Abstract:
A digital signal processing (DSP)-based approach to parameter estimation modulation identification and interference charaterization in connection with a satellite Communication Monitoring System (CSM). The techniques descried here also allow automatic generation of satellite frequency plans (S 74 ) without any a priori knowledge of such plans. Individual processes for carrier isolation (S 71 ), segmentation (S 72 ), frequency estimation (S 73 ), symbol rate estimation, bit error rate estimation, modulation identification and interference characterization are disclosed may be combined in a totally automated process.

Description:
[0001]     This application claims the benefit of U.S. Provisional Application Ser. No. 60/289,389, filed on May 8, 2002. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The invention relates generally to a satellite communication monitoring (CSM) method and apparatus for providing parameter estimation, modulation classification, and interference characterization in communication satellite systems.  
       BACKGROUND  
       [0003]     In a satellite communication system, particularly a system where the satellite is deployed in a geostationary orbit, the satellite will be able to receive signals transmitted to the satellite by earth stations at an allocated uplink frequency band and will be operative to transmit signals to earth stations on allocated downlink frequency bands. The uplink bands are selected to be spaced apart from the downlink bands in order to avoid interference. Nonetheless, interference may be generated due to transmissions from adjacent earth stations or adjacent satellites having overlapping beams. In addition, interference may arise from natural phenomena, such as rainfall, scattering, terrestrial communications and the like.  
         [0004]     With respect to the downlink, the signal received at an earth station from the satellite is frequency-down-converted and digitized by means of an analog-to-digital (A/D) converter. A typical value for the bandwidth of the A/D converted frequency band is 36 MHz. The A/D converter output is a stream of bits which essentially captures all the information in the received signal.  
         [0005]      FIG. 1  illustrates a satellite system  10  having a plurality of satellites  11 ,  12 ,  13 ,  14  in geostationary orbit, including a satellite  13  that is intended to communicate with an earth station  15  and several adjacent satellites  11 ,  12  and  14 . Satellite  13  transmits signals on a downlink band to the earth station  15  having a frequency down converter, A/D converter and CSM equipment  18  that can provide conventional CSM functions. The CSM  18  has an adequate processing capability, which may be provided by a conventional processor (not shown) with appropriate software modules.  
         [0006]     The CSM system  18  includes a digital spectrum analyzer, operating on the A/D output bits, that provides a panoramic look of the carriers in the entire frequency band that was digitized. In order to properly monitor the received signal, the carriers must be separated or isolated, and subdivided as needed. Then, an estimation made of their parameters, identifying their modulation types, as well as detecting and characterizing any interferer that may be present in the digitized frequency band. The successive steps involve carrier isolation, segmentation, frequency estimation, symbol rate estimation, bit error rate estimation, modulation classification and interference characterization.  
         [heading-0007]     Carrier Isolation:  
         [0008]     Carrier isolation consists of identifying and separating the individual carriers in the digitized frequency band. After carrier isolation has been performed, each carrier is processed separately to estimate its parameters, determine its modulation type, etc. Typically, the carriers are identified on a spectrum analyzer by a human operator, in a straightforward and well known process.  
         [0009]     However, automated carrier detection is difficult, as the process must be capable of differentiating true carriers from thermal noise, statistical fluctuations, side lobes, intermodulation products, and spurious spikes.  
         [heading-0010]     Segmentation:  
         [0011]     For the sake of computational simplicity, it is often necessary to segment the time domain data record containing the digital samples into segments of appropriate size, and to process each segment separately. Furthermore, when the channel is not constant, segmentation has the additional advantage of providing a channel which is approximately constant over each segment. Examples of non-constant channels include bursty channels, fading channels, and voice activated channels. The size of the segment is usually chosen as a power of 2 because such a choice leads to the use of efficient FFT processing. FFT processing is the backbone of the digital spectrum analysis to be performed on such segments.  
         [heading-0012]     Frequency Estimation:  
         [0013]     There are several well-known techniques to carrier frequency estimation.  
         [0014]     One popular technique is the centroid method. In this method, the center frequency is estimated as a weighted average frequency, where the weights are taken as the squares of the spectral coefficients. A second method consists of fitting a straight line to the instantaneous phase data. Finding the best straight-line fit is a simple mean square error minimization problem, where the slope of the line provides the frequency estimate and the value at the origin provides the initial phase. When using this technique, the phase values must be unwrapped before the straight line fit A third method consists of passing the received waveform through a nonlinearity, such as quadrupling, and detecting spectral lines at harmonics of the carrier. The frequency location of these spectral lines, which are obtained via a high resolution FET, would provide an accurate estimate of the carrier frequency.  
         [0015]     While the above three methods are suitable in many situations, they each have their shortcomings, making them unsuitable for some applications. For example, the centroid method is not suitable if the frequency spectrum is not symmetric. The instantaneous phase square error minimization is best suited to constant envelope modulations, and the nonlinearity does not always produce line spectra at harmonics of the carrier frequency. Furthermore, the accuracy provided by these methods may sometimes be insufficient.  
         [heading-0016]     Symbol Rate Estimation:  
         [0017]     There are several well-known techniques for symbol rate estimation. One conventional scheme is the delay and multiply method, where the received waveform is multiplied by a replica of itself, that has been delayed by a fraction of the symbol rate. Spectral lines will then appear in the spectrum at harmonics of the symbol rate when the delay is properly chosen. The amount of delay, and the number and magnitude of spectral lines are modulation scheme-dependent and well known in each case. Those spectral lines therefore provide a signature identifying the symbol rate, and may also be used for modulation discrimination.  
         [0018]     Another method is to use a first order phase lock loop (PLL) to track the timing of the received signal. This is a typical way of achieving clock synchronization in digital modems.  
         [0019]     While the above methods are suitable for many situations, they each have their shortcomings, making them unsuitable for some applications. For example, the delay and multiply method does not always produce spectral lines at harmonics of the symbol rate. As to the PLL tracking method, it needs a sufficiently accurate knowledge of the symbol rate at the start.  
         [heading-0020]     BER Estimation:  
         [0021]     When a signal is demodulated and FEC is decoded, it is possible to obtain an accurate estimate of the BER, without having access to the actual transmitted bits. BER is determined by a well-known procedure based on re-encoding the decoded bits.  
         [0022]     In the absence of FEC decoding, an accurate BER estimate (coded or uncoded) may be obtained over an AWGN (additive white gaussian noise) channel from accurate estimation of energy per bit/noise density (Eb/No), and knowledge of the modulation format and FEC type and rate.  
         [0023]     Estimating the uncoded and coded BER becomes more difficult if the channel is not AWGN. In order to provide a fairly accurate BER estimate in this case, understanding the nature and magnitude of the various channel impairments is paramount. Indeed, if by a process of reverse engineering one is able to completely determine all the channel impairments, then one could in principle reconstruct a waveform statistically identical to the one under examination, and therefore one would be able to accurately estimate the BER. In reality of course, it is not possible to completely determine all the channel impairments, and one would attempt to estimate them as accurately as possible.  
         [heading-0024]     Modulation Classification:  
         [0025]     There are a number of well-know techniques for modulation classification. They mostly fall into one of two categories: pattern-recognition based and decision theory-based. The most practical techniques are a hybrid of these two approaches, where a set of key features is extracted from the modulated waveform (as in pattern recognition), and the principles of decision theory are applied to classify the modulation based on those features.  
         [0026]     Numerous key features have been used for modulation classification. A partial list of those features include: amplitude histograms, frequency histograms, phase histograms, phase difference histograms, the variance of the amplitude, frequency, and phase, higher order moments, kurtosis, cumulants, the square of the signal envelope, zero crossings, the power spectrum of the received signal, the presence of harmonics at selected frequencies, the magnitude of the spectral component at twice the carrier frequency of the signal squared, the magnitude of the spectral component at 4 times the carrier frequency of the signal raised to the fourth power, and the power spectrum asymmetry.  
         [0027]     If properly chosen and applied, the key features can help discriminate among different modulation formats, even under adverse conditions, such as low signal to noise ratio (SNR), limited amount of data, presence of interference, and channel impairments.  
         [0028]     Existing modulation classification schemes typically have several shortcomings. One shortcoming is that the key features computation does not take into account that different samples have different reliability values, as they are often taken asynchronously with the signal symbols. Another shortcoming is that the band-limited nature of the waveform (which causes signal fluctuations around the symbol edges) is usually not taken into account A third shortcoming is that the outcome of a classification scheme is often dependent on the sequence of applying the key features. Another shortcoming is that the thresholds used in determining the decision regions are independent of SNR. A further shortcoming is that simple majority rule is used to make a final decision based on the individual segments decisions. Last but not least, is the fact that many existing classification schemes require exact knowledge of the signal parameters, and are not robust to inaccuracies in the value of those parameters. Unfortunately, the schemes that perform the best under idealized conditions tend to be the least robust.  
         [heading-0029]     Interference Characterization:  
         [0030]     Interference identification and characterization can significantly enhance the utility of a Communication System Monitoring system. In this regard, “characterization” refers to determining the power level; carrier frequency and occupied bandwidth of the interferer, plus any other transmission parameters that may be estimated. Generalizing the interference characterization to the case of multiple interferers is done iteratively.  
         [0031]     There are many potential sources of interference in a satellite communication system such as inclined satellites, radars, terrestrial microwave links, in-orbit test equipment generated carriers, rogue transmitters, and carriers on mistaken frequencies and/or directions. In addition, as previously noted, adjacent satellites in the geostationary arc are a main source of interference.  
         [0032]     Adjacent Satellite Interference (ASI) can occur on the uplink and on the downlink. While the interference mechanism is different in these two cases, both uplink ASI and downlink ASI result in the presence of interfering signals in a frequency band. An interferer&#39;s power may be sufficiently low to make its detection and identification difficult, yet sufficiently high to cause noticeable performance degradation to desired signals.  
         [0033]     Furthermore, the capability to characterize interferers in a desired frequency band can provide useful data on whether other satellite systems are abiding by the frequency coordination agreements to which they are party.  
         [0034]     A practical algorithm for interference identification and characterization is known in the art. The received waveform consists of a distorted version of the desired signal, thermal noise, and an unknown interferer. It is desired to characterize the interferer to the extent possible. In other words, it is desired to determine the interferer power, center frequency, occupied bandwidth, modulation type, symbol rate, and any other potentially useful information. If one could completely cancel out the desired signal, standard correlation techniques could be used to extract interferer information from the thermal noise. However, the distortion of the desired signal makes its complete cancellation impractical. The goal is then to cancel the desired signal as much as possible so that any residual energy is small and does not mask the presence of an interferer.  
         [0035]     Impairments that are expected to distort the desired signal waveform include: the non-ideal channel, phase noise, oscillator drift, transmitter non-linearities, non-ideal filtering, clock jitter, intermodulation products, and quadrature imbalance. In order to perform a fairly complete cancellation of the strong signal in this case, understanding the nature and magnitude of the various channel impairments is paramount. Indeed, if by a process of reverse engineering one is able to completely determine all the channel impairments, then one could in principle reconstruct a noise-free, identical copy of the desired signal in the received waveform. Subtracting this constructed replica from the received waveform would leave the interferer and the noise. In reality of course, it is not possible to construct a perfect noise-free copy of the desired signal in the received waveform. The desired approach is to construct as close a replica as possible of the received desired signal by estimating the impairments as accurately as possible. The extent to which it is possible to estimate those impairments and cancel out their effect will determine the degree of success in characterizing the interference.  
         [0036]     As many of the foregoing processes and procedures are manual or only semi-automated, it is an object of the present invention to provide fully automated procedures for determining each of these satellite performance related parameters.  
         [0037]     It is also an object of the invention to provide a combination of automated procedures that can attain an automatic generation of satellite frequency plans.  
         [0038]     It is yet an object of the invention to provide a combination of at least two and possibly all of the automated procedures in order to obtain an optimum result.  
       SUMMARY OF THE INVENTION  
       [0039]     The present invention is a digital signal processing (DSP)-based approach to parameter estimation, modulation identification and interference characterization in connection with a satellite Communication Monitoring System (CSM). The techniques described here allow automatic generation of satellite frequency plans without any a priori knowledge of such plans. When combined with information publicly available about a given satellite, these techniques will give very precise information of the frequency plan of that satellite. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0040]      FIG. 1  is a schematic illustration of a satellite system where CSM would be utilized.  
         [0041]      FIG. 2  is a flowchart for a procedure that performs an automated carrier isolation process.  
         [0042]      FIG. 3  is a flowchart for a procedure that performs an automated carrier segmentation process.  
         [0043]      FIG. 4  is a flowchart for a procedure that performs an automated carrier frequency estimation process.  
         [0044]      FIG. 5  is a flowchart for a procedure that performs an automated symbol rate estimation process.  
         [0045]      FIG. 6  is a flowchart for a procedure that performs an automated bit error rate (BER) estimation process.  
         [0046]      FIG. 7  is a flowchart for a procedure that performs an automated modulation classification process.  
         [0047]      FIG. 8  is a flowchart for a procedure that performs an automated interference identification and characterization process.  
         [0048]      FIG. 9A  is a flowchart for a procedure that integrates three of the foregoing automated processes to achieve an automatic generation of a satellite frequency plan.  
         [0049]      FIG. 9B  is a flowchart for a procedure that integrates all of the foregoing automated processes. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0050]     In a satellite communication system as illustrated in  FIG. 1 , where a CSM system is available to perform various system monitoring, analysis and estimation functions, the processor resident at the CSM may be operative to perform a variety of procedures, consistent with the algorithms identified subsequently in flowchart form, to automatically estimate parameters, classify modulation and characterize interference in the system. While the invention is disclosed in connection with various specific embodiments, it is not limited thereto and a wide variety of alternative approaches may be evident to one skilled in the art upon reading the following disclosure. For example, the processing performed may be distributed or centralized, with communication with an earth station provided by well known network and system arrangements.  
         [0051]     Turning now to the individual elements of the signal processing performed in a CSM system contemplated by the present invention, the following procedures may be employed.  
         [heading-0052]     Carrier Isolation:  
         [0053]     Carrier isolation would be automatically performed in accordance with the following procedure, consistent with the flowchart illustrated in  FIG. 2 . In a first step S 1 , the processor serving the CSM would perform an FFT of size N FFT  on the composite waveform of bandwidth W. The value of N FFT  is programmable, and may be given a default value, such as but not limited to 1024. In step S 2 , the power spectrum is obtained from the FFT output by computing the squared magnitude of each FFT coefficient. This procedure is repeated M times according to step S 3  and averaged out in step S 4  to smooth out the statistical fluctuations in the spectrum. The value of M is programmable, and in an exemplary embodiment, may have a default value of 16, although other values would be readily apparent to one skilled in the art. Then, a noise floor p n  is determined in step S 5 .  
         [0054]     With these basic parameters in hand, the power spectrum is filtered in step S 6  in order to mitigate the impact of any statistical fluctuations, and to gloss over spurious spikes and frequency nulls between sidelobes. Then, in step S 7 , a minimum carrier level p c  X dB above the noise floor p n  is set, where X is a programmable parameter, which may have a default value of 3 dB, or other value as would be apparent to one skilled in the art.  
         [0055]     The processing will proceed through the individual frequency points from the lowest to the highest, in step S 8 . When a value higher than p c  is first detected at a certain frequency, that frequency is taken as the lower frequency limit of a carrier in step S 8 . Also, in that same step, when the value at the filter output drops first to a level below p c , the corresponding frequency is taken as the upper frequency limit of the carrier. The entire spectrum is processed according to the procedure of step S 8 , as indicated in step S 9 , thus identifying the lower and upper frequency limits for each carrier. Finally, in step S 10 , the individual carriers are digitally filtered out, one by one, in accordance with the procedure identified above. Thereafter, the procedure comes to an end.  
         [heading-0056]     Segmentation:  
         [0057]     Segmentation would be automatically performed in accordance with the following procedure, consistent with the flowchart illustrated in  FIG. 3 . In a first step S 11 , a number of samples that are to be included in a segment are determined and a suitable power of 2 is identified to represent the selected number of samples in the segment. Then, in step S 12 , the instantaneous power in each sample is computed. Next, in step S 13 , the instantaneous power values are filtered out in order to remove large deviations. In step S 14 , the average and the standard deviation of the instantaneous power is computed and, in step S 15 , the normalized standard deviation is computed and compared to a threshold based on the value of Eb/No, where Eb is the signal strength and No is a corresponding noise value. In step S 16 , it is determined whether the threshold is exceeded. If not exceeded, the segment is rejected (N), otherwise (Y), it is accepted in step S 17 . Then in step S 18 , it is determined whether the analyzed segment is the last segment and, if not, the process proceeds to test the next segment If it is the last segment, the process ends.  
         [heading-0058]     Frequency Estimation:  
         [0059]     Frequency estimation is automatically performed in accordance with the following procedure, consistent with the flowchart illustrated in  FIG. 4 . In a first step S 21 , the processor would compute a frequency estimate using the well known centroid method. Then, in step S 22 , the instantaneous phase method is modified. The modification would be made as follows. Assign a weight proportional to the square of the magnitude to each instantaneous phase value, so that samples with higher SNR are given more weight. Use a weighted minimum mean square error criterion. Then, in step S 23 , a second frequency estimate is computed using the modified instantaneous phase method as described above.  
         [0060]     In step S 24 , the waveform is passed through a non-linearity and any harmonics in the spectrum are detected. In step S 25 , the FFT-based location of harmonics is enhanced by using unbiased interpolation of the FFT coefficients. Finally, in step S 26 , a third frequency estimate is determined on the basis of the enhanced harmonics location process, as previously disclosed.  
         [0061]     Once the three frequency estimates are obtained, although more may be obtained if desired, a weighted average of the frequency estimates is determined in step S 27 . The weights are assigned on the basis of spectral symmetry, envelope fluctuations, and strength of the frequency harmonics.  
         [0062]     As would be understood by one skilled in the art, if only a moderate frequency estimation accuracy is sought, a subset of the above set of estimates would be adequate. On the other hand, if higher frequency accuracy is still needed, supplement the estimate obtained above with a phase locked loop to track the received carrier.  
         [heading-0063]     Symbol Rate Estimation:  
         [0064]     Symbol rate estimation is automatically performed in accordance with the following procedure, consistent with the flowchart illustrated in  FIG. 5 , using a modification of the conventional delay and multiply technique. According to the modification, in a step S 31 , both the received signal and its delayed replica are passed through a nonlinearity to produce harmonics at the symbol rate. Then, in step S 32 , the processor would compute the number of crossings per unit time where the signal envelope crosses the half power level. In step S 33 , the timing (clock frequency and phase) of the received waveform would be tracked, in an exemplary embodiment, by using a second order PLL.  
         [0065]     In a subsequent process represented by step S 34 , a non-uniform sampling approach would be used. For example, but without limitation, a non-uniformly sampled set may be generated by digital interpolation between the available uniformly sampled samples. The proposed non-uniform sampling rate is slowly and monotonically increasing, and covers the range of uncertainty in the symbol rate. This provides the ability to home in on the true sample rate. Once lock is achieved, uniform sampling is resumed and a PLL is used to fine tune the symbol rate estimate.  
         [0066]     If only a moderate symbol rate estimation accuracy is sought, a subset of the above set of estimates would be adequate.  
         [heading-0067]     BER Estimation:  
         [0068]     Bit error rate estimation is automatically performed in accordance with the following procedure, consistent with the flowchart illustrated in  FIG. 6 . According to step S 41 , the process begins with an estimate the waveform parameters and a determine the modulation type, if it is not already known, as described above. Then, in step S 42 , there is a processing of the received samples with a properly matched and equalized filter, followed by a tracking of the carrier phase and the clock phase in step S 43 . In step S 44 , the well known maximum likelihood techniques are used to estimate the phase noise, intermodulation products, quadrature imbalances, and non-linearity&#39;s.  
         [0069]     Any side information available regarding the transmitter characteristics, such as for example the power amplifier specifications, may be used for this purpose in step S 45 . The information may be available beforehand and either input manually or accessible automatically by the processor on the basis of pre-stored information in RAM or auto detected characteristics of the equipment, in a manner known in the art.  
         [0070]     The process proceeds in option 1 to the construction of a waveform with the estimated parameters and modulation type, subject it to the estimated impairments, and estimate the BER, in step S 46 .  
         [0071]     Alternatively, the process may proceed as option 2 to step S 47  by first constructing a noise-free scattering diagram based on the estimated impairments. Then, an estimate of the uncoded and coded BER, using maximum likelihood, may be obtained from the noise-free scattering diagram, and the estimated Eb/No in step S 48 .  
         [heading-0072]     Modulation Classification:  
         [0073]     Modulation classification is automatically performed in accordance with the following procedure, consistent with the flowchart illustrated in  FIG. 7 . According to step S 51 , an estimate is automatically made of the waveform parameters as accurately as possible, as outlined above. Then, an estimate of the signal-to-noise ratio (SNR) of the received waveform is obtained in step S 52 .  
         [0074]     Available side information, if any, may be used to narrow down the set of potential modulation formats at this point, according to step S 53 . The information may be available beforehand and either input manually or accessible automatically by the processor on the basis of pre-stored information in RAM or auto detected characteristics of the equipment, in a manner known in the art. Then several modification steps occur.  
         [0075]     In step S 54 , the key features computation is modified such that each sample contributing to a key feature is assigned a weight proportional to its SNR. (Some phase samples are more sensitive to noise than others, depending on the magnitude of those samples.) In step S 55 , the key features computation is modified such that each sample contributing to a key feature is assigned a weight proportional to its distance from the symbol edges. (Band limiting causes envelope fluctuations around the symbol edges). In step S 56 , based on the side information, a subset of key features from the set listed above is computed. Then, in step S 57 , the sub-optimum hierarchical classification approach to a vector approach is modified, where several features are applied simultaneously to a multidimensional threshold. The threshold setting is made SNR-dependent. (Actual threshold values for different SNRs are computed offline).  
         [0076]     In step S 58 , the number of segments processed is made SNR-dependent to achieve a given confidence level. And, in step S 59 , for each segment processed, a ranking is assigned as to how likely it is that the waveform under examination belongs to each of the modulation classes under consideration.  
         [0077]     Finally, in step S 60 , a soft combining of all the segment rankings is performed to arrive at the most likely overall classification of a modulation type.  
         [heading-0078]     Interference Characterization:  
         [0079]     Interference characterization is automatically performed in accordance with the following procedure, consistent with the flowchart illustrated in  FIG. 8 . According to step S 61 , an estimate is made of the waveform parameters and a determination is made of the modulation type of the desired signal, if it is not already known, as described earlier.  
         [0080]     In step S 62 , the received samples are processed with a properly matched and equalized filter. Then, in step S 63 , the carrier phase and the clock phase are tracked.  
         [0081]     Any side information available regarding the transmitter characteristics, such as for example the power amplifier specifications, may be used in this regard and optionally input. The information may be available beforehand and either input manually or accessible automatically by the processor in step S 63 A on the basis of pre-stored information in RAM or auto detected characteristics of the equipment, in a manner known in the art.  
         [0082]     In step S 64 , the well known maximum likelihood techniques is used to estimate the phase noise, intermodulation products, quadrature imbalances, and nonlinearities. Then, in step S 65 , the received signal is demodulated and the transmitted bits are recovered. Optionally, if the SNR is low and the error rate is high, FEC decoding of the signal to recover the information bits can be beneficial in this step. If FEC decoding was performed, the information bits must be re-encoded.  
         [0083]     In step S 66 , the transmitted bits are remodulated on a carrier according to the known (or estimated) modulation type, symbol rate, and filter characteristics. The remodulated signal is subjected to the impairments estimated above in step S 67  and the remodulated signal from the received waveform in step S 68 . A standard correlation and spectral analysis techniques is performed on the residual signal to extract interferer information from the noise, in step S 69 .  
         [0084]     The several processes for automated determination of parameters may be combined to provide an automatic generation of a satellite frequency plan, as illustrated in  FIG. 1 , and according to the process of  FIG. 9A . Specifically, the carrier is isolated automatically, according to the process in  FIG. 2 , in step S 71 . The carrier isolation is followed by a segmentation processing in step S 72 , according to the flowchart of  FIG. 3 . Thereafter, a frequency estimation process according to the method of  FIG. 4  is conducted automatically in step S 73 . The result of this combination of outputs would be automatically combined into a frequency plan for a satellite by the CSM in step S 74 .  
         [0085]     The several processes disclosed in  FIGS. 2-8  may be conducted automatically, in any combination, as would be known in the art, including a combination of all of the processes as illustrated in  FIG. 9B . There, as in  FIG. 9A , the carrier isolation, segmentation and frequency estimation processes, which derive a frequency plan in step  81 , may be accompanied by the estimation of symbol rate according to the process of  FIG. 5  in step S 82  and the estimation of BER according to the process of  FIG. 6  in step S 83  The modulation classification according to  FIG. 7  may be performed in step S 84  and the interference characterization according to  FIG. 8  may be performed in step S 85 .  
         [0086]     While the present invention has been described in accordance with certain embodiments and examples, it is not limited thereto.