# Patent

## Title
MIMO OFDM system

## Abstract

A MIMO OFDM system includes a plurality of space-time encoders for encoding respective data blocks with independent space-time codes. The transformed data block signals are transmitted by a plurality of transmit antennas and received by a plurality of receive antennas. The received data is pre-whitened prior to maximum likelihood detection. In one embodiment, successive interference cancellation can be used to improve system performance. Channel parameter estimation can be enhanced by weighting the channel impulse response estimates based upon a deviation from average.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
This application claims the benefit of U.S. Provisional Patent Application No. 60/206,182, filed on May, 22, 2000.


STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH
Not Applicable.
FIELD OF THE INVENTION
The present invention relates generally to communication systems and, more particularly, to Orthogonal Frequency Division Multiplexed (OFDM) communication systems.
BACKGROUND OF THE INVENTION
High data-rate wireless access is demanded by many applications. Traditionally, more bandwidth is required for higher data-rate transmission. However, due to spectral limitations, techniques for increasing bandwidth are often impractical and/or expensive.
In one known system, multiple transmit and receive antennas are used to obtain spectrally efficient data transmission. Multiple transmit antennas can be used to obtain transmit diversity or to form multiple-input multiple-output (MIMO) channels. Multiple transmit antennas have also been used to provide diversity in wireless systems. Transmit diversity can be based on linear transforms or by space-time coding. Space-time coding in particular is characterized by high code efficiency and can improve the efficiency and performance of Orthogonal Frequency Division Multiplexing (OFDM) systems. The system capacity can be further improved if multiple transmit and receive antennas are used to form MIMO channels. Compared with a single-input single-output (SISO) system with flat Rayleigh fading or narrowband channels, a MIMO system can improve the capacity by a factor of the minimum of the number of transmit and receive antennas.
FIG. 1 shows a conventional OFDM system 10 including subsystems for transmission and reception of data. A coding subsystem 12 encodes binary data from a data source. The coded data is interleaved by an interleaving subsystem 14 and then mapped onto multi-amplitude multi-phase constellation symbols by a mapping subsystem 16. In one particular embodiment, the multi-amplitude multi-phase constellation symbols include quadrature phase shift keying (QPSK) symbols. Pilot signals can then inserted by a pilot insertion subsystem 18 to estimate the channel at the remote subscriber unit receivers. A serial-to-parallel conversion subsystem 20 converts the serial data stream to a parallel data stream that is provided to an inverse fast Fourier transform (IFFT) subsystem 22. The transformed data is converted to serial data stream by a parallel-to-serial converter 24. Cyclic extension and windowing can be added by a subsystem 26 prior to digital-to-analog conversion by a DAC 28 and transmission by an antenna system 30. The receive portion 32 of the OFDM system includes similar corresponding components for extracting the data from the received OFDM signal.
As shown in FIG. 2, the known OFDM system 10 utilizes an overlapping orthogonal multicarrier modulation technique having a plurality of subcarriers 50. FIG. 3 shows the orthogonal nature of the subcarriers. More particularly, each of four subcarriers 60 of one OFDM data symbol has an integral number of cycles in the interval T. The number of cycles between adjacent subcarriers differs by one.
In one known OFDM transmission system, the complexity of the space-time processor increases as the bandwidth increases and the performance of the space-time processor is significantly degraded when estimated channel parameters are used to construct space-time processors.
It would, therefore, be desirable to provide a MIMO OFDM system having enhanced signal detection. It would further be desirable to increase the accuracy of channel parameter estimates.
SUMMARY OF THE INVENTION
The present invention provides a MIMO OFDM system utilizing independent space-time codes for multiple transmit antenna sets. The receiver decodes the space-time codes using pre-whitening followed by maxiumum likelihood decoding. With this arrangement, the MIMO OFDM system provides spectrally efficient wideband communication. The MIMO-OFDM system determines and uses channel delay profile estimates to achieve more accurate channel parameter estimation.
In one aspect of the invention, a MIMO OFDM communication system includes a plurality of transmit antennas and a plurality of receive antennas. First and second data blocks are each transformed into two signals by respective first and second space-time encoders. Each of the four resultant signals form an OFDM block that is transmitted by a respective transmit antenna. Each receive antenna receives a signal that is the superposition of the four transmitted OFDM blocks. When detecting and decoding the coded signal for the first data block, the coded signal for the second data block is treated as an interfering signal. Similarly, the first data block signal is treated as an interfering signal when detecting and decoding the second data block signal. The received signals are pre-whitened prior to maximum likelihood decoding, which can include Viterbi decoding. In one embodiment, pre-whitening for the maximum likelihood decoding includes minimum mean square error (MMSE) restoration of the desired signals followed by whitening of the residual interfering signals and noise.
Successive interference cancellation can improve performance of the system. More particularly, after the first and second data blocks are decoded, it is determined whether the decoded signals contain errors. In the case where one decoded data block has an error and the other data block does not contain an error, the correct data block signal is regenerated and removed from the received signal. The other data block is then re-detected and decoded from the modified signal.
In a further aspect of the invention, a MIMO OFDM system enhances channel parameter estimation by utilizing relatively accurate channel delay profiles derived from the spatial correlation of the channel impulse responses. In general, the estimated channel responses are weighted based upon a deviation from the average channel response. By more heavily weighting relatively accurate channel responses, the channel parameter estimations are more accurate.



BRIEF DESCRIPTION OF THE DRAWINGS
The invention will be more fully understood from the following detailed description taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a prior art orthogonal frequency division multiplexing (OFDM) system;
FIG. 2 is a prior art graphical depiction showing subchannels used in the OFDM system of FIG. 1;
FIG. 3 is a prior art graphical depiction showing orthogonal subcarriers used in the OFDM system of FIG. 1;
FIG. 4 is a block diagram of a portion of a MIMO-OFDM system in accordance with the present invention;
FIGS. 5A–6B are graphical representations of MIMO-OFDM systems in accordance with the present invention having various channel delay profiles, numbers of receive antennas, and detection techniques;
FIGS. 7A–B are graphical comparisons of MIMO-OFDM systems in accordance with the present invention with ideal and estimated channel parameters; and
FIGS. 8A–D are graphical representations of MIMO-OFDM systems in accordance with the present invention with various Doppler frequencies.



DETAILED DESCRIPTION OF THE INVENTION
In general, the present invention provides an orthogonal frequency division multiplexing (OFDM) system having multiple transmit and receive antennas for forming MIMO channels. With this arrangement, channel estimation and signal detection is enhanced.
FIG. 4 shows a MIMO-OFDM system 100 having multiple, here shown as four, transmit antennas TA1-4 and a plurality of receive antennas RA1-P. Although the MIMO-OFDM system is shown having four transmit antennas, it is understood that any number of transmit antennas can be used. In addition, the number of receive antennas should be equal to or greater than the number of transmit antennas.
The MIMO-OFDM system 100 includes a first space time encoder STE1 that receives a first data block b1[n,k] and a second space-time encoder STE2 that receives a second data block b2[n,k]. At time n at tone k, each of the two data blocks, {bi[n,k]: k=0, 1, . . . } for i=1 and 2, is transformed into two signals, {t2i+j[n,k]: k=0, 1, . . . ,& j=1, 2} for i=1 and 2, respectively, (Equations 1–3) through the first and second space-time encoders STE1,STE2. Each of the coded signals forms an OFDM block. The transmit antennas TA1-4 transmit the OFDM signals after respective inverse fast Fourier transform IFFT1-4 modulation by respective signals tmi[n,k] for i=1, . . . , 4.
The signals sent by the transmit antennas TA1-4 are received by the receive antennas RA1-RAP. The received signals r1[n,k], r2[n,k], . . . , rP[n,k] are transformed by respective fast Fourier transform (FFT) subsystems FFT1–FFTP to generate signals that are provided to a space-time processor STP, which provides detected signal information to respective first and second space-time decoders STD1, STD2. A channel parameter estimator CPE receives the transformed signals from which channel parameter information is determined and then provided to the space-time processor STP for use in decoding the signals.
The received signal at each receive antenna RA1-RAP is the superposition of the four distorted transmitted signals, which can be expressed below in Equation 1:




  
    
      
        
          
            
              r
              j
            
            ⁡
            
              [
              
                n
                ,
                k
              
              ]
            
          
          =
          
            
              
                ∑
                
                  i
                  =
                  1
                
                4
              
              ⁢
              
                
                  
                    H
                    ij
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
                ⁢
                
                  
                    t
                    i
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
              
            
            +
            
              
                w
                j
              
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
          
        
        ,
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          1
          )
        
      
    
  




for j=1, . . . , p, where p corresponds to the number of receive antennas, Hij[n,k] denotes the channel frequency response for the k-th tone at time n, corresponding to the i-th transmit and the j-th receive antenna, and wj[n,k] denotes the additive complex Gaussian noise on the j-th receive antenna. The noise is assumed to be zero-mean with variance σn2 and uncorrelated for different times n's, tones k's, and receive antennas j's.

The input-output relationship for the OFDM signals can be also expressed in vector form as set forth in Equation 2–4 below:

r[n,i:]=H1[n,k]t1[n,k]+H2[n,k]t2[n,k]+w[n,k],  Eq. (2)

where





  
    
      
        
          
            r
            ⁡
            
              [
              
                n
                ,
                k
              
              ]
            
          
          ⁢
          
            =
            Δ
          
          ⁢
          
            (
            
              
                
                  
                    
                      r
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    
                      r
                      4
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
              
            
            )
          
        
        ,
        
          
            w
            ⁡
            
              [
              
                n
                ,
                k
              
              ]
            
          
          ⁢
          
            =
            Δ
          
          ⁢
          
            (
            
              
                
                  
                    
                      w
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
              
              
                
                  ⋮
                
              
              
                
                  
                    
                      w
                      4
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
              
            
            )
          
        
        ,
        
          

        
        ⁢
        
          
            
              t
              i
            
            ⁡
            
              [
              
                n
                ,
                k
              
              ]
            
          
          ⁢
          
            =
            Δ
          
          ⁢
          
            
              (
              
                
                  
                    
                      
                        t
                        
                          
                            2
                            ⁢
                            i
                          
                          +
                          1
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                
                
                  
                    
                      
                        t
                        
                          
                            2
                            ⁢
                            i
                          
                          +
                          2
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                
              
              )
            
            ⁢
            
              
            
            ⁢
            and
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          3
          )
        
      
    
  
  
    
      
        
          
            H
            i
          
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        ⁢
        
          =
          Δ
        
        ⁢
        
          (
          
            
              
                
                  
                    H
                    
                      
                        2
                        ⁢
                        i
                      
                      +
                      11
                    
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
              
              
                
                  
                    H
                    
                      
                        2
                        ⁢
                        i
                      
                      +
                      21
                    
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
              
            
            
              
                ⋮
              
              
                ⋮
              
            
            
              
                
                  
                    H
                    
                      
                        2
                        ⁢
                        i
                      
                      +
                      
                        1
                        ⁢
                        p
                      
                    
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
              
              
                
                  
                    H
                    
                      
                        2
                        ⁢
                        i
                      
                      +
                      
                        2
                        ⁢
                        p
                      
                    
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
              
            
          
          )
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          4
          )
        
      
    
  




To achieve transmit diversity gain and detection of the transmitted signals, the space-time processor STP extracts the required signals for decoding by the first and second space-time decoders STD1, STD2. The space-time processor and space-time decoders each require channel state information.
In one embodiment, the CPE utilizes conventional training sequences to exploit time and frequency domain correlations of the channel parameters. Exemplary channel estimation techniques are described in Y. Li, et al., “Channel Estimation for OFDM Systems with Transmitter Diversity in Mobile Wireless Channels,” IEEE Journal of Selected Areas in Comm., Vol. 17, pp. 461–471, March 1999, and Y. Li., “Simplified Channel Estimation for OFDM Systems with Multiple Transmit Antennas,” IEEE Journal of Selected Areas in Comm., Vol. ______, pp. ______, ______, which are incorporated herein by reference.
The complex baseband representation of a mobile wireless channel impulse response can be described by Equation 5 below:




  
    
      
        
          h
          ⁡
          
            (
            
              t
              ,
              τ
            
            )
          
        
        =
        
          
            ∑
            k
          
          ⁢
          
            
              
                γ
                k
              
              ⁡
              
                (
                t
                )
              
            
            ⁢
            
              c
              ⁡
              
                (
                
                  τ
                  -
                  
                    τ
                    k
                  
                
                )
              
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          5
          )
        
      
    
  




where τκ is the delay of the k-th path, γk(t) is the corresponding complex amplitude, and c(t) is a shaping pulse having a frequency response, which can be a square-root raised-cosine Nyquist filter. Due to the motion of the vehicle, the complex amplitudes γk(t) are wide-sense stationary (WSS), narrow-band complex Gaussian processes, which are independent for each path. The average powers of the complex amplitudes γk(t) depend on the channel delay profiles, e.g., hilly terrain (HT) and typical urban (TU), which are determined by the environment. The channels typically have the same delay profiles.

From Equation 5 above, it follows that the frequency response at time t can be expressed as set forth below in Equation 6:




  
    
      
        
          
            
              
                H
                ⁡
                
                  (
                  
                    t
                    ,
                    f
                  
                  )
                
              
              ⁢
              
                =
                Δ
              
              ⁢
              
              ⁢
              
                
                  ∫
                  
                    -
                    ∞
                  
                  
                    +
                    ∞
                  
                
                ⁢
                
                  
                    h
                    ⁡
                    
                      (
                      
                        t
                        ,
                        τ
                      
                      )
                    
                  
                  ⁢
                  
                    e
                    
                      
                        -
                        j2π
                      
                      ⁢
                      
                        
                      
                      ⁢
                      jτ
                    
                  
                  ⁢
                  
                    
                  
                  ⁢
                  
                    d
                    τ
                  
                
              
            
          
        
        
          
            
              
                =
                
                ⁢
                
                  
                    C
                    ⁡
                    
                      (
                      f
                      )
                    
                  
                  ⁢
                  
                    
                      ∑
                      k
                    
                    ⁢
                    
                      
                        
                          γ
                          k
                        
                        ⁡
                        
                          (
                          t
                          )
                        
                      
                      ⁢
                      
                        e
                        
                          
                            -
                            j2π
                          
                          ⁢
                          
                            
                          
                          ⁢
                          f
                          ⁢
                          
                            
                          
                          ⁢
                          
                            τ
                            k
                          
                        
                      
                    
                  
                
              
              ,
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          6
          )
        
      
    
  
  
    
      where
    
    
      
        
      
    
  
  
    
      
        
          C
          ⁡
          
            (
            f
            )
          
        
        ⁢
        
          =
          Δ
        
        ⁢
        
          
            ∫
            
              -
              ∞
            
            
              +
              ∞
            
          
          ⁢
          
            
              c
              ⁡
              
                (
                τ
                )
              
            
            ⁢
            
              e
              
                
                  -
                  j2π
                
                ⁢
                
                  
                
                ⁢
                f
                ⁢
                
                  
                
                ⁢
                τ
              
            
            ⁢
            
              
            
            ⁢
            
              d
              τ
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          7
          )
        
      
    
  




In an OFDM system with proper cyclic extension and timing, the channel frequency response, with tolerable leakage, can be represented by Equation 8 below:





  
    
      
        
          H
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        ⁢
        
          =
          Δ
        
        ⁢
        
          
            H
            ⁡
            
              (
              
                
                  n
                  ⁢
                  
                    
                  
                  ⁢
                  
                    T
                    f
                  
                
                ,
                
                  k
                  ⁢
                  
                    
                  
                  ⁢
                  Δ
                  ⁢
                  
                    
                  
                  ⁢
                  f
                
              
              )
            
          
          =
          
            
              ∑
              
                l
                =
                0
              
              
                
                  K
                  o
                
                -
                1
              
            
            ⁢
            
              
                h
                ⁡
                
                  [
                  
                    n
                    ,
                    l
                  
                  ]
                
              
              ⁢
              
                
                  W
                  K
                  kl
                
                .
              
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          8
          )
        
      
    
  




where the channel response is h[n,l]{circumflex over (=)}h(nTf,k Ts/K),WK=exp(−j2π/K), K is the number of tones in an OFDM block, Tf and Δf are the block length and tone spacing, respectively, and Ts is the symbol duration of OFDM, which is related to Δf by Ts=1/Δf. The channel responses h[n,l], for l=0, 1, . . . , K0−1, are WSS, narrow-band complex Gaussian processes. The average power of the channel h[n,l] and index K0(<K) depend on the delay profiles, e.g., HT and TU, of the wireless channels.

In accordance with the present invention, signal detection is enhanced by utilizing spatial pre-whitening followed by maximum-likelihood (ML) decoding. While joint detection of multiple inputs may be optimal, the concomitant computational complexity renders such an approach impractical.
In contrast to joint detection, in accordance with the present invention the coded signals for the second data block b2[n,k] are treated as interfering signals when detecting and decoding the first data block b1[n,k] signals. Similarly, the coded signals for the first data block b1[n,k] are treated as interfering signals when detecting and decoding the second data block b2[n,k]. In addition, the transmitted signals are considered to be uncorrelated and Gaussian processes.
For example, the second data block signal b2[n,k], which is transmitted by the third and fourth transmit antennas TA3, TA4, is treated as an interfering signal when detecting and decoding the first data block b1[n,k]. Therefore, the interfering signal v[n, k] at the receivers is equal to the channel response vector H2[n,k] multiplied by the transmitted signal vector t2[n,k] for the interfering signal plus Gaussian noise w[n,k] as set forth below in Equation 9:

v[n, k]=H2[n, k]t2[n, k]+w(n, k)  Eq. (9)

The vectors in Equation 9 are derived from Equations 2–4 above.

If v[n, k] is spatially and temporally white, then the minimum Euclidian distance decoder is equivalent to maximum likelihood (ML) decoder. However, if v[n,k] is spatially or temporally correlated, then pre-whitening is used for the ML decoder. Pre-whitening for ML decoding is well known to one of ordinary skill in the art and is described below. In general, the space-time codes for the first and second data blocks are decoded using pre-whitening for flattening the receiver response to facilitate ML detection. The detected constellation points are mapped to the sequence nearest in Euclidean distance.
From the ML criterion, ML decoding is equivalent to finding the estimated first data block {{circumflex over (b)}1[n, k] that minimizes the value of Equation 10 below:




  
    
      
        
          C
          ⁡
          
            (
            
              {
              
                
                  b
                  1
                
                ⁡
                
                  [
                  
                    n
                    ,
                    k
                  
                  ]
                
              
              }
            
            )
          
        
        =
        
          
            ∑
            
              k
              =
              1
            
            K
          
          ⁢
          
            
              m
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
            .
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          10
          )
        
      
    
  




where the minimum Euclidean distance is defined in Equations 11–12 below:





  
    
      
        
          
            
              
                m
                ⁡
                
                  [
                  
                    n
                    ,
                    k
                  
                  ]
                
              
              ⁢
              
                =
                Δ
              
              ⁢
              
              ⁢
              
                
                  
                    (
                    
                      
                        r
                        ⁡
                        
                          [
                          
                            n
                            ,
                            k
                          
                          ]
                        
                      
                      -
                      
                        
                          
                            H
                            1
                          
                          ⁡
                          
                            [
                            
                              n
                              ,
                              k
                            
                            ]
                          
                        
                        ⁢
                        
                          
                            t
                            1
                          
                          ⁡
                          
                            [
                            
                              n
                              ,
                              k
                            
                            ]
                          
                        
                      
                    
                    )
                  
                  H
                
                ⁢
                
                  
                    R
                    v
                    
                      -
                      1
                    
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
                ⁢
                
                  (
                  
                    
                      r
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    -
                  
                
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    
                      H
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      t
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
                )
              
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          11
          )
        
      
    
  
  
    
      and
    
    
      
        
      
    
  
  
    
      
        
          
            
              
                
                  R
                  v
                
                ⁡
                
                  [
                  
                    n
                    ,
                    k
                  
                  ]
                
              
              ⁢
              
                =
                Δ
              
              ⁢
              
              ⁢
              
                E
                ⁢
                
                  {
                  
                    
                      v
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        v
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                  }
                
              
            
          
        
        
          
            
              =
              
              ⁢
              
                
                  
                    
                      H
                      2
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      H
                      2
                      H
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
                +
                
                  
                    σ
                    n
                    2
                  
                  ⁢
                  I
                
              
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          12
          )
        
      
    
  




As known to one of ordinary skill in the art, the inverse of the matrix Rv[n,k], which is derived from the cross correlation H2[n,k]H2H[n,k] of the interfering channel response, can be used to whiten the signal.

Direct calculation then yields that the minimum Euclidean distance can be defined as set forth in Equation 13




  
    
      
        
          
            
              
                m
                ⁡
                
                  [
                  
                    n
                    ,
                    k
                  
                  ]
                
              
              =
              
              ⁢
              
                
                  
                    
                      r
                      H
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      R
                      v
                      
                        -
                        1
                      
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    r
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
                -
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    
                      t
                      1
                      H
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      H
                      1
                      H
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      R
                      v
                      
                        -
                        1
                      
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    r
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
                -
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    
                      r
                      H
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      R
                      v
                      
                        -
                        1
                      
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      H
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      t
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
                +
              
            
          
        
        
          
            
              
              ⁢
              
                
                  
                    t
                    1
                    H
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
                ⁢
                
                  
                    H
                    1
                    H
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
                ⁢
                
                  
                    R
                    v
                    
                      -
                      1
                    
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
                ⁢
                
                  
                    H
                    1
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
                ⁢
                
                  
                    
                      t
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  .
                
              
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          13
          )
        
      
    
  




Denoting {tilde over (H)}[n,k] as a two by two matrix satisfying Equation 14 and 15





  
    
      
        
          
            
              
                H
                1
                H
              
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
            ⁢
            
              
                R
                v
                
                  -
                  1
                
              
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
            ⁢
            
              
                H
                1
              
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
          
          ⁢
          
            =
            Δ
          
          ⁢
          
            
              
                
                  H
                  _
                
                H
              
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
            ⁢
            
              
                H
                _
              
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
          
        
        ⁢
        
          

        
        ⁢
        and
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          14
          )
        
      
    
  
  
    
      
        
          
            L
            1
          
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        ⁢
        
          =
          Δ
        
        ⁢
        
          
            
              (
              
                
                  H
                  1
                
                ⁢
                
                  
                    H
                    
                      _
                      ⁢
                      
                        
                      
                    
                  
                  1
                  
                    -
                    1
                  
                
              
              )
            
            H
          
          ⁢
          
            
              
                R
                v
                
                  -
                  1
                
              
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
            .
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          15
          )
        
      
    
  




it then follows that the minimum Euclidean distance can be represented in Equation 16





  
    
      
        
          
            
              
                
                  m
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
                =
                
                ⁢
                
                  
                    
                      
                        r
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        R
                        v
                        
                          -
                          1
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      r
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                  -
                
              
            
          
          
            
              
                
                ⁢
                
                  
                    
                      
                        t
                        1
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        
                          H
                          _
                        
                        1
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        L
                        1
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      r
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                  -
                
              
            
          
          
            
              
                
                ⁢
                
                  
                    
                      
                        r
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        L
                        1
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        
                          H
                          _
                        
                        1
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        t
                        1
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                  +
                
              
            
          
          
            
              
                
                ⁢
                
                  
                    
                      t
                      1
                      H
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      
                        H
                        _
                      
                      1
                      H
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      
                        H
                        _
                      
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      t
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
              
            
          
          
            
              
                =
                
                ⁢
                
                  
                    
                      
                        r
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        R
                        v
                        
                          -
                          1
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      r
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                  -
                
              
            
          
          
            
              
                
                ⁢
                
                  
                    
                      
                        t
                        1
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        
                          H
                          _
                        
                        1
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        
                          r
                          _
                        
                        1
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                  -
                
              
            
          
          
            
              
                
                ⁢
                
                  
                    
                      
                        
                          r
                          _
                        
                        1
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        
                          H
                          _
                        
                        1
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        t
                        1
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                  +
                
              
            
          
          
            
              
                
                ⁢
                
                  
                    
                      t
                      1
                      H
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      
                        H
                        _
                      
                      1
                      H
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      
                        H
                        _
                      
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      t
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
              
            
          
          
            
              
                =
                
                ⁢
                
                  
                    
                      
                        r
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        R
                        v
                        
                          -
                          1
                        
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      r
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                  -
                
              
            
          
          
            
              
                
                ⁢
                
                  
                    
                      
                        
                          r
                          _
                        
                        1
                        H
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                    ⁢
                    
                      
                        
                          r
                          _
                        
                        1
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          k
                        
                        ]
                      
                    
                  
                  +
                
              
            
          
          
            
              
                
                ⁢
                
                  
                    
                      
                      
                        
                          
                            
                              r
                              _
                            
                            1
                          
                          ⁡
                          
                            [
                            
                              n
                              ,
                              k
                            
                            ]
                          
                        
                        -
                        
                          
                            
                              
                                H
                                _
                              
                              1
                            
                            ⁡
                            
                              [
                              
                                n
                                ,
                                k
                              
                              ]
                            
                          
                          ⁢
                          
                            
                              t
                              1
                            
                            ⁡
                            
                              [
                              
                                n
                                ,
                                k
                              
                              ]
                            
                          
                        
                      
                      
                    
                    2
                  
                  ,
                
              
            
          
        
        ⁢
        
          

        
        ⁢
        where
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          16
          )
        
      
    
  
  
    
      
        
          
            
              r
              ~
            
            1
          
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        ⁢
        
          =
          Δ
        
        ⁢
        
          
            
              L
              1
            
            ⁡
            
              [
              
                n
                ,
                k
              
              ]
            
          
          ⁢
          
            
          
          ⁢
          
            
              r
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
            .
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          17
          )
        
      
    
  




When the well known Viterbi algorithm is used for the ML decoding of the space-time codes, the first two terms in the above equation for m[n,k] are independent of the detected data and only the third term, i.e., ∥{tilde over (r)}1[n,k]−{tilde over (H)}1[n,k]t1[n,k]∥2, is related to the detected data and affects the metric in the trellis search when the Viterbi algorithm is used. Trellis searching is well known to one of ordinary skill in the art. Therefore, the ML decoding is equivalent to finding the estimated first data block {{circumflex over (b)}1[n,k] that minimizes the value of Equation 18 below:




  
    
      
        
          
            C
            _
          
          ⁡
          
            (
            
              {
              
                
                  b
                  1
                
                ⁡
                
                  [
                  
                    n
                    ,
                    k
                  
                  ]
                
              
              }
            
            )
          
        
        =
        
          
            ∑
            
              k
              =
              1
            
            K
          
          ⁢
          
            
              
              
                
                  
                    
                      r
                      _
                    
                    1
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
                -
                
                  
                    
                      
                        H
                        _
                      
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  ⁢
                  
                    
                      t
                      1
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
              
              
            
            2
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          18
          )
        
      
    
  




Thus, after pre-whitening, a conventional space-time decoder for a 2-transmit and 2-receive antenna system can be used.

Note that L1[n,k] can be rewritten as shown in Equation 19:




  
    
      
        
          
            L
            1
          
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        =
        
          
            
              (
              
                
                  
                    H
                    _
                  
                  
                    -
                    1
                  
                
                ⁡
                
                  [
                  
                    n
                    ,
                    k
                  
                  ]
                
              
              )
            
            H
          
          ⁢
          
            
              H
              1
              H
            
            ⁡
            
              [
              
                n
                ,
                k
              
              ]
            
          
          ⁢
          
            
              
                R
                0
                
                  -
                  1
                
              
              ⁡
              
                [
                
                  n
                  ,
                  k
                
                ]
              
            
            .
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          19
          )
        
      
    
  




A predetermined weight matrix H1H[n,k]Rv−1[n,k] for minimum mean-square error (MMSE) restoration of the desired signal t1[n,k] suppresses the interfering signal t2[n,k]. After MMSE signal restoration, the correlation matrix of the residual interferers and noise can be represented as set forth in Equation 20:





  
    E
    ⁢
    
      {
      
        
          
            H
            1
            H
          
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        ⁢
        
          
            R
            v
            
              -
              1
            
          
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        ⁢
        
          v
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        ⁢
        
          
            (
            
              
                
                  H
                  1
                  H
                
                ⁡
                
                  [
                  
                    n
                    ,
                    k
                  
                  ]
                
              
              ⁢
              
                
                  R
                  v
                  
                    -
                    1
                  
                
                ⁡
                
                  [
                  
                    n
                    ,
                    k
                  
                  ]
                
              
              ⁢
              
                v
                ⁡
                
                  [
                  
                    n
                    ,
                    k
                  
                  ]
                
              
            
            )
          
          H
        
      
      }
    
  
  =
  
    
      
        H
        1
        H
      
      ⁡
      
        [
        
          n
          ,
          k
        
        ]
      
    
    ⁢
    
      
        R
        v
        
          -
          1
        
      
      ⁡
      
        [
        
          n
          ,
          k
        
        ]
      
    
    ⁢
    
      
        
          H
          1
        
        ⁡
        
          [
          
            n
            ,
            k
          
          ]
        
      
      .
    
  




The term {tilde over (H)}−1[n,k]H whitens the residual interferers and noise. Therefore, the pre-whitening processing for the ML decoder includes MMSE restoration of the desired signals followed by whitening of the residual interferers and noise.

In another aspect of the invention, successive interference cancellation is utilized to improve the overall system performance. The successive interference cancellation can be based upon cyclic redundancy check (CRC) codes and/or signal quality.
In one embodiment, a MIMO-OFDM system includes successive interference cancellation based upon CRC codes for identifying decoding errors. First and second data blocks b1[n,k], b2[n,k] can be decoded as described above. If an error is detected in one of the data blocks, such as the first data block b1[n,k], and no errors are detected in the other data block, such as the second data block b2[n,k], then the coded signals for the correct (second) data block are regenerated at the receiver and removed from the received signal. That is, the coded signals for second data block b2[n,k] are removed from the received signal such that cleaner signals can be used to re-detect and decode the first data block b1[n,k], which originally contained an error. More particularly, the first data block can be re-detected and decoded without interference from the second data block signals.
In a further embodiment, a MIMO-OFDM system detects and decodes each of the data block signals, which do not include error codes such as CRC codes. As is known to one of ordinary skill in the art, some systems do not utilize error coding when signal quality is expected to be above a predetermined threshold. In accordance with the present invention, each decoded signal has an associated MMSE. The signal with the higher quality, e.g., lower MMSE, is removed such that it does not interference with the other signal.
In another aspect of the invention, a MIMO-OFDM system includes enhanced channel parameter estimation using relatively accurate channel delay profiles. In one embodiment, a known decision-directed channel parameter estimator along with optimum training sequences for OFDM systems with multiple transmit antennas are used to estimate the channel delay profiles. Illustrative parameter estimations and training sequences are described in Y. (Geoffrey) Li, et al, “Channel Estimation for OFDM Systems with Transmitter Diversity and its Impact on High-Rate Data Wireless Networks,” IEEE Journal of Selected Areas in Comm., vol. 17, pp. 461–471, March 1999, and Y. Li. et al., “Simplified Channel Estimation for OFDM Systems with Multiple Transmit Antennas,” ______. The estimated channel delay profiles are used to determine channel parameter estimations.
In general, the time and frequency correlation of the channel profiles are used to more accurately estimate the channel parameter estimation. More particularly, channel profiles are correlated in time since the change over time is relatively slow. Similarly, adjacent channels have similar frequency responses and are thus correlated with respect to frequency. By determining the average channel impulse response for example, a deviation from the average can form the basis to weight each channel impulse response. With this weighting arrangement, the channel delay estimates can be more accurately estimated to enhance channel parameter estimation.
The channel impulse response hij[n,l] can be estimated using the correlation of channel parameters in the time and frequency domains. The estimated channel impulse response ĥij[n,l] can be reconstructed using a discrete Fourier transform (DFT) as shown below in Equation 21




  
    
      
        
          
            
              H
              ^
            
            ij
          
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        =
        
          
            ∑
            
              l
              =
              0
            
            
              
                K
                o
              
              -
              1
            
          
          ⁢
          
            
              
                
                  h
                  ^
                
                ij
              
              ⁡
              
                [
                
                  n
                  ,
                  l
                
                ]
              
            
            ⁢
            
              W
              K
              kl
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          21
          )
        
      
    
  




where ĥij[n,l] contains the true channel parameter hij[n,l], WKkl is described above in Equation 5, and an estimation error eij[n,l] as expressed below in Equation 22:

ĥij[n,l]=hij[n,l]+eij[n,l]  Eq. (22)

The estimation error eij[n,l] can be Gaussian with zero-mean and variance σ2. The parameter estimation quality can be measured with a normalized MSE (NMSE) defined as follows in Equation 23:





  
    
      
        NMSE
        ⁢
        
          =
          Δ
        
        ⁢
        
          
            E
            ⁢
            
              
                
                
                  
                    
                      
                        H
                        ^
                      
                      ij
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                  -
                  
                    
                      H
                      ij
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        k
                      
                      ]
                    
                  
                
                
              
              2
            
          
          
            E
            ⁢
            
              
                
                
                  
                    H
                    ij
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      k
                    
                    ]
                  
                
                
              
              2
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          23
          )
        
      
    
  




Thus, the NMSE for the channel response can be expressed as set forth in Equation 24:

NMSEr=Koσ2  Eq. (24)

assuming that the NMSE is normalized as shown in Equation 25:





  
    
      
        
          
            
              ∑
              
                l
                =
                0
              
              
                
                  K
                  o
                
                -
                1
              
            
            ⁢
            
              E
              ⁢
              
                
                  
                  
                    
                      h
                      ij
                    
                    ⁡
                    
                      [
                      
                        n
                        ,
                        l
                      
                      ]
                    
                  
                  
                
                2
              
            
          
          =
          
            
              
                ∑
                
                  l
                  =
                  0
                
                
                  
                    K
                    o
                  
                  -
                  1
                
              
              ⁢
              
                σ
                l
                2
              
            
            =
            
              1
              ⁢
              
                
              
              ⁢
              with
            
          
        
        ⁢
        
          

        
        ⁢
        
          σ
          ⁢
          
            =
            Δ
          
          ⁢
          
            E
            ⁢
            
              
                
                
                  
                    h
                    ij
                  
                  ⁡
                  
                    [
                    
                      n
                      ,
                      l
                    
                    ]
                  
                
                
              
              2
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          25
          )
        
      
    
  




If the channel delay profile is known, that is, σl2 for l=0, . . . , K0−1 is known, and is used to reconstruct channel frequency response from ĥij[n,l], the MSE of Ĥij[n,k], can be significantly reduced. In this case, if weighting factors α1's are selected to minimize the NMSE of the estimated channel response as in Equation 26:




  
    
      
        
          
            
              H
              ^
            
            ij
          
          ⁡
          
            [
            
              n
              ,
              k
            
            ]
          
        
        ⁢
        
          =
          Δ
        
        ⁢
        
          
            ∑
            
              l
              =
              0
            
            
              
                K
                o
              
              -
              1
            
          
          ⁢
          
            
              α
              l
            
            ⁢
            
              
                
                  h
                  ^
                
                ij
              
              ⁡
              
                [
                
                  n
                  ,
                  l
                
                ]
              
            
            ⁢
            
              W
              K
              kl
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          26
          )
        
      
    
  




then the optimal weighting factor α1 can be defined in Equation 27:





  
    
      
        
          α
          l
        
        =
        
          
            
              σ
              l
              2
            
            
              
                σ
                l
                2
              
              +
              
                σ
                2
              
            
          
          
            
              ∑
              
                m
                =
                0
              
              
                
                  K
                  o
                
                -
                1
              
            
            ⁢
            
              
                σ
                m
                4
              
              
                
                  σ
                  m
                  2
                
                +
                
                  σ
                  2
                
              
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          27
          )
        
      
    
  




which can also be expressed as an inverse of the sum of one plus a ratio of noise power to a power of channel response estimates averaged over the receive antennas, i.e.,





  1
  
    1
    +
    
      
        σ
        2
      
      
        σ
        l
        2
      
    
  




and the resultant NMSE is expressed in Equation 28:





  
    
      
        
          NMSE
          o
        
        =
        
          
            
              σ
              2
            
            ⁢
            
              
                ∑
                
                  m
                  =
                  0
                
                
                  
                    K
                    o
                  
                  -
                  1
                
              
              ⁢
              
                
                  σ
                  m
                  2
                
                
                  
                    σ
                    m
                    2
                  
                  +
                  
                    σ
                    2
                  
                
              
            
          
          
            
              ∑
              
                m
                =
                0
              
              
                
                  K
                  o
                
                -
                1
              
            
            ⁢
            
              
                σ
                m
                4
              
              
                
                  σ
                  m
                  2
                
                +
                
                  σ
                  2
                
              
            
          
        
      
    
    
      
        Eq
        .
        
          
        
        ⁢
        
          (
          28
          )
        
      
    
  




Channel delay profiles depend upon the environment and therefore are usually unknown to users of the system. However, for MIMO-OFDM systems, channels corresponding to different transmit or receive antennas should have the same delay profiles. Thus,




  
    σ
    l
    2
  
  =
  
    E
    ⁢
    
      
        
        
          
            h
            ij
          
          ⁡
          
            [
            
              n
              ,
              l
            
            ]
          
        
        
      
      2
    
  




can be estimated by averaging the estimated channel impulse response for the channels formed by the four transmit antennas and the p receive antennas as shown below in Equation 29:





  
    
      
        
          ∂
          l
          2
        
        ⁢
        
          =
          
            
              1
              
                4
                ⁢
                p
              
            
            ⁢
            
              
                ∑
                
                  i
                  =
                  1
                
                4
              
              ⁢
              
                
                  ∑
                  
                    j
                    =
                    1
                  
                  p
                
                ⁢
                
                  
                    
                    
                      
                        
                          h
                          ^
                        
                        ij
                      
                      ⁡
                      
                        [
                        
                          n
                          ,
                          l
                        
                        ]
                      
                    
                    
                  
                  2
                
              
            
          
        
      
    
    
      
        Eq.  (29)
      
    
  




With the estimated variance, channel delay profile estimates are more accurate so as to improve channel parameter estimation.
EXAMPLE
An exemplary MIMO-OFDM system in accordance with the present invention was simulated. The known typical urban (TU) and hilly terrain (HT) delay profiles were used with Doppler frequencies of 5, 40, 100, and 200 Hz, respectively. The channels corresponding to different transmit or receive antennas have the same statistics. Four transmit antennas and different numbers of receive antennas were used to form a 4-input multiple-output OFDM systems.
To construct an OFDM signal, the entire channel bandwidth, 1.25 MHz, is divided into 256 subchannels. The 2 subchannels on each end are used as guard tones, and the remaining (252 tones) are used to transmit data. To make the tones orthogonal to each other, the symbol duration is about 204.8 microseconds. An additional 20.2 microseconds guard interval is used to provide protection from intersymbol interference due to channel multipath delay spread. This results in a total block length Tf of about 225 microseconds and a subchannel symbol rate rb of 4.44 kbaud.
A 16-state space-time code with 4-PSK is used. Each data block, containing 500 bits, is coded into two different blocks, each of which has exactly 252 symbols, to form an OFDM block. Therefore, the OFDM system with 4 transmit antennas can transmit 2 space-time codewords (1000 bits in total). Each time slot includes 10 OFDM blocks, with the first block used for training and the remaining nine blocks used for data transmission. Thus, the system can transmit data at a rate of 4 Mbits/sec over a 1.25 MHz channel, i.e., the transmission efficiency is 3.2 bits/sec/Hz.
FIGS. 5A–6B show the simulated performance of MIMO-OFDM systems in accordance with the present invention with different channel delay profiles, numbers of receive antennas, and detection techniques. FIG. 5A demonstrates the effect of interleaving on the performance improvement. By interleaving, the required SNR for a 10% WER is improved by 1.5 dB for the TU channel and by 0.7 dB for the HT channel. Since the HT channel has more diversity than the TU channel before interleaving, interleaving has less gain for the HT channel than for the TU channel.
FIGS. 6A–B compare the WERs of a system with interleaving for different detection techniques. As shown, the system with successive interference cancellation based on CRC and signal quality (MMSE) can reduce the required WERs for a 10% WER by 2.5 and 1.8 dB, respectively. All the performance curves in FIGS. 5A–5B are for OFDM with 4 transmit and 4 receive antennas. As the number of receive antennas increases, performance improves, as can be seen from FIGS. 6A–6B. In particular, if the receive antenna number is increased from 4 to 6, the OFDM system with either the TU or HT channels will have about 4 dB performance improvement.
FIGS. 7A–7B compare the performance of MIMO-OFDM systems with the ideal or the estimated channel parameters for different channels with a 40 Hz Doppler frequency. From FIG. 7A it can be seen that the required SNRs for a 10% WER are 10–11 dB for a MIMO-OFDM system with estimated channel parameters for successive interference suppression and space-time decoding, which is 1.5–2 dB higher than with ideal channel parameters for signal detection and decoding. With additional receive antennas, performance improves, as shown in FIG. 7B. In particular, for a system with estimated channel parameters, the required SNR for a 10% WER is reduced by 4.5 dB and 2 dB when the number of receive antennas is increased from 4 to 6 and 6 to 8, respectively.
FIGS. 8A–D compare the performance of OFDM systems with different Doppler frequencies. As the Doppler frequency becomes higher, the channel estimation error increases, and therefore the system suffers more degradation. For a MIMO-OFDM system with 4 transmit and 4 receive antennas, the required SNR for a 10% WER is degraded by 2.4 dB when the Doppler frequency is increased from 40 Hz to 100 Hz. However, with more receive antenna numbers, the degradation is reduced. The degradation is only about 0.4 dB with 10 receive antennas.
The present invention provides an OFDM system having multiple transmit and receive antennas to form a multiple-input multiple-output (MIMO) system that increases system capacity. A pre-whitening technique for ML decoding and successive interference cancellation technique are disclosed. Using these techniques in a four input/four output OFDM system, the net data transmission rate can reach 4 Mbits/sec over a 1.25 MHz wireless channel with a 10–12 dB SNR required for a 10% WER, depending on the radio environment and signal detection technique for word lengths up to 500 bits. A MIMO-OFDM system in accordance with the present invention can be effectively used in high data-rate wireless systems
One skilled in the art will appreciate further features and advantages of the invention based on the above-described embodiments. Accordingly, the invention is not to be limited by what has been particularly shown and described, except as indicated by the appended claims. All publications and references cited herein are expressly incorporated herein by reference in their entirety.

## Claims

1. A method for MIMO-OFDM communication, comprising:
1. on a single transmitting computing device:
(a) encoding a first data block into a first plurality of encoded signals;
(b) encoding a second data block into a second plurality of encoded signals;
(c) transmitting each of the first and second pluralities of encoded signals on respective transmit antennas; and

2. on a single receiving computing device:
(a) simultaneously receiving the transmitted signals on a plurality of receive antennas;
(b) pre-whitening the received signals for each of the first and second data block signals;
(c) performing maximum likelihood detection on each of the pre-whitened received signals;
(d) after decoding the first data block and the second data block of the received signals, performing successive interference cancellation on the received signals by modifying the received signal by re-encoding one of the first or second data block and removing the one of the first or second data block from the received signals; and
(e) and re-decoding the modified received signals.

2. The method according to claim 1, further comprising using CRC codes to perform the successive interference cancellation.

3. The method according to claim 1, further comprising using MMSE levels to perform the successive interference cancellation.

4. The method according to claim 1, further comprising performing channel estimation by weighting channel delay response estimates.

5. The method according to claim 4, wherein performing channel estimation further comprises weighting the channel response estimates based upon a deviation from an average channel response estimate for each delay.

6. The method according to claim 1, further comprising minimizing an NMSE of a channel by weighting channel response estimates.

7. A method for MIMO-OFDM communication, comprising;
1. on a single transmitting computing device:
providing a first data block to a first space-time encoder that generates first and second coded signals;
transmitting the first coded signal from a first transmit antenna;
transmitting the second coded signal from a second transmit antenna;
providing a second data block to a second space-time encoder that generates third and fourth coded signals, wherein each of the first, second, third and fourth coded signals forms a respective OFDM block;
transmitting the third coded signal from a third transmit antenna;
transmitting the fourth coded signal from a fourth transmit antenna; and
2. on a receiving computing device:
simultaneously receiving the first, second, third and fourth coded signals on a plurality of receive antennas;
pre-whitening the received signals for the first data block signal;
performing maximum likelihood decoding on the pre-whitened first data block signal;
pre-whitening the received signals for the second data block signal;
performing maximum likelihood decoding on the pre-whitened second data block signal; and
regenerating the received signal with the first data block removed from the received signal, and re-decoding the second data block signal when the decoded first data block has a higher signal quality than the decoded second data block.

8. The method according to claim 7, wherein the signal quality is based upon MMSE.

9. The method according to claim 7, further comprising regenerating the received signal, removing the first data block signal from the received signal, and re-decoding the second data block signal when the decoded first data block does not have decoding errors and the second data block signal does have a decoding error.

10. The method according to claim 7, further comprising using Viterbi decoding.

11. The method according to claim 7, further comprising encoding the first and second data block signals with independent space-time codes.

12. The method according to claim 7, further comprising MMSE restoration of the first and second data block signals.

13. The method according to claim 7, wherein the plurality of receive antennas comprises at least four receive antennas.

14. The method according to claim 7, further comprising weighting channel response estimates based upon channel delay profile information.

15. The method according to claim 7, further comprising performing a weighted DFT of estimated channel responses.

16. The method according to claim 7, further comprising performing channel estimation by computing a weighting factor corresponding to an inverse of a sum of one plus a ratio of noise power to a power of channel response estimates averaged over the receive antennas.

17. A method for MIMO-OFDM communication, comprising:
1. on a single transmitting computing device:
encoding a first data block into a first plurality of encoded signals;
encoding a second data block into a second plurality of encoded signals;
transmitting each of the first and second pluralities of encoded signals on respective transmit antennas; and
2. on a receiving computing device:
simultaneously receiving the transmitted signals on a plurality of receive antennas;
decoding the first and second data block signals; and
estimating channel parameters by weighting channel response estimates based upon a deviation from average.

18. The method of claim 1, wherein the step of successive interference cancellation further comprises:
treating the second data block as interference when detecting and decoding the first data block; and
treating the first data block as interference when detecting and decoding the second data block.

19. The method of claim 18, further comprising determining whether the first data block and the second data block contain errors or were correct, wherein the removed data block from the received signals is the data block determined to be correct.

20. The method of claim 19, further comprising, before removing the correct data block from the received signals, regenerating the encoded signals for the correct data block at the receiver.

21. The method of claim 1, further comprising determining a signal quality for each of the first data block and the second data block, wherein the removed data block from the received signals is the data block with a higher signal quality relative to the other data block.

22. The method of claim 21, wherein the removed data block with a higher signal quality is removed from the received signal because the signal quality for the removed data block is above a predetermined threshold.

23. The method of claim 21, wherein the signal quality is associated with a minimum mean-square error.

24. An apparatus for decoding data in a MIMO-OFDM communication, the data being transmitted from a single computing device, the apparatus comprising:
a module that receives a first plurality of encoded signals;
a module that receives a second plurality of encoded signals, the first plurality of encoded signals and the second plurality of encoded signaled being received simultaneously;
a module that pre-whitens the received signals for (1) a first data block associated with the first plurality of encoded signals and (2) a second data block associated with the second plurality of encoded signals;
a module that performs maximum likelihood detection on each of the pre-whitened signals;
a module that, after decoding the first data block and the second data block of the received signals, modifies the received signals by re-encoding the first or second data block and removing the re-encoded first or second data block from the received signals and re-decodes the modified received signals.

25. The apparatus of claim 24, wherein the module that modifies and re-decodes the modified received signals further treats the second data block as interference when re-decoding the first data block and treats the first data block as interference when re-decoding the second data block.

26. The apparatus of claim 24, wherein the first or the second data block that is not removed is determined to have errors.

27. The method of claim 1, wherein the first or the second data block that is not removed is determined to have errors.

28. A computing device for decoding data in a MIMO-OFDM communication, the data being transmitted from a single transmitting computing device, the computing device comprising:
a module that receives a first plurality of encoded signals from a first transmit antenna on the single transmitting computing device;
a module that receives a second plurality of encoded signals from a second transmit antenna on the single transmitting computing device;
a module that, after decoding the first data block and the second data block of the received signals, re-encodes the first or second data block, removes the re-encoded first or second data block from the received signals and re-decodes the received signals.

29. The computing device of claim 28, further comprising:
a module that pre-whitens the received signals for (1) a first data block associated with the first plurality of encoded signals and (2) a second data block associated with the second plurality of encoded signals.

30. The computing device of claim 29, further comprising a module that performs maximum likelihood detection on each of the pre-whitened signals.

31. The computing device of claim 28, wherein the process of re-encoding the first or second data block, removing the re-encoded first or second data block from the received signals and re-decoding the received signals further comprises performing successive interference cancellation on the received signals.

32. The computing device of claim 28, wherein the first or second data block that is not removed from the received signal is determined not to have errors.

33. A method for decoding data in a MIMO-OFDM communication, the data being transmitted from a single transmitting computing device, the method comprising:
receiving a first plurality of encoded signals from a first transmit antenna on the single transmitting computing device;
receiving a second plurality of encoded signals from a second transmit antenna on the single transmitting computing device, the first plurality of encoded signals and the second plurality of encoded signaled being received simultaneously;
after decoding the first data block and the second data block of the received signals, re-encoding the first or second data block, removing the re-encoded first or second data block from the received signals to generate modified received signals; and
re-decoding the modified received signals.

34. The method of claim 33, wherein modifying and re-decoding the modified received signals further comprises treating the second data block as interference when re-decoding the first data block and treats the first data block as interference when re-decoding the second data block.

35. The method of claim 33, further comprising:
pre-whitening the received signals for (1) a first data block associated with the first plurality of encoded signals and (2) a second data block associated with the second plurality of encoded signals.

36. The method of claim 35, further comprising performing maximum likelihood detection on each of the pre-whitened signals.

37. The method of claim 33, wherein re-encoding the first or second data block, removing the re-encoded first or second data block from the received signals and re-decoding the received signals further comprises performing successive interference cancellation on the received signals.

38. The method of claim 33, further comprising determining that the first or second data block that is not removed from the received signal is determined not to have errors.

39. A computer-readable medium storing instructions for controlling a computing device to decode data in a MIMO-OFDM communication, the data being transmitted from a single transmitting computing device, the instructions comprising:
receiving a first plurality of encoded signals from a first transmit antenna on the single transmitting computing device;
receiving a second plurality of encoded signals from a second transmit antenna on the single transmitting computing device, the first plurality of encoded signals and the second plurality of encoded signaled being received simultaneously;
after decoding the first data block and the second data block of the received signals, re-encoding the first or second data block, removing the re-encoded first or second data block from the received signals to generate modified received signals; and
re-decoding the modified received signals.

40. The computer-readable medium of claim 39, wherein modifying and re-decoding the modified received signals further comprises treating the second data block as interference when re-decoding the first data block and treats the first data block as interference when re-decoding the second data block.

41. The computer-readable medium of claim 39, wherein the instructions further comprise:
pre-whitening the received signals for (1) a first data block associated with the first plurality of encoded signals and (2) a second data block associated with the second plurality of encoded signals.

42. The computer-readable medium of claim 41, wherein the instructions further comprise performing maximum likelihood detection on each of the pre-whitened signals.

43. The computer-readable medium of claim 39, wherein re-encoding the first or second data block, removing the re-encoded first or second data block from the received signals and re-decoding the received signals further comprises performing successive interference cancellation on the received signals.

44. The computer-readable medium of claim 33, wherein the instructions farther comprise determining that the first or second data block that is not removed from the received signal is determined not to have errors.