Classification of Digitally Modulated Signals in Presence of Non-Gaussian HF Noise Alharbi Hazza1, Mobien Shoaib2, Alshebeili Saleh1,2, Alturki Fahd1 1
Electrical Engineering Department Prince Sultan Advanced Technologies Research Institute/STC-Chair College of Engineering, King Saud University Riyadh, Saudi Arabia
2
[email protected] [email protected] {dsaleh, falturki}@ksu.edu.sa Abstract— Automatic Modulation Classification (AMC) is the process of classifying the received signals without prior information. This process is an intermediate step between signal detection and demodulations. It serves both military and civilian applications, such as spectrum monitoring and general-purpose universal demodulators. In this paper, we propose a Decision Tree (DT) algorithm to classify a wide class of the single carrier modulations used in High Frequency (HF) band. Specifically, the proposed algorithm addresses the classification of 2FSK, 4FSK, 8FSK, 2PSK, 4PSK, 8PSK, 16QAM, 32QAM, 64QAM, and OQPSK using three features: Temporal Time Domain (TTD), spectral peaks, and number of amplitude levels. Almost all previous research work in AMC assumes the noise model to be Additive White Gaussian Noise (AWGN). Although this assumption is valid in many communications environments, recent literatures show that the HF noise is fluctuating between AWG and Bi-kappa distributions. This work, first, considers the effect of noise model on the previously mentioned features, and then presents simulation results showing the performance of proposed algorithm in such an environment.
r(t) Signal Detection
Modulation Classification
Automatic modulation classification system
s(t) Mdemodulators
Figure 1. The AMC based receiver architecture.
Fig. 1 shows the classification task in a smart radio. The task of the signal detection block is to identify signal transmission. The FB AMC contains a feature extractor followed by a classifier. The classifier can be based on fixed threshold as in DT methods, or based on Pattern Recognition (PR) methods as in neural networks (NN) and Support Vector Machines (SVM) [3, 4]. Although the PR techniques give high classification rate; see for example [3], they suffer from high computational complexity compared to DT techniques. On the other hand, DT methods give acceptable performance with low computational cost. Different features such as wavelet coefficients [11, 12], instantaneous values of amplitude, frequency and phase [13, 14], and Higher-Order Statistics (HOS) [15-17] have been considered in the development of DT algorithms. Some proposed algorithms make use of more than one feature to enhance the classification performance [18, 19]. However, to the best of our knowledge, none of the available AMC methods addressed the modulation set considered in this work, nor did they investigate the effect of non-Gaussian HF noise on classification performance. In this paper, we present a novel approach to classify ten modulations commonly used in HF band, i.e., 2FSK, 4FSK, 8FSK, 2PSK, 4PSK, 8PSK, 16QAM, 32QAM, 64QAM, and OQPSK [10]. The proposed algorithm is based on five features. Three features are related to the instantaneous values of phase, amplitude, and Power Spectral Density (PSD) [7]. The forth feature is the number of spectral peaks calculated from the impulse response of estimated auto-regressive model coefficients [8]. And the final feature is the number of amplitude levels in uniformly quantized signal. We also investigate the behavior of the features in presence of AWGN
Keywords- Automatic modulation classification; temporal time domain features; spectral peaks estmation; uniform quintization; bi-kappa noise; HF band.
I.
Feature Extraction
INTRODUCTION
AMC is the process of identifying modulation type of a detected signal without prior information. This technique has both military and civilian applications, and is currently an important research subject in the design of cognitive radios. AMC is a very complex task especially in a non co-operative environment as in HF communications, where transmission is affected by atmospheric conditions and other transmission interferences [1]. AMC methods are grouped into two categories: Likelihood Based (LB) and Feature Based (FB) methods. LB methods have two steps: calculating the likelihood function of the received signal for all candidate modulations, and using Maximum Likelihood Ratio Test (MLRT) for decision-making. In FB methods, features are extracted from the received signal and used with classification algorithm for decision making. Most of the recent literature uses the FB methods due to their low processing complexity and high performance. More details about AMC methods with a comprehensive literature review are presented in [2]. This work was supported by a grant (No. 08-ELE263-2) from The Unit of Science and Technology at King Saud University
978-1-4244-6317-6/10/$26.00 © 2010 IEEE
815
ISWCS 2010
and Bi-kappa noise [5, 6], where we identify the features that are not affected by the noise model. The signal and channel models are presented in Sections II and III respectively. Section IV presents the five features in more details, while in Section V the proposed DT AMC algorithm is developed. Section VI shows the performance of proposed algorithm using simulation results. Finally, Section V presents concluding remarks and suggestions for possible future research directions. II.
SIGNALS MODEL
The general form of received signal encompassing all the modulation schemes under consideration is given by: r t
Re C t e
(1)
n t
where is the complex envelope of modulated signal, n(t) is band limited noise, is the carrier frequency, and denotes the real part. The complex envelope is characterized by the constellation points , signal power E, and pulse shaping function p(t). For symbols with periodicity , the general form of complex envelope can be expressed as: √E ∑N C p t
C t
kT
Figure 2. Histograms of Bi-kappa noise and AWGN for unity standard deviation.
A more realistic noise model can be constructed by passing the bi-kappa noise through a band-limiting band-pass transmit filter. The bandwidth of this filter is set to 8 where, is the symbol rate. This filter is practically used to minimize the transmission bandwidth. Fig. 2 shows the histogram of the bikappa and AWG random variables after the filtering; for fair comparison the standard deviation of both distributions is set to unity. The figure shows that the bi-Kappa distribution approaches the AWG distribution when the shaping parameter is increased. On contrary a decrease in shaping parameter results in deviation of the Bi-kappa distribution from AWG distribution. In this research, the worst case scenario is considered, i.e., the parameters of Bi-Kappa distribution are set to, σ=20, k=1.
(2)
The constellation points of digital modulation of order M considered in this paper are formulated in Table 1; see [9]. TABLE I. CONSTELLATION POINTS OF SOME DIGITAL MODULATIONS.
Modulation
Constellation point
M-PSK M-QAM QPSK
Ck∈e-j[2π(m)/M + π/M]; m ∈ {0,1,2,3, …, M-1} Ck = ak + jbk; ak, bk ∈{2m -1 – M1/2} C exp , C; m ∈ {0,1,2,3} 1,3,5,7 a , bk in QPSK are staggered to allow ±π/2 change between each symbol. Ck=cos (2πfmt)+jsin (2πfmt); fm∈{0, …, M-1}
OQPSK MFSK
III.
IV.
This section gives the general formulas and descriptions of the features used in designing the proposed AMC. Moreover, it investigates the effect of noise models on TTD features. The effect of noise model on spectral peaks and number of signal levels is also discussed.
NOISE MODELS
Noise model assumed in most of the research related to AMC is AWGN. This research focuses on AMC in HF band, where the AWGN assumption no longer remains valid for all transmission times [5,6]. Instead the noise varies between AWGN and Bi-kappa distributions. The Bi-Kappa distribution is characterized by the following probability distribution function: 1 1√ ,
1
1
1 1√
1
A. Maximum value of the spectral power density of the normalized-centered instantaneous amplitude Maximum value of the power spectral density of the normalized - centered instantaneous amplitude is given by:
0 0
1√
FEATURES AND EFFECT OF NOISE MODEL
γ
max|DFT N
i |
(4) where Ns is the number of samples, , is the 1 m absolute value of the analytic form of the received signal, and is its mean value.
(3)
0
where σ and k are the shaping parameter and tuning factor respectively. Practical values of these parameters are σ=46, k=1.1, and σ=20, k=1 [5].
816
B. Standard deviation of the absolute value of the centered, non-linear component of the instantaneous phase This feature is concerned with signal phase characteristics, and is given by: 1
|
(5)
|
OQPSK QPSK
40 γmax in Bi-Kappa (dB)
1
50
32QAM 64QAM
30
16QAM 8FSK
20
4FSK 10
2FSK 8PSK
0
where is the centered non-linear components of the instantaneous phase, is the threshold value of the non weak signal, L is the number of samples in .
-10 0
15
20 SNR
25
30
35
40
computed in the presence of Bi-kappa (σ=20 , k=1 ) noise
OQPSK QPSK
0.8
32QAM 64QAM
(6)
|
10
1
σap in AWGN
|
2PSK 5
Figure 4.
C. Standard deviation of the absolute value of the normalized-centered instantaneous amplitude This feature is used to classify QAM signals against other modulations at a specific value of SNR. The following expression is used to calculate this feature. 1
4PSK
0.6
16QAM 8FSK 4FSK
0.4
2FSK 8PSK
0.2
4PSK
D. Effect of noise models on TDD features Figs. 3-8 show the values of the TDD features in presence of both noise models, where SNR ranges from -5 to 30 dB. Note that each modulation sub-group has different color. Each plot is obtained by averaging over 50 simulation runs. It can be seen that the parameters are highly dependent on the noise model at low SNR values, whereas, at higher SNR, there is no significant difference.
0 0
20 SNR
25
30
35
computed in the presence of AWGN
QPSK 0.8
32QAM
σap in Bi-Kappa
64QAM 0.6
16QAM 8FSK 4FSK
0.4
2FSK 8PSK
0.2
4PSK 0 0
2PSK 5
Figure 6.
10
15
20 SNR
25
30
35
0.7
OQPSK QPSK
0.6
32QAM
64QAM
0.5
16QAM 8FSK
σaa in AWGN
20
4FSK 10
2FSK 8PSK
0
4PSK
Figure 3.
10
15
20 SNR
25
30
35
64QAM 16QAM
0.4
8FSK 0.3
4FSK 2FSK
0.2
8PSK
2PSK 5
40
computed in the presence of Bi-kappa (σ=20 , k=1 ) noise.
QPSK
30
40
OQPSK
32QAM σap in AWGN (dB)
15
1
OQPSK
40
-10 0
10
Figure 5.
E. Number of peaks in frequency response of prediction coefficients Spectral peaks of the prediction coefficients are an efficient statistical feature for FSK modulation classification. The forward prediction coefficients of the received signal are computed and then the number of peaks is estimated from the normalized frequency response of the coefficients using a fixed pre-defined threshold. The number of peaks corresponds to the order of the FSK signal. 50
2PSK 5
0.1
4PSK
40
0 0
2PSK 5
computed in the presence of AWGN Figure 7.
817
10
15
20 SNR
25
30
35
computed in the presence of AWGN
40
0.7
Finally, OPSK is separated from MFSK signals using . And, FSK modulations are separated using and threshold spectral peak estimation. The values of thresholds are given in Table II, and are selected by observing the values of the features at different SNR values in presence of both AWGN and Bi-Kappa noise. The Figs. 3-8 show that the feature affected most by the change in noise model is , therefore, the threshold is selected so that it works for both noise models. We find that =30 is an optimum value.
OQPSK
0.6
QPSK 32QAM
σaa in Bi-Kappa
0.5
64QAM 16QAM
0.4
8FSK 0.3
4FSK 2FSK
0.2
8PSK 0.1 0 0
Figure 8.
4PSK 2PSK 5
10
15
20 SNR
25
30
35
40
computed in the presence of Bi-kappa (σ=20 , k=1 ) noise.
F. Number of levels of quantized instantaneous absolute amplitude The absolute value of the analytic form of QAM signal cannot distinguish between all the constellation points having the same radius. As a result, there is distinct number of radii corresponding to each MQAM, e.g., the number of radii in 16QAM, 32QAM, and 64QAM are 3, 5, and 9 respectively. In order to obtain this number, the absolute value of QAM signal is normalized and quantized into 100 levels. The average over a segment gives the required level value, where each segment length is defined as ⁄ . This procedure of QAM classification can also be used for classification of ASK modulations.
Figure 9. Tree based classifier.
VI.
To evaluate the performance of proposed AMC method, all the modulations schemes under test were generated and classified in presence of band-limited AWGN and Bi-kappa noise, where the bandwidth of the band-limiting filter is 8 [7]. The SNR is adjusted by multiplying the output noise by the following factor:
G. Effect of noise models The last two parameters presented in subsections E and F are insensitive to the noise model. The estimate of the number of peaks remains same for both noise models at -5dB SNR, similarly, the number of levels of quantization do not overlap at low SNR values for both noise models. Therefore they are very useful for developing AMC algorithms. V.
SIMULATION RESULTS
R sn =
TREE-BASED CLASSIFIER
⎞ E ⎛ − SNR ⎜ 10 20 ⎟ No ⎝ ⎠
(7)
where E, N , SNR are the signal power, noise power, and desired SNR respectively. All constellation points are normalized such that the absolute value of highest constellation point is 1. The simulation parameters are given in Table III. The classification rate is computed by averaging over 500 realizations and is illustrated in Fig. 10. To show performance improvement the classification rate of two DT AMCs are compared. The first AMC uses thresholds based only on features computed under the assumption of AWGN. Whereas,
In the proposed tree-based classifier, the parameters presented in Section IV are used for modulation classification. The proposed approach identifies the sub-groups within the set of modulation schemes under consideration before classifying the individual modulations. There are three sub-groups considered in this paper, i.e., MPSK, MFSK and MQAM. OPSK is placed in the MFSK sub-group. The main idea in treebased classifier is to compute the features and compare the values with pre-computed thresholds, in order to identify the sub-groups and finally the exact modulation type. The tree-based classifier is illustrated in Fig. 9. The first step separates MFSK sub-group from MPSK and MQAM subgroups, by comparing the feature against threshold . The MPSK subgroup is then separated from MQAM sub-group based on feature using the threshold . Each modulation against in MPSK is then identified using feature and . The quantization level estimation thresholds: procedure described in Section IV.F is used to classify the modulations in MQAM sub-group.
TABLE II. AMC ALGORITHM THRESHOLDS Component
Threshold for number of peaks calculations
818
Value 26 30 0.34 0.78 0.87 -5 dB
REFERENCES
TABLE III. SIMULATION PARAMETERS Parameter Carrier Frequency
= 2400 Hz
Sampling rate
= 153.6 KHz
of
[2]
= 24 kHz
Symbol rate
No.
[1]
Value
symbols
required
for
[3]
256 [4]
classification Total number of samples
16384
Frequency separation
Δf =
[5]
the second considers threshold values selected for both noise models under consideration. Fortunately, the threshold values for both algorithms are the same except which is modified for the two cases and shown in Table II. Fig. 10, shows that the first AMC performs well for AWG noise model (~90% at 6dB SNR), however, the classification rate deteriorates in Bi-Kappa noise (~85% at 6dB SNR). The second AMC on the other hand shows an average classification rate of more than 90% at SNR = 6 dB for both AWG and Bi-kappa noise models, with an improvement of 8% in the classification rate over the first AMC when Bi-Kappa noise model is used.
[6]
[7] [8]
[9] [10] [11]
[12]
[13]
[14] Figure 10. Average classification rate of the propposed algorithm.
[15]
VII. CONCLUSIONS [16]
In this paper, we proposed a novel AMC algorithm for the classifications of most commonly used single carrier digital modulations in the HF band. Furthermore, we investigated the effect of HF noise models on features extraction and classification rate. The simulation results show the effect of noise models on the three temporal time domain features. The shows greater deviation in presence of Bi-Kappa feature γ noise. Consequently, the performance of DT algorithm deteriorates to less than 85% at 6 dB SNR. The threshold is in therefore re-selected by observing the values of feature γ presence of both noise models. As a result the classification rate of the proposed algorithm improves to more than 90% at SNR=6 dB in the presence of either AWGN or Bi-kappa noise. This performance has been achieved by adjusting the threshold based on the results of Section IV. ts of
[17]
[18]
[19]
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