Patent Publication Number: US-8976886-B2

Title: Method and apparatus for jointly performing channel estimation and interference estimation in a wireless communication system

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This claims priority to U.S. Provisional Patent Application 61/620,911, filed on Apr. 5, 2012, which is incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The technology described in this document relates generally to wireless communications and more particularly to systems and methods for estimating characteristics of a wireless communication channel. 
     BACKGROUND 
     In the field of wireless communications, MIMO-OFDM (Multiple-Input and Multiple-Output, Orthogonal Frequency-Division Multiplexing) technology has been used to achieve increased data throughput and link range without requiring additional bandwidth or increased transmission power. MIMO-OFDM technology utilizes multiple transmission antennas at a transmitter and multiple receive antennas at a receiver to enable a multipath rich environment with multiple orthogonal channels existing between the transmitter and the receiver. Data signals can be transmitted in parallel over these channels, thus enabling the increased data throughput and link range. Because of its advantageous properties, MIMO-OFDM is the air-interface technology used in numerous wireless communication standards, such as IEEE 802.11n (WiFi), 4G, 3GPP Long Term Evolution (LTE), WiMAX, and HSPA+. For efficient operation, in terms of capacity, block error rate, and other metrics, estimation of the communication channel between the receiver and transmitter may be performed at the receiver. 
     SUMMARY 
     The present disclosure is directed to systems and methods for estimating characteristics of a channel. In a method for estimating characteristics of a channel, a transmission of known reference data is received at a receiving device. The reference data is transmitted over the channel that includes one or more desired layers and one or more interfering layers. Characteristics of the channel are determined based on the known reference data, where the determining includes a joint estimation of the one or more desired layers and the one or more interfering layers. The determining includes selecting certain of the layers to be estimated at each of the known reference data. The determining also includes selecting certain of the layers to be estimated over a range of the known reference data. The determining further includes solving an equation to jointly estimate the one or more desired layers and the one or more interfering layers based on the selections. The selections reduce a number of unknown values in the equation. 
     In another example, a receiver for estimating characteristics of a communication channel includes a processing system and a memory coupled to the processing system. The processing system is configured to execute steps including receiving a transmission of known reference data, where the reference data is transmitted over the channel that includes one or more desired layers and one or more interfering layers. The steps also include determining characteristics of the channel based on the known reference data, where the determining includes a joint estimation of the one or more desired layers and the one or more interfering layers. The determining includes selecting certain of the layers to be estimated at each of the known reference data and selecting certain of the layers to be estimated over a range of the known reference data. The determining further includes solving an equation to jointly estimate the one or more desired layers and the one or more interfering layers based on the selections. The selections reduce a number of unknown values in the equation. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1A  is a block diagram of an example Multiple-Input and Multiple-Output (MIMO) communication system including a channel with one or more desired layers and one or more interfering layers. 
         FIG. 1B  depicts an example of known reference data used by a receiver to estimate a communication channel. 
         FIG. 1C  depicts an equation used to jointly estimate one or more desired layers and one or more interfering layers of a communication channel. 
         FIG. 1D  depicts example steps performed by a receiver to perform joint estimation of one or more desired layers and one or more interfering layers of a communication channel. 
         FIG. 2  depicts example systems in which a joint estimation of one or more desired layers and one or more interfering layers may be performed. 
         FIG. 3  depicts a matrix including known reference data for various time-frequency positions and an equation that may be solved to jointly estimate one or more desired layers and one or more interfering layers based on the known reference data. 
         FIG. 4  illustrates proposed solutions for estimating characteristics of a communication channel that include selection of certain aspects of the channel to be frequency-flat and selection of certain aspects of the channel to be frequency-selective in the estimation. 
         FIG. 5  is a flowchart illustrating an example method for estimating characteristics of a communication channel. 
     
    
    
     DETAILED DESCRIPTION 
       FIG. 1A  is a block diagram of an example Multiple-Input and Multiple-Output (MIMO) communication system  100  including a channel  112  with one or more desired layers and one or more interfering layers. In the example communication system  100  of  FIG. 1A , an input data stream  106  is received by a transmitter  108  and subsequently transmitted over a plurality of transmission antennas  110 . The transmission antennas  110  transmit the input data stream  106  over the channel  112 , which includes the one or more desired layers and the one or more interfering layers. The data transmission over the plurality of transmission antennas  110  is received at a plurality of receive antennas  114  of a receiver  102 . The channel  112  affects the data transmitted between the transmitter  108  and the receiver  102 , such that a modified version of the transmitted signal is received at the receive antennas  114 . The received signal may be modified from the transmitted signal due to properties of the channel  112 , interference at the receive antennas  114 , or by noise of the channel  112 , among other reasons. The system  100  can be described generally via the following equation:
 
 y=Hx+n,  
 
where H is a channel matrix that defines characteristics of the channel  112 , x is a data matrix that defines the signal transmitted by the transmitter  108 , y is a data matrix that defines the signal received by the receiver  102 , and n is a noise matrix that affects the transmitted signal. Pre-coding or beamforming may be used at the transmitter  108  when multiple transmitter antennas  110  are employed. In the equation above, the channel matrix H defines characteristics of the one or more desired layers, as well as characteristics of the one or more interfering layers. Note that the transmitter  106  transmits both the desired layers and the interfering layers in  FIG. 1A . This is only used for an example. Alternatively, multiple transmitters may transmit simultaneously, from some of which the desired layers are transmitted, and from others of which the interfering layers are transmitted. In such a case, the transmitter  106  can be assumed as a superset of transmitters, and the following discussions still apply.
 
     For efficient operation (i.e., in terms of capacity, block error rate, etc.) of the system  100 , an estimation of the channel  112  is performed at the receiver  102 . To perform channel estimation, a transmission of known reference data (i.e., pilot symbols or cell-specific reference signals) is received at the receiver  102 . The known reference data is transmitted over the channel  112  including the one or more desired layers and the one or more interfering layers at predetermined time and frequency positions. The receiver  102  uses the known reference data to estimate characteristics of the channel  112  in all time and frequency positions. In the system  100  of  FIG. 1A , the receiver  102  performs a joint estimation of the one or more desired layers and the one or more interfering layers of the channel  112 . An estimation of the noise and/or residual interference of the system  100  may also be included in the joint estimation process. The joint estimation is performed instead of an independent estimation of the one or more desired layers and the one or more interfering layers. For example, an independent estimation may involve estimation of a desired layer that is separate and independent of a desired layer, and/or an interference and noise estimation. 
     An example of the known reference data used by the receiver  102  to estimate the channel  112  is depicted at  120  of  FIG. 1B . An x-axis of data matrix S(f, t) varies with time, and a y-axis of the data matrix S(f, t) varies with frequency. The darkened cells of the matrix represent known pilot symbols transmitted at predetermined time and frequency positions, which are known in advance by the receiver  102 . In the matrix, the known reference data may be considered to be overhead. Thus, to achieve higher throughput, it may be desirable to use a smaller number of reference symbols, as a higher number of reference symbols may degrade spectral efficiency of the system  100 . However, if the known reference signal is too sparse, the receiver  102  may have difficulty in accurately estimating the channel  112 . 
     As noted above, the estimation of the channel  112  is a joint estimation, where the one or more desired layers and the one or more interfering layers of the channel  112  are estimated together, rather than via separate, independent estimations. At  100  in  FIG. 1A , the channel  112  is illustrated as including layers (i.e., channels, streams) h 1 , h 2 , h 3 , and h 4 , and certain of these layers are desired layers and certain of these layers are interfering layers. At  140  in  FIG. 1C , an equation to jointly estimate the one or more desired layers and the one or more interfering layers is as follows: 
                 y   ⁡     (   f   )       =         S   ⁡     (   f   )       ⁡     [             h   1     ⁡     (   f   )                   h   2     ⁡     (   f   )                   h   3     ⁡     (   f   )                   h   4     ⁡     (   f   )             ]       +     n   ⁡     (   f   )           ,         
where y(f) is a matrix including observations made at the receiver  102 , S(f) is a matrix including the known reference data transmitted by the transmitter  108 ,
 
               [             h   1     ⁡     (   f   )                   h   2     ⁡     (   f   )                   h   3     ⁡     (   f   )                   h   4     ⁡     (   f   )             ]               
is a matrix including variables representing the one or more desired layers and the one or more interfering layers to be estimated, and n(f) is a matrix representing a noise component of the received signal y(f). All variables of the equation are dependent only upon frequency, such that the estimation process includes making an assumption that the one or more desired layers and the one or more interfering layers are constant in time as an example. The equation above is solved as part of the estimation process.
 
     At  160  of  FIG. 1D , example steps  162 ,  164 ,  166 ,  168  are performed by the receiver  102  to perform the joint estimation of the one or more desired layers and the one or more interfering layers. At  162 , the receiver  102  receives the matrix S(f, t) including the known reference data (i.e., the known pilot symbols depicted at  120  of  FIG. 1B ). The matrix S(f, t) including the known reference data is transmitted over the channel  112  and is thus affected by the characteristics of the channel  112 . At  164 , certain of the layers h 1 , h 2 , h 3 , and h 4  of the channel  112  are selected to be frequency-flat in the estimation. At  166 , certain of the layers h 1 , h 2 , h 3 , and h 4  are selected to be frequency-selective in the estimation. The receiver  102  thus performs a partitioning process, such that not all layers are selected as being frequency-flat and not all layers are selected to be frequency-selective in the estimation. The partitioning process may also leave certain layer(s) out of channel estimation process by not selecting such layer(s) in both  164  and  166 . At  168 , the equation at  140  of  FIG. 1C  is solved to jointly estimate the one or more desired layers and the one or more interfering layers. The equation at  140  is solved based on the matrix S(f, t) including the known reference data and based on the selections. A number of unknown values in the equation at  140  is reduced by the selection of certain of the layers as being frequency-flat. 
     Alternatively, the channel estimation may assume the channels for all layers are constant over frequency, and select the layers to be time-flat in  164  and select layers to be time-selective in  166 . In yet another example, the channel estimation assumes the channel is not constant over time and frequency, and  164  and  166  can be extended to sub-steps to select layers to be one of (1) time-frequency-flat, (2) time-flat, frequency-selective, (3) time-selective, frequency-flat, (4) time-frequency-selective. Certain layers can still be left out of channel estimation by the partitioning process. Hereafter, the time-constant assumption is used for illustration purposes where it applies. 
     The selection of certain of the layers to be frequency-flat in the estimation and the selection of certain of the layers to be frequency-selective in the estimation may be made based on a variety of factors. In one example, the selections are made based on an importance of one or more of the layers, a determination of one or more of the interfering layers as being dominant over others of the one or more interfering layers, a degree of mutual correlation among variables to be estimated in reference to the operating regime (e.g., signal to interference ratio, signal to noise ratio), a desired performance and stability in the receiver, or an instrumentation complexity of the receiver. In other examples, the selections are based on one or more design tradeoffs. For example, the selections may be based on a balance between performance (e.g., signal to noise ratio, throughput, etc.) versus computational complexity, where selection of a greater number of layers to be frequency-selective may result in higher performance but may also require a higher computational complexity. The higher computational complexity may, for example, affect a battery life or power consumption of the receiver. 
     In one example, the one or more desired layers are selected to be frequency-selective, and the one or more interfering layers are selected to be frequency-flat. In another example, a dominant interfering layer of the one or more interfering layers is selected to be frequency-selective, and others of the one or more interfering layers are selected to be frequency-flat. In one example, statistics of the frequency-flat layers may be used instead of instantaneous values associated with these layers. 
     The system  100  of  FIG. 1A  was described above as being characterized by the equation y=Hx+n. This equation may be rewritten as follows to further describe the system  100 : 
               y   ⁡     (     f   ,   t     )       =         ∑     i   =   1     K     ⁢           ⁢         h   i     ⁡     (     f   ,   t     )       ⁢       x   i     ⁡     (     f   ,   t     )           +     n   ⁡     (     f   ,   t     )               
where y is a data matrix that defines the signal received by the receiver, h i  is a matrix representing the channel, which includes one or more desired layers and one or more interfering layers, x i  is a matrix including the known reference data (i.e., pilot symbols) transmitted over the channel, and n is a matrix representing noise in the received signal. In this equation, y, h i , x i , and n are functions of both frequency (f) and time (t). Further, the following equality may be used:
 
| S |=size( S )= N,  
 
where N is a number of observations that are made at the receiver. The receiver is configured to estimate characteristics of the channel h i  for all values of i (i.e., the one or more desired layers and the one or more interfering layers of the channel, and for the case that certain layers are left out of channel estimation, partitioning is assumed to be done before where this model applies), f, and t (i.e., all relevant time and frequency positions), given the N noisy observations that define the matrix y. In matrix form, the input-output relationship defined by the system may be written as follows:
 
     
       
         
           
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       FIG. 2  depicts example systems in which a joint estimation of one or more desired layers and one or more interfering layers may be performed. At  200 , a MIMO-OFDM system is depicted, where a receiver makes three noisy observations of the channel between a transmitter and a receiver. MIMO-OFDM systems may create parallel layers (i.e., channels, streams) in time and frequency, as illustrated by the three parallel layers h(f 1 , t 1 ), h(f 2 , t 1 ), and h(f 2 , t 2 ). The three different observations made at the receiver may be represented by the following equations, where y represents a signal received at the receiver, h is the channel, and n is a noise component of the received signal:
 
 y ( f   1   ,t   1 )= h ( f   1   ,t   1 )+ n   1  
 
 y ( f   2   t   1 )= h ( f   2   ,t   1 )+ n   2  
 
 y ( f   2   ,t   2 )= h ( f   2   ,t   2 )+ n   3  
 
In the equations above, both y and h are dependent on frequency (f) and time (t). The variables n 1 , n 2 , and n 3  illustrate that the receiver observes three different noise values in making the observations. Performing the joint estimation of the variables in the equations above may be preferable to performing an independent estimation of the variables. For example, if each of the variables is independently estimated, the effect of receiver noise may not be reduced, and thus, an estimation error N 0  may result. Further, the actual channel variables are likely not independent, due to limited degrees of freedom in the physical channel. Performing a joint estimation of the variables of the system  200  may provide an estimate of the channel that accounts for such dependencies between variables.
 
     At  220 , another MIMO-OFDM system is depicted, where a receiver makes two observations, with each of the observations including a term representing one or more desired layers and a term representing one or more interfering layers. The two observations made at the receiver may be represented by the following equations, where y represents a signal received at the receiver, h represents a desired layer, q represents an interfering layer, and n is a noise component of the received signal:
 
 y ( f   1   ,t   1 )= h ( f   1   ,t   1 )+ q ( f   1   ,t   1 )+ n   1  
 
 y ( f   2   ,t   1 )= h ( f   2   ,t   1 )+ q ( f   2   ,t   1 )+ n   2  
 
In the equations above, y, h, and q are dependent on frequency (f) and time (t). In performing a joint estimation of the desired and interfering layers, a more accurate estimation of the one or more desired layers may result by performing a lower-resolution frequency estimation of the one or more interfering layers. The lower-resolution frequency estimation of the one or more interfering layers may involve estimating only statistics of the interfering layers (e.g., rather than instantaneous values of the interfering layers), such that more resources can be devoted to estimating the one or more desired layers. Generally, it may be preferable to use a higher-resolution frequency estimation of the desired layers, as compared to the interfering layers.
 
     At  240 , a multi-user MIMO (MU-MIMO) system is depicted. The MU-MIMO system includes a transmission from a transmitter to multiple receivers (i.e., multiple users) at the same time. The MU-MIMO architecture may improve a capacity of MIMO transmission by creating additional spatial degrees of freedom. The MU-MIMO architecture may have a higher spatial multiplexing gain and system capacity as versus single-user MIMO (SU-MIMO) systems. The transmitter may use precoding vectors u 1 , u 2 , and u 3 , which correspond to the three receivers of the system. As illustrated at  240 , each of the receivers receives data over three layers, where two of the three layers are interfering layers, and one of the layers is a desired layer. The two interfering layers may be caused due to the parallel transmissions from the transmitter to the other receivers of the system. Each of the receivers may estimate the channel by performing a joint estimation of the two interfering layers and the desired layer. 
     At  260 , a coordinated multi-point transmission (CoMP) technique is depicted. The system at  260  includes three base station antennas transmitting data to a single receiver (i.e., a single user device). Interfering layers may be caused by interference from base stations other than the one transmitting a desired signal to the receiver. In CoMP, the channel to be estimated may correspond to multiple cells, and the desired layers and the interfering layers of the channel may be estimated at different frequency slots from received channel state information reference symbols (CSI-RS). However, the number of reference signals for CSI-RS may be limited, such that a number of variables may be larger than a number of equations. To allow for reliable estimation of the channel, the interfering layers may be assigned to have a lower frequency resolution than the desired layers during the estimation. 
       FIG. 3  depicts a matrix  300  including known reference data for various time-frequency positions and an equation  340  that may be solved to jointly estimate one or more desired layers and one or more interfering layers based on the known reference data. The matrix  300  and equation  340  may be used in performing channel estimation in a long-term evolution (LTE) wireless communication system. In LTE Release 10, dynamic switching between Single-User MIMO (SU-MIMO) and Multi-User MIMO (MU-MIMO) is supported. For MU-MIMO transmission, up to four users (i.e., UEs) and up to four layers (i.e., spatial streams) in total are supported (e.g., two desired layers and two interfering layers, three desired layers and one interfering layer, and other combinations). In the LTE system of  FIG. 3 , channel estimation for demodulation may be performed via demodulation reference signal (DMRS) ports  7  and  8 . In the matrix  300  including known reference data used for performing channel estimation, an x-axis represents time, and a y-axis represents frequency. Darkened elements in the matrix  300  represent the known reference data (i.e., pilot symbols), as discussed above with respect to  FIG. 1A . Three frequencies ( 1 ,  2 , and  3 ) are highlighted in the matrix  300  of  FIG. 3 . At each of these three frequencies, a receiver in the LTE system makes four observations at four different times ( 1 ,  2 ,  3 , and  4 ). In total, for the three frequencies, twelve observations are made at the receiver in a resource block (RB). 
     Using the twelve observations made at the receiver, an equation may be solved to jointly estimate the one or more desired layers and the one or more interfering layers: 
               y   ⁡     (   f   )       =         S   ⁡     (   f   )       ⁡     [             h   1     ⁡     (   f   )                   h   2     ⁡     (   f   )                   h   3     ⁡     (   f   )                   h   4     ⁡     (   f   )             ]       +     n   ⁡     (   f   )               
The above equation is depicted at  340  of  FIG. 3 . In the equation, y(f) is a matrix including data related to the observations made at the receiver, S(f) is a matrix including the known reference data transmitted by the transmitter and is a 4×4 DMRS sequence,
 
               [             h   1     ⁡     (   f   )                   h   2     ⁡     (   f   )                   h   3     ⁡     (   f   )                   h   4     ⁡     (   f   )             ]               
is a matrix including data for variables representing the one or more desired layers and the one or more interfering layers to be estimated, and n(f) is a matrix representing a noise component of the received signal y(f). As indicated at  340 , the matrix n(f) may be typically modeled as a complex white Gaussian noise with variance σ 0   2 , i.e., n(f)˜CN(0, σ 0   2 I 4 ), where σ 0   2  captures the effect of intercell interference. In term of channel estimation on DMRS port 7 and 8 in LTE system, equation  340  in  FIG. 3  can be expressed as follows:
 
     
       
         
           
             
               
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     Solving the equation  340  may allow the channel to be estimated for all potential users and at all time-frequency positions. When the transmitter of the known reference data is operating in a MIMO transmission mode, the channel can be assumed to be constant in time within an RB. Conversely, however, rather than assuming the channel to be frequency-flat within an RB, in solving the equation, it may instead be assumed that the channel is frequency-selective within the RB. As a result of these assumptions, there are twelve variables to be estimated in solving the equation  340 : the four layers of the channel in three frequency positions (i.e., h 1 (f), h 2 (f), h 3 (f), and h 4 (f), for f equal to 1, 2, and 3). S(f) should be invertible for all frequency positions (1, 2, and 3) to solve the equation  340 . However, the individual DMRS sequences are randomly generated, and S(f) may not be full rank with considerable probability (e.g., S(f) may be rank 2 or 3). 
     To solve the equation  340 , a frequency selectivity of the layers h 1 , h 2 , h 3 , and h 4  may be captured to the extent possible, and a lower frequency resolution may be used for certain layers as necessary. Thus, to solve the equation  340 , certain of the layers are selected to be frequency-flat in the estimation process, and certain of the layers are selected to be frequency-selective in the estimation. Selecting certain of the layers, typically interfering layers, to be frequency-flat may allow the equation  340  to be solved by reducing a number of unknown values in the equation  340 . Further, the selection of certain of the layers as being frequency-flat may allow more resources to be devoted to estimating the frequency-selective layers, such that the frequency-selective layers may be estimated with higher accuracy. 
       FIG. 4  illustrates proposed solutions  400 ,  440  for estimating characteristics of a communication channel by solving the equation  340  of  FIG. 3 . In the solutions  400 ,  440 , the channel is assumed to include four layers, with one or more desired layers and one or more interfering layers. Further, in both of the solutions  400 ,  440 , the four layers are partitioned based on importance, such that certain of the layers are selected as being frequency-flat and certain of the layers are selected to be frequency-selective in the estimation (e.g., layers that may have a greater effect on performance measures may be selected to be frequency-selective, in order to allow them to have a higher frequency resolution as versus the frequency-flat layers). In the first solution  400  of  FIG. 4 , two of the four layers are selected as being frequency-selective, and the other two layers are selected as being frequency-flat. The two layers selected to be frequency-selective are the two desired layers in the case of rank 2 allocation, and two layers selected to be frequency-selective are the desired layer and a layer corresponding to the orthogonal DMRS sequence in the case of rank 1 allocation. The other two layers that are not selected to be frequency-selective are selected to be frequency-flat, which results in the modeling of the received signal illustrated at  400 : 
               [           y   ⁡     (   1   )                 y   ⁡     (   2   )                 y   ⁡     (   3   )                 y   ⁡     (   4   )                 y   ⁡     (   5   )                 y   ⁡     (   6   )                 y   ⁡     (   7   )                 y   ⁡     (   8   )                 y   ⁡     (   9   )                 y   ⁡     (   10   )                 y   ⁡     (   11   )                 y   ⁡     (   12   )             ]     =         [           a   1           a   1         0       0       0       0         b   1           b   1               a   2           -     a   2           0       0       0       0         b   2           -     b   2                 a   3           a   3         0       0       0       0         b   3           b   3               a   4           -     a   4           0       0       0       0         b   4           -     b   4               0       0         a   5           a   5         0       0         b   5           b   5             0       0         a   6           -     a   6           0       0         b   6           -     b   6               0       0         a   7           a   7         0       0         b   7           b   7             0       0         a   8           -     a   8           0       0         b   8           -     b   8               0       0       0       0         a   9           a   9           b   9           b   9             0       0       0       0         a   10           -     a   10             b   10           -     b   10               0       0       0       0         a   11           a   11           b   11           b   11             0       0       0       0         a   12           -     a   12             b   12           -     b   12             ]     ⁡     [             h   1     ⁡     (   1   )                   h   2     ⁡     (   1   )                   h   1     ⁡     (   2   )                   h   2     ⁡     (   2   )                   h   1     ⁡     (   3   )                   h   2     ⁡     (   3   )                 h   3               h   4           ]       +   n           
In the equation above, y(1) through y(12) represent the twelve observations made at the receiver, and the variable n represents a noise in the signal received at the receiver. Variables h 1  and h 2  represent the layers selected to be frequency-selective, and thus, these layers are functions of frequencies  1 ,  2 , and  3 . Variables h 3  and h 4  represent the layers selected to be frequency-flat. The matrix including the h 1 , h 2 , h 3 , and h 4  variables is multiplied by a matrix including the known reference data S(f) transmitted by the transmitter to the receiver. The selection of certain of the channel layers as being frequency-flat reduces a number of unknown values in the equation.
 
     A least-squares approach to solving the first solution  400  of  FIG. 4  is as follows:
 
 ĥ= ( X   H   X ) −1   X   H   y  
 
where ( ) H  is an operation of Hermitian transpose of a complex matrix. To help ensure full rank and to decrease a dynamic range of the matrix elements after the inverse, a small loading factor may be incorporated as follows:
 
 ĥ= ( X   H   X+D ) −1   X   H   y,  
 
where D may take the form:
 
               D   =         mI   8     ⁢           ⁢   D     =     [             m   1     ⁢     I   6           0           0           m   2     ⁢     I   2             ]         ,         
where m, m 1 , and m 2  are fixed constants. Further, the solution may also be regularized with an SNR estimate to minimize noise amplification at low SNR as follows:
 
                 h   ^     =         (         X   H     ⁢   X     +   D   +       1     SNR   est       ⁢     I   8         )       -   1       ⁢     X   H     ⁢   y       ,         
where the
 
             1     SNR   est           
term is a scaling factor that takes into account the SNR estimate.
 
     To estimate interference covariance, ĥ i  may represent the least-squares solution for an i th  receiver antenna. To determine an interference covariance matrix, the interfering channel estimates from the least squares solution may be correlated across receive antennas, as follows: 
               R   =         [             h   ^     3     (   1   )               ⋮               h   ^     3     (   R   )             ]     ⁡     [         h   ^     3       (   1   )     *       ⁢           ⁢   …   ⁢           ⁢       h   ^     3       (   R   )     *         ]       +       [             h   ^     4     (   1   )               ⋮               h   ^     4     (   R   )             ]     ⁡     [         h   ^     4       (   1   )     *       ⁢           ⁢   …   ⁢           ⁢       h   ^     4       (   R   )     *         ]       +       σ   0   2     ⁢   I         ,         
where R is equal to a number of receiver antennas. If one of the frequency-selective layers is also interference, the channel of the entire time-frequency slots in an RB may be estimated via interpolation and averaging and may use the following equation:
 
               R   ⁡     (     f   ,   t     )       =         [             h   ^     3     (   1   )               ⋮               h   ^     3     (   R   )             ]     ⁡     [         h   ^     3       (   1   )     *       ⁢           ⁢   …   ⁢           ⁢       h   ^     3       (   R   )     *         ]       +       [             h   ^     4     (   1   )               ⋮               h   ^     4     (   R   )             ]     ⁢             [         h   ^     4       (   1   )     *       ⁢           ⁢   …   ⁢           ⁢       h   ^     4       (   R   )     *         ]     +       [               h   ^     2     (   1   )       ⁡     (     f   ,   t     )               ⋮                 h   ^     2     (   R   )       ⁡     (     f   ,   t     )             ]     ⁡     [           h   ^     2       (   1   )     *       ⁡     (     f   ,   t     )       ⁢           ⁢   …   ⁢           ⁢         h   ^     2       (   R   )     *       ⁡     (     f   ,   t     )         ]       +       σ   0   2     ⁢   I                   
A MIMO equalizer may account for the effect of the interference for every time-frequency slot before decoding. For example, a whitening filter may be used to eliminate interference in the received signal y prior to its receipt at the receiver. The whitened signal y w  may be determined as follows:
 
 y   w   =R   −1/2   y  
 
     In the second solution  440  of  FIG. 4 , only a single desired layer is selected to be frequency-selective, and the other layers are selected to be frequency-flat. By contrast, in the first solution  400  of  FIG. 4 , the receiver (i.e., user or UE) selects two layers for frequency-selective estimation regardless of its rank. Thus, the second solution  440  may decrease the estimation complexity as versus the first solution  400  of  FIG. 4 . For example, in the case of rank 1, there may be a single desired layer and three interference layers, and under the second solution  440 , even a dominant interference layer may be assumed to be frequency-flat. The second solution  440  thus causes a loss of frequency granularity in the estimation, but this may be acceptable if the interference layers do not appear to be too strong. Making these assumptions, modeling of the received signal may be represented via the formulation  440  of  FIG. 4 : 
               [           y   ⁡     (   1   )                 y   ⁡     (   2   )                 y   ⁡     (   3   )                 y   ⁡     (   4   )                 y   ⁡     (   5   )                 y   ⁡     (   6   )                 y   ⁡     (   7   )                 y   ⁡     (   8   )                 y   ⁡     (   9   )                 y   ⁡     (   10   )                 y   ⁡     (   11   )                 y   ⁡     (   12   )             ]     =         [           a   1         0       0         a   1           b   1           b   1               a   2         0       0         -     a   2             b   2           -     b   2                 a   3         0       0         a   3           b   3           b   3               a   4         0       0         -     a   4             b   4           -     b   4               0         a   5         0         a   5           b   5           b   5             0         a   6         0         -     a   6             b   6           -     b   6               0         a   7         0         a   7           b   7           b   7             0         a   8         0         -     a   8             b   8           -     b   8               0       0         a   9           a   9           b   9           b   9             0       0         a   10           -     a   10             b   10           -     b   10               0       0         a   11           a   11           b   11           b   11             0       0         a   12           -     a   12             b   12           -     b   12             ]     ⁡     [             h   1     ⁡     (   1   )                   h   1     ⁡     (   2   )                   h   1     ⁡     (   3   )                 h   2               h   3               h   4           ]       +   n           
In the equation above, y(1) through y(12) represent the twelve observations made at the receiver, and the variable n represents a noise in the signal received at the receiver. Variable h 1  represents the single layer selected to be frequency-selective, and thus, this layer is a function of frequencies  1 ,  2 , and  3 . Variables h 2 , h 3 , and h 4  represent the layers selected to be frequency-flat. The matrix including the h 1 , h 2 , h 3 , and h 4  variables is multiplied by a matrix including the known reference data S(f) transmitted by the transmitter to the receiver. The selection of the three layers as being frequency-flat reduces a number of unknown values in the equation and may reduce a complexity of the estimation process.
 
     Both of the solutions  400  and  440  involve selection of certain layers as being frequency-selective and selection of certain layers as being frequency-flat. This partitioning of layers may be achieved based upon a variety of considerations and guidelines. The partitioning may be based on a balance between performance (e.g., SNR, throughput, etc.) and computational complexity, battery life, or power consumption of the receiver. For example, by selecting more channels to be frequency-selective, a higher accuracy estimation may be achieved, but the higher accuracy may come at an expense of a higher computational complexity in the receiver. The higher computational complexity may cause the receiver to consume power faster, thus reducing its battery life. The partitioning process may also be based on the various layers&#39; impact on performance measures, a degree of mutual correlation among the variables to be estimated in reference to an operating regime (e.g., SIR, SNR), a desired performance level, or an instrumentation complexity. For example, if a layer is determined to have a great impact on a performance measure, then the layer may be selected to be frequency-selective, thus enabling a higher resolution frequency estimation for the layer. Further, a combination of the aforementioned considerations may be used in the partitioning. The selection of the layers as being frequency-flat and frequency-selective may allow an increase in throughput as compared to other channel estimation methods. 
     A least-squares approach to solving the second solution  440  of  FIG. 4  may be as follows:
 
 ĥ= ( X   H   X ) −1   X   H   y,  
 
To help ensure full rank and to decrease a dynamic range of the matrix elements after the inverse, a small loading factor may be incorporated as follows:
 
 ĥ= ( X   H   X+D ) −1   X   H   y,  
 
where D may take the form:
 
               D   =         mI   6     ⁢           ⁢   D     =     [             m   1     ⁢     I   4           0           0           m   2     ⁢     I   2             ]         ,         
where m, m 1 , and m 2  are fixed constants. Further, the solution may also be regularized with an SNR estimate to minimize noise amplification at low SNR as follows:
 
                 h   ^     =         (         X   H     ⁢   X     +   D   +       1     SNR   est       ⁢     I   6         )       -   1       ⁢     X   H     ⁢   y       ,         
where the
 
             1     SNR   est           
term is a scaling factor that takes into account the SNR estimate. A minimum-mean-square-error (MMSE) approach to solve the equation may be as follows:
 
 ĥ ( X   H   X+σ   0   2   R   h   −1 ) −1   X   H   y.  
 
Solving the equation typically involves a matrix inversion. Given the large size of such a matrix, (e.g., 4×4, 8×8, or 12×12, depending on the number of unknowns), it is computationally prohibitive. Based on the observation that such a matrix is structural, a low-computational-complexity matrix inversion can be applied. For example, for equation  400 , inverting a 8×8 matrix can be implemented efficiently by
 
     
       
         
           
             
               
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       FIG. 5  is a flowchart  500  illustrating an example method for estimating characteristics of a communication channel. At  502 , a transmission of known reference data is received at a receiving device. The reference data is transmitted over the channel that includes one or more desired layers and one or more interfering layers. The known reference data is used to determine characteristics of the channel, where the determining includes a joint estimation of the one or more desired layers and the one or more interfering layers. At  504 , certain of the layers are selected to be estimated at each of the known reference data. At  506 , certain of the layers are selected to be estimated over a range of the known reference data. At  508 , an equation is solved to jointly estimate the one or more desired layers and the one or more interfering layers based on the selections. A number of unknown values in the equation is reduced by the selection of certain of the layers as being frequency-flat. 
     This written description uses examples to disclose the invention, including the best mode, and also to enable a person skilled in the art to make and use the invention. The patentable scope of the invention may include other examples. Additionally, the methods and systems described herein may be implemented on many different types of processing devices by program code comprising program instructions that are executable by the device processing subsystem. The software program instructions may include source code, object code, machine code, or any other stored data that is operable to cause a processing system to perform the methods and operations described herein. Other implementations may also be used, however, such as firmware or even appropriately designed hardware configured to carry out the methods and systems described herein. 
     The systems&#39; and methods&#39; data (e.g., associations, mappings, data input, data output, intermediate data results, final data results, etc.) may be stored and implemented in one or more different types of computer-implemented data stores, such as different types of storage devices and programming constructs (e.g., RAM, ROM, Flash memory, flat files, databases, programming data structures, programming variables, IF-THEN (or similar type) statement constructs, etc.). It is noted that data structures describe formats for use in organizing and storing data in databases, programs, memory, or other computer-readable media for use by a computer program. 
     The computer components, software modules, functions, data stores and data structures described herein may be connected directly or indirectly to each other in order to allow the flow of data needed for their operations. It is also noted that a module or processor includes but is not limited to a unit of code that performs a software operation, and can be implemented for example as a subroutine unit of code, or as a software function unit of code, or as an object (as in an object-oriented paradigm), or as an applet, or in a computer script language, or as another type of computer code. The software components and/or functionality may be located on a single computer or distributed across multiple computers depending upon the situation at hand. 
     It should be understood that as used in the description herein and throughout the claims that follow, the meaning of “a,” “an,” and “the” includes plural reference unless the context clearly dictates otherwise. Also, as used in the description herein and throughout the claims that follow, the meaning of “in” includes “in” and “on” unless the context clearly dictates otherwise. Further, as used in the description herein and throughout the claims that follow, the meaning of “each” does not require “each and every” unless the context clearly dictates otherwise. Finally, as used in the description herein and throughout the claims that follow, the meanings of “and” and “or” include both the conjunctive and disjunctive and may be used interchangeably unless the context expressly dictates otherwise; the phrase “exclusive of” may be used to indicate situations where only the disjunctive meaning may apply.