Abstract:
An apparatus and method for providing spectrum sensing. The invention accepts as inputs a spectrogram or any other time frequency representation of signals in which the resulting two-dimensional output representation provides useful characteristics or features of the original time/series signal being analyzed. The invention employs both time and frequency averaging to exploit signal persistence in either domain.

Description:
STATEMENT OF GOVERNMENT INTEREST 
       [0001]    The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    Energy detector-based spectrum sensing is typically implemented using the periodogram. By including the time dimension, an image can be formed from consecutive periodograms referred to as the spectrogram. Such time-varying spectral representations are needed to address the dynamics of the signal environment in spectrum sensing applications. As indicated in reference [3] below, challenges associated with traditional implementations of energy detection schemes include: i) selection of the threshold for detecting primary users, ii) inability to differentiate interference from primary users and noise, and iii) poor performance under low signal-to-noise ratio (SNR) conditions. 
         [0003]    In this sense, the spectrogram, which is referenced widely in the open literature, could be thought of as “prior art”. More appropriately, it would be the spectrogram combined with Welch&#39;s method of time averaging [4]. Also included in the prior art is the Adjustable Bandwidth Concept [1], which extends Welch&#39;s method to include the ability to average over frequency, and allows for operation on log-scaled amplitudes in the input spectrogram. 
       OBJECTS AND SUMMARY OF THE INVENTION 
       [0004]    The purpose of the present invention is to provide a method of analyzing time-frequency representations (or other two-dimensional inputs) which are characterized by the bandwidths or persistence of the multitude of components that can comprise the original two-dimensional representation. In short, the present invention accomplishes this by generating M additional two-dimensional representations based on an input two-dimensional representation. 
         [0005]    One object of the present invention is to provide an apparatus and method for detecting electronic signals. 
         [0006]    Another object of the present invention is to provide an apparatus and method for detecting interfering electronic signals. 
         [0007]    Still another object of the present invention is to separate signal components according to their bandwidth. 
         [0008]    Still yet another object of the present invention is to provide both time and frequency averaging to increase detection and reduce false-alarm probabilities. 
         [0009]    Briefly stated, the present invention provided an apparatus and method for spectrum sensing. The invention accepts as inputs a spectrogram or any other time frequency representation of signals in which the resulting two-dimensional output representation provides useful characteristics or features of the original time/series signal being analyzed. The invention employs both time and frequency averaging to exploit signal persistence in either or both domains. 
       INCORPORATED BY REFERENCE  
       [0000]    
       
         [1] A. J. Noga, “Adjustable Bandwidth Concept (ABC) Performance Evaluation,” AFRL-IF-RS-TR-2003-184, July 2003. 
         [2] L. Galleani, L. Cohen, A. J. Noga, “A Time Frequency Approach to the Adjustable Bandwidth Concept,” Elsevier Journal on Signal Processing, August 2006. 
         [3] T. Yucek, H. ArsIan, “A Survey of Spectrum Sensing Algorithms for 
       
     
         [0013]    Cognitive Radio Applications,” IEEE Communications Surveys &amp; Tutorials, Vol. 11, No. 1, First Quarter 2009.
   [4] P. D Welch, “The use of Fast Fourier Transform for the Estimation of Power Spectra,” IEEE Trans. Audio Electroacoust., Vol. AU-15, June 1967, pp. 70-73.   
 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]      FIG. 1  depicts a functional block diagram of the present invention, a detection-enhanced adjustable bandwidth apparatus. 
           [0016]      FIG. 2  depicts band-pass filter responses of the present invention. 
           [0017]      FIG. 3  depicts a spectrogram of a three-component test signal in noise as a two-dimensional input to the present invention. 
           [0018]      FIG. 4   a  depicts a first stage output of a prior art 3-stage apparatus. 
           [0019]      FIG. 4   b  depicts a first stage output of a 3-stage embodiment of the present invention. 
           [0020]      FIG. 5   a  depicts a second stage output of a prior art 3-stage apparatus. 
           [0021]      FIG. 5   b  depicts a second stage output of a 3-stage embodiment of the present invention. 
           [0022]      FIG. 6   a  depicts a third stage output of a prior art 3-stage apparatus. 
           [0023]      FIG. 6   b  depicts a third stage output of a 3-stage embodiment of the present invention. 
           [0024]      FIG. 7  depicts a functional block diagram of a M-stage embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0025]    Referring to  FIG. 1 , the present invention, a Detection-Enhanced Adjustable Bandwidth (ABC++) apparatus is depicted. The invention as tested comprises a computer running a computer software program which executes a sequence of computer performed steps. For tests performed to date, the invention comprised a desktop computer running scripts within MatLab® to implement the apparatus. 
         [0026]    The invention accepts as inputs sequential vectors of digital spectral data, {right arrow over (X)} in (n), over the segment index, n. The N elements of the input vector can be derived from an external process that estimates the Power Spectral Density (PSD) of a data sequence to be processed by the present ABC++ invention. When for example, the data sequence is a function of time, an increase in the segment index corresponds to an increase in time, and the overall sequence of PSD estimates provides a two-dimensional representation of the variations in spectral content of the data sequence over time and frequency. The ABC++ device is an M-stage process, M&gt;1, which generates M additional two-dimensional representations from the input two-dimensional representation. Although a common application of the ABC++ device will be for automated signal energy detection, other applications can be anticipated where two-dimensional matrices of data such as images are to be analyzed. For the purposes of this description, the signal energy detection application of the invention is assumed. 
         [0027]    Still referring to  FIG. 1 , an N-element data vector, {right arrow over (X)} in , is filtered over elements k=1, 2, . . . N, through a parallel set of M Band-pass Filters  101 ,  102 , . . . ,  103 . The resulting set of M vectors are designated as {right arrow over (X)} 1 , {right arrow over (X)} 2 , . . . {right arrow over (X)} M , each also consisting of N-elements. In prior art without detection enhancement, these vectors would then be processed by Ensemble Averagers, {right arrow over (A)} 1 , {right arrow over (A)} 2 , . . . {right arrow over (A)} M , respectively. Each averager performs an ensemble average over K i  segments, for any given stage, i. After averaging over consecutive segments, the resulting vectors can then be compared to thresholds η 1 , η 2 , . . . , η M  respectively, resulting in the binary-valued detection vectors, {right arrow over (D)} 1 , {right arrow over (D)} 2 , . . . {right arrow over (D)} M . For the energy detection application of the device, components  101 ,  102 , . . . ,  103  each accomplish a weighted average over the frequency dimension, and Ensemble Averager/Detectors  801 ,  802 , . . . ,  803  each accomplish an average over the time segment dimension. Generally, the parameters of the filters and averagers are chosen to provide more frequency filtering and less time averaging in earlier stages. Likewise, less frequency filtering and more time segment averaging is provided in later stages. Here, the terms earlier and later are used in reference to the stage number and are not in reference to time. 
         [0028]    The parameters of the Band-Pass Filters  101 ,  102 , . . . ,  103 , are chosen to achieve unity gain in their pass-bands, and to ensure the perfect reconstruction property, 
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         [0000]    For many useful data sequences of interest, the convolutions of the input data vector with the filters can be implemented as circular convolutions, leveraging fast transformation algorithms such as the Fast Fourier Transform (FFT). By choice of filter coefficients, each filter can then be designed to achieve zero delay over frequency elements to maintain correspondence between the elements of the input vector and the output vectors. In the original patent, the same processing effect was accomplished using a set of M low-pass filters, one per stage, and configuring the connections between stages to achieve this alignment between input and output vectors. A representative set of magnitude responses for the Band-pass Filters  101 ,  102 , . . . ,  103  (as depicted in  FIG. 2 ), for the case of M=3 stages. Note that strictly speaking, the first stage filter is actually low-pass in nature, and the last stage filter will be high-pass, but herein, we are generally referring to each filter as a band-pass filter. Note also that the coefficients for these filters can be derived from the low-pass filters of the configuration described in U.S. Pat. No. 5,257,211, incorporated herein by reference. In this case, each low-pass filter is chosen to provide an integer valued delay over frequency elements, to more easily achieve input and output vector alignments. The length of the filters in this mathematically equivalent original configuration directly corresponds to the amount of frequency averaging accomplished in each stage, as described in the original patent. 
         [0029]    Detection enhancement is accomplished by taking advantage of the characteristics of the spectral components that occur in stages 1 through i-1, relative to stage i. The Band-pass Filters  101 ,  102 , . . . ,  103 , are designed to sort the spectral content of the input vector, {right arrow over (X)} in , based on bandwidth. Therefore, the spectral components contained in {right arrow over (X)} 1  are more persistent over the frequency dimension relative to components in {right arrow over (X)} 2 , {right arrow over (X)} 3 , . . . {right arrow over (X)} M . In general, the spectral components of {right arrow over (X)} i  are more persistent over the frequency dimension relative to components in {right arrow over (X)} i+1 , {right arrow over (X)} i+2 , . . . , {right arrow over (X)} M . Conversely, this implies that due to relatively less persistence, the spectral components of {right arrow over (X)} i  behaved as nascent Kronecker delta sequences in the Band-pass filters of stages 1 through i-1. As a result, these nascent Kronecker delta sequences elicited responses in these Band-pass Filters that are a function of the impulse response of the filters. Furthermore, due to the perfect reconstruction property of the set of Band-pass Filters, negated versions of these undesired responses are then present in stage i. This cross-contamination between stages is a natural consequence of the perfect reconstruction property, combined with the non-ideal nature of practical filters. To achieve perfect reconstruction with practical filters, overlap between frequency responses will occur and lead to useful but imperfect separation of signal components. 
         [0030]    Still referring to  FIG. 1 , detection enhancement is accomplished by a series of additional processing steps after the initial set of Band-pass Filters  101 ,  102 , . . . ,  103 . Subtractor  201  forms the difference of the vector, {right arrow over (X)} in , minus the output vector of Band-pass Filter  101 . Summer  202  sums the scalar threshold parameters, η 0  and η M . The output vector from the stage M Band-pass Filter  103  is processed by Detector  203  using as a threshold the output of Summer  202 . Detector  203  compares each element of the input vector to the scalar sum threshold η M +η 0  from  202  and creates a new vector with elements of value 1 or 0. For elements of the input vector that are greater than or equal to the threshold, the corresponding element of the output vector is 1. Otherwise, the output vector elements are 0. The Detector  203  output vector and the output vector of Subtractor  201  are multiplied element by element in Multiplier  204 . The resulting output vector from  204  is then filtered over the frequency dimension, i.e., over the elements of the vector, in Band-pass Filters  301 ,  302 , . . .  303 . The parameters of filter  301  are identical to those of filter  101 , the parameters of filter  302  are identical to those of filter  102 , and so on. The output vectors of Band-pass Filters  301 ,  302 , . . . ,  303  are summed with the output vector of Band-pass Filter  103 , in Summer  403 . The output vector of Summer  403  is now a final corrected version of the vector {right arrow over (X)} M . 
         [0031]    In preparation for final corrections to vector {right arrow over (X)} M-1 , Subtractor  401  forms the difference of the output vector of Band-pass filter  101  minus the output vector of Band-pass Filter  301 . Likewise, Subtractor  402  forms the difference of the output vector of Band-pass Filter  102  minus the output vector of Band-pass Filter  302 . These difference vectors are formed for the first M-1 stages. In this manner, the perfect reconstruction property is maintained across the output vectors of Subtractors  401 ,  402 , and Summer  403 , and these output vectors have been corrected based on detections from stage M. In the next step, final corrections are made to stage M-1, and initial corrections are made to stages 1 through M-2, based on detections from stage M-1 using threshold η M-1 +η 0 . These final and initial correction processes continue likewise for stages M-1 to 2. The correction process is completed when stage 2 detections are used to correct stages 1 and 2. 
         [0032]    Still referring to  FIG. 1 , Summer  502  forms the sum of the scalar η 2  and η 0  for the threshold of Detector  503 . The current version of the corrected vector {right arrow over (X)} 2  from the last Subtractor in stage 2 is compared element by element to this threshold and creates a new vector with elements of value 1 or 0. For elements of the input vector that are greater than or equal to the threshold, the corresponding element of the output vector is 1. Otherwise, the output vector elements are 0. Multiplier  504  performs an element by element multiply of the detection vector from Detector  503 , with the output difference vector of Subtractor  201 . The output vector of Multiplier  504  is filtered over elements by Band-pass Filter  601 . In Summer  702 , the output vector of Band-pass Filter  601  is summed with the current version of the corrected vector {right arrow over (X)} 2  from the last Subtractor in stage 2. The output of Summer  702  is the final corrected version of {right arrow over (X)} 2 . Finally, Subtractor  701  forms the difference of the most recent corrected version of {right arrow over (X)} 1  minus the output vector of Band-pass Filter  601 . All final corrected versions of vectors {right arrow over (X)} 1 , {right arrow over (X)} 2 , . . . , {right arrow over (X)} M  are then independently averaged over the time dimension in Ensemble Averager/Detectors  801 ,  802 , . . . ,  803  as described for the prior art. Although detection vectors are shown at the outputs of Averager/Detectors  801 ,  802 , . . . ,  803 , resulting vectors from the ensemble averages can also be output for further external processing and analysis. 
         [0033]    To demonstrate the effectiveness of the ABC++ process, comparisons to the conventional ABC process of U.S. Pat. No. 5,257,211 can be made using a two-dimensional input which by design, contains signal components of multiple bandwidths. The signal simulations and results were obtained using Matlab™. For the results presented, both the ABC and ABC++ were 3-stage processes, i.e., M=3, configured with the same Band-pass filters  101 ,  102  and  103  parameters. The band-pass filter parameters were derived from the equivalent low-pass ABC implementation. These low-pass filter parameters were created using the Matlab fir1 command, as fir1(64,0.01) and fir1(64,0.1) for stage 1 and stage 2 respectively. The corresponding band-pass filter responses are shown  FIG. 2 . No time averaging was used in the results presented, i.e., the selected parameters of the averagers are K 1 =1, K 2 =1 and K 3 =1. 
         [0034]    For the demonstration, the two-dimensional input is a spectrogram containing three signal components, each of increasingly wider bandwidth. As seen in  FIG. 3 , a narrow bandwidth component is present in the center of the frequency range. 
         [0035]    Additionally, a wide bandwidth component is located in the upper frequency range, and a medium bandwidth component is located in the lower frequency range. Noise is also present across the entire frequency range, resulting in a spectrogram that simulates data acquired from an actual communication receiver. The frequency dimension of the test input is 512 elements or frequency bins and the time dimension is 50 segments. 
         [0036]    Referring to  FIG. 4   a , the first stage of the conventional, prior art ABC process performs reasonably well in that the wide bandwidth component is present and the narrow bandwidth component is almost completely attenuated, although some small remnants of signal energy can be seen. Although greatly reduced relative to the input, the medium bandwidth component is still present in sufficient amount due to the non-ideal nature of practical filters. Comparing this result to that of the ABC++ process shown in  FIG. 4   b , the narrow bandwidth component has been effectively eliminated in stage 1, and the medium bandwidth component is significantly reduced, without reducing the wide bandwidth component. 
         [0037]    Referring to  FIG. 5   a  and  FIG. 5   b  depicts the stage 2 results. Again, it is readily apparent that although the conventional ABC process of U.S. Pat. No. 5,257,211 does predominantly yield the medium bandwidth signal component in this stage, some of the narrow bandwidth component is still present. For the present invention&#39;s ABC++ process, both the wide bandwidth and narrow bandwidth components have been effectively eliminated in this stage. 
         [0038]    Referring to  FIG. 6   a  and  FIG. 6   b  depicts the stage 3 results, the conventional ABC process very effectively eliminates the wide bandwidth and medium bandwidth components, but has slightly attenuated the narrow bandwidth component. The present invention&#39;s ABC++ process likewise eliminates the wide bandwidth and the medium bandwidth components, but has less attenuation of the narrow bandwidth component when compared to the conventional ABC process of U.S. Pat. No. 5,257,211. 
         [0039]    Referring to  FIG. 7  shows a M-order embodiment of the present invention having a quantity of M band-pass filters in the first filter bank, the second filter bank having M-1 band-pass filters, and the third, fourth, etc. each having one less band-pass filter than the prior bank of filters. It follows that the number of multipliers, subtractors, detectors, etc. will be scaled appropriately to the M-order of the apparatus. It is clearly within the scope of the present invention that the apparatus can be scaled, as just described, to any degree as applications may require. 
         [0040]    Having described preferred embodiments of the invention with reference to the accompanying drawings, it is to be understood that the invention is not limited to those precise embodiments, and that various changes and modifications may be effected therein by one skilled in the art without departing from the scope or spirit of the invention as defined in the appended claims.