Abstract:
A method transmits data streams in a multiple-input/multiple-output (MIMO) wireless communication systems, where the number of receiving antennas q is less than a number of the transmitting antennas p. The data streams are precoded with a set of finite impulse response filters according to a transfer function of the MIMO channels. The precoded data streams are transmitted over multiple-input/multiple-output channels to a receiver, where the transmitted precoded data stream are detected and decoded to perfectly recover the plurality of data streams without the use of an equalizer.

Description:
FIELD OF INVENTION  
         [0001]    The present invention relates generally to the field of wireless communications, and more particularly to transmitters in multi-input/multi-output (MIMO) communication systems.  
         BACKGROUND OF THE INVENTION  
         [0002]    Rapid progress in wireless communications, such as cellular networks, has led to an increasing demand for adaptive and efficient signal processing. Transmitter and receiver diversities in multi-input/multi-output (MIMO) channels play a key role in wireless communications. In practical applications, multi-path propagation and limited bandwidth can severely degrade receiver performance.  
           [0003]    Inter-symbol interference (ISI) is a critical problem in MIMO channels used by wireless communication systems, such as terrestrial television broadcasting and cellular networks. In addition to ISI, inter-channel interference (ICI), is also a problem in MIMO channels. Therefore, ISI/ICI reduction is a critical component for any MIMO communication systems.  
           [0004]    In cellular networks, up-link channels run from mobile transmitters to base station receivers, and down-link channels run from the base station transmitters to mobile receivers. The base station usually has substantial processing power, and is typically equipped with multiple transmitting and receiving antennas. In contrast, the mobile transceiver has limited processing power and only a single antenna.  
           [0005]    In the prior art, Bezout equalizers have been used in receivers to limit ISI and ICI, see Kung et al.,  “An associative memory approach to blind signal recovery for SIMO/MIMO systems,”  Proceedings of IEEE Workshop on Neural Networks for Signal Processing, September 2001. With the Bezout equalizer, the MIMO dispersive channel is converted into several single-input/single-output non-dispersive channels. However, the Bezout equalizer requires that the number of outputs, which is equal to the number of receiver antennas, is greater than the number of inputs or transmitter antennas. Such a requirement can be satisfied easily by the base station but not the mobile transceiver. Bezout equalizers greatly increase the complexity of the receivers.  
           [0006]    Therefore, there still is a need for reducing ISI/ICI in receivers of a MIMO system where the number of the receiver antennas at a mobile receiver is limited, and where joint processing is not practical due to the physical separation of the receiving antennas of different transceivers.  
         SUMMARY OF THE INVENTION  
         [0007]    The present invention provides a precoder for a transmitter, such as a base station in a cellular network, to eliminate inter-symbol and inter-channel interference (ISI/ICI) in a receiver, e.g., a cellular telephone. The precoder includes a set of linear finite impulse response (FIR) filters. These filters are designed and optimized to completely eliminate the ISI/ICI on a down-link channel from a transmitter to a receiver. Therefore, the complexity of the mobile receiver can be reduced while still eliminating ISI/ICI.  
           [0008]    The present invention applies to single user MIMO system, where the output signals correspond to different antennas of a single user, and to distributed multi-user systems, where the output signals correspond to different antennas of different users. By feeding back channel information in a frequency division duplex (FDD) system, or by estimating a reverse channel in a time division duplex (TDD) system, the channel characteristics can be determined by the transmitter at the base station. The transmitter then uses the channel characteristics to precode the out-going signals. The fact that channels in a time-division system are reciprocal is described by Esmailzadeh et al. “Time-division duplex CDMA communications,” IEEE Personal Communications, Volume: 4 Issue: 2, pp. 51-56, April 1997.  
           [0009]    The invention provides a precoder in a transmitter to eliminate ISI and ICI in a receiver. The receiver, in contrast with the prior art, does not include a Bezout equalizer. Due to the optimum precoder design, the received signal is free of ISI and ICI. The receiver is therefore very simple, only including standard components for timing recovery, demodulation, and decoding, and some other basic functionality. An equalizer is no longer required at the receiver. Note that the Bezout equalizer is a left delay-permissive inverse of the channel, while the precoder is a right delay-permissive inverse of a channel transfer function.  
           [0010]    More particularly, the invention provides a method which transmits data streams in a multiple-input/multiple-output (MIMO) wireless communication system, where the number of receiving antennas q is less than a number of the transmitting antennas p.  
           [0011]    The data streams are precoded with a set of finite impulse response filters according to a transfer function of the MIMO channels. The precoded data streams are transmitted over multiple-input/multiple-output channels to a receiver, where the transmitted precoded data stream are detected and decoded to recover the plurality of data streams without the use of an equalizer. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]    [0012]FIG. 1 is a block diagram of a MIMO system with a Bezout precoder according to the invention; and  
         [0013]    [0013]FIG. 2 is a block diagram of a method for determining filter coefficients for the precoder according to the invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0014]    MIMO System Model with Precoder  
         [0015]    [0015]FIG. 1 shows a multi-input/multi-output (MIMO) system  100  according to the invention. The MIMO system  100  includes a precoder  110 , a transmitter with p transmitting antennas  120 , a MIMO channel  130 , and a receiver with q receiving antennas  140 , where q&lt;p. The precoder  110  includes a filter bank F(D)  112  described in greater detail below. In one implementation of the invention, the receiver is a cellular telephone with a single antenna.  
         [0016]    The receiver includes standard components  150  for timing recovery, demodulation, and decoding, and some other basic receiver functionality. However, the receiver does not include a Bezout equalizer for ISI/ICI reduction, as in the prior art. Instead, ISI\ICI reduction is accomplished by the precoder  110  in the transmitter.  
         [0017]    The precoder  110  takes q data streams s q (n)  111  as input and produces p data streams  s′   p (n)  115  as output for the p transmitting antennas  120  using the filter bank F(D)  112 . The transmitter sends the signals over the MIMO channel  130 . The receiving antennas  140  detect p transmitted signals, and perfectly recover q data streams x q (n)  141 , without the use of an equalizer.  
         [0018]    If s′hd j(k)  115  denotes the sequence of symbols produces by the precoder  110  for the p transmitting antennas  120 , for j=1, . . . , p, and h ij (k) is the channel response from transmitter j to receiver i=1, . . . , q, then,  
             x   i          (   k   )       =       ∑     j   =   1     p                       ∑     l   =   0     d              h   ij          (   l   )              s   j   ′          (     k   -   l     )               ,                         
 
         [0019]    where d denotes a maximal ISI length.  
         [0020]    The above convolution can be expressed equivalently in a z-transform domain as: 
           H ( D ) s ′( D )= x ( D ) 
         [0021]    where,  
         [0022]    s′(D)=[s′ 1 (D) s′ 2 (D) . . . s′ p (D)] T , x(D)=[x 1 (D) x 2 (D) . . . x q (D)] T  and H(D)={h ij (D)} are the z-transform vectors (matrix) of the corresponding sequences or impulse responses of the channels  130 .  
         [0023]    Departing from the traditional z-transform notation, here the delay operator is denoted by D instead of by z −1 . The p-input-q-output MIMO channel  130  can then be represented by a q×p matrix H(D)  121 , which is referred to as the transfer function of the MIMO system  100 .  
         [0024]    The precoder&#39;s filters F(D)  112  takes the data streams s i (k), i=1, . . . , q  111 , as inputs and generates the p transmitted signals s′ j (k), j=1, . . . , p as outputs  115 . With the preceding filters F(D)  112 , the received signal x(D) can be expressed as: 
           H ( D ) F ( D ) s ( D )= x ( D ) 
         [0025]    where s(D) is the z-transform vector of the data streams s i (k), for i=1, . . . , q.  
         [0026]    Definition of the Bezout Precoder  
         [0027]    If q&lt;p, then the FIR filter bank F(D)  112  is a Bezout precoder for the channel transfer function H(D)  121 , if and only if  
           H        (   D   )            F        (   D   )         =     [           D     k   1                       0                       ⋰                       0                     D     k   q             ]                           
 
         [0028]    This is called Bezout precoder because this equation satisfies the generalized Bezout identity. The Bezout precoder exploits the polynomial algebra property of the channel to eliminate ISI and ICI. From the polynomial algebra associated with the generalized Bezout identity, signal recoverability condition, and the relationship between the transmitted and received data can be determined.  
         [0029]    With the Bezout precoder  110 , the symbols received by the receiver are ISI and ICI-free. In the absence of noise, the received symbols are a delayed version of the transmitted symbols, hence the input data streams are perfectly recoverable.  
         [0030]    Existence Conditions of Bezout Precoder  
         [0031]    The MIMO system  100  with the matrix transfer function H(D)  121  is perfectly recoverable by the Bezout precoder  110  if and only if H(D) is left coprime, except for a left common factor with determinant D k .  
         [0032]    Optimal Bezout Precoder  
         [0033]    With the Bezout precoder  110 , the receiver can perfectly recover the input streams under an idealistic assumption that the system  100  is noise free. However, noise is pervasive in all practical applications. Therefore, it is important to understand the performance of Bezout precoder&#39;s filter bank F(D)  112  for noisy channels and select the one with the best noise resilience.  
         [0034]    For the Bezout precoder  110  H(D)F(D)=Diag[D k     i   ], one column of F(D)  112  is denoted by f(D)=f 0 +Df 1 + . . . +D ρ−1 f ρ−1 , and its expanded column vector is denoted by 
           {right arrow over (f)}=[f   0   T   f   1   T    . . . f   ρ−1   T ], 
         [0035]    where ρ denotes the tap-length of the precoder&#39;s filter.  
         [0036]    In order to have an ISI/ICI-free communication, the following requirement are met 
           H ( D ) f   i ( D )=[0 . . .  D   k     i    . . . 0] T   , i= 1, . . . ,  q   
         [0037]    The received SNR (signal-to-noise ratio) for the i-th stream is  
             (     σ   s   i     )     2       σ   n   2       ,                         
 
         [0038]    where (σ s   i ) 2  is the signal power of the i-th stream, and σ n   2  is the noise power for the i-th stream. The total transmission power at the transmitting antennas due to the i-th stream is (σ s   i ) 2 ∥{right arrow over (f)} i ∥ 2 ,because each FIR filter f i (D) amplifies the signal power by a factor of ∥{right arrow over (f)} i ∥ 2 , when the input sequences are independent from sample to sample. Therefore, the optimal Bezout precoder filter for the source inputs  111  is equivalent to multiple individually optimized precoder filters, one for each input.  
         [0039]    Consequently, in the optimal individual Bezout precoder, the ith filter f i (D) has a minimal two-norm (largest singular value in a matrix) ∥f i (D)∥ 2 ≡∥{right arrow over (f)} i ∥ 2 , such that 
           H ( D ) f   i ( D )=[0 . . .  D   k     i    . . . 0] T   , i= 1, . . .  q.   
         [0040]    It should be noted that the system delay k i  is a design parameter, thus, the two-norm of f i (D) can be reduced.  
         [0041]    [0041]FIG. 2 shows the steps of a method  200  for designing the optimal f i (D) using a resultant matrix.  
         [0042]    Step  210  constructs a MIMO channel resultant matrix  211  from the transfer function H(D)  121 . If the transfer function H(D)  121  of the channel  130  is expressed in terms of coefficient matrices as H(D)=H 0 +H 1 D+ . . . +H d−1 D d−1 +H d D d , then the resultant matrix  211  is defined as:  
           Γ        [     H        (   D   )       ]       =     [           H   0                                                 ⋮         H   0                                       H   d         ⋮       ⋰                                     H   d         ⋮         H   0                                     ⋰       ⋮                                                 H   d           ]       ,                         
 
         [0043]    where the size of the resultant matrix  211  is (d+ρ)q×ρp, d is the maximal ISI length of the channel, and ρ is defined as the tap-length of the FIR filter of the precoder  110 .  
         [0044]    Step  220  performs a singular value decomposition (SVD) on the channel resultant matrix  121  and solves for the expanded vector {right arrow over (f)} i . Thus, the equation H(D)f i (D)=[0 D k     i   . . . 0] T , i=1, . . . , q can be expressed in matrix notation as: 
           Γ[H ( D )] {right arrow over (f)}   i   =e   m   , m=   1, . . . , (   d+ρ ) q.   
         [0045]    where e m  is a column vector with all zeros, except an entry of one at 
           m=i+qk   i   , k   i =0, . . . , d+ρ− 1. 
         [0046]    A singular value decomposition (SVD) is taken of Γ[H(D)]  211 , with Σ being a square positive-definite diagonal matrix Σ=diag(σ 1 , . . . σ r ), where r is the rank of Γ[H(D)], U and V are unitary matrices trimmed to the proper size conformant with Σ:  
         [0047]    Γ[H(D)]=UΣV H    221 . For a given index i, a Bezout precoder filter {right arrow over (f)} exists if and only if a solution b for Ub=e m  exists. In other words, {right arrow over (f)} i  is obtained by solving the equation: UΣV H {right arrow over (f)} i =e m .  
         [0048]    Step  230  selects the optimum of all feasible solutions to determine the filter coefficients  231  of the Bezout precoder  110 . This Bezout precoder is 
           {right arrow over (f)}   i   =VΣ   −1   U   H   e   m with the 2-norm, 
           ∥{right arrow over (f)}   i ∥ 2 =( UΣ   −2   U   H ) mm , 
         [0049]    where the two-norm, by definition, is the largest singular value in a matrix.  
         [0050]    The optimal integer m* corresponding to the optimal delay k i , with minimal 2-norm, is: 
         [0051]    [0051]         m   *     =     arg                     min   m          {         (     U          ∑     -   2            U   H         )       m                 m                     m   =     i        (     mod                 q     )         ,       e   m     ∈     Column                 Span        {   U   }           }     .                                     
         [0052]    In other words, of the possible solution, the one with the smallest two-norm is the optimal solution.  
         [0053]    Effect of Bezout Precoding  
         [0054]    The main advantage of Bezout precoder  110  lies in its ability to completely eliminate ISI/ICI for wireless MIMO channels with more inputs than outputs. The low complexity precoder can be implemented in a transmitter, such as a base station of a cellular network, to simplify the design of wireless receivers. In fact, there is no need for an equalizer in the receiver.  
         [0055]    The Bezout precoder according to the invention provides quality-of-service (QoS) for streaming date through power control. This is useful for multi-media communications with video and audio streams at different levels of priority. With the Bezout precoder, scaling the transmitting powers scales the output signal-to-noise ratios (SNRs) by the same factor.  
         [0056]    In other words, a diagonal power control matrix Λ can be used at the transmitter to change the system 
           H ( D ) F ( D )=Diag[ D   k     i   ] 
         [0057]    to 
           H ( D ) F ( D )Λ=Diag[ D   k     i   ]Λ 
         [0058]    so that the output SNR or bit error rate (BER) requirements are met for selected data streams.  
         [0059]    Bezout preceding according to the invention can deliver the same optimal BER, at half the power, as techniques that use a space time block coder (STBC), see Alamouti,  “A simple transmit diversity technique for wireless communications,”  IEEE Journal on Selected Areas in Communications, Vol. 16, No. 8, pp. 1451-1458, October 1998.  
         [0060]    Although the invention has been described by way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications can be made within the spirit and scope of the invention. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.