least partly at the point at which the transmit signals are being generated at the transmit station. See, for example:

    
    
        M. Meurer, P. W. Baier, T. Weber, Y. Lu, A. Papathanassiou, “Joint Transmission, an advantageous downlink concept for CDMA mobile radio system using time division duplexing”, IEE Electronics Letters, Bd. 36, 2000, S. 900-901 [1] and
        P. W. Baier, M. Meurer, T. Weber, H. Tröger, “Joint Transmission (JT), an alternative rationale for the downlink of time division CDMA using multi-element transmit antennas”, Proc. IEEE 7th International Symposium on Spread Spectrum Techniques & Applications (ISSSTA'2000), Parsippany/N.J., 2000, S. 1-5 [2].

The cited documents present a Joint Transmission (JT) transmission method, especially for downlink mobile radio systems from the base station to the subscriber stations, which allows simultaneous provision to a number of subscribers. The transmit signals propagated by the transmit antennas of the base station or transmit station (AP) are generated in a common process in this case and optimized with respect to the transmit energy to be used.

    
    


In Joint Transmission systems with at least one transmit station having at least one transmit antenna and with at least one receiver station having at least one receive antenna, the linear receive-side signal processing, referred to below as demodulation, is described by receiver station-specific demodulator matrices [2].
In conventional Joint-Transmission systems [2], the subscriber-specific demodulation matrices are defined by fixed signatures; e.g., CDMA codes. This process is particularly determined due to the fact that no information about the space and time transmission characteristics of the mobile radio channels operating between transmit stations and receiver stations is included in the design of the subscriber-specific demodulation matrices.
Similar to the process used in the Joint Transmission (JT) method, such transmit signals also may be generated when receiver stations with a number of receive antennas are employed, by using

    
    
        information about the effective radio channels and
        information about the receive-side-specific processing methods defined a priori for detection,

which, theoretically, perfectly eliminates the interference occurrences discussed at the point of transmission.

    
    


The present invention is, thus, directed toward a method and an improved transmit device which, for the effective transmission channels, takes account both of a minimization of the transmit power and also of further quality criteria, such as a directional characteristic of the transmit signal for example.
SUMMARY OF THE INVENTION
In accordance with present invention, transmit signals propagated from the antenna elements of the transmit station are generated in a common process and matched with regard to the transmit energy to be used for radiation, with the receive signal received by the antenna elements of the receive antennas of the receiver station being detected in a linear signal process.
Advantageously, the individual signals for the antenna elements of the transmit antenna of the transmit station can be calculated before radiation with the aid of a modulator matrix M.
In this case, a transmit signal vector t= M· d can, in particular, be generated by essentially linear modulation of at least one data vector d to be transmitted with the modulator matrix M.
In a further embodiment of the present invention, demodulation is undertaken with linear receiver-side signal processing, taking account of the space and time transmission characteristics between transmit stations and receiver stations.
In particular, receive-station-specific demodulator matrices D can be employed for the linear receive-side signal processing.
Advantageously, each transmit station (AP) and each receiver station (MT) is connected via at least one radio channel characterized by a channel matrix H.
The system matrix B= D· H contained in the modulator matrix M  is preferably given by the product of the demodulator matrix D and channel matrix H.
With the inventive radio communication system in which the transmit station features a transmit antenna with KB antenna elements (with KB≧1) and the receiver stations each feature one transmit antenna with KM antenna elements (with KM≧1), parts are provided for generating the transmit signals propagated from the antenna elements of the transmit antenna of the transmit station (AP) in a shared process and for matching with regard to the transmit energy to be used for radiation, as well as parts for detecting the receive signals received from the antenna elements of the receive antennas of the receiver stations in a linear signal process.
The radio communication system in accordance with the present invention is particularly suitable for executing a method in accordance with the present invention.
In a Multi-User MIMO transmission system, the present invention combines, on the one hand:

    
    
        the generation of access-point-specific transmit signals in accordance with Joint Transmission,

and one the other hand:

        the demodulation, taking into consideration information about the space and time division transmission devices, of the effective mobile radio channels between the transmit stations and the receiver stations.
    
    


Technical implementations of this innovative combined method allow the benefits of both methods to be profitably employed.
Information about the space and time transmission characteristics of the effective mobile radio channels between transmit stations and receiver stations can be taken into account when determining the access-point-specific demodulation.
Some of the benefits offered by the inclusion of channel characteristics are as follows:

    
    
        Reduction of the total transmit energy,
        Avoiding combinations of mobile radio channels and incorrectly matched demodulation matrices,
        Improvement of the intercell interference situation in cellular Joint-Transmission systems,
        Reduction of the SNR degradation (see [3]),
        Increase in transmission efficiency (see [3]),
        Increase in system capacity.
    
    


More details can be found, for example, in

    
    
        H. Tröger, T. Weber, M. Meurer, P. W. Baier, “Performance Assessment of Joint Transmission (JT) Multi User Downlink with Multi-Element Transmit Antennas”, European Transmission on Telecommunications, ETT Vol. 12, No. 5, September/October 2001 [3],
    
    


Additional features and advantages of the present invention are described in, and will be apparent from, the following Detailed Description of the Invention and the Figures.



BRIEF DESCRIPTION OF THE FIGURES
FIG. 1 shows a system model of an MIMO JT system in accordance with the invention.
FIG. 2 shows the structure of a channel matrix H0(k) in accordance with equation (21) below.
FIG. 3 shows the structure of a channel matrix D(k) in accordance with equation (38) below.



DETAILED DESCRIPTION OF THE INVENTION
Joint Transmission (JT) is a highly promising transmission method for the downlink [1, 2, 3] which is proposed for mobile radio systems using the hybrid multiple access method TDMA/CDMA. With JT, the transmission signals are advantageously generated jointly for all receiver stations MT. JT is based on prespecified demodulators, wherein on the basis of the characteristics of these demodulators and the channel pulse responses, the modulator in the transmit station AP is defined a posteriori so that intersymbol interference (ISI) and Multiple Access Interference (MAI) are completely eliminated. To date, investigations into JT have only taken account of multi-element antennas at the transmit station AP. Statistical investigations [3] have revealed the benefit of transmit antenna groups. The present invention relates to JT for transmission systems with a number of subscribers, where multi-element antennas are used both at the transmit station AP and at the receiver stations MT. A system model of such a MIMO JT method is presented below.
Signal Transmission Model of MIMO Systems with a Number of Subscribers
At the AP, a group of KB transmit antenna elements is used and at each MT μk k=1 . . . K) a group of KM receive antenna elements is set up. The channel impulse responses




  
    
      
        
          
            
              h
              _
            
            
              (
              
                k
                ,
                
                  k
                  B
                
                ,
                
                  k
                  M
                
              
              )
            
          
          =
          
            
              (
              
                
                  
                    h
                    _
                  
                  1
                  
                    (
                    
                      k
                      ,
                      
                        k
                        B
                      
                      ,
                      
                        k
                        M
                      
                    
                    )
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  
                    h
                    _
                  
                  W
                  
                    (
                    
                      k
                      ,
                      
                        k
                        B
                      
                      ,
                      
                        k
                        M
                      
                    
                    )
                  
                
              
              )
            
            T
          
        
        ,
        
          k
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            K
          
        
        ,
        
          
            k
            B
          
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            
              K
              B
            
          
        
        ,
        
          
            k
            M
          
          =
          
            1
            ⁢
            
              
            
            ⁢
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            ⁢
            
              
            
            ⁢
            
              K
              M
            
          
        
        ,
      
    
    
      
        (
        1
        )
      
    
  




of the dimension W characterize the mobile radio channel between the transmit antenna element kB and the receive antenna element km of MT μk. The transmit antenna-specific transmit signal of dimension S





  
    
      
        
          
            
              t
              _
            
            
              (
              
                k
                B
              
              )
            
          
          =
          
            
              (
              
                
                  
                    t
                    _
                  
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                    (
                    
                      k
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                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  
                    t
                    _
                  
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                      k
                      B
                    
                    )
                  
                
              
              )
            
            T
          
        
        ,
        
          
            k
            B
          
          =
          
            1
            ⁢
            
              
            
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            ...
            ⁢
            
              
            
            ⁢
            
              K
              B
            
          
        
        ,
      
    
    
      
        (
        2
        )
      
    
  




is injected into each of the kB transmit antenna elements. The KB antenna-specific transmit signals t(kB) from (2) can be combined to form the overall transmit signal





  
    
      
        
          t
          _
        
        =
        
          
            (
            
              
                
                  t
                  _
                
                
                  
                    (
                    1
                    )
                  
                  T
                
              
              ⁢
              
                
              
              ⁢
              ...
              ⁢
              
                
              
              ⁢
              
                
                  t
                  _
                
                
                  
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                      K
                      B
                    
                    )
                  
                  T
                
              
            
            )
          
          T
        
      
    
    
      
        (
        3
        )
      
    
  




of the dimension KBS. With the channel impulse responses h(k,kB,kM) from (1) the MT and antenna-specific channel folding matrices





  
    
      
        
          
            
              H
              _
            
            
              (
              
                k
                ,
                
                  k
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          =
          
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              ⁢
              
                
              
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            1
          
        
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        ⁢
        
          
            
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                  ⁢
                  k
                
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                  ⁢
                  
                    
                  
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                  ...
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                  ⁢
                  K
                
              
              ,
              
                
                  k
                  B
                
                =
                
                  1
                  ⁢
                  
                    
                  
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                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    K
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              ,
              
                
                  k
                  M
                
                =
                
                  1
                  ⁢
                  
                    
                  
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                  ⁢
                  
                    K
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              ,
            
          
        
      
    
    
      
        (
        4
        )
      
    
  




can be formed. h(k,kB,kM) of (4) has the dimension (S+W−1)×S.

With t(kB) of (2) and h(k,kB,kM) of (4) the signal received at the receive antenna kM from MT μk can be expressed as vector




  
    
      
        
          
            
              
                
                  r
                  _
                
                
                  (
                  
                    k
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                  )
                
              
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                      H
                      _
                    
                    
                      (
                      
                        k
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                          M
                        
                      
                      )
                    
                  
                  ⁢
                  
                    
                      t
                      _
                    
                    
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                        k
                        B
                      
                      )
                    
                  
                
              
            
          
        
        
          
            
              =
              
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                    (
                    
                      
                        
                          H
                          _
                        
                        
                          (
                          
                            k
                            ,
                            1
                            ,
                            
                              k
                              M
                            
                          
                          )
                        
                      
                      ⁢
                      ...
                      ⁢
                      
                        
                      
                      ⁢
                      
                        
                          H
                          _
                        
                        
                          (
                          
                            k
                            ,
                            
                              K
                              B
                            
                            ,
                            
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                              M
                            
                          
                          )
                        
                      
                    
                    )
                  
                  
                    }
                    
                      
                        
                      
                      
                        
                          H
                          _
                        
                        
                          (
                          
                            k
                            ,
                            
                              k
                              M
                            
                          
                          )
                        
                      
                    
                  
                
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                  _
                
              
            
          
        
        
          
            
              
                =
                
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                      _
                    
                    
                      (
                      
                        k
                        ,
                        
                          k
                          M
                        
                      
                      )
                    
                  
                  ⁢
                  
                    t
                    _
                  
                
              
              ,
              
                k
                =
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  K
                
              
              ,
              
                
                  k
                  M
                
                =
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      K
                      M
                    
                    .
                  
                
              
            
          
        
      
    
    
      
        (
        5
        )
      
    
  




r(k,kM) and H(k,kM) have the dimensions (S+W−1)×1 or (S+W−1)×(KBS). The MT and receive-antenna-specific channel folding matrix is designated as H(k,kM).
The KM signals r(k,kM) received at MT μk k=1 . . . K) of (5) can be arranged in a vector




  
    
      
        
          
            
              r
              _
            
            
              (
              k
              )
            
          
          =
          
            
              (
              
                
                  
                    r
                    _
                  
                  
                    
                      (
                      
                        k
                        ,
                        1
                      
                      )
                    
                    T
                  
                
                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  
                    r
                    _
                  
                  
                    
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                        k
                        ,
                        
                          K
                          M
                        
                      
                      )
                    
                    T
                  
                
              
              )
            
            T
          
        
        ,
        
          k
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            K
          
        
        ,
      
    
    
      
        (
        6
        )
      
    
  




of dimension KM(S+W−1) which is designated as the MT-specific receive signal at MT μk.

With the [KM(S+W−1)]×(KBS) MT-specific channel folding matrices




  
    
      
        
          
            
              H
              _
            
            
              (
              k
              )
            
          
          =
          
            
              (
              
                
                  
                    H
                    _
                  
                  
                    
                      (
                      
                        k
                        ,
                        1
                      
                      )
                    
                    T
                  
                
                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  
                    H
                    _
                  
                  
                    
                      (
                      
                        k
                        ,
                        
                          K
                          M
                        
                      
                      )
                    
                    T
                  
                
              
              )
            
            T
          
        
        ,
        
          k
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            K
          
        
        ,
      
    
    
      
        (
        7
        )
      
    
  




the MT-specific receive signal r(k) of (6) becomes

r(k)=H(k)t.  (8)

The K MT-specific receive signals r(k) of (6) are combined to form the overall receive signal




  
    
      
        
          
            
              
                r
                _
              
              =
              
              ⁢
              
                
                  (
                  
                    
                      
                        r
                        _
                      
                      
                        
                          (
                          1
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                    ⁢
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                        r
                        _
                      
                      
                        
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                        (
                        
                          
                            
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                              _
                            
                            
                              
                                (
                                1
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                              T
                            
                          
                          ⁢
                          
                            
                          
                          ⁢
                          ...
                          ⁢
                          
                            
                          
                          ⁢
                          
                            
                              H
                              _
                            
                            
                              
                                (
                                K
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                        )
                      
                      T
                    
                    }
                  
                  ⁢
                  
                    t
                    _
                  
                
                
                  H
                  _
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  H
                  _
                
                ⁢
                
                  t
                  _
                
              
            
          
        
      
    
    
      
        (
        9
        )
      
    
  




r and H from (9) have the dimensions KKM(S+W−1) or [KKM(S+W−1)]×(KBS) respectively.
Data Transmission and Recognition
It is assumed that in a TDMA burst, N data symbols are to be transmitted from the AP to the MT μk k=1 . . . K). The dnk), k=1 . . . N intended for MT μk, k=1 . . . K are assigned in the data vector




  
    
      
        
          
            d
            _
          
          
            (
            k
            )
          
        
        =
        
          
            (
            
              
                
                  d
                  _
                
                1
                
                  (
                  k
                  )
                
              
              ⁢
              
                
              
              ⁢
              ...
              ⁢
              
                
              
              ⁢
              
                
                  d
                  _
                
                N
                
                  (
                  k
                  )
                
              
            
            )
          
          T
        
      
    
    
      
        (
        10
        )
      
    
  




the dimension N. The K data vectors dk) (k=1 . . . K) are combined to form the overall data vector





  
    
      
        
          d
          _
        
        =
        
          
            
              (
              
                
                  
                    d
                    _
                  
                  
                    
                      (
                      1
                      )
                    
                    T
                  
                
                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  
                    d
                    _
                  
                  
                    
                      (
                      K
                      )
                    
                    T
                  
                
              
              )
            
            T
          
          =
          
            
              (
              
                
                  
                    d
                    _
                  
                  1
                
                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  
                    d
                    _
                  
                  KN
                
              
              )
            
            T
          
        
      
    
    
      
        (
        11
        )
      
    
  




of dimension KN. To transmit data from the AP to the MT, the overall transmit signal t of (3) must be expressed by the overall data vector d of (11). If linear modulation is assumed, the modulation process can be expressed as

t=Md.  (12)

The matrix M is called the modulator matrix and has the dimension (KBS)×(KN).
According to the observations made in [3], for each K MT μk k=1 . . . K) a demodulator matrix D(k) of dimension N×[KM(S+W−1)] must be defined in advance and the overall demodulator matrix of the dimension (KN)×[KKM(S+W−1)] is then specified as

D=diagonal block matrix (D(1) . . . D(k))  (13)

FIG. 1 shows the system model of the MIMO-JT method. In the case of the JT, the modulator matrix M of (12) is determined taking into account the demodulator matrix D of (13) and the channel folding matrix H of (9) a posteriori, such that




  
    
      
        
          d
          _
        
        ⁢
        
          =
          j
        
        ⁢
        
          
            
              D
              _
            
            ⁢
            
              r
              _
            
          
          =
          
            
              
                D
                _
              
              ⁢
              
                H
                _
              
              ⁢
              
                t
                _
              
            
            =
            
              
                D
                _
              
              ⁢
              
                H
                _
              
              ⁢
              
                M
                _
              
              ⁢
              
                d
                _
              
            
          
        
      
    
    
      
        (
        14
        )
      
    
  




applies. According to the representation in [1, 2, 3] one selection option is





  
    
      
        
          M
          _
        
        =
        
          
            
              (
              
                
                  D
                  _
                
                ⁢
                
                  
                
                ⁢
                
                  H
                  _
                
              
              )
            
            
              *
              T
            
          
          ⁢
          
            
              
                (
                
                  
                    D
                    _
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        H
                        _
                      
                      ⁡
                      
                        (
                        
                          
                            D
                            _
                          
                          ⁢
                          
                            
                          
                          ⁢
                          
                            H
                            _
                          
                        
                        )
                      
                    
                    
                      *
                      T
                    
                  
                
                )
              
              
                -
                1
              
            
            .
          
        
      
    
    
      
        (
        15
        )
      
    
  




In this case, for a given H and D the overall transmit energy ∥t∥2/2 is minimized. A major problem in designing this type of MIMO-JT method is that of defining the demodulator matrix D in order to obtain an advantageous system performance.
To aid clarity, a MIMO system with only one subscriber is considered below.
In the investigations of JT systems conducted thus far, multiple antennas have only been taken into account at the transmit station (AP) and not at the receiver stations (MT), wherein MIMO antenna arrangements are not included in the considerations. The important point when including these types of antenna arrangements in JT systems is the definition of a suitable demodulator matrix.
Elementary JT System with One MIMO Antenna Arrangement
In this section, an elementary JT system is considered, in which the AP communicates with just one MT μk, kε(1 . . . K) from a collective of K MT μk (k=1 . . . K) and in which an individual data symbol is transmitted to this MT. This situation with just one MT and just one data symbol is indicated below by the index “0”.
The MIMO antenna arrangement considered consists of KB transmit antennas at the AP and KM receive antennas at each MT μk (k=1 . . . K). The names and dimensions of the vectors and matrices introduced in the course of this section are summarized in Tables 1 and 2.
In each of the KB transmit antennas the transmit antenna-specific transmit signal




  
    
      
        
          
            
              t
              _
            
            0
            
              (
              
                k
                ,
                
                  k
                  B
                
              
              )
            
          
          =
          
            
              (
              
                
                  
                    t
                    _
                  
                  
                    0
                    ,
                    1
                  
                  
                    (
                    
                      k
                      ,
                      
                        k
                        B
                      
                    
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  
                    t
                    _
                  
                  
                    0
                    ,
                    
                      S
                      0
                    
                  
                  
                    (
                    
                      k
                      ,
                      
                        k
                        B
                      
                    
                    )
                  
                
              
              )
            
            T
          
        
        ,
        
          
            k
            B
          
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            
              K
              B
            
          
        
        ,
      
    
    
      
        (
        16
        )
      
    
  




of dimension S0 is injected. If S0 is greater than 1, the transmitted data symbol is spread spectrally. S0 is thus called the spread factor. The KB antenna-specific transmit signals t0k,kB) of (16) are combined into the overall transmit signal





  
    
      
        
          
            t
            _
          
          0
          
            (
            k
            )
          
        
        =
        
          
            (
            
              
                
                  t
                  _
                
                0
                
                  
                    (
                    
                      k
                      ,
                      1
                    
                    )
                  
                  T
                
              
              ⁢
              
                
              
              ⁢
              ...
              ⁢
              
                
              
              ⁢
              
                
                  t
                  _
                
                0
                
                  
                    (
                    
                      k
                      ,
                      
                        K
                        B
                      
                    
                    )
                  
                  T
                
              
            
            )
          
          T
        
      
    
    
      
        (
        17
        )
      
    
  




of dimension KBS0.

The radio channel between the transmit antenna kB and the receive antenna kM of the MT μk is characterized by the channel response word




  
    
      
        
          
            h
            _
          
          
            (
            
              k
              ,
              
                k
                B
              
              ,
              
                k
                M
              
            
            )
          
        
        =
        
          
            (
            
              
                
                  h
                  _
                
                1
                
                  (
                  
                    k
                    ,
                    
                      k
                      B
                    
                    ,
                    
                      k
                      M
                    
                  
                  )
                
              
              ⁢
              
                
              
              ⁢
              ...
              ⁢
              
                
              
              ⁢
              
                
                  h
                  _
                
                W
                
                  (
                  
                    k
                    ,
                    
                      k
                      B
                    
                    ,
                    
                      k
                      M
                    
                  
                  )
                
              
            
            )
          
          T
        
      
    
    
      
        (
        18
        )
      
    
  




of the dimension W. With h(k,kB,kM) from (18) the MT- and antenna-specific channel matrix





  
    
      
        
          
            
              H
              _
            
            0
            
              (
              
                k
                ,
                
                  k
                  B
                
                ,
                
                  k
                  M
                
              
              )
            
          
          =
          
            (
            
              
                H
                _
              
              
                
                  0
                  ⁢
                  
                    
                  
                  ⁢
                  i
                
                ,
                j
              
              
                (
                
                  k
                  ,
                  
                    k
                    B
                  
                  ,
                  
                    k
                    M
                  
                
                )
              
            
            )
          
        
        ,
        
          i
          =
          
            
              1
              ⁢
              
                
              
              ⁢
              ...
              ⁢
              
                
              
              ⁢
              
                S
                0
              
            
            +
            W
            -
            1
          
        
        ,
        
          j
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            
              S
              0
            
          
        
        ,
        
          

        
        ⁢
        
          
            
              H
              _
            
            
              
                0
                ⁢
                
                  
                
                ⁢
                i
              
              ,
              j
            
            
              (
              
                k
                ,
                
                  k
                  B
                
                ,
                
                  k
                  M
                
              
              )
            
          
          =
          
            {
            
              
                
                  
                    
                      
                        
                          
                            h
                            _
                          
                          
                            i
                            -
                            j
                            +
                            1
                          
                          
                            (
                            
                              k
                              ,
                              
                                k
                                B
                              
                              ,
                              
                                k
                                M
                              
                            
                            )
                          
                        
                      
                      
                        
                          
                            1
                            ≤
                            
                              i
                              -
                              j
                              +
                              1
                            
                            ≤
                            W
                          
                          ,
                        
                      
                    
                    
                      
                        0
                      
                      
                        
                          sonst
                          ,
                        
                      
                    
                  
                  ⁢
                  
                    

                  
                  ⁢
                  
                    k
                    M
                  
                
                =
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    K
                    M
                  
                
              
              ,
              
                k
                =
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  K
                
              
              ,
              
                
                  k
                  B
                
                =
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    K
                    B
                  
                
              
              ,
            
          
        
      
    
    
      
        (
        19
        )
      
    
  




can be formed. H0(k,kB,kM) has the dimension (S0+W−1)×S0.

With t0(k) of (17) and H0(k,kB,kM) of (19) the signal received at the receive antenna kM of MT μk can be expressed as a vector




  
    
      
        
          
            
              
                
                  r
                  _
                
                0
                
                  (
                  
                    k
                    ,
                    
                      k
                      M
                    
                  
                  )
                
              
              =
              
              ⁢
              
                
                  ∑
                  
                    
                      k
                      B
                    
                    =
                    1
                  
                  
                    K
                    B
                  
                
                ⁢
                
                  
                    
                      H
                      _
                    
                    0
                    
                      (
                      
                        k
                        ,
                        
                          k
                          B
                        
                        ,
                        
                          k
                          M
                        
                      
                      )
                    
                  
                  ⁢
                  
                    
                      t
                      _
                    
                    0
                    
                      (
                      
                        k
                        ,
                        
                          k
                          B
                        
                      
                      )
                    
                  
                
              
            
          
        
        
          
            
              
                =
                
                ⁢
                
                  
                    
                      
                        (
                        
                          
                            
                              H
                              _
                            
                            0
                            
                              (
                              
                                k
                                ,
                                1
                                ,
                                
                                  k
                                  M
                                
                              
                              )
                            
                          
                          ⁢
                          
                            
                          
                          ⁢
                          ...
                          ⁢
                          
                            
                          
                          ⁢
                          
                            
                              H
                              _
                            
                            0
                            
                              (
                              
                                k
                                ,
                                
                                  K
                                  B
                                
                                ,
                                
                                  k
                                  M
                                
                              
                              )
                            
                          
                        
                        )
                      
                      }
                    
                    
                      
                        H
                        _
                      
                      0
                      
                        (
                        
                          k
                          ,
                          
                            k
                            M
                          
                        
                        )
                      
                    
                  
                  ⁢
                  
                    
                      t
                      _
                    
                    0
                    
                      (
                      k
                      )
                    
                  
                
              
              ,
              
                
                  k
                  M
                
                =
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    K
                    M
                  
                
              
              ,
            
          
        
      
    
    
      
        (
        20
        )
      
    
  




of dimension S0+W−1. H0(k,kM) in (20) has the dimension (S0+W−1)×(KBS0). r0(k,kM) of (20) is an MT- and receive antenna-specific signal. With r0(k,kM) the overall signal received at MT μk is received as





  
    
      
        
          
            
              
                
                  r
                  _
                
                0
                
                  (
                  k
                  )
                
              
              =
              
              ⁢
              
                
                  (
                  
                    
                      
                        r
                        _
                      
                      0
                      
                        
                          (
                          
                            k
                            ,
                            1
                          
                          )
                        
                        T
                      
                    
                    ⁢
                    
                      
                    
                    ⁢
                    ...
                    ⁢
                    
                      
                    
                    ⁢
                    
                      
                        r
                        _
                      
                      0
                      
                        
                          (
                          
                            k
                            ,
                            
                              K
                              M
                            
                          
                          )
                        
                        T
                      
                    
                  
                  )
                
                T
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    
                    ⁢
                    
                      
                        
                          (
                          
                            
                              
                                H
                                _
                              
                              0
                              
                                
                                  (
                                  
                                    k
                                    ,
                                    1
                                  
                                  )
                                
                                T
                              
                            
                            ⁢
                            
                              
                            
                            ⁢
                            ...
                            ⁢
                            
                              
                            
                            ⁢
                            
                              
                                H
                                _
                              
                              0
                              
                                
                                  (
                                  
                                    k
                                    ,
                                    
                                      K
                                      M
                                    
                                  
                                  )
                                
                                T
                              
                            
                          
                          )
                        
                        T
                      
                      }
                    
                  
                  
                    
                      H
                      -
                    
                    0
                    
                      (
                      k
                      )
                    
                  
                
                ⁢
                
                  
                    t
                    _
                  
                  0
                  
                    (
                    k
                    )
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    H
                    _
                  
                  0
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  
                    t
                    _
                  
                  0
                  
                    (
                    k
                    )
                  
                
              
            
          
        
      
    
    
      
        (
        21
        )
      
    
  




r0k) and H0k) from (21) have the dimensions KM (S0+W−1) or [KM(S0+W−1)×(KBS0). FIG. 2 shows the structure of the matrix H0k).
With t0k) from (2) and r0k) from (21), the energies transmitted by the AP and received by MT μk become




  
    
      
        
          T
          0
          
            (
            k
            )
          
        
        =
        
          
            
              t
              _
            
            0
            
              
                (
                k
                )
              
              
                *
                T
              
            
          
          ⁢
          
            
              t
              _
            
            0
            
              (
              k
              )
            
          
          ⁢
          
            
          
          ⁢
          or
        
      
    
    
      
        (
        22
        )
      
    
  
  
    
      
        
          
            
              
                R
                0
                
                  (
                  k
                  )
                
              
              =
              
              ⁢
              
                
                  
                    r
                    _
                  
                  0
                  
                    
                      (
                      k
                      )
                    
                    
                      *
                      T
                    
                  
                
                ⁢
                
                  
                    r
                    _
                  
                  0
                  
                    (
                    k
                    )
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    t
                    _
                  
                  0
                  
                    
                      (
                      k
                      )
                    
                    
                      *
                      T
                    
                  
                
                ⁢
                
                  
                    H
                    _
                  
                  0
                  
                    
                      (
                      k
                      )
                    
                    
                      *
                      T
                    
                  
                
                ⁢
                
                  
                    H
                    _
                  
                  0
                  
                    (
                    k
                    )
                  
                
                ⁢
                
                  
                    
                      t
                      _
                    
                    0
                    
                      (
                      k
                      )
                    
                  
                  .
                
              
            
          
        
      
    
    
      
        (
        23
        )
      
    
  




One would also require that the ratio R0k)/T0k) f R0k) from (23) and T0k) from (22) is to be maximized by the correct choice of t0k) from (17). To achieve this maximization, t0k) from (17) should be selected as follows:




  
    
      
        
          
            
              t
              _
            
            0
            
              (
              k
              )
            
          
          =
          
            arg
            ⁢
            
              
            
            ⁢
            
              
                max
                
                  
                    t
                    _
                  
                  0
                  
                    (
                    k
                    )
                  
                
              
              ⁢
              
                (
                
                  
                    
                      
                        t
                        _
                      
                      0
                      
                        
                          (
                          k
                          )
                        
                        
                          *
                          T
                        
                      
                    
                    ⁢
                    
                      
                        H
                        _
                      
                      0
                      
                        
                          (
                          k
                          )
                        
                        
                          *
                          T
                        
                      
                    
                    ⁢
                    
                      
                        H
                        _
                      
                      0
                      
                        (
                        k
                        )
                      
                    
                    ⁢
                    
                      
                        t
                        _
                      
                      0
                      
                        (
                        k
                        )
                      
                    
                  
                  
                    
                      
                        t
                        _
                      
                      0
                      
                        
                          (
                          k
                          )
                        
                        
                          *
                          T
                        
                      
                    
                    ⁢
                    
                      
                        t
                        _
                      
                      0
                      
                        (
                        k
                        )
                      
                    
                  
                
                )
              
            
          
        
        ,
      
    
    
      
        (
        24
        )
      
    
  




which corresponds to a Rayleigh quotient. With H0k) from (21) the transmit signal t0k) determined by (24) is the inherent vector u0k) of the matrix H0k)r with H0k) belonging to the largest inherent value of this matrix, meaning

t0(k)=u0(k).  (25)

By substitution of t0k) from (25) in (21) the overall receive signal

r0(k)=H0(k)u0(k).  (26)

is produced.

The best demodulator for this signal is a filter adapted to the signal, which with r0k) from (21), leads to the demodulator matrix




  
    
      
        
          
            
              
                
                  D
                  _
                
                0
                
                  (
                  k
                  )
                
              
              =
              
              ⁢
              
                
                  r
                  _
                
                0
                
                  
                    (
                    k
                    )
                  
                  
                    *
                    T
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    u
                    _
                  
                  0
                  
                    
                      (
                      k
                      )
                    
                    
                      *
                      T
                    
                  
                
                ⁢
                
                  
                    H
                    _
                  
                  0
                  
                    
                      (
                      k
                      )
                    
                    
                      *
                      T
                    
                  
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                (
                
                  
                    
                      D
                      _
                    
                    0
                    
                      (
                      
                        k
                        ,
                        1
                      
                      )
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      D
                      _
                    
                    0
                    
                      (
                      
                        k
                        ,
                        
                          K
                          M
                        
                      
                      )
                    
                  
                
                )
              
            
          
        
      
    
    
      
        (
        27
        )
      
    
  
  
    
      
        
          
        
        ⁢
        
          =
          
            (
            
              
                
                  D
                  _
                
                
                  0
                  ,
                  1
                
                
                  (
                  k
                  )
                
              
              ⁢
              
                
              
              ⁢
              ...
              ⁢
              
                
              
              ⁢
              
                
                  D
                  _
                
                
                  0
                  ,
                  
                    
                      K
                      M
                    
                    ⁡
                    
                      (
                      
                        
                          S
                          0
                        
                        +
                        W
                        -
                        1
                      
                      )
                    
                  
                
                
                  (
                  k
                  )
                
              
            
            )
          
        
      
    
    
      
        (
        28
        )
      
    
  




of dimension 1×[KM(S0+W−1)], where the receive antenna-specific demodulator matrices





  
    
      
        
          
            
              D
              _
            
            o
            
              (
              
                k
                ,
                
                  k
                  M
                
              
              )
            
          
          =
          
            
              τ
              _
            
            0
            
              
                (
                
                  k
                  ,
                  
                    k
                    M
                  
                
                )
              
              *
              T
            
          
        
        ,
        
          
            k
            M
          
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            
              K
              M
            
          
        
        ,
      
    
    
      
        (
        29
        )
      
    
  




have the dimension 1×(S0+W−1).

Multiple MT-JT System with a Number of Symbols with One MIMO Antenna Arrangement

a) Transmission Model
If we now look at the more realistic situation in which the AP communicates simultaneously with all K MT μk (k=1 . . . K) and where, instead of only one data symbol per MT, N>1 data symbols are transmitted, with each of these data symbols being spectrally spread by the factor S0 already introduced in Section 2.







TABLE 1







Names and dimensions of vectors introduced in Section 2.











Vector
Name
Dimension







t0k,kB)
MT- and transmit antenna-
S0




Specific transmit signal



t0k)
MT-specific transmit signal
KBS0



h(k,kB,kM)
MT- and antenna-specific
W




Channel response word



r0k,kB)
MT- and receive antenna-
S0 + W − 1




Specific receive signal



r0k)
MT-specific
KM(S + W − 1)




Receive signal



u0k)
Inherent vector of
KBS0




Hk)*τ Hk)




belonging to the largest inherent




value

















TABLE 2







Names and dimensions of matrices introduced in Section 2.









Matrix
Name
Dimension





H0k,kB,kM)
MT- and antenna-
(S0 + W − 1) × S0



specific channel matrix


H0k,kM)
MT- and receive
(S0 + W − 1) × (KBS0)



antenna-specific channel



matrix


H0k)
MT-specific
[KM (S0 + W − 1)] × (KBS0)



channel matrix


D0k)
MT-specific
1 × [KM (S0 + W − 1)]



demodulator matrix


D0k,kM)
MT- and receive
1 × (S0 + W − 1)



antenna specific



demodulator matrix









As before, the AP is equipped with KB transmit antennas and each MT μk features KM receive antennas. Below, the signal descriptions introduced in Section 2 are first adapted to this new situation. Then, on the basis of the demodulator matrices D0k) from (27) a demodulator matrix D is created. The names and dimensions of the vectors and matrices introduced in the course of Section 3 are summarized in Tables 3 or 4.
Instead of t0k,kB) from (16) there is the transmit antenna-specific transmit signal




  
    
      
        
          
            
              t
              _
            
            
              (
              
                k
                B
              
              )
            
          
          =
          
            
              (
              
                
                  
                    t
                    _
                  
                  1
                  
                    (
                    
                      k
                      B
                    
                    )
                  
                
                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  t
                  S
                  
                    (
                    
                      k
                      B
                    
                    )
                  
                
              
              )
            
            T
          
        
        ,
        
          
            k
            B
          
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            
              K
              B
            
          
        
        ,
      
    
    
      
        (
        30
        )
      
    
  




of the dimension

S=NS0,  (31)

and instead of t0k) from (17) the overall transmit signal





  
    
      
        
          t
          _
        
        =
        
          
            (
            
              
                
                  t
                  _
                
                
                  
                    (
                    1
                    )
                  
                  T
                
              
              ⁢
              ...
              ⁢
              
                
              
              ⁢
              
                
                  
                    t
                    _
                  
                  
                    (
                    
                      K
                      B
                    
                    )
                  
                
                T
              
            
            )
          
          T
        
      
    
    
      
        (
        32
        )
      
    
  




of the dimension KBS is produced.

Instead of H0k,kB,kM) from (19) the MT- and antenna-specific channel matrix




  
    
      
        
          
            
              H
              _
            
            
              (
              
                k
                ,
                
                  k
                  B
                
                ,
                
                  k
                  M
                
              
              )
            
          
          =
          
            (
            
              
                H
                _
              
              
                i
                ,
                j
              
              
                (
                
                  k
                  ,
                  
                    k
                    B
                  
                  ,
                  
                    k
                    M
                  
                
                )
              
            
            )
          
        
        ,
        
          i
          =
          
            
              1
              ⁢
              
                
              
              ⁢
              ...
              ⁢
              
                
              
              ⁢
              S
            
            +
            W
            -
            1
          
        
        ,
        
          j
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            S
          
        
        ,
        
          

        
        ⁢
        
          
            
              H
              _
            
            
              i
              ,
              j
            
            
              (
              
                k
                ,
                
                  k
                  B
                
                ,
                
                  k
                  M
                
              
              )
            
          
          =
          
            {
            
              
                
                  
                    
                      
                        
                          
                            h
                            _
                          
                          
                            i
                            -
                            j
                            +
                            1
                          
                          
                            (
                            
                              k
                              ,
                              
                                k
                                B
                              
                              ,
                              
                                k
                                M
                              
                            
                            )
                          
                        
                      
                      
                        
                          
                            1
                            ≤
                            
                              i
                              -
                              j
                              +
                              1
                            
                            ≤
                            W
                          
                          ,
                        
                      
                    
                    
                      
                        0
                      
                      
                        
                          sonst
                          ,
                        
                      
                    
                  
                  ⁢
                  
                    

                  
                  ⁢
                  
                    k
                    M
                  
                
                =
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    K
                    M
                  
                
              
              ,
              
                k
                =
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  K
                
              
              ,
              
                
                  k
                  B
                
                =
                
                  1
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      K
                      B
                    
                    .
                  
                
              
            
          
        
      
    
    
      
        (
        33
        )
      
    
  




is produced.

H0k,kB,kM) from (33) has the dimension (S+W−1)×S.
Instead of r0k,kB) from (20), t from (32) and H0k,kB,kM) from (33) produce the MT- and receive antenna-specific receive signal




  
    
      
        
          
            r
            _
          
          
            (
            
              k
              ,
              
                k
                M
              
            
            )
          
        
        =
        
          
            
              ∑
              
                
                  k
                  B
                
                =
                1
              
              
                K
                B
              
            
            ⁢
            
              
            
            ⁢
            
              
                
                  H
                  _
                
                
                  (
                  
                    k
                    ,
                    
                      k
                      B
                    
                    ,
                    
                      k
                      M
                    
                  
                  )
                
              
              ⁢
              
                
                  t
                  _
                
                
                  (
                  
                    k
                    B
                  
                  )
                
              
            
          
          ⁢
          
            

          
          ⁢
          
            
          
          =
          
            
              
                (
                
                  
                    
                      H
                      _
                    
                    
                      (
                      
                        k
                        ,
                        1
                        ,
                        
                          k
                          M
                        
                      
                      )
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      H
                      _
                    
                    
                      (
                      
                        k
                        ,
                        
                          K
                          B
                        
                        ,
                        
                          k
                          M
                        
                      
                      )
                    
                  
                
                )
              
              
                }
                
                  
                    
                      H
                      _
                    
                    ⁢
                    
                      
                    
                  
                  
                    (
                    
                      k
                      ,
                      
                        k
                        M
                      
                    
                    )
                  
                
              
            
            ⁢
            
              
                t
                _
              
              .
            
          
        
      
    
    
      
        (
        34
        )
      
    
  




rk,kB) and Hk,kM) from (34) have the dimensions (S+W−1) or (S+W−1)×(KBS).
With Hk,kM) from (34) and t from (32) the overall signal received by MT μk can be written as follows:




  
    
      
        
          
            r
            _
          
          
            (
            k
            )
          
        
        =
        
          
            
              (
              
                
              
              ⁢
              
                
                  
                    
                      r
                      _
                    
                    
                      (
                      
                        k
                        ,
                        1
                      
                      )
                    
                  
                  T
                
                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  
                    
                      r
                      _
                    
                    
                      (
                      
                        k
                        ,
                        
                          K
                          M
                        
                      
                      )
                    
                  
                  T
                
              
              )
            
            T
          
          ⁢
          
            

          
          ⁢
          
            
          
          =
          
            
              
                
                  
                    (
                    
                      
                        
                          H
                          _
                        
                        
                          
                            (
                            
                              k
                              ,
                              1
                            
                            )
                          
                          T
                        
                      
                      ⁢
                      
                        
                      
                      ⁢
                      ...
                      ⁢
                      
                        
                      
                      ⁢
                      
                        
                          
                            H
                            _
                          
                          
                            (
                            
                              k
                              ,
                              
                                k
                                M
                              
                            
                            )
                          
                        
                        T
                      
                    
                    )
                  
                  }
                
                ⁢
                
                  t
                  _
                
              
              
                
                  
                    H
                    _
                  
                  ⁢
                  
                    
                  
                
                
                  (
                  k
                  )
                
              
            
            ⁢
            
              
            
            ⁢
            
              

            
            ⁢
            
              
            
            =
            
              
                
                  H
                  
                    (
                    k
                    )
                  
                
                _
              
              ⁢
              
                
              
              ⁢
              
                t
                _
              
            
          
        
      
    
    
      
        (
        35
        )
      
    
  




rk) and Hk) from (35) have the dimensions KM(S+W−1) or [KM(S+W−1)]×KBS. As an extension of the observations in the previous section, an overall receive signal




  
    
      
        
          r
          _
        
        =
        
          
            
              (
              
                
              
              ⁢
              
                
                  
                    
                      r
                      _
                    
                    
                      (
                      1
                      )
                    
                  
                  T
                
                ⁢
                
                  
                
                ⁢
                ...
                ⁢
                
                  
                
                ⁢
                
                  
                    
                      r
                      _
                    
                    
                      (
                      K
                      )
                    
                  
                  T
                
              
              )
            
            T
          
          ⁢
          
            

          
          ⁢
          
            
          
          =
          
            
              
                (
                
                  
                    
                      H
                      _
                    
                    
                      
                        (
                        1
                        )
                      
                      T
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  ...
                  ⁢
                  
                    
                  
                  ⁢
                  
                    
                      
                        H
                        _
                      
                      
                        (
                        K
                        )
                      
                    
                    T
                  
                
                )
              
              T
            
            ⁢
            
              
            
            ⁢
            
              

            
            ⁢
            
              
            
            =
            
              
                H
                _
              
              ⁢
              
                t
                _
              
            
          
        
      
    
    
      
        (
        36
        )
      
    
  




is now introduced with the K receive signals rk) from (34) of all K MT μk (k=1 . . . K). r and H from (35) have the dimensions KKM(S+W−1) or [KKM(S+W−1)]×KBS.

b) Determining the Demodulator Matrix D
According to the observations made in [2], for each of the K MT μk (k=1 . . . K) a demodulator matrix Dk) of dimension N×[KM(S+W−1)] must be determined and then the overall demodulator matrix of the dimension (KN)×[KKM(S+W−1)] is produced as

D=diagonal block matrix (D(1) . . . D(k))  (37)








TABLE 3







Names and dimensions of vectors introduced in this section











Vector
Name
Dimension







tka)
transmit antenna-specific transmit
S = NS0




signal



t
Overall transmit signal
KBS



rk,ka)
MT- and receive antenna specific
S + W − 1




receive signal



rk)
MT-specific receive signal
KM(S + W − 1)



r
Overall receive signal
KKM(S + W − 1)



d
Overall data vector
KN

















TABLE 4







Names and dimensions of matrices introduced in this section.









Matrix
Designation
Dimension





Hk,ka,kM) H
MT- and antenna-
(S + W − 1) × S



specific channel matrix


H0k,kM)
MT- and receive
(S + W − 1) × (KBS)



antenna-specific channel



matrix


Hk)
MT-specific
[Km (S + W − 1) ] × (KBS)



channel matrix


H
Overall channel
[KKM(S + W − 1) ] × (KBS)



matrix


Dk)
MT-specific
N × [KM(S + W − 1)



demodulator matrix


D
Overall
(KN) × [KKM(S + W − 1) ]



demodulator matrix


B
System matrix
(KN) × (KBS)


M
Modulator matrix
(KBS) × (KN)









The decisive point of the proposal for constructing the demodulator matrix D(k) taking into consideration the channel characteristics lies in the demodulator matrix D0k) introduced in (27). The N lines of D(k) are obtained as shifted versions of D0k) from (27) in accordance with the method




  
    
      
        
          
            
              D
              _
            
            
              i
              ,
              j
            
            
              (
              k
              )
            
          
          =
          
            (
            
              
                D
                _
              
              
                i
                ,
                j
              
              
                (
                k
                )
              
            
            )
          
        
        ,
        
          i
          =
          
            1
            ⁢
            
              
            
            ⁢
            ...
            ⁢
            
              
            
            ⁢
            N
          
        
        ,
        
          j
          =
          
            1
            ⁢
            
              
            
            ⁢
            
              ...
              ⁢
              
                
              
              [
              
                
                  K
                  M
                
                ⁡
                
                  (
                  
                    
                      
                        S
                        0
                      
                      ⁢
                      N
                    
                    +
                    W
                    -
                    1
                  
                  )
                
              
              ]
            
          
        
        ,
        
          

        
        ⁢
        
          
            
              D
              _
            
            
              i
              ,
              j
            
            
              (
              k
              )
            
          
          =
          
            {
            
              
                
                  
                    
                      
                        D
                        _
                      
                      
                        0
                        ,
                        p
                      
                      
                        (
                        k
                        )
                      
                    
                  
                  
                    
                      
                        1
                        ≤
                        
                          
                            (
                            
                              j
                              -
                              
                                
                                  (
                                  
                                    i
                                    -
                                    1
                                  
                                  )
                                
                                ⁢
                                
                                  S
                                  0
                                
                              
                            
                            )
                          
                          ⁢
                          mod
                          ⁢
                          
                            
                          
                          ⁢
                          
                            (
                            
                              
                                
                                  S
                                  0
                                
                                ⁢
                                N
                              
                              +
                              W
                              -
                              1
                            
                            )
                          
                        
                        ≤
                        
                          
                            S
                            0
                          
                          +
                          W
                          -
                          1
                        
                      
                      ,
                    
                  
                
                
                  
                    0
                  
                  
                    
                      sonst
                      ,
                    
                  
                
              
              ⁢
              
                

              
              ⁢
              with
            
          
        
      
    
    
      
        (
        38
        )
      
    
  
  
    
      
        
          p
          =
          
            
              
                (
                
                  j
                  -
                  
                    
                      (
                      
                        i
                        -
                        1
                      
                      )
                    
                    ⁢
                    
                      S
                      0
                    
                  
                
                )
              
              ⁢
              
                mod
                ⁡
                
                  (
                  
                    
                      
                        S
                        0
                      
                      ⁢
                      N
                    
                    +
                    W
                    -
                    1
                  
                  )
                
              
            
            +
            
              
                (
                
                  
                    S
                    0
                  
                  +
                  W
                  -
                  1
                
                )
              
              ·
              
                [
                
                  j
                  
                    
                      
                        S
                        0
                      
                      ⁢
                      N
                    
                    +
                    W
                    -
                    1
                  
                
                ]
              
            
          
        
        ,
      
    
    
      
        (
        39
        )
      
    
  




and [ ] designating the integer part. The structure of D(k) from (38) is shown in FIG. 3.

D from (37) can be formed with the K matrices D(k) from (38). With D from (37) and H from (36) the system matrix

B=DH  (40)

of the dimension KN×KBS is obtained. As shown in [2], the overall transmit signal t from (22) and the overall data vector d [2] of the dimension KN can be obtained as





  
    
      
        t
        =
        
          
            
              
                
                  
                    
                      B
                      
                        *
                        T
                      
                    
                    ⁡
                    
                      (
                      
                        
                          BB
                          _
                        
                        
                          *
                          T
                        
                      
                      )
                    
                  
                  
                    -
                    1
                  
                
                }
              
              
                
                  M
                  _
                
                ⁢
                
                  
                
              
            
            ⁢
            
              d
              _
            
          
          ⁢
          
            

          
          ⁢
          
            
          
          =
          
            
              M
              _
            
            ⁢
            
              
            
            ⁢
            
              d
              _
            
          
        
      
    
    
      
        (
        41
        )
      
    
  




with the modulator matrix M from (41) possessing the dimension (KBS)×(KN).

Although the present invention has been described with reference to specific embodiments, those of skill in the art will recognize that changes may be made thereto without departing from the spirit and scope of the present invention as set forth in the hereafter appended claims.

## Claims

1. A method of transmitting information in a radio communication system, the method comprising:
connecting a transmit station to at least two receiver stations via a radio communication interface;
including a transmit antenna with at least two antenna elements at the transmit station and including a transmit antenna with at least two antenna elements at each of the receiver stations, wherein the transmit station and the receiver stations communicate using MIMO transmission;
generating transmit signals for radiation from the antenna elements of the transmit antenna of the transmit station in a common process and matching the transmit signals with regards to a transmit energy to be used for radiation;
detecting received signals received by antenna elements of receive antennas of the receiver stations in a linear signal processing through demodulation, taking into account space and time transmission characteristics between the transmit station and the respective receiver stations, wherein a receiver station specific transmit signal corresponds to a Rayleigh quotient;
calculating individual transmit signals for the antenna elements of the transmit antenna of the transmit station before radiation using a modulator matrix;
generating a transmit signal vector using a linear modulation of a data vector to be transmitted with the modulator matrix;
processing the received signals, the processing including using a demodulation matrix for linear receive-side signal processing;
connecting the transmit station to the receiver stations using at least one radio channel having a channel matrix; and
including a system matrix in the modulator matrix specified by a product of the demodulator matrix and the channel matrix.

2. A radio communication system for transmitting information, comprising:
at least one transmit station including a transmit antenna with at least two antenna elements;
at least two receiver stations each including a transmit antenna with at least two antenna elements; and
a radio communication interface for connecting the at least one transmit station and the at least two receiver stations;
wherein the transmit station generates transmit signals which are radiated by the antenna elements of the transmit antenna of the transmit station in a common process and matches the transmit signals with regards to a transmit energy to be employed for radiation;
wherein each of the receiver stations detect receive signals received by antenna elements of receive antennas of the receiver stations in a linear signal processing through demodulation, taking into account space and time transmission characteristics between the transmit station and the respective receiver stations;
wherein a receiver station specific transmit signal corresponds to a Rayleigh quotient;
wherein individual transmit signals are calculated for the antenna elements of the transmit antenna of the transmit station before radiation using a modulator matrix;
wherein a transmit signal vector is generated using a linear modulation of a data vector to be transmitted with the modulator matrix;
wherein the received signals are processed using a demodulation matrix for linear receive-side signal processing;
wherein the transmit station and the receiver stations are connected using at least one radio channel having a channel matrix; and
wherein a system matrix is included in the modulator matrix as specified by a product of the demodulator matrix and the channel matrix.