Modulation Recognition in Multipath Fading ... - Semantic Scholar
Modulation Recognition In Multipath Fading Channels Using Cyclic Spectral Analysis Eric Like
Vasu Chakravarthy
Robert Husnay
Zhiqiang Wu
Air Force Institute of Technology
Air Force Research Lab
Air Force Research Lab
Dept of EE Wright State University
Abstract—In this paper, we propose a novel signal classification method using cyclic spectral analysis and neural networks for multipath fading channels. The proposed system provides excellent classification performance in realistic multipath fading channels at low SNR, while assuming no a priori knowledge of the signal statistics, including carrier frequency, phase offset, or symbol rate. Due to its insensitivity to these statistics and its robustness to multipath fading channels, the Spectral Coherence Function (SOF) is employed in the proposed system to produce a highly reliable classifier. Additionally, by employing a multipleantenna based system, even greater advantages are achieved by exploiting spatial diversity. Numerical results demonstrate the classifier performance under a variety of channel conditions.
I. I NTRODUCTION With the current increased demand for spectrum usage, the need to efficiently utilize the available spectrum is at an all time high. Until recently, communication devices could only operate in the spectrum allocated to them by the FCC. However, with the arrival of cognitive radio, the ability to adapt to the current environment and take advantage of spectrum holes has the potential to significantly increase the amount of useable spectrum [1][2]. With this capability, any area of the spectrum that is not currently being occupied can be capitalized on by other devices wishing to make the fullest use of the spectrum. In addition to merely looking for areas of the spectrum that are completed unoccupied, a more flexible option for a cognitive radio is to assess whether it can transmit in an occupied frequency band at a low enough power level to avoid interference with the current system. Since different modulation schemes can tolerate different interference levels, the modulation scheme of the existing inband signal will have to be determined. The ability to autonomously perform modulation recognition will greatly enhance the ability of cognitive radios to maximize the use of the entire spectrum. Attempts to perform modulation recognition have been ongoing for over two decades. Methods can be generally classified into either likelihood-based (LB) or feature-based (FB) approaches. In LB systems, the likelihood functions for each potential modulation scheme is computed, and the scheme with the greatest likelihood is selected. This offers a method that is optimal in the Bayesian sense, but a complete mathematical representation is often very complex. Additionally, the system can be highly susceptible to modelling errors, and is commonly too computationally burdensome to operate in real time [14][15]. FB approaches attempt to extract the significant information from the received signal and perform
a classification based on the reduced data. Even though these methods are suboptimal to the LB approaches, they are much more computationally efficient and have been demonstrated to provide near-optimal performance [3]. FB approaches have utilized a variety of features based on variations of the signal’s instantaneous frequency, amplitude, and phase, their moments, as well as other derived values. However, most require the modulation classifier to have a priori knowledge of critical signal statistics and to have some level of synchronization with the signal. This data would not normally be known to a cognitive radio searching for under-utilized spectrum on an noncooperative basis, and greatly reduces the utility of the classifier. Furthermore, many require unreasonably high signal to noise ratio (SNR), and completely fail in multipath or fading environments [4][5]. The Spectral Coherence Function (SOF) has been demonstrated to be insensitive to noise, and to produce highly distinct features for signals with different modulation schemes without requiring any a priori knowledge of the signal’s carrier frequency, phase, or timing offset [8][9]. However, due to the large amount of data generated by cyclic spectral analysis, the feature set must be reduced in some way in order for a classifier to be able to utilize it. In [8] the authors proposed using only the cycle frequency profile of the SOF, which was shown to achieve excellent classification results in AWGN channels at SNR levels down to -5 dB. In our previous work [9] it was shown that with only the marginal increase of computational complexity incurred by using both the spectral and cycle frequency profiles, the system can be significantly improved. In this paper, we extend our previous work in [9] to evaluate the ability of the SOF’s performance as a reliable feature in multipath fading channels, and compare its performance to that of the benchmark system given in [8]. By exploiting the SOF’s insensitivity to additive noise as well as channel corruption, the resulting classifier is shown to be robust both to low SNR as well as multipath fading channels. To increase the capacity even further, two combining schemes are proposed to exploit spatial diversity by combining the data received from multiple antennas. The resulting classifier is demonstrated against AM, BPSK, 16QAM, 8PSK, BFSK, CDMA, and OFDM signals down to an SNR of -5 dB, in several multipath fading channels. In Section II, the underlying theory utilized by the proposed classifier is provided and the features of interest are developed. In Section III the classifier design is described, and simulation
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
results are given in Section IV. Conclusions drawn from the data are given in Section V. II. S IGNAL S TATISTIC D EVELOPMENT A. Signal Model Cyclic spectral analysis is based on the concept that communications signals are appropriately modeled as cyclostationary signals, rather than merely as stationary signals. This means that the signal statistics vary periodically in time. As a result the spectral components of the signal become temporally correlated. These correlations arise due to underlying periodicities in the signal, such as sampling, scanning, modulating, multiplexing and coding. The spectral correlation function (SCF) has been developed as a key feature to measure the amount of correlation between spectral components. The estimate of a signal’s SCF is given by [6][7]: N/2−1 α (f ) SX
= lim
lim
N →∞ N →∞
XT (r, f1 )XT∗ (r, f2 )
(1)
r=−N/2
N /2−1
XT (n, fk ) =
x(n − r)e−j2πfk (n−r)Ts
(2)
r=−N /2
where Ts is the sampling period, T = N Ts , α ≡ f1 − f2 , f ≡ (f1 + f2 )/2, fk ∈ 1/T · {−N /2, . . . , N /2 − 1}, and N and N are assumed to be even with N > N . Here it can be seen that the SCF can be interpreted as a formal correlation between the two time signals XT (n, f + α2 ) and XT (n, f − α2 ). Since the spectral components of white noise are uncorrelated, it does not contribute to the resulting image. It should be noted that this is the case even when the power spectrum of the noise exceeds the power of the signal of interest, indicating the robustness of cyclic spectral analysis to additive noise. The magnitude of the spectral coherence function (SOF) is then defined as the correlation coefficient between these signals: α SX (f ) (3) ∗ α α 1/2 0 0 ] f− [SX f + SX 2 2 Examples of the SOF of common signals are shown in Fig 1 and 2 below. As can been seen, the SOF of each modulation scheme produces highly unique images, which act as a spectral fingerprint for each scheme. These fingerprints can then be used to distinguish between different modulation schemes. For this reason, SOF images have been demonstrated to be highly effective in classifying various signals in AWGN channels [8][9]. However, wireless communications channels are rarely purely AWGN channels. Airborne signals are typically subject to multipath propagation as well as fading. The resulting SCF of the signal is given by [6]. α α α ∗ H f− Sx (f ) (4) SYα (f ) = H f + 2 2 α = CX
where it is subject to a potentially significant degree of corruption. However, by substituting (4) into (3) and forming the SOF, it can readily be seen that the effects due to channel distortion are removed and the resulting SOF of the received signal is equal to the SOF of the original undistorted signal [6]. This result predicts the SOF to be insensitive to multipath effects, as long as no frequency of interest in the signal is completely nullified by the channel distortion. Additionally, assuming a sufficiently slowly fading channel, the resulting SOF image will merely be a negligibly corrupted version of that obtained in a nondispersive channel. Examples of SCF and SOF estimates of a various signals in multipath channels are shown in Fig 3 and 4. When computing the SCF, N and N from (1) and (2) must be made finite, and an estimate of the SCF is obtained. These values limit the temporal and cyclic resolutions to Δt ≈ N Ts and Δf ≈ 1/T = 1/N Ts , respectively. Additionally, the cycle frequency resolution is limited to Δα = 1/Δt . However, to achieve statistical reliability, the time frequency resolution product must be made very large, ΔtΔf 1 , or equivalently Δf 1/Δα [10]. This results in a computationally infeasible number of cycle frequencies to be computed in search of only the few cyclic features actually present. A solution to this problem is to first estimate the cycle frequencies where features occur using an efficient temporal smoothing approach, such as the Strip Spectrum Correlation Algorithm (SSCA) outlined in [11]. After the cycle frequencies of interest are identified, the SCF can be estimated at those points through the equivalent method of frequency smoothing as outlined in the equation below [10]: N/2−1 α (f ) = lim SX
lim
r r XT (0, f1 + )XT∗ (0, f2 + ) (5) T T
N →∞ N →∞ r=−N/2
where now N > N and XT (n, fk ) is defined in (2). The resulting SOF is a three dimensional image. The amount of data is too large for any classifier to utilize in a reasonable amount of time, and must be reduced in some manner. In [8], the authors suggested using only the cycle frequency profile of the SOF. However, with only a modest gain in computational complexity, we propose using the spectral frequency profile as well. We define the cycle frequency profile as − → α ] α = maxf [CX
(6)
and the spectral frequency profile as → − α f = maxα [CX ]
(7)
to be the feature set used for classification. III. C LASSIFIER D ESIGN Due to its ease of implementation and ability to generalize to any carrier frequency and symbol rate, the proposed classifier employs a neural network based system to perform signal
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
classification. This is done with five neural networks each trained to classify a signal as either AM, BPSK, BFSK, CDMA, or one of OFDM, 16QAM, or 8PSK. In general, OFDM signals will contain unique cyclic features due caused by the symbol rate of each subcarrier. However, due to the fact that each subcarrier overlaps with adjacent subcarriers, the resulting SOF of the OFDM signal will be affected. Under the assumption that each subcarrier is modulated with independent data symbols, the cyclic features in the SOF for each subcarrier will be reduced by the adjacent subcarriers. As a result, the cycle frequency and spectral frequency profiles of the SOF estimated for OFDM signals appear negligibly different from those estimated for higher order QAM and PSK signals. Therefore, the neural networks are trained to group these signals together into a single classification. If a finer classification is needed for to discriminate between each of these subclassifications, it can be handed off to a second stage to compute higher order cyclic statistics of the signal [12][13][14]. The resulting classifier diagram is shown in Fig 5. Each network is composed of four neurons in their hidden layer and one neuron in their output layer, with each layer employing a hyperbolic tangent sigmoid transfer function. The inputs to the network are the concatenated cycle and frequency profiles of the SOF. Each neural network will output a value in the range of (-1,1) and the modulation scheme corresponding to the network with the highest output will be selected. The distance between the highest output and its closest competitor can be used as a pseudo-confidence parameter, with a larger distance corresponding to a higher degree of confidence in correct classification, and a smaller distance to a lower degree of confidence[8]. To take advantage of the presence of spatial diversity in fading channels, the effect of using an L branch antenna receiver array is also investigated, where the fading among the different antennas are assumed to be independent. Two methods of combining the data are implemented based on the estimated SNR of the signal for the given receiver. The first method is to implement a selection combining (SC) algorithm before computing the SOF of the received signal. This is done by estimating the SNR on each of the L branches, and retaining only the signal residing on the branch with the highest SNR. By assuming that each branch has identical noise powers, the branch with the highest SNR can be found by noting that it will also be the branch with the highest total power. This results in an extremely simple combining method that provides excellent performance gains with a very moderate increase in computational complexity. The classifier diagram modified for SC with multiple antennas is shown in Fig 6. Maximum ratio combining (MRC) is a powerful scheme used to combine signals from multiple antennas [12][13]. In MRC, the estimates of the SNR of the received signals are used to constructively combine the signals, while suppressing noise affects. However, due to the unknown relative phase
differences of the channels for each receiver, the signals cannot be weighted and added directly. Instead, a variation of MRC is proposed by adding weight values of the SOF profiles. This method computes the SOF profile of the signal received on each antenna. Each SOF is then weighted by the SNR of the signal that generated it. After the SOF from each antenna has been computed and weighted, all the SOF profiles are added together to generate a “combined” SOF profile. This new pseudo SOF profile is then passed to the neural networks to resume processing. The classifier diagram implementing the MRC variant is shown in Fig 7. IV. S IGNAL C LASSIFICATION R ESULTS Simulations were run with AM, BPSK, 16QAM, 8PSK, BFSK, CDMA, and OFDM signals. Both the proposed system as well as the benchmark system utilizing only the cycle frequency profile were tested for comparison purposes. For each signal simulated, the IF carrier frequency was uniformly distributed between .23 and .27 times the sampling rate, and the bandwidth of the signals were uniformly distributed between .16 and .24 times the sampling rate. The system was trained and tested with 4096 samples for its classification decision, corresponding to approximately 410 symbols for the digital modulation schemes. The proposed system was evaluated in a flat, 2-path, and 20-path Rayleigh fading channels with an SNR ranging from -5 dB to 10 dB. The 2-path and 20-path channels were modeled with independently varying, equal power paths. For all channels, each path was modeled with a coherence of 0.9 over 500 samples. In the 2-path channel, the delay between the first path and the second path was uniformly distributed between one and nineteen samples. In the 20-path channel, there was a delay of one sample between the arrival of each consecutive path. Figures 8 and 9 depict the performance of the proposed system and the benchmark system under a flat fading channel. As can be seen, the proposed system significantly outperforms the benchmark system in all cases. The proposed system experiences only a moderate performance degradation even without any combining methods implemented as compared to the benchmark system. The result when implementing either of the combiners yield a significant gain, even with the case of just L = 2 antennas. Figures 10 and 11 demonstrate the system performance in the 2-path channel. Here, the single antenna performance is more degradated than in the flat fading channel. However, each of the combining schemes give a substantial performance increase compared to the single antenna case. Again, the addition of a single antenna significantly enhances the classification performance. The system performance under the harsh 20-path channel is shown in Figures 12 and 13. Here, the use of the combining techniques is of the greatest benefit. Due to the relative increase in noise power when the signal is in a deep fade, the SOF can be significantly corrupted. However, the SOF is still subject to significant corruption if a there is a
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
particularly low channel response at a feature of interest. The performance of the MRC variant is substantially higher than the SC system in this case, where its ability to constructively add the cyclic features while suppressing noise and smoothing channel distortion enables it to provide the greatest benefit. V. C ONCLUSION In this paper we proposed a multi-antenna modulation recognition system utilizing the Spectral Coherence Function (SOF) of received signals in several fading channels. The SOF proved to be a robust feature to use for signal classification. The SOF’s insensitivity to the unknown statistics of received signals and its robustness to multipath fading channels make it an exceptional choice for modulation recognition. The system was further enhanced by using a selection combining (SC) scheme and a variation of maximum ratio combining (MRC) to exploit spatial diversity with multiple antennas. The SC scheme demonstrated considerable gains over the single antenna case with a minimal amount of computational requirements, while the MRC variant demonstrated exceptional results with only a moderate increase in computational requirements. ACKNOWLEDGMENT
[5] W. Su and J. Kosinski, “Comparison and modification of automated communication modulation recognition methods”, IEEE Milcom’02, October, 2002 [6] W. A. Gardner, Cyclostationarity in communications and signal processing, IEEE Press, New Jersey, 1993 [7] W. A. Gardner, W. A. Brown and C.-K. Chen, “Spectral correlation of modulated signals: part II - digital modulation”, IEEE Transactions on Communications, vol. 35, no. 6, pp. 595-601, June 1987 [8] A. Fehske, J. Gaeddert and J. H. Reed, “A new approach to signal classification using spectral correlation and neural networks”, 1st IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, pp. 144-150, Baltimore, 2005 [9] E. Like, V. Chakravarthy, and Z. Wu, “Reliable Modulation Classification at Low SNR Using Spectral Correlation,” IEEE Consumer Communications and Networking Conference, January 2007. [10] W. A. Gardner, “Measurement of spectral correlation”, IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 34, no. 5, October 1986 [11] R. S. Roberts, W. A. Brown and H. H. Loomis, “Computationally efficient algorithms for cyclic spectral analysis”, IEEE Signal Processing Magazine, April 1991 [12] O. Dobre, Y. Bar-Ness, and W. Su, “Higher Order Cyclic Cumulants for High Order Modulation Classification,” Proc. IEEE MILCOM’03, 2003 [13] P Marchard, J Lacoume, and C Martret, “Multiple Hypothesis Modulation Classification Based On Cyclid Cumlants of Different Orders,” Proc. ICASSP, 1998, pp.2157-2160. [14] O. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Selection Combining for Modulation Recognition in Fading Channels,” IEEE Milcom’05, 2005 [15] A. Swami and B. Sadler, “Hierarchical digital modulation classification using cumulants”,IEEE Transactions on Communication, vol. 48, pp.416429, 2000.
This work is sponsored by the Air Force Research Laboratory via DAGSI program. R EFERENCES [1] J. Mitola, “Cognitive radio: an integrated agent architecture for software defined radio”, Ph.D. dissertation, KTH Royal Institute of Technology, Stockholm, Sweden, 2000. [2] The proceedings of the 1st IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, Baltimore, 2005 [3] O Dobre, A Abdi, Y Bar-Ness, and W. Su, “A Survey of Automatic Modulation Classification Techniques: Classical Approaches and new Trends,” IEEE Proceedings on Communications, 2006. [4] E. Azzouz and A. Nandi, “Automatic modulation recognition of communication signals”, Kluwer Academic Publishers, 1996
Fig. 1.
BPSK in AWGN Channel, 5 dB SNR
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
Fig. 5. Fig. 2.
2FSK in AWGN Channel, 5 dB SNR
Fig. 6. Fig. 3.
System Diagram with Selection Combining
BPSK in Multipath Fading Channel, 5 dB SNR
Fig. 7. Fig. 4.
System Diagram
System Diagram with MRC Variant
2FSK in Multipath Fading Channel, 5 dB SNR
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
Fig. 8.
SC System Performance in Flat Fading
Fig. 9.
MRC System Performance in Flat Fading
Fig. 10.
SC System Performance in 2 Path Fading
Fig. 11.
Fig. 12.
Fig. 13.
MRC System Performance in 2 Path Fading
SC System Performance in Multi-Path Fading
MRC System Performance in Multi-Path Fading
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
Vasu Chakravarthy
Robert Husnay
Zhiqiang Wu
Air Force Institute of Technology
Air Force Research Lab
Air Force Research Lab
Dept of EE Wright State University
Abstract—In this paper, we propose a novel signal classification method using cyclic spectral analysis and neural networks for multipath fading channels. The proposed system provides excellent classification performance in realistic multipath fading channels at low SNR, while assuming no a priori knowledge of the signal statistics, including carrier frequency, phase offset, or symbol rate. Due to its insensitivity to these statistics and its robustness to multipath fading channels, the Spectral Coherence Function (SOF) is employed in the proposed system to produce a highly reliable classifier. Additionally, by employing a multipleantenna based system, even greater advantages are achieved by exploiting spatial diversity. Numerical results demonstrate the classifier performance under a variety of channel conditions.
I. I NTRODUCTION With the current increased demand for spectrum usage, the need to efficiently utilize the available spectrum is at an all time high. Until recently, communication devices could only operate in the spectrum allocated to them by the FCC. However, with the arrival of cognitive radio, the ability to adapt to the current environment and take advantage of spectrum holes has the potential to significantly increase the amount of useable spectrum [1][2]. With this capability, any area of the spectrum that is not currently being occupied can be capitalized on by other devices wishing to make the fullest use of the spectrum. In addition to merely looking for areas of the spectrum that are completed unoccupied, a more flexible option for a cognitive radio is to assess whether it can transmit in an occupied frequency band at a low enough power level to avoid interference with the current system. Since different modulation schemes can tolerate different interference levels, the modulation scheme of the existing inband signal will have to be determined. The ability to autonomously perform modulation recognition will greatly enhance the ability of cognitive radios to maximize the use of the entire spectrum. Attempts to perform modulation recognition have been ongoing for over two decades. Methods can be generally classified into either likelihood-based (LB) or feature-based (FB) approaches. In LB systems, the likelihood functions for each potential modulation scheme is computed, and the scheme with the greatest likelihood is selected. This offers a method that is optimal in the Bayesian sense, but a complete mathematical representation is often very complex. Additionally, the system can be highly susceptible to modelling errors, and is commonly too computationally burdensome to operate in real time [14][15]. FB approaches attempt to extract the significant information from the received signal and perform
a classification based on the reduced data. Even though these methods are suboptimal to the LB approaches, they are much more computationally efficient and have been demonstrated to provide near-optimal performance [3]. FB approaches have utilized a variety of features based on variations of the signal’s instantaneous frequency, amplitude, and phase, their moments, as well as other derived values. However, most require the modulation classifier to have a priori knowledge of critical signal statistics and to have some level of synchronization with the signal. This data would not normally be known to a cognitive radio searching for under-utilized spectrum on an noncooperative basis, and greatly reduces the utility of the classifier. Furthermore, many require unreasonably high signal to noise ratio (SNR), and completely fail in multipath or fading environments [4][5]. The Spectral Coherence Function (SOF) has been demonstrated to be insensitive to noise, and to produce highly distinct features for signals with different modulation schemes without requiring any a priori knowledge of the signal’s carrier frequency, phase, or timing offset [8][9]. However, due to the large amount of data generated by cyclic spectral analysis, the feature set must be reduced in some way in order for a classifier to be able to utilize it. In [8] the authors proposed using only the cycle frequency profile of the SOF, which was shown to achieve excellent classification results in AWGN channels at SNR levels down to -5 dB. In our previous work [9] it was shown that with only the marginal increase of computational complexity incurred by using both the spectral and cycle frequency profiles, the system can be significantly improved. In this paper, we extend our previous work in [9] to evaluate the ability of the SOF’s performance as a reliable feature in multipath fading channels, and compare its performance to that of the benchmark system given in [8]. By exploiting the SOF’s insensitivity to additive noise as well as channel corruption, the resulting classifier is shown to be robust both to low SNR as well as multipath fading channels. To increase the capacity even further, two combining schemes are proposed to exploit spatial diversity by combining the data received from multiple antennas. The resulting classifier is demonstrated against AM, BPSK, 16QAM, 8PSK, BFSK, CDMA, and OFDM signals down to an SNR of -5 dB, in several multipath fading channels. In Section II, the underlying theory utilized by the proposed classifier is provided and the features of interest are developed. In Section III the classifier design is described, and simulation
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
results are given in Section IV. Conclusions drawn from the data are given in Section V. II. S IGNAL S TATISTIC D EVELOPMENT A. Signal Model Cyclic spectral analysis is based on the concept that communications signals are appropriately modeled as cyclostationary signals, rather than merely as stationary signals. This means that the signal statistics vary periodically in time. As a result the spectral components of the signal become temporally correlated. These correlations arise due to underlying periodicities in the signal, such as sampling, scanning, modulating, multiplexing and coding. The spectral correlation function (SCF) has been developed as a key feature to measure the amount of correlation between spectral components. The estimate of a signal’s SCF is given by [6][7]: N/2−1 α (f ) SX
= lim
lim
N →∞ N →∞
XT (r, f1 )XT∗ (r, f2 )
(1)
r=−N/2
N /2−1
XT (n, fk ) =
x(n − r)e−j2πfk (n−r)Ts
(2)
r=−N /2
where Ts is the sampling period, T = N Ts , α ≡ f1 − f2 , f ≡ (f1 + f2 )/2, fk ∈ 1/T · {−N /2, . . . , N /2 − 1}, and N and N are assumed to be even with N > N . Here it can be seen that the SCF can be interpreted as a formal correlation between the two time signals XT (n, f + α2 ) and XT (n, f − α2 ). Since the spectral components of white noise are uncorrelated, it does not contribute to the resulting image. It should be noted that this is the case even when the power spectrum of the noise exceeds the power of the signal of interest, indicating the robustness of cyclic spectral analysis to additive noise. The magnitude of the spectral coherence function (SOF) is then defined as the correlation coefficient between these signals: α SX (f ) (3) ∗ α α 1/2 0 0 ] f− [SX f + SX 2 2 Examples of the SOF of common signals are shown in Fig 1 and 2 below. As can been seen, the SOF of each modulation scheme produces highly unique images, which act as a spectral fingerprint for each scheme. These fingerprints can then be used to distinguish between different modulation schemes. For this reason, SOF images have been demonstrated to be highly effective in classifying various signals in AWGN channels [8][9]. However, wireless communications channels are rarely purely AWGN channels. Airborne signals are typically subject to multipath propagation as well as fading. The resulting SCF of the signal is given by [6]. α α α ∗ H f− Sx (f ) (4) SYα (f ) = H f + 2 2 α = CX
where it is subject to a potentially significant degree of corruption. However, by substituting (4) into (3) and forming the SOF, it can readily be seen that the effects due to channel distortion are removed and the resulting SOF of the received signal is equal to the SOF of the original undistorted signal [6]. This result predicts the SOF to be insensitive to multipath effects, as long as no frequency of interest in the signal is completely nullified by the channel distortion. Additionally, assuming a sufficiently slowly fading channel, the resulting SOF image will merely be a negligibly corrupted version of that obtained in a nondispersive channel. Examples of SCF and SOF estimates of a various signals in multipath channels are shown in Fig 3 and 4. When computing the SCF, N and N from (1) and (2) must be made finite, and an estimate of the SCF is obtained. These values limit the temporal and cyclic resolutions to Δt ≈ N Ts and Δf ≈ 1/T = 1/N Ts , respectively. Additionally, the cycle frequency resolution is limited to Δα = 1/Δt . However, to achieve statistical reliability, the time frequency resolution product must be made very large, ΔtΔf 1 , or equivalently Δf 1/Δα [10]. This results in a computationally infeasible number of cycle frequencies to be computed in search of only the few cyclic features actually present. A solution to this problem is to first estimate the cycle frequencies where features occur using an efficient temporal smoothing approach, such as the Strip Spectrum Correlation Algorithm (SSCA) outlined in [11]. After the cycle frequencies of interest are identified, the SCF can be estimated at those points through the equivalent method of frequency smoothing as outlined in the equation below [10]: N/2−1 α (f ) = lim SX
lim
r r XT (0, f1 + )XT∗ (0, f2 + ) (5) T T
N →∞ N →∞ r=−N/2
where now N > N and XT (n, fk ) is defined in (2). The resulting SOF is a three dimensional image. The amount of data is too large for any classifier to utilize in a reasonable amount of time, and must be reduced in some manner. In [8], the authors suggested using only the cycle frequency profile of the SOF. However, with only a modest gain in computational complexity, we propose using the spectral frequency profile as well. We define the cycle frequency profile as − → α ] α = maxf [CX
(6)
and the spectral frequency profile as → − α f = maxα [CX ]
(7)
to be the feature set used for classification. III. C LASSIFIER D ESIGN Due to its ease of implementation and ability to generalize to any carrier frequency and symbol rate, the proposed classifier employs a neural network based system to perform signal
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
classification. This is done with five neural networks each trained to classify a signal as either AM, BPSK, BFSK, CDMA, or one of OFDM, 16QAM, or 8PSK. In general, OFDM signals will contain unique cyclic features due caused by the symbol rate of each subcarrier. However, due to the fact that each subcarrier overlaps with adjacent subcarriers, the resulting SOF of the OFDM signal will be affected. Under the assumption that each subcarrier is modulated with independent data symbols, the cyclic features in the SOF for each subcarrier will be reduced by the adjacent subcarriers. As a result, the cycle frequency and spectral frequency profiles of the SOF estimated for OFDM signals appear negligibly different from those estimated for higher order QAM and PSK signals. Therefore, the neural networks are trained to group these signals together into a single classification. If a finer classification is needed for to discriminate between each of these subclassifications, it can be handed off to a second stage to compute higher order cyclic statistics of the signal [12][13][14]. The resulting classifier diagram is shown in Fig 5. Each network is composed of four neurons in their hidden layer and one neuron in their output layer, with each layer employing a hyperbolic tangent sigmoid transfer function. The inputs to the network are the concatenated cycle and frequency profiles of the SOF. Each neural network will output a value in the range of (-1,1) and the modulation scheme corresponding to the network with the highest output will be selected. The distance between the highest output and its closest competitor can be used as a pseudo-confidence parameter, with a larger distance corresponding to a higher degree of confidence in correct classification, and a smaller distance to a lower degree of confidence[8]. To take advantage of the presence of spatial diversity in fading channels, the effect of using an L branch antenna receiver array is also investigated, where the fading among the different antennas are assumed to be independent. Two methods of combining the data are implemented based on the estimated SNR of the signal for the given receiver. The first method is to implement a selection combining (SC) algorithm before computing the SOF of the received signal. This is done by estimating the SNR on each of the L branches, and retaining only the signal residing on the branch with the highest SNR. By assuming that each branch has identical noise powers, the branch with the highest SNR can be found by noting that it will also be the branch with the highest total power. This results in an extremely simple combining method that provides excellent performance gains with a very moderate increase in computational complexity. The classifier diagram modified for SC with multiple antennas is shown in Fig 6. Maximum ratio combining (MRC) is a powerful scheme used to combine signals from multiple antennas [12][13]. In MRC, the estimates of the SNR of the received signals are used to constructively combine the signals, while suppressing noise affects. However, due to the unknown relative phase
differences of the channels for each receiver, the signals cannot be weighted and added directly. Instead, a variation of MRC is proposed by adding weight values of the SOF profiles. This method computes the SOF profile of the signal received on each antenna. Each SOF is then weighted by the SNR of the signal that generated it. After the SOF from each antenna has been computed and weighted, all the SOF profiles are added together to generate a “combined” SOF profile. This new pseudo SOF profile is then passed to the neural networks to resume processing. The classifier diagram implementing the MRC variant is shown in Fig 7. IV. S IGNAL C LASSIFICATION R ESULTS Simulations were run with AM, BPSK, 16QAM, 8PSK, BFSK, CDMA, and OFDM signals. Both the proposed system as well as the benchmark system utilizing only the cycle frequency profile were tested for comparison purposes. For each signal simulated, the IF carrier frequency was uniformly distributed between .23 and .27 times the sampling rate, and the bandwidth of the signals were uniformly distributed between .16 and .24 times the sampling rate. The system was trained and tested with 4096 samples for its classification decision, corresponding to approximately 410 symbols for the digital modulation schemes. The proposed system was evaluated in a flat, 2-path, and 20-path Rayleigh fading channels with an SNR ranging from -5 dB to 10 dB. The 2-path and 20-path channels were modeled with independently varying, equal power paths. For all channels, each path was modeled with a coherence of 0.9 over 500 samples. In the 2-path channel, the delay between the first path and the second path was uniformly distributed between one and nineteen samples. In the 20-path channel, there was a delay of one sample between the arrival of each consecutive path. Figures 8 and 9 depict the performance of the proposed system and the benchmark system under a flat fading channel. As can be seen, the proposed system significantly outperforms the benchmark system in all cases. The proposed system experiences only a moderate performance degradation even without any combining methods implemented as compared to the benchmark system. The result when implementing either of the combiners yield a significant gain, even with the case of just L = 2 antennas. Figures 10 and 11 demonstrate the system performance in the 2-path channel. Here, the single antenna performance is more degradated than in the flat fading channel. However, each of the combining schemes give a substantial performance increase compared to the single antenna case. Again, the addition of a single antenna significantly enhances the classification performance. The system performance under the harsh 20-path channel is shown in Figures 12 and 13. Here, the use of the combining techniques is of the greatest benefit. Due to the relative increase in noise power when the signal is in a deep fade, the SOF can be significantly corrupted. However, the SOF is still subject to significant corruption if a there is a
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
particularly low channel response at a feature of interest. The performance of the MRC variant is substantially higher than the SC system in this case, where its ability to constructively add the cyclic features while suppressing noise and smoothing channel distortion enables it to provide the greatest benefit. V. C ONCLUSION In this paper we proposed a multi-antenna modulation recognition system utilizing the Spectral Coherence Function (SOF) of received signals in several fading channels. The SOF proved to be a robust feature to use for signal classification. The SOF’s insensitivity to the unknown statistics of received signals and its robustness to multipath fading channels make it an exceptional choice for modulation recognition. The system was further enhanced by using a selection combining (SC) scheme and a variation of maximum ratio combining (MRC) to exploit spatial diversity with multiple antennas. The SC scheme demonstrated considerable gains over the single antenna case with a minimal amount of computational requirements, while the MRC variant demonstrated exceptional results with only a moderate increase in computational requirements. ACKNOWLEDGMENT
[5] W. Su and J. Kosinski, “Comparison and modification of automated communication modulation recognition methods”, IEEE Milcom’02, October, 2002 [6] W. A. Gardner, Cyclostationarity in communications and signal processing, IEEE Press, New Jersey, 1993 [7] W. A. Gardner, W. A. Brown and C.-K. Chen, “Spectral correlation of modulated signals: part II - digital modulation”, IEEE Transactions on Communications, vol. 35, no. 6, pp. 595-601, June 1987 [8] A. Fehske, J. Gaeddert and J. H. Reed, “A new approach to signal classification using spectral correlation and neural networks”, 1st IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, pp. 144-150, Baltimore, 2005 [9] E. Like, V. Chakravarthy, and Z. Wu, “Reliable Modulation Classification at Low SNR Using Spectral Correlation,” IEEE Consumer Communications and Networking Conference, January 2007. [10] W. A. Gardner, “Measurement of spectral correlation”, IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 34, no. 5, October 1986 [11] R. S. Roberts, W. A. Brown and H. H. Loomis, “Computationally efficient algorithms for cyclic spectral analysis”, IEEE Signal Processing Magazine, April 1991 [12] O. Dobre, Y. Bar-Ness, and W. Su, “Higher Order Cyclic Cumulants for High Order Modulation Classification,” Proc. IEEE MILCOM’03, 2003 [13] P Marchard, J Lacoume, and C Martret, “Multiple Hypothesis Modulation Classification Based On Cyclid Cumlants of Different Orders,” Proc. ICASSP, 1998, pp.2157-2160. [14] O. Dobre, A. Abdi, Y. Bar-Ness, and W. Su, “Selection Combining for Modulation Recognition in Fading Channels,” IEEE Milcom’05, 2005 [15] A. Swami and B. Sadler, “Hierarchical digital modulation classification using cumulants”,IEEE Transactions on Communication, vol. 48, pp.416429, 2000.
This work is sponsored by the Air Force Research Laboratory via DAGSI program. R EFERENCES [1] J. Mitola, “Cognitive radio: an integrated agent architecture for software defined radio”, Ph.D. dissertation, KTH Royal Institute of Technology, Stockholm, Sweden, 2000. [2] The proceedings of the 1st IEEE International Symposium on New Frontiers in Dynamic Spectrum Access Networks, Baltimore, 2005 [3] O Dobre, A Abdi, Y Bar-Ness, and W. Su, “A Survey of Automatic Modulation Classification Techniques: Classical Approaches and new Trends,” IEEE Proceedings on Communications, 2006. [4] E. Azzouz and A. Nandi, “Automatic modulation recognition of communication signals”, Kluwer Academic Publishers, 1996
Fig. 1.
BPSK in AWGN Channel, 5 dB SNR
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
Fig. 5. Fig. 2.
2FSK in AWGN Channel, 5 dB SNR
Fig. 6. Fig. 3.
System Diagram with Selection Combining
BPSK in Multipath Fading Channel, 5 dB SNR
Fig. 7. Fig. 4.
System Diagram
System Diagram with MRC Variant
2FSK in Multipath Fading Channel, 5 dB SNR
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
Fig. 8.
SC System Performance in Flat Fading
Fig. 9.
MRC System Performance in Flat Fading
Fig. 10.
SC System Performance in 2 Path Fading
Fig. 11.
Fig. 12.
Fig. 13.
MRC System Performance in 2 Path Fading
SC System Performance in Multi-Path Fading
MRC System Performance in Multi-Path Fading
US Government work not protected by US Copyright This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE "GLOBECOM" 2008 proceedings.
