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- Open Access
Automatic modulation classification of digital modulations in presence of HF noise
- Hazza Alharbi^{3}Email author,
- Shoaib Mobien^{2},
- Saleh Alshebeili^{1, 2, 3} and
- Fahd Alturki^{3}
https://doi.org/10.1186/1687-6180-2012-238
© Alharbi et al.; licensee Springer. 2012
Received: 13 March 2012
Accepted: 18 October 2012
Published: 14 November 2012
Abstract
Designing an automatic modulation classifier (AMC) for high frequency (HF) band is a research challenge. This is due to the recent observation that noise distribution in HF band is changing over time. Existing AMCs are often designed for one type of noise distribution, e.g., additive white Gaussian noise. This means their performance is severely compromised in the presence of HF noise. Therefore, an AMC capable of mitigating the time-varying nature of HF noise is required. This article presents a robust AMC method for the classification of FSK, PSK, OQPSK, QAM, and amplitude-phase shift keying modulations in presence of HF noise using feature-based methods. Here, extracted features are insensitive to symbol synchronization and carrier frequency and phase offsets. The proposed AMC method is simple to implement as it uses decision-tree approach with pre-computed thresholds for signal classification. In addition, it is capable to classify type and order of modulation in both Gaussian and non-Gaussian environments.
Keywords
- Automatic modulation classification
- Feature-based classification
- Bi-kappa noise
- HF communications
Introduction
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[3].
Till now, designing AMC algorithms in presence of non-Gaussian noise has not received sufficient attention. The reason is that Gaussianity assumption often matches the observed statistical characteristics of channel noise. However, for HF channel the case is different as the noise is better described by a model fluctuating between G and BK distributions. Therefore, this new noise model must be considered during the development of an AMC for HF band. Existing AMC methods (that assume G noise only) 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 then using maximum likelihood ratio test for decision-making [5]. In FB methods, features are first extracted from the received signal and then applied to a classifier in order to recognize the modulation type and possibly its order.
Attempts to classify signals in HF noise have been reported in the literature. In [24–26], entropic distance feature has been exploited for a classification of constant envelope digital signals, such as PSK and FSK modulations. In[26], this feature has been further explored for signals propagating via multiple ionospheric modes with co-channel interference and non-Gaussian noise for different types of PSK and FSK modulations. The basic idea of entropic distance is to compress the received signal using a compression algorithm and use the compression ratio as entropy measure of the received signal of an unknown modulation type. Therefore, normalized entropic distance can be used to classify different modulation schemes. It is also demonstrated in[24, 26] that entropic distance is a useful feature in separating narrow band as well as wide band FSK modulations. Its robustness against parameters variations such as quantization resolution, signal length, and compression algorithm is also verified.
Motivated by the observations noted in [4], effect of BK distribution on AMC design has been investigated in [27, 28]. The results in [27] show that the performance of an AMC algorithm designed for G noise model significantly deteriorates in presence of BK noise, specifically at low signal-to-noise ratio (SNR). In addition, the investigation in [28] shows that it is possible to design features that are reasonably robust in presence of HF noise.
The objective in this article is to develop a new decision tree-based AMC algorithm well-suited for the classification of most popular single carrier modulations used in HF communication systems, i.e., 2FSK, 4FSK, 8FSK, 2PSK, 4PSK, 8PSK, 16QAM, 32QAM, 64QAM, 16 amplitude-phase shift keying (APSK), and 32APSK [1]. APSK is a digital modulation scheme that can be considered as a class of QAM in which symbols are always placed on equidistant concentric circles in the constellation diagram. This modulation scheme is known to have fewer problems with nonlinear amplifiers due to its constellation shape[29].
To achieve the above objective, the following features are considered: the maximum value of power spectral density (PSD) of normalized-centered instantaneous amplitude, the maximum value of magnitude of discrete fourier transform (DFT) of k th power of received signal (Γ_{ k }), and number of points in pre-defined ranges of partitioned signal constellation magnitude. The first feature is well known in the literature[7–9]. The second feature with k = 2, 4 has previously been proposed in [30] for blind estimation of frequency offset of PSK and QAM signals and in[31] for the classification of MPSK modulations. The third feature is new; it is based on counting the number of points of the magnitude of received signal constellation in a certain predefined range. This feature has a desirable property in that its value remains almost constant even when the noise model gets changed from Gaussian distribution to BK distribution. Another important property of this feature is its low computational cost, as it only requires addition and comparison operations. It is worth noting that all three features are insensitive to symbol synchronization and carrier frequency and phase offsets.
The rest of the article is organized as follows. A unified mathematical model for all the modulation schemes under consideration is presented in Section 2. The proposed AMC and its computational complexity are detailed out in Section 3. Simulation results are presented and discussed in Section 4. Finally, conclusions are drawn in Section 5.
Signal model
Constellation points of digital modulation schemes
Modulation | Constellation point |
---|---|
MPSK | C_{ i } ∈ exp(−j 2πm/M), m = 0, 1,., M − 1 |
MQAM | ${C}_{i}={a}_{K}+j{b}_{k},{a}_{k},{b}_{k}\phantom{\rule{0.5em}{0ex}}\in \left\{2m-1-\sqrt{M}\right\},\phantom{\rule{1em}{0ex}}m=1,2,.,\sqrt{M}$ |
OQPSK | C_{ i } ∈ 4PSK staggered to allow ±π/2 change between symbols. |
MFSK | ${C}_{i}\phantom{\rule{1em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}cos\phantom{\rule{0.5em}{0ex}}\left(\frac{2\pi {f}_{m}}{{f}_{s}}n\right)+j\phantom{\rule{0.5em}{0ex}}sin\left(\frac{2\pi {f}_{m}}{{f}_{s}}\right);\cdot m\phantom{\rule{0.5em}{0ex}}\in \left\{0,\dots ,M-1\right\},n=0,1,\dots ,{N}_{f}-1$ |
MAPSK | ${C}_{i}\phantom{\rule{0.5em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}rexp\left(-\frac{j2\pi m}{{M}_{s}}\right),where\left\{\begin{array}{l}r\phantom{\rule{0.5em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}\left[1,2\right],\phantom{\rule{1.5em}{0ex}}{M}_{s}\phantom{\rule{0.5em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}\left[4,12\right],\phantom{\rule{1em}{0ex}}m\phantom{\rule{0.5em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}[0,\dots ,11],\phantom{\rule{0.5em}{0ex}}if\phantom{\rule{0.5em}{0ex}}M=16\\ r\phantom{\rule{0.5em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}\left[1,2,3\right],\phantom{\rule{1em}{0ex}}{M}_{s}\phantom{\rule{0.5em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}\left[4,12,16\right],\phantom{\rule{1em}{0ex}}m\phantom{\rule{0.5em}{0ex}}\in \phantom{\rule{0.5em}{0ex}}\left[0,\dots ,15\right],\phantom{\rule{0.5em}{0ex}}if\phantom{\rule{0.5em}{0ex}}M=32\end{array}\phantom{\rule{6.5em}{0ex}}\right\}$ |
where N_{0} is the noise power and SNR is in dB.
The proposed AMC
The proposed AMC features
Simulation parameters
Parameter | Value |
---|---|
Carrier frequency | f_{c}= 24 kHZ |
Symbol rate | r_{s}= 2400 Hz |
Sampling rate | f_{s}= 19.2 kHz |
Number of symbols | N = 512 |
Total number of samples | N_{s}= 4096 |
The maximum value of PSD of normalized-centered instantaneous amplitude
The maximum value of DFT magnitude of the kth power of analytic form of received signal
Number of points of partitioned magnitude of constellation diagram
QAM/APSK modulation symbols are defined in terms of phase and amplitude variations and are represented in the form of a constellation diagram. This diagram is extracted from the analytic form of the IF signal after down conversion to the baseband. Many features exist in literature that exploit different aspects of the constellation diagram for classification of 16, 32, and 64QAM modulations[38–42]. In this article, a new feature based on partitioning magnitude of constellation diagram is proposed. This feature makes use of the observation that the noise-free normalized constellation points of PSK and FSK modulations are on the unit circle, whereas the normalized constellation points of QAM and APSK modulations may lie on, inside, and/or outside the unit circle. Therefore, this feature is useful in separating near constant amplitude modulations from amplitude varying modulations, and also in determining the order of amplitude varying modulations.
Regions of partitioned magnitude of constellation diagram
Region | Range | |
---|---|---|
Starting point | Ending point | |
R _{1} | 0 | 0.2 |
R _{2} | 0.2 | 0.3 |
R _{3} | 0.3 | 0.4 |
R _{4} | 0.4 | 0.6 |
R _{5} | 0.6 | 0.8 |
R _{6} | 1.00 | 1.25 |
R _{7} | 1.6 | 1.7 |
Structure of the AMC algorithm
Computational complexity
Computational complexity of the proposed algorithm
Feature | Number of operations | ||
---|---|---|---|
Complex multiplication | Complex addition | Comparison | |
K _{1} | 0 | N_{s} – 1 | 2N_{s} + 1 |
K _{2} | 0 | N_{s} – 1 | 3N_{s} + 1 |
K _{3} | 0 | N_{s} – 1 | 2N_{s} + 1 |
K _{4} | 0 | N_{s} – 1 | 4N_{s} + 1 |
K _{max} | N_{s}/2log(N_{s}) + N_{s} + 1 | N_{s} log(N_{s}) | N _{s} |
Γ_{1} | N_{s}/2log(N_{s}) + N_{s} + 1 | N_{s} log(N_{s}) | N _{s} |
Γ_{2} | N_{s}/2log(N_{s}) + 2N_{s} + 1 | N_{s} log(N_{s}) | N _{s} |
Γ_{4} | N_{s}/2log(N_{s}) + 4N_{s} + 1 | N_{s} log(N_{s}) | N _{s} |
Results
This section presents results that show the overall performance of the proposed AMC algorithm in the presence of either G or BK noise for classifying the type and order of a particular modulation. Features described in Section 3 are extracted from the signal under consideration and utilized in the proposed AMC scheme according to Figure14. Simulation results are presented at different values of SNR using parameters’ values given in Table2. The performance is measured in terms of probability of correct classification (P_{cc}) averaged over 100 independent trials.
Conclusions
In this article, a new features-based decision tree AMC algorithm is developed for the classification of most popular single carrier modulations used in HF communications systems, i.e., 2FSK, 4FSK, 8FSK, 2PSK, 4PSK, 8PSK, 16QAM, 32QAM, 64QAM, 16APSK, and 32APSK. Towards this objective, three features are employed that include PSD and DFT of k th power of received signal. A new constellation-based feature for the classification of QAM and APSK signals is also proposed.
In practice, the received signal is often corrupted by HF noise whose statistical characteristics have PDF best described by a model that fluctuates between G and BK distributions; in addition the received signal may have frequency, phase, and symbol synchronization errors. Extensive simulations results have shown that the proposed features are insensitive to noise model variation or synchronization errors.
The proposed AMC method has an advantage of being simple to implement as it uses decision-tree with pre-computed thresholds for signal classification. In addition, it is capable to classify type and order of modulation in band-limited HF noise environment at relatively low SNR.
Declarations
Acknowledgments
The authors would like to thank the reviewers for their time and effort spent in carefully reviewing the manuscript, and for their valuable comments that have greatly contributed to the enhancement of article’s quality. This study was supported by Grant no. 08-ELE 263–2 from the unit of Science and Technology at King Saud University.
Authors’ Affiliations
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