Classical methods use statistical-moments to determine the type of modulation in question. This essentially correct approach for discerning amplitude modulation (AM) from frequency modulation (FM) fails for more demanding cases such as AM vs. AM-LSB (lower side-band rejection) - radio signals being richer in information than statistical moments. Parameters with good discriminating power were selected in a data conditioning phase and binary deep-learning classifiers were trained for AM-LSB vs. AM-USB, FM vs. AM, AM vs. AM-LSB, etc. The parameters were formed as features, from wave reconstruction primary parameters: rolling pedestal, amplitude, frequency and phase. Very encouraging results were obtained for AM-LSB vs. AM-USB with stochastic training, showing that this particularly difficult case (inaccessible with stochastic moments) is well solvable with multi-layer perceptron (MLP) neuromorphic software.
Signals Intell (SIGINT) is a branch of the military and civilian intell services monitoring
(mainly) the RF communications. Automated Modulation Classifiers (AMC’s) are of 2 types:
likelihood classifiers (LC’s) [
Before attempting to constitute any particular feature quantities, it is important to foresee how the procedure would be immune to noise and jamming. The best approach is to base the features on physially understood quantities, thus the reconstruction of the fundamental wave: where f, p, A are slowly varying
Pedestal reconstruction perform the wave average between ti and tf: functions of time. - for this the simplest method is to where sinc(x) = sin(x) / x and Ae = Asinc(f) – with the duration of one sample. Since the sin term does not vanish, we try to zero the sinc term. For tf-ti = n, the n m/f, condition must be met, with m N. Basically m is scanned until the relation gives a close-enough integer (in our case n = 11) and then p = u.
Amplitude reconstruction – following the same idea, we designed a similar formula for the amplitude: Through a coincidence the “magic number” n for double the frequency is very similar to n = 11 from pedestal determination and we can use the same loop for the averages.
Frequency reconstruction - similar to amplitude, we determined frequency with an OII dipolar moment, which basically differentiates the sine wave: where k indexes u(t-k). We used k=1.
Phase reconstruction – similar to frequency we determined phase with an OII dipolar moment taking reference to a fixed phase sine: where for = 0 the error may be significant, however phase is not absolute, rather relative to the previous sample’s phase, as such such errors tend to systematically cancel out.
Feature creation – having pedestal, amplitude, frequency and phase for each sample, we accumulated these quantities in histograms looking for discriminating features. We devised similar other parameters (in number of 12) to capture the differences between various modulation types. As an example, the figure above shows the distribution of the full width at ¼ maximum for the phase distribution histograms - with red, again, AM modulation and with blue, FM modulation.
Using this set of 12 parameters we trained (with BFGS – Broyden-Fletcher-Goldfarb-Shanno algorithm for AM vs. FM, or stochastic for AM-LSB vs. AM-USB) deep learning neural networks for binary sets of modulations.
The results were excellent for instance AM vs. FM, and the most difficult case (and notable result too) was AM-LSB vs. AM-USB which are essentially the same type of modulation, and is known to be practically impossible to discern with the classical statistical-moments method. The figure below shows this result.
Concluding, our deep learning neuromorphic software approach to AMC’s confirms the promising results of a pleiad of other such approaches. What distinguishes our approach is a 2 step feature creation method. The first step reconstructs the basic signal parameters, pedestal, amplitude, frequency and phase and creates histograms with 1000 such samples (each n=11, “magic number” samples long). The second step analyses these histograms and draws parameters out of them. We found these parameters to be much better performing than the primary raw parameters.
As showcase for this conclusion stands the difficult case of discriminating AM-LSB vs. AMUSB modulation, which flags the correct modulation in 95% of cases. [4] J. Liu, Q. Luo, A novel modulation classification algorithm based on daubechies5 wavelet and fractional fourier transform in cognitive radio, 14th IEEE ICCT Communication Technology Conference, document/6511199, pp. 115–120, (2012); Y. Lv, Y. Liu, F. Liu, J. Gao, K. Liu, G. Xie, Automatic modulation recognition of digital signals using CWT based on optimal scales, IEEE Conference On Computer and Information Technology, document/6984692, pp. 430–434, (2014). [5] D. Das, A. Anand, P. K. Bora, R. Bhattacharjee, Cumulant based automatic modulation classification of QPSK, OQPSK, π/4-QPSK and 8-PSK in MIMO environment, IEEE Conference On Signal Processing and Communications, document/7439996, pp. 1–5, (2016); A. Hazza, M. Shoaib, A. Saleh, A. Fahd, Robustness of digitally modulated signal features against variation in HF noise model, EURASIP J. Wirel. Commun. Netw. 2011, 24, (2011).