Abstract:
A method of estimating the Doppler spread of a communication channel includes computing a first sum defined by a difference between the pilot tones of a first group of N symbols and a corresponding pilot tones of a second group of N symbols preceding the first group of N symbols, computing a second sum defined by the pilot tones of the second group of N symbols, and computing a ratio of the first sum and the second sum for each of the N symbols of the first and second group of symbols to generate N ratios representative of the Doppler spread of the channel. The first sum is further defined by the square of the difference between the pilot tones of the first group of N symbols and the corresponding pilot tones of the second group of N symbols.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
       [0001]    The present application claims benefit under 35 USC 119(e) of U.S. provisional application No. 61/253,433, filed Oct. 20, 2009, entitled “Doppler Estimator for OFDM Systems,” the content of which is incorporated herein by reference in its entirety. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    Channel estimation is commonly used in OFDM systems with coherent demodulation for channel equalization of the received signal. The transmitted OFDM signal includes pre-defined pilots at known sub-carrier locations, which are used for channel estimation. The transmitted pilots are sometimes scattered in the frequency domain to maintain a high utilization ratio. The receiver applies interpolation techniques to reconstruct interpolated pilots at locations where the actual scattered pilots are absent. A need continues to exist for improved estimation of Doppler spread of the channel in OFDM systems. 
       BRIEF SUMMARY OF THE INVENTION 
       [0003]    A method of estimating the Doppler spread of a communication channel includes, in part, computing a first sum defined by a difference between the pilot tones of a first group of N symbols and a corresponding pilot tones of a second group of N symbols preceding the first group of N symbols, wherein N is an integer greater than one. The method further includes computing a second sum defined by the multitude of pilot tones of the second group of N symbols, and computing a ratio of the first sum and the second sum for each of the N symbols of the first and second group of symbols to generate N ratios representative of the Doppler spread of the channel. 
         [0004]    In one embodiment, the first sum is further defined by the square of the difference between the pilot tones of the first group of N symbols and the corresponding pilot tones of the second group of N symbols. The second sum is further defined by the pilot tones of the second group of N symbols. 
         [0005]    In one embodiment, the first pilot tones of each symbol of the first group of N symbols includes the entire set of pilot tones of the symbol of the first group of N symbols, and the second pilot tones of each symbol of the second group of N symbols includes the entire set of pilot tones of the symbol of the second group of N symbols. In one embodiment, the pilot tones of the first group of N symbols include in-phase and quadrature-phase pilot tones, and the pilot tones of the second group of N symbols include in-phase and quadrature-phase pilot tones. In one embodiment, the N ratios are normalized. 
         [0006]    A system operative to estimate the Doppler spread of a communication includes, in part, first and second summing blocks, a memory and a processing block. The first summing block is operative to compute a first sum defined by a difference between the pilot tones of a first group of N symbols and the corresponding pilot tones of a second group of N symbols preceding the first group of N symbols, where N is an integer greater than one. The second summing block is operative to compute a second sum defined by the pilot tones of the second group of N symbols. The memory is operative to store the first and second sums. The processing block is operative to compute the ratio of the first sum and the second sum for each of the N symbols of the first and second group of symbols so as to generate N ratios representative of the Doppler spread of the channel. 
         [0007]    In one embodiment, the first sum is further defined by a square of the difference between the pilot tones of the first group of N symbols and the corresponding pilot tones of the second group of N symbols. In such embodiments, the second sum is defined by the pilot tones of the second group of N symbols. 
         [0008]    In one embodiment, the pilot tones of each symbol of the first group of N symbols includes the entire set of pilot tones of the symbols of the first group of N symbols, and the second pilot tones of each symbol of the second group of N symbols includes the entire set of pilot tones of the symbol of the second group of N symbols. 
         [0009]    In one embodiment, the pilot tones of the first group of N symbols include in-phase and quadrature-phase pilot tones, and the pilot tones of the second group of N symbols include in-phase and quadrature-phase pilot tones. In one embodiment, the processing block further normalizes the N ratios. 
         [0010]    A system operative to estimate the Doppler spread of a communication channel includes a processing unit, and a memory. The processing unit is operative to compute a first sum defined by a difference between the pilot tones of a first group of N (N is an integer) symbols and a corresponding pilot tones of a second group of N symbols preceding the first group of N symbols. The processing unit is further operative to compute a second sum defined by the pilot tones of the second group of N symbols. The processing unit computes a ratio of the first and second sums for each of the N symbols of the first and second group of symbols thereby to generate N ratios representative of the Doppler spread of the channel. The memory stores the first and second sums. 
         [0011]    In one embodiment, first sum is further defined by a square of the difference between the pilot tones of the first group of N symbols and the corresponding pilot tones of the second group of N symbols. IN such embodiments, the second sum is defined by the pilot tones of the second group of N symbols. 
         [0012]    In one embodiment, the pilot tones of each symbol of the first group of N symbols includes the entire set of pilot tones of the symbol of the first group of N symbols, and the second pilot tones of each symbol of the second group of N symbols includes the entire set of pilot tones of the symbols of the second group of N symbols. 
         [0013]    In one embodiment, the pilot tones of the first group of N symbols include in-phase and quadrature-phase pilot tones, and the pilot tones of the second group of N symbols include in-phase and quadrature-phase pilot tones. In one embodiment, the processing unit is further operative to normalize the N ratios. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIG. 1  is a flowchart of steps performed to estimate the Doppler spread of a channel, in accordance with one embodiment of the present invention. 
           [0015]      FIG. 2  is a block diagram of a system adapted to estimate the Doppler spread of a channel, in accordance with one exemplary embodiment of the present invention. 
           [0016]      FIG. 3  is a block diagram of a system adapted to estimate the Doppler spread of a channel, in accordance with another exemplary embodiment of the present invention. 
           [0017]      FIG. 4  shows, in part, a number of plots of a scaled RMS channel change averaged over a multitude of symbols as a function of actual Doppler spread at different signal-to-noise ratios. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0018]    In accordance with one embodiment of the present invention, channel estimates at scattered and interpolated pilot locations from successive symbols are used to estimate the Doppler spread of the channel. Using scattered and interpolated pilot locations to estimate the Doppler spread of the channel leads to enhanced immunity against noise and channel delay spread. The Doppler estimation algorithm is used to tune the demodulator performance in mobile and portable applications. 
         [0019]    The Doppler estimation algorithm, in accordance with embodiments of the present invention, uses interpolated pilots to measure the channel change from symbol to symbol. Assume H n (k) is the channel estimate at the k th  pilot sub-carrier in the n th  symbol, then the following expression (1) is used, as described further below, to determine the Doppler estimate: 
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         [0020]    As shown in the numerator of expression (1), the square of the absolute value of the difference between H n+1 (k) and H n (k) is computed over the entire pilot tones. Likewise, as shown in the denominator of expression (1), the square of the absolute value of H n (k) is computed over the entire pilot tones. Using the above expression (1), a value associated with each pair of symbols n th  and (n+1) th  is obtained, where n is an integer. The root mean squared (RMS) of a predefined number of such values represents a measure of the channel change and an accurate indication of the Doppler spread of the channel. In one example, 100 symbols may be used to estimate the Doppler spread of the channel (alternatively referred to herein as Doppler spread.) In other examples, more or fewer than 100 symbols may be used to estimate the Doppler spread. The Doppler spread may be used to enable the demodulation of the received signal. 
         [0021]      FIG. 1  is a flowchart  100  of steps performed to estimate the Doppler spread of a channel, in accordance with one embodiment of the present invention. The received  102  OFDM symbols are transformed  104  from time domain to frequency domain using, for example, a fast Fourier transform. Next, the pilot tones are extracted  106  and the channel is estimated  108 . Next, the extracted pilots are used to generate  110  a pilot channel estimate H n (k). The pilot channel estimate represents the estimated channel at pilot carrier locations. The pilot carriers are a sub-set of all carriers. The pilot channel estimate H n (k) is stored  120 , and subsequently squared and added  122  to the pilot channel estimate obtained using other pilot tones, as shown in the denominator of expression (1). The squaring and the summation operations in act  122  when carried out over the entire pilot channel estimates results in obtaining a value corresponding to the denominator of expression (1) above. 
         [0022]    The pilot channel estimate H n (k) obtained in  110  is then subtracted  112  from the previous pilot channel estimate H n−1 (k) to obtain the difference between the two. This difference is thereafter squared and added  114  to the values obtained during prior operations of act  114 . The squaring and the summation operations in act  114  when carried out over the entire pilot channel estimates results in obtaining a value corresponding to the numerator of expression (1) above. The ratio obtained by dividing  124  the final value (i.e., computed over all the pilot tones) of the act  114  by the final value of act  122  represents the Doppler estimate of the channel. In some embodiments, normalization and smoothing  126  operations are performed on the Doppler estimated obtained in act  124 . Normalization and smoothing operations are known and are described in, for example: “A Robust Channel Estimator At The High Doppler Frequency Via Matching Pursuit Technique” by Lei Chen and Bernard Mulgrew, 16th European Signal Processing Conference (EUSIPCO 2008), August 2008, available at: http://www.eurasip.org/Proceedings/Eusipco/Eusipco2008/papers/1569104708.pdf; 
         [0023]    Further description of normalization and smoothing are described in, for example “A Maximum Likelihood Doppler Frequency Estimator for OFDM Systems” by Yang-Seok Choi, O. Can Ozdural, Huaping Liu, and Siavash Alamouti, IEEE International Conference on Communications, 2006, ICC &#39;06, pp. 4572-4576, June 2006, available at: http://web.engr.oregonstate.edu/˜hliu/papers/COLA_ICC06.pdf; 
         [0024]    Additional description for data smoothing is provided on the following web page: http://reference.wolfram.com/applications/eda/SmoothingDataFillingMissingDataAndNonparametricFitting.html. The contents of all of the above three publications are incorporated herein by reference in their entirety. 
         [0025]    Furthermore, in some embodiments, curve fitting  128  is applied to the results obtained in act  128 . In some embodiments, a linear curve fitting algorithm is applied to the square root of the smoothed values. In some embodiments, after obtaining the ratios in act  124 , curve fitting  128  is performed. In such embodiments, normalization and smoothing operations may be optionally performed during curve fitting  128 . In some embodiments, non-linear curve fitting is applied to the values obtained in act  124  or act  126 . 
         [0026]      FIG. 2  is a block diagram of a system  200  adapted to estimate the Doppler spread of a channel, in accordance with one exemplary embodiment of the present invention. System  200  is shown as including squaring blocks  202 ,  204 ,  206 ,  208 , summing blocks  210 ,  212 , difference blocks  218 ,  220 , processor  240 , and symbol delay block  222 . The in-phase component pilot_i of each pilot is squared by squaring block  202  and supplied to summing block  210 . The quadrature-phase component pilot_q of each pilot is squared by squaring block  204  and supplied to summing block  210 . Summing block adds the values it receives from squaring blocks  202  and  204  and stores the result in memory  242  disposed in processor  240 . 
         [0027]    Symbol delay block  222  supplies the in-phase and quadrature-phase components of the corresponding pilots of the preceding symbol to difference blocks  218  and  220  respectively. Difference block  218  computes the difference between corresponding in-phase pilots of the currently received symbol and the preceding symbol, and supplies the result to squaring block  206 . Likewise, difference block  220  computes the difference between corresponding quadrature-phase pilots of the currently received symbol and the preceding symbol, and supplies the result to squaring block  208 . Summing block  212  adds the values it receives from squaring blocks  206 ,  208  and stores the result in memory  242  of processor  240 . Each data stored by summing block  210  in memory  242  corresponds to the squared value of one pilot, as shown in denominator |H n (k)| 2  of expression (1). Likewise, each data stored by summing block  212  in memory  242  corresponds to the square of the difference between the current pilot and the preceding pilot, as shown in numerator |H n+1 (k)−H n (k)| 2  of expression (1). The process of storing the data by summing blocks  210  and  212  continues for all or a subset of the pilots associated with a multitude of symbols, e.g., 100. 
         [0028]    In one embodiment, for each symbol, processing block  244  forms the ratio of the data stored by summing block  212  and the data stored by summing block  210 , in accordance with expression (1). In yet other embodiments, the processing block  244  performs this division for a subset of symbols. Processing block then generates the root mean squared (RMS) of the values associated with the predefined number of symbols, e.g., 100, to determine the Doppler spread of the channel. It is understood that in other embodiments of the present invention, a mathematical operation other than the square operation may be applied to the pilots. 
         [0029]    As described above, an optional smoothing operation i is performed to increase the accuracy of the Doppler estimate. A normalizing function, such as func 1   −1  or func 2   −1  may be applied to the square root of the smoothed value of the division result. Since these estimates are obtained by averaging over a number of symbols, the noise immunity is improved. 
         [0030]    In some embodiments, estimating the Doppler spread of a channel in accordance with expression 1 is performed using software running on a computer system.  FIG. 3  shows a computer system having disposed therein, in part, processor  302 , memory  304 , and network interface  306  that communicate with one another using bus  308 . Memory  304  is shown as including ROM  310  and RAM  312 . 
         [0031]    Network interface subsystem  306  provides an interface to other computer systems, networks, and storage resources. The networks may include the Internet, a local area network (LAN), a wide area network (WAN), a wireless network, an intranet, a private network, a public network, a switched network, or any other suitable communication network. Network interface subsystem  306  serves as an interface for receiving data from other sources and for transmitting data to other sources. 
         [0032]    Memory  304  may be configured to store the basic programming and data constructs that provide the functionality in accordance with embodiments of the present invention. For example, according to one embodiment of the present invention, software modules implementing the functionality of the present invention may be stored in memory  304 . These software modules may be executed by processor(s)  302 . Memory  304  may also provide a repository for storing data used in accordance with the present invention. Memory  304  may include a number of memories including a random access memory (RAM)  418  for storage of instructions and data during program execution and a read only memory (ROM)  420  in which fixed instructions are stored. 
         [0033]      FIG. 4  shows plots  410  and  420  of a scaled RMS channel change averaged over 200 symbols as a function of actual Doppler spread at SNR of 10 dB and 20 dB, respectively. Also shown are two functions of Fd, namely square root function func 2  (Fd)  430  and generalized function func 1  (Fd)  440 . It is seen that both of these functions approximate the RMS channel change well. In one embodiment, Fd may be obtained as func 1   −1  (scaled RMS channel change) or as func 2   −1  (scaled RMS channel change). 
         [0034]    The above embodiments of the present invention are illustrative and not limitative. Various alternatives and equivalents are possible. The invention is not limited by the summing block, squaring block, difference block, delay block, memory or processing block, etc. used. The invention is not limited by the number of pilot tones in each symbol. Nor is it limited by the number of symbols used to estimate the channel. The invention is not limited by the normalization function that may be used. The invention is not limited by the type of integrated circuit in which the present disclosure may be disposed. Nor is the disclosure limited to any specific type of process technology, e.g., CMOS, Bipolar, or BICMOS that may be used to manufacture the present disclosure. Other additions, subtractions or modifications are obvious in view of the present disclosure and are intended to fall within the scope of the appended claims.