Abstract:
The present invention provides a method of accurately determining the signal to noise ratio (SNR) using filters. Three embodiments of the invention are disclosed: the use of fixed filters, multiple filters and dynamic filters. The total noise energy is calculated by applying low pass and high pass filters. The minimum of the two noise energies estimated by the low pass and high pass filters is selected to calculate the total noise energy in the signal. The present invention provides an accurate method of SNR estimation in conditions of low SNR and high carrier offsets, without the requirement for bringing the signal to base band. The use of multiple filters provides accurate SNR measurement even in the presence of discrete interferences.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     The present invention, in general, relates to the estimation of signal to noise ratio (SNR) in digital communication receivers and specifically relates to SNR estimation using fixed, dynamic and multiple filters in the applications of low earth orbit (LEO) communication satellites.  
         [0002]     The accurate estimation of SNR is a critical requirement in satellite communications applications. SNR estimation is required for the monitoring of impairments in the received signal in digital mobile radio systems and satellite modems. A typical satellite communications receiver or a digital mobile receiver is activated only at predetermined SNR thresholds. When the minimum SNR level is reached, the satellite communications receiver or a digital mobile receiver is switched on. The SNR value indicates whether the target satellite is within the permissible range of the receiver.  
         [0003]     The methods in the art for SNR estimation are effective in medium (approximately 12 dB) to high SNR conditions. However, in the case of satellite modem applications in low SNR conditions, the relative strength of noise is high, hence the methods currently used in the art yield inaccurate results in SNR estimation.  
         [0004]     Methods in the art for SNR estimation require the signal to be completely brought to base band. In satellite communication applications, it is difficult to bring the signal to base band, since there will be an uncertainty in the frequency estimation of the signal due to the Doppler shift induced by the high velocity of the LEO satellites.  
         [0005]     Carrier offsets resulting from Doppler shifts are a recurring problem in LEO satellite communication systems. The methods disclosed in the art for SNR estimation typically fail in the presence of carrier offsets.  
         [0006]     Discrete interference external radiation sources result in non-uniformity in the pattern of noise energy. The methods disclosed in the art for SNR estimation typically fail in the presence of discrete interferences.  
         [0007]     Hence, there is an unsatisfied market need for an accurate method for SNR estimation, that can be effectively applied in conditions of low SNR and high carrier offsets, and that does not require the signal to be brought to base band. There is also an unsatisfied market need for an accurate method of SNR estimation in the presence of discrete interferences.  
       SUMMARY OF THE INVENTION  
       [0008]     The present invention provides a method of accurately determining SNR using filters. The following three embodiments of the invention are disclosed: a method for accurately determining SNR using fixed filters, multiple filters and dynamic filters. The noise energy value is calculated by applying low pass and high pass filters. The minimum amongst the energy values estimated by the low pass and high pass filters, is selected to calculate the actual noise energy in the signal. The present invention provides an accurate method for SNR estimation in conditions of low SNR and high carrier offsets, and also provides a method that does not require the signal to be brought to base band. The use of multiple filters provides an accurate SNR measurement even in the presence of discrete interferences.  
         [0009]     This invention proposes a method of filter selection and application and a method of SNR computation. The method of this invention, including all its embodiments will be hereafter referred to as the selective filter application (SFA) method.  
         [0010]     One advantage of the SFA method is that SNR is accurately estimated even in the conditions of extreme frequency variations. Extreme frequency variations typically exist in the signals received from LEO satellites. The Doppler shift varies significantly in the signals transmitted by LEO satellites, for example, from −3000 Hz to +3000 Hz, varying at a maximum rate of 27 Hz/sec.  
         [0011]     Another advantage of the SFA method is that SNR is accurately estimated even in low SNR conditions.  
         [0012]     Another advantage of the SFA method is that SNR is accurately estimated even in the presence of high carrier offsets.  
         [0013]     Another advantage of the SFA method is that it can be used for different types of modulation schemes, such as binary phase shift keying (BPSK), M-ary phase shift keying (mPSK), M-ary frequency shift keying (mFSK), and differential modulation schemes.  
         [0014]     Another advantage of the SFA method is that the signal does not have to be brought to base band for SNR estimation. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]      FIG. 1A  illustrates the graphical representation of the equation 2W+W sig ≦f s /2 for the first embodiment of the invention that uses a fixed filter low pass and high pass filter.  
         [0016]      FIG. 1B  illustrates the intersection of signal and filter spectra that occurs when the equation 2W+W sig ≦f s /2 is not satisfied.  
         [0017]      FIG. 1C  illustrates the signal and filter spectrum for the second embodiment of the invention that uses dynamic filters.  
         [0018]      FIG. 1D  illustrates an example of a sampled signal spectrum with discrete interferences.  
         [0019]      FIG. 1E  illustrates the application of the first multiple filter to the signal spectrum.  
         [0020]      FIG. 1F  illustrates the application of the second multiple filter to the signal spectrum.  
         [0021]      FIG. 1G  illustrates the application of the third multiple filter to the signal spectrum.  
         [0022]      FIG. 1H  illustrates the application of the fourth multiple filter to the signal spectrum.  
         [0023]      FIG. 1I  illustrates the original signal spectrum.  
         [0024]      FIG. 1J  is a representation of the outputs of the multiple filters as illustrated in  FIG. 1E ,  FIG. 1F ,  FIG. 1G ,  FIG. 1H  and the original signal spectrum shown in  FIG. 1I .  
         [0025]      FIG. 2  illustrates the method of SNR computation.  
         [0026]      FIG. 3A  illustrates a graph that compares the SNR estimated by the proposed SFA method with the methods of prior art for a quadrature phase shift keying (QPSK) modulated base band signal at 10 Hz frequency offset.  
         [0027]      FIG. 3B  illustrates a graph that compares the SNR estimated by the proposed SFA method with the methods of prior art for a QPSK modulated base band signal at 1000 Hz frequency offset.  
         [0028]      FIG. 4A  illustrates a graph that compares the SNR estimated using the SFA method with the SNR estimated using a method of prior art for a symmetrical differential phase shift keying (SDPSK) modulated base band signal at 0 Hz frequency offset.  
         [0029]      FIG. 4B  illustrates a graph that compares the true SNR with the estimated SNR using the SFA method for a SDPSK modulated base band signal at a high frequency offset of 1000 Hz.  
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0030]      FIG. 1A  illustrates the graphical representation  101  of the equation 2W+W sig ≦f s /2 for the first embodiment of the invention that uses a fixed filter at both ends of the signal spectrum  105 . The sampling rate, abbreviated as f s , is determined by an analog to digital converter (ADC). The bandwidth of the low pass  103  and high pass  104  filters are fixed at W Hz. The maximum signal bandwidth required is assumed to be W sig  Hz. The bandwidth W of the low and high pass frequency bands are selected such that the spectrum of one of those filters does not intersect with that of the incoming signal  105 . This is ensured by compliance to the equation: 
 2 W+W   sig   ≦f   s /2  
         [0031]      FIG. 1B  illustrates the graphical representation  102  intersection of signal spectrum  105  and filter spectra  103 ,  104  that occurs when the equation 2W+W sig ≦f s /2 is not satisfied. Ideally at least one of the two filters, i.e., either the low pass filter  103  or high pass filter  104  must estimate only the noise energy and should not estimate the energy in any section of the signal spectrum  105 . However, when the signal spectrum  105  and filter spectrum  103 ,  104  intersect as illustrated in  FIG. 1B  when the equation 2W+W sig ≦f s /2 is not satisfied, both the high pass  104  and low pass filters  103  estimate not only the noise, but also a section of the signal spectrum  105 , as depicted by the shaded areas  106 .  
         [0032]      FIG. 1C  illustrates the signal spectrum  105  and dynamic filter spectrum  108  for the second embodiment of the invention that uses dynamic filters  108 . When the characteristics of the signal  105  change to signal  107  due to frequency shift, the filter  108  dynamically shifts to a new position  109 .  
         [0033]     The center frequency W c  of the received signal is estimated by the receiver. The bandwidth of the filter (B) is also known, for example B can be equal to signal bandwidth W sig . For a modulated signal, W sig =B+α B, where B is the baud rate and α is the roll off factor of the pulse shaping filter.  
         [0034]     A single dynamic filter  108  is used at one end of the signal spectrum  105  for noise energy estimation. The same method, as illustrated under the description of  FIG. 2  is applied for the estimation of SNR using dynamic filters.  
         [0035]     When the center frequency of the signal  105  shifts to a new position  107  as illustrated in  FIG. 1C , the filter response shifts correspondingly  109  and thereby, overlap of the shifted filter response  109  with the actual signal  105  is avoided.  
         [0036]     A method for deriving a dynamic filter is given below. The filter coefficients of the dynamic filter are calculated. The dynamic filter is defined by its filter coefficients. The following values are known: bandwidth of the filter B, center frequency of the original signal W C , frequency shift f sh , shift in center frequency of the signal W DC  and sampling duration T s . The objective is to derive the filter coefficients, thereby creating the dynamic filter.  
         [0037]     Given the center frequency W C  and the frequency shift f sh  of the original signal, the center frequency of the shifted signal is defined by the equation, 
 
 W   DC   =W   C   +f   sh  
 
         [0038]     The design and application of a dynamic filter comprises of first creating a filter and shifting it appropriately as the original signal shifts.  
         [0039]     The following example describes the method of creating a Butterworth filter and dynamically shifting it. Note that this invention is not restricted to the use of a particular type of filter, such as the filter provided below. The filter coefficients of a second order Butterworth band pass filter are given as n 0 , n 1 , n 2 , d 0 , d 1  and d 2 . T s  is the sampling duration and B is the bandwidth of the filter. 
 
 C =cot( W   DC   ×T   s /2) 
 
 n   0   =B.C  
 
n 1 =0 
 
 n   2   =−B.C  
 
 d   0   =B.C+C   2 +1 
 
 d   1 =−2( C   2 −1) 
 
 d   2   =−B.C+C   2 +1 
 
         [0040]     The filter transform function H(z) is given as, 
 
 H ( z )=( n   0   +n   1   z   −1   +n   2   z   −2 )/( d   0   +d   1    z   −1   +d   2   z   −2 ) 
 
         [0041]     When the center frequency of the original signal shifts, the frequency shift is known and accordingly the dynamic filter parameters are determined. After the dynamic filter is applied to the signal spectrum, E Noise  is determined by computing the dynamic filter output.  
         [0042]      FIG. 1D  illustrates an example of a sampled signal spectrum  105  with discrete interferences. Discrete interferences to the signal cause non-uniform noise  110  in the frequency domain. However, the non-uniform noise  110  or discrete interferences in the frequency domain may or may not reside in the signal spectrum  105 .  
         [0043]      FIG. 1E  illustrates the application of the first multiple filter  111  to the signal spectrum  105 .  
         [0044]      FIG. 1F  illustrates the application of the second multiple filter  112  to the signal spectrum.  
         [0045]      FIG. 1G  illustrates the application of the third multiple filter  113  to the signal spectrum.  
         [0046]      FIG. 1H  illustrates the application of the fourth multiple filter  114  to the signal spectrum.  
         [0047]      FIG. 1I  illustrates the original signal spectrum  105 .  
         [0048]      FIG. 1J  is a representation of the outputs of the multiple filters as illustrated in  FIG. 1E ,  FIG. 1F ,  FIG. 1G ,  FIG. 1H  and the original signal spectrum  105  shown in  FIG. 1I .  
         [0049]     Consider the case of a discrete interference or a non uniform noise  110  illustrated in  FIG. 1D . Consider the case when M multiple filters are used. The actual white noise energy E Noise  is best represented by the filter that measures the least energy. 
 
 E   Noise   =[W   sig   /w ](min( E   1   ,E   2    . . . E   M )) 
 
 where W sig  is the maximum signal bandwidth, M is the number of multiple filters, w is the bandwidth of each multiple filter, and E 1 , E 2  . . . E M  are the noise values estimated by the filters. 
 
         [0050]      FIG. 2  illustrates the method of computation of SNR. The in-phase sample I d (n) of the incoming signal is passed through a low pass filter  201   a , while the quadrature phase sample Q d (n) is passed through another low pass filter  201   b , both the filters having a bandwidth W. I dL  is the in-phase sample of the digital signal after the application of the low pass filter  201   a  to the in-phase sample I d (n) of the sampled signal. Q dL  is the quadrature phase sample after the application of the low pass filter  201   b  to the quadrature phase sample Q d (n) of the sampled signal.  
         [0051]     The application of the filters is illustrated by the following equations: 
 
 I   dL   =I   d   *h   L , 
 
 Q   dL   =Q   d   *h   L  
        where h L  is the filter coefficient and * represents convolution.        
 
         [0053]     The relation between the input χ n  and the output y n  of the filter is given by the equation: 
 
( y   n   ×b   0 )+( y   n-1   ×b   1 )+( y   n-2   ×b   2 )+ . . . =(χ n   ×a   0 )+(χ n-1   ×a   1 ) 
        where a 0 , a 1 , . . . , and b 1 , b 2  . . . are filter coefficients.        
 
         [0055]     The filter may be of infinite impulse response (IIR) or finite impulse response (FIR). The output in frequency domain is given by: 
 
 Ĩ   dL ( w )= H ( w )× Ĩ   d ( w ) 
 
 {tilde over (Q)}   dL ( w )= H ( w )× {tilde over (Q)}   d ( w ) 
 
         [0056]     The outputs of the low pass filter  201   a  and  201   b  are fed to the squaring elements  203   c  and  203   d  respectively, that square both the in-phase I dL  and quadrature phase Q dL  low pass filtered samples. The low pass signal energy (E L ) is obtained by summing the squares of the quadrature phase sample of the noise energy and the in-phase sample of the noise energy in a summer  205 . The summer is fed with a one step delay z −1    212   a . The summing operation is illustrated by the following equation  
         E   L     =         ∑     P   =   0       P   -   1       ⁢       I   dL   2     ⁡     [   p   ]         +       Q   dL   2     ⁡     [   p   ]             
 
 wherein, p is the time index with a predetermined limit. 
 
         [0057]     The in-phase sample I d (n) of the incoming signal is passed through a high pass filter  202   a , while the quadrature phase samples Q d (n) is passed through another high pass filter  202   b , both the filters having a bandwidth W. I dH  is the in-phase sample of the digital signal after the application of the high pass filter  202   a , while Q dH  is the quadrature phase sample after the application of the high pass filter  202   b.    
         [0058]     Application of the filters is illustrated by the following equation: 
 
 I   dH   =I   d   *h   H  
 
 Q   dH   =Q   d   *h   H  
 
 where h H  is the filter coefficient of the high pass filter. 
 
         [0059]     Outputs of the high pass filters  202   a  and  202   b  are fed to the squaring elements  203   e  and  203   f  respectively, that square both the in-phase and quadrature phase high pass filtered output samples. The high pass signal energy (E H ) is obtained by summing the squares of the quadrature phase samples of the noise energy and the in-phase sample of the noise energy in a summer  206 . The summer is also fed with one step delay z −1    212   b .  
         E   H     =         ∑     n   =   0       n   -   1       ⁢       I   dH   2     ⁡     [   n   ]         +       Q   dH   2     ⁡     [   n   ]             
 
 Wherein n is the time index with a predetermined limit. 
 
         [0060]     The minimum of the low pass signal energy and high pass signal energy is determined. This minimum is represented by min (E L , E H )  204 . The minimum is chosen because if any one of the two low pass filters  201   a  or  201   b , or the high pass filters  202   a  or  202   b , filters a section of the actual signal along with the noise. That particular filter will provide a higher value for noise compared to the filter that filters only the noise. Hence, the minimum of E L  and E H    204  is the most representative of the noise energy without discrete components. In case there is a discrete noise component, which comes in the region of the low or high pass filters, the minimum value of E L  and E H  ensures that the discrete noise is not measured.  
         [0061]     The minimum of E L  and E H    204  is fed to the distributor  208 . The ratio of maximum signal bandwidth W sig  to bandwidth W of the high pass filters  202   a  or  202   b  and the low pass filters  201   a  or  201   b , W sig /W is also fed to the distributor  208 .  
         [0062]     Assuming additive white noise, the total noise energy (E Noise ) is calculated by the formula: 
 
 E   Noise   =W   sig   /W [min( E   L   ,E   H )]
 
         [0063]     The in-phase I d  (n) and quadrature phase Q d  (n) samples are fed to the squaring elements  203   a  and  203   b  respectively. The squared samples are summed using a summer  207 . 
 
 The total energy of the incoming signal T is represented by  
       T   =         ∑     K   =   0       N   -   1       ⁢       I   d   2     ⁡     [   k   ]         +       Q   d   2     ⁡     [   k   ]             
 
         [0064]     where I d  [k] and Q d  [k] are the in-phase and quadrature phase samples of the incoming signal respectively.  
         [0065]     The total noise energy (E Noise ) is subtracted 210 from the energy of the received signal (T). The output of this operation provides the actual signal energy (S). 
 
 S=T −( fs/ 2)* E   Noise   /Wsig  
 
         [0066]     The calculated total noise energy (E Noise ) is fed to an inverter  209  in order to determine 1/E Noise , and is forwarded to a distributor  211 . The actual signal energy (S) is also fed to the distributor  211 . The signal to noise ratio (SNR) determined at the distributor  211  is the ratio of actual signal energy (S) to the total noise energy (E Noise ). 
 
SNR= S/E   Noise  
 
         [0067]      FIG. 3A  illustrates a graph that compares the SNR estimated by the SFA method with two methods known in the art for a quadrature phase shift keying (QPSK) modulated base band signal at 10 Hz frequency offset. The two methods in the art are the SNR estimator techniques of Paulizzi&#39;s, et al., illustrated as equations (3) and (4) in the literature “A Comparison of SNR Estimation Techniques for QPSK Modulations” by David R. Pauluzzi, Andrew S. Toms and Norman C. Beaulieu, IEEE Transactions on Communications, Vol. 4, No. 2, February 2000. The plots of the two equations (3) and (4) are depicted as plot  303  and  304  in  FIG. 3A . It can be observed from  FIG. 3A  that the above two methods yield SNR measurements that significantly deviate from the true SNR values. Plot  302  of the SFA method lies closest to the true SNR plot  301 , even at low SNRs.  
         [0068]      FIG. 3B  illustrates a graph that compares the SNR estimated by the proposed SFA method with the true SNR for a QPSK modulated base band signal at a 1000 Hz frequency offset. It is observed that even at high frequency offsets, the plot  306  of the SFA method lies closest to the true SNR plot  305 . Note that the prior art is not plotted in  FIG. 3B  as it significantly fails in the accuracy of SNR estimation.  
         [0069]      FIG. 4A  illustrates a graph that compares the SNR estimated using the SFA method against the SNR estimated using a method in the art for a symmetrical differential phase shift keying (SDPSK) modulated base band signal at 0 Hz frequency offset. The four methods in the art considered are the SNR estimator techniques of Pauluzzi et al., illustrated as equations (3), (4), (5) and (6) “A Comparison of SNR Estimation Techniques for QPSK Modulations” by David R. Pauluzzi, Andrew S. Toms and Norman C. Beaulieu, IEEE Transactions on Communications, Vol. 4, No. 2, February 2000”. The results of the method using equation (3) disclosed above by Paulizzi, et al. is depicted as plot  403 , the result of the method using equation (4) is depicted as  404 , the result of the method using equation (5) is depicted as plot  401  in  FIG. 4A  and the result of the method using equation (6) is depicted as plot  402 . It can be observed from  FIG. 4A  that the plot of the SFA method  406  of this invention lies closest to the true SNR  405 .  
         [0070]      FIG. 4B  illustrates a graph that compares true SNR against the SNR estimated using the SFA method for a SDPSK modulated base band signal at a high frequency offset of 1000 Hz. It can be observed from  FIG. 4B  that the plot  408  of the SFA method of this invention lies very close to the true value of the true SNR  407 .  
         [0071]     In summary, it can be observed from  FIG. 3A ,  FIG. 3B ,  FIG. 4A  and  FIG. 4B  that the SFA method provides an accurate estimation of SNR, and the accuracy is not significantly affected by low SNR and high frequency offset conditions.