Patent Publication Number: US-2006002414-A1

Title: Statistical data rate allocation for MIMO systems

Description:
FIELD OF THE INVENTION  
      This invention relates generally to multiple-input, multiple-output communication systems, and more particularly to allocating data rates to layers in MIMO systems.  
     BACKGROUND OF THE INVENTION  
      A general architecture for multiple-input, multiple-output (MIMO) communications systems is well known, E. Telatar, “Capacity of multi-antenna Gaussian channels,”  European Tansactions on Telecommunications , vol. 10, pp. 585-595, November-December 1999, and G. J. Foschini and M. J. Gans, “On the limits of wireless communications in a fading environment when using multiple antennas,”  Wireless Personal Commun ., vol. 6, pp. 315-335, March 1998. However, it is still a problem to develop practical systems based on the MIMO architecture that approach a theoretical channel capacity.  
      MIMO systems can use closed-loop or open-loop architectures. In a closed-loop system, the transmitter uses feedback information from the receiver to determine data rates based on instantaneous channel conditions. This improves the system&#39;s capacity but increases the complexity, overhead and cost of the system. In an open-loop system, the transmitter does not require instantaneous feedback from the receiver to determine data rates. Therefore, it is preferred to use an open-loop architecture.  
      In space-time coded systems, one method uses bit interleaved coded modulation (BICM), B. M. Hochwald and S. ten Brink, “Achieving near-capacity on a multiple-antenna channel,”  IEEE Trans. Wireless Commun ., vol. 51, pp. 389-399, March 2003. BICM uses list sphere decoding and iterative channel decoding to approach the capacity of MIMO channels for low and medium data rate transmission with a moderate number of transmit antennas. However, for a large number of transmit antennas and high order modulation, the limited size of the list used in the sphere decoding severely degrades performance.  
      Another method for MIMO systems uses vertical Bell Laboratory layered space-time structure (V-BLAST), G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas,”  Bell Labs Technical Journal , pp. 41-59, August 1996, P. W. Wolniansky, G. J. Foschini, G. D. Golden, and R. A. Valenzuela, “V-BLAST: An architecture for realizing very high data rate over the rich-scattering wireless channel,”  Proc. URSI Int. Symp. Signals, Systems, and Electronics , pp. 295-300, October 1998, and H. E. Gamal and J. A. R. Hammons, “A new approach to layered space-time coding and signal processing,”  IEEE Trans. Inform. Theory , vol. 47, pp. 2321-2334, September 2001.  
      In V-BLAST, the input data stream is demultiplexed to multiple substreams or ‘layers’. Each layer is encoded independently using one-dimensional encoding, and each encoded layer is sent concurrently via a different antenna to receiver antennas.  
      To detect each layer in the receiver, a linear processing according to zero-forcing (ZF) or minimum mean square-error (MMSE) criteria can be used to null undetected layers in the received signal. The contribution of detected layers is subtracted by decision-directed successive interference cancellation (SIC).  
      In a V-BLAST system, the input data stream is typically divided evenly into the layers, and all layers have an identical data rate. As a result, the layers, which are detected first, are more prone to error due to a loss of signal energy by the nulling. Therefore, the prior art V-BLAST system does not approach the theoretical channel capacity, even with an optimal ordering of the detection.  
      Therefore, there is a need for an open-loop MIMO system that approaches the theoretical channel capacity for high data rates or for a large number of antennas.  
     SUMMARY OF THE INVENTION  
      The invention provides a MIMO system that uses a layered structure with unequal rate allocation. Instead of allocating the data rates among the layers equally, or according to instantaneous data rate feedback in a closed loop system, the invention uses statistical information of the channel based on past observations to determine the data rate allocated to each layer.  
      It is an objective of the invention to allocate data rate according to quality of channels for the layers. Layers to be detected first have a lower data rates because those layers have a lower quality channel due to the nulling of undetected layers. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  is a block diagram of a transmitter for a layered MIMO system according to the invention;  
       FIG. 2  is a block diagram of a receiver for the layered MIMO system according to the invention; and  
       FIG. 3  is a flow diagram of a method for allocating data rates among layers according to the invention; 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
      Transmitter Structure  
       FIG. 1  shows a transmitter  100  for a layered MIMO system according to the invention. An input data stream  101  is demultiplexed  110  to N t  substreams or ‘layers’  111 . Each layer is encoded  120  independently. The encoded layers are interleaved (Π)  130  and modulated  140  and sent concurrently to different transmit antennas  141  to be transmitted as transmit signals  102  through a channel. In the example shown, N t =2, although it should be understood that any practical number of transmit and receive antennas can be used with the invention.  
      The demultiplexing  110  and encoding  120 , according to the invention, use a statistical rate allocation  150  as described herein. The statistics are based on past observations of the layer capacities, as opposed to instantaneous feedback.  
      Receiver Structure  
       FIG. 2  shows a receiver  200  in the layered MIMO system according to the invention. Signals  201  are received by N r  receive antennas  210 . Linear processing  220  is applied to null undetected layers. The processed signals are decoded  230 , and de-interleaved (Π −1 )  240  before sent to the multiplexer  250  where the decoded layers are combined into a reconstructed output signal  202  corresponding to the input signal  101 . Successive interference-cancellation  260 , in the receiver, is according to decision feedback information  261 .  
      System Model  
      In a flat-fading MIMO system with N t  transmit antennas and N r  receive antennas, a relationship between transmitted signals  102  and received signals  201  can be expressed as 
 
 r=Hs+n,  
 
 where r is a N r ×1 vector representing the received signals  201 , s is a N t ×1 vector representing the transmitted signals  102 , and H is a N r ×N t  channel matrix representing an impulse response of the channel. A N r ×1 noise vector n has entries that are independent and identically distributed (i.i.d.) zero-mean circular complex Gaussian random variables with a variance N 0 . 
 
      An open-loop channel capacity is given by  
           C   ⁡     (     H   ,   SNR     )       =       log   2     ⁢           ⁢     det   ⁡     (       I     N   r       +       SNR     N   t       ⁢     HH   H         )           ,       
 
 where I N     r    is a N r ×N r  identity matrix, and SNR is the signal-to-noise ratio. 
 
      Without loss of generality, we assume that each layer l  111  is sent via transmit antenna l  141 , and the order of detection is from 1 to N t . Then, at the receiver  200 , layer i is decoded  230 , based on z i  determined as follows,  
           z   i     =       w   i   H     (     r   -       ∑     l   =   1       i   -   1       ⁢       h   l     ⁢       s   ^     l           )       ,       
 
 where the N r ×1 unit-norm weight vector w i    221  nulls  220  signals from all other undecoded layers. The weight vector  221  is determined according to zero-forcing or MMSE criterion. The reconstructed signals  261  from decoded layers are ŝ l . The value h l  is the l th  column of the channel matrix H. 
 
      After the linear processing  220  and the interference cancellation  260 , layer i is decoded  230  using a one-dimensional code.  
      Data Rate Allocation for Layered Systems  
      In the MIMO system, the optimal data rate to be allocated to layer l should be  
                 C   l     =         log   2     ⁢           ⁢     det   (       I     N   r       +       SNR     N   t       ⁢     H     (     l   -   1     )       ⁢     H     (     l   -   1     )     H         )       -       log   2     ⁢           ⁢     det   (       I     N   r       +       SNR     N   t       ⁢     H     (   l   )       ⁢     H     (   l   )     H         )           ,           (   1   )             
 
 where H (l) =[h l+1  h l+2  . . . h N     t   ], and h l  is the l th  column of the channel matrix H. 
 
      The capacity of a MIMO channel such as the first and the second term in the equation (1), whether Rayleigh or Ricean, can be approximated accurately by a Gaussian distribution, at medium and high SNRs, P. J. Smith and M. Shafi, “On a Gaussian approximation to the capacity of wireless MIMO systems,”  Proc. ICC  2002, pp. 406-410, April  2002 , M. A. Kamath, B. L. Hughes, and X. Yu, “Gaussian approximations for the capacity of MIMO Rayleigh fading channels,”  IEEE Asilomar Conference on Signals, Systems, and Computers , November 2002.  
      Thus, the capacity of each layer C l  is also Gaussian distributed, and can be denoted by 
 
C l ˜N(η l ,σ l   2 ), 
 
 where η l , and σ l   2  are the mean and variance of the capacity of layer l, respectively. The important point here is that the capacity is expressed statistically, instead of being based on actual capacity derived from instantaneous feedback information. It should also be noted that other statistics, such as a Gamma distribution and higher order statistics, can be used express the capacity of the channel. 
 
      In our MIMO system, instead of dynamically changing the data rate for each layer, we fix layer l to a data rate u l , which is based on the means and variances of all the layer capacities, i.e., first and second order statistics. Minimizing a probability of not achieving a required performance, i.e., the outage probability P out , of a layered system is equivalent to maximizing a probability  
           1   -     P   out       =       ∏     l   =   1     M     ⁢       ∫     u   l     ∞     ⁢       1         2   ⁢   π       ⁢     σ   l         ⁢     ⅇ     -         (     t   -     η   l       )     2       2   ⁢     σ   l   2             ⁢     ⅆ   t             ,       
 
 when no layer has a data rate greater than the respective capacity of the layer, and subject to the constraint that a total data rate C T  of the channel is fixed, i.e.,  
           ∑     l   =   1     M     ⁢     u   l       =       C   T     .         
 
      Let the data rate of a layer be a difference x l =u l −ρ l . By setting up an equivalent Lagrangean objective function, we find a stationary point, that is, a point where a derivative of the function vanishes, from the objective function  
       J   =       log   ⁡     (       ∏     l   =   1     M     ⁢       ∫     x   l     ∞     ⁢       1         2   ⁢   π       ⁢     σ   l         ⁢     ⅇ     -       t   2       2   ⁢     σ   l   2             ⁢     ⅆ   t           )       -       λ   ⁡     (         ∑     l   =   1     M     ⁢     x   l       +       ∑     l   =   1     M     ⁢     η   l       -     C   T       )       .           
 
      We can verify that the stationary point satisfies  
           -       ⅇ       x   l   2       2   ⁢     σ   l   2               ∫     x   l     ∞     ⁢       1         2   ⁢   π       ⁢     σ   l         ⁢     ⅇ     -       t   2       2   ⁢     σ   l   2             ⁢     ⅆ   t             =   λ     ,           ⁢     l   =   1     ,   2   ,   …   ⁢           ,     M   .     
     ⁢   because         
             ∫     x   l     ∞     ⁢       1         2   ⁢   π       ⁢     σ   l         ⁢     ⅇ     -       t   2       2   ⁢     σ   l   2             ⁢     ⅆ   t         ≈   1     ,           ⁢         x   l     /     σ   l       ⪡   0.         
 
      Therefore, the difference between the optimum data rate and the mean of the capacity of a layer is  
           x   l   *     ≈         σ   l         ∑     m   =   1     M     ⁢     σ   m         ⁢     (       C   T     -       ∑     m   =   1     M     ⁢     η   m         )         ,       
 
 and an optimum data rate u* for the layer l is  
               u   l   *     ≈       η   l     +         σ   l         ∑     m   =   1     M     ⁢     σ   m         ⁢       (       C   T     -       ∑     m   =   1     M     ⁢     η   m         )     .                 (   2   )             
 
      Therefore, the outage probability for each layer is  
           P   l   *     =         ∫     -   ∞       x   l   *       ⁢       1         2   ⁢   π       ⁢     σ   l         ⁢     ⅇ     -       t   2       2   ⁢     σ   l   2             ⁢     ⅆ   t         =       ∫     -   ∞         (       C   T     -       ∑     m   =   1     M     ⁢     η   m         )         ∑     m   =   1     M     ⁢     σ   m           ⁢       1       2   ⁢   π         ⁢     ⅇ     -       t   2     2         ⁢     ⅆ   t             ,       
 
 which is the same for all layers. Thus, a minimum total outage probability is achieved when the outage probability of each layer is identical. 
 
      We define a normalized capacity margin as  
             φ   ⁢     =   Δ     ⁢         (         ∑     m   =   1     M     ⁢     η   m       -     C   T       )         ∑     m   =   1     M     ⁢     σ   m         .             (   3   )             
 
      Then, an optimum total outage probability is  
           P   out   *     =       1   -       ∏     l   =   1     M     ⁢     (     1   -     P   l   *       )         =     1   -       (       ∫   φ   o     ⁢       1       2   ⁢   π         ⁢     ⅇ     -       t   2     2         ⁢     ⅆ   t         )     M           ,       
 
 which states an interesting fact. The minimum total outage probability of a layered system is uniquely determined by the normalized capacity margin. 
 
      That is, if we properly select the data rate for each layer, the sum of capacities of all layers, with perfect SIC, is exactly the same as that obtained by instantaneous feedback. To achieve that capacity, instantaneous data rate feedback is needed. However, if the channel is ergodic enough, such as those with enough frequency selectivity or time variation, we can approach that capacity by statistically determining the data rate for each layer, with a small penalty. Our approach is to minimize the overall outage probability given the total data rate. Because of the results above, we use a statistical approach for allocating bits to different layers.  
      We use an asymptotic expansion according to M. A. Kamath, B. L. Hughes, and X. Yu, “Gaussian approximations for the capacity of MIMO Rayleigh fading channels,”  IEEE Asilomar Conference on Signals, Systems, and Computers , November 2002, which is  
             ∫   φ   o     ⁢       1       2   ⁢   π         ⁢     ⅇ     -       t   2     2         ⁢     ⅆ   t         ≈         2   ⁢   π       -         ⅇ       x   2     2       x     ⁢     (     1   -     1     x   2       +         1   ·   3         (     x   2     )     2       ⁢           ⁢   …       )           ,           ⁢     x   ⁢     &lt;&lt;     ⁢   0     ,     
     ⁢       then   ⁢           ⁢     P   out   *       ≈       M       2   ⁢   πφ         ⁢       ⅇ       -     φ   2       /   2       .             
 
      Similarly, we derive an asymptotic outage probability of the MIMO channel with the total overall data rate C T  as  
           P   ch     ≈       1       2   ⁢     πφ   ch           ⁢     ⅇ       -     ϕ   ch   2       /   2           ,       where   ⁢           ⁢     φ   ch       =         η   ch     -     C   T         σ   ch         ,       
 
 where η ch  is an ergodic MIMO channel capacity, i.e., every sequence or sizable sample is equally representative of the whole as in regard to a statistical parameter, and σ ch   2  is the variance of the MIMO channel capacity. Note that  
           η   ch     =       ∑     l   =   1     M     ⁢     η   l         ,       and   ⁢           ⁢     σ   ch       ≤       ∑     l   =   1     M     ⁢     σ   l         ,   because       
           E   ⁢     {       (       ∑   l     ⁢     v   l       )     2     }       ≤       (       ∑   l     ⁢       E   ⁢     {     v   l   2     }           )     2       ,       
 
 for any set of random variables {v l ′s}. 
 
      Thus,  
           φ   ch     ≤   φ     ,   and       
           P   out     ≥     P   out   *     ≈       M       2   ⁢   πφ         ⁢     ⅇ       -     φ   2       /   2         ≥     M   ⁢     1       2   ⁢     πφ   ch           ⁢     ⅇ       -     φ   ch   2       /   2         ≈     MP   ch       ,       
 
 which implies that with the identical data rates, the asymptotic outage probability of the layered structure is at least M times that of the MIMO channel. 
 
      Because of the above results, we provide a statistical method for determining the data rate allocation, subject to the following constraints.  
      In practical communication systems, there are only a limited number of combinations of modulation and coding rate. Therefore, a set of N available data rates c 1 &lt;c 2 &lt; . . . &lt;c N    302  is discrete, see  FIG. 3 . Here, the data rates are arranged in a low to high order, where c 1  is a minimum available data rate and c N  is a maximum available data rate of the set.  
      Any Gaussian distribution has a negative tail, therefore, our analysis above applies primarily to systems with a high SNR, where an optimum data rate u l * of each layer is guaranteed to be positive.  
      Statistical Data Rate Allocation Method  
       FIG. 3  shows our method  300  for allocating data rates among multiple layer in a MIMO communications system.  
      First, we determine  310  statistics  311 , e.g., a mean TI, and a variance σ l   2  of a capacity of each layer based on past observations  301  of capacities of layers as the layers were transmitted through a channel, as given by Equation (1). The means and variances can be determined entirely in the transmitter, based on signals sent from the receiver as acknowledgement to transmitted messages. It should be noted that other statistics can be used.  
      It should be made clear, that the statistics do not need to be based on instantaneous actual channel condition, but rather the statistics can be based only on historical data.  
      In the beginning of transmission, where no historical data are available, empirically derived statistics can be used to set the initial data rates for the layers. The empirical data can be obtained from experiments or simulation using standard channel models.  
      For a total data rate C T , determine  320 , for each layer, an optimum data rate u l *  321  according to Equation (2), based on the layer capacity statistics  311  of each layer.  
      Determine  330  if the optimum data rate u l * is less than a minimum data rate of a set of available data rates  302 .  
      If false  331 , then select  340  a closest data rate c l * of the available data rates  302  that is less than the optimum data rate u l *.  
      Otherwise, if true  332 , then select  350  the data rate c; to be a minimum of the set of available data rates.  
      Note in the system described, we may use different modulations for different layers depending on the chosen data rates.  
      Variations  
      The approach proposed above can also be applied to the cases where the association of transmit antennas with layers varies, or is frequency-selective such as in OFDM systems. We only have to sum up all the data rates as given by Equation (1) for each layer and determine the corresponding mean and variance of the channel capacity for each layer.  
      Although the invention has been described by way of examples of preferred embodiments, it is to be understood that various other adaptations and modifications may be made within the spirit and scope of the invention. Therefore, it is the object of the appended claims to cover all such variations and modifications as come within the true spirit and scope of the invention.