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This paper deals with modulation classification under the alpha-stable noise condition. Our goal is to discriminate orthogonal frequency division multiplexing (OFDM) modulation type from single carrier linear digital (SCLD) modulations in this scenario. Based on the new results concerning the generalized cyclostationarity of these signals in alpha-stable noise which are presented in this paper, we construct new modulation classification features without any priori information of carrier frequency and timing offset of the received signals, and use support vector machine (SVM) as classifier to discriminate OFDM from SCLD. Simulation results show that the recognition accuracy of the proposed algorithm can be up to 95% when the mix signal to noise ratio (MSNR) is up to ?1 dB.

With wide application of OFDM, the recognition of OFDM signal has become a hot issue in various fields of applications among cognitive radio and military applications. Algorithms for the recognition of OFDM versus SCLD signals in AWGN scenario have been reported in [

The rest of the paper is organized as follows. The SCLD and OFDM signal models is presented in Sections 2, the proposed recognition algorithm is introduced in Section 3 and simulation results are discussed in Section 4. Finally, our conclusions are presented in Section 5.

The received signal can be written as,

where

If the modulation type of the transmitted signal is OFDM,

where

If the modulation type of the transmitted signal is SCLD,

where

The alpha-stable noise

In (4),

and

where

where

Alpha-stable noise does not have second-order and higher order statistics so that many traditional OFDM identification algorithms will be invalid. To solve the problem that traditional second-order cyclic statistics significantly degenerate in the alpha-stable noise, the concept of generalized second-order cyclic statistics was proposed in [

where

The autocorrelation function of signal

When MSNR is higher enough,

where

of

where

where

for operator, which maintain the phase of signal,

where

where

analytical expressions for the generalized second-order cyclic statistics at

As one can notice, when processing the received signal

Similarly, for the SCLD signal, we obtain

where

Based on the above results on signal the generalized cyclic statistics, here we develop a novel algorithm for the recognition of OFDM and SCLD signals in alpha-stable noise.

Under the assumption of no aliasing, for the discrete-time signal

sampling rate

Then, for the OFDM signal,

where

prefix length. From (17) one can see that

where

Similarly, for the SCLD signal, we obtain

where

and the data is assumed to be independent and identically distributed.

When comparing (18) and (19), one can easily notice the additional factor

The estimate of the generalized cyclic statistics

where

with covariance estimators are respectively given by,

and

where

According to the above analysis, the steps of recognizing OFDM against SCLD modulations may be obtained as follows:

Step 1: The magnitude of the generalized second-order cyclic statistics

Step 2: The modulation classification features

Step 3: The modulation type is decided. Classify the test signal by employing the SVM classifier defined in the training procedure.

A. Simulation setup

For the SCLD signals, we consider a pool of QPSK and 16-QAM. With the OFDM signals, the subcarriers are modulated using QPSK or 16-QAM. Unless otherwise mentioned, for the OFDM signal, the number of subcarriers is set to 64, the useful time period of the OFDM symbol is set to 0.0128 s and the cyclic prefix period is set to 0.0032s. In addition, frequency offset is set to 1 kHz and 2 kHz for SCLD and OFDM signals, and

B. Generalized second-order cyclic statistics magnitude estimates for the OFDM and SCLD signals

The estimated magnitude of the generalized cyclic statistics of OFDM and SCLD is plotted. For SαS noise, MSNR = 10 dB and

When comparing results presented in

the magnitude of the generalized cyclic statistics of the OFDM signal (at

C. Performance of proposed recognition algorithm

Without loss of generality, set

In

method is almost 100% at 0 dB. This simulation results for the algorithm performance confirm its effectiveness in alpha- stable distribution noise.

D. Effect of the a value on algorithm performance

In this experiment, set MSNR = 0 dB, a changes with the step 0.1 in the interval [0.1, 1.9]. The observation interval is set to 0.32 s, and 200 tests for each a value. The simulation results are shown in

This paper proposes a novel modulation identification algorithm for OFDM and SCLD in alpha-stable distributed noise. The generalized second-order cyclic statistics can be exploited for the recognition of OFDM against SCLD signals. The proposed recognition algorithm eliminates the need for preprocessing tasks, such as symbol timing estimation, carrier and waveform recovery, and signal and noise power estimation. Simulation results show that the algorithm have good estimation performance and high robustness.

Zhang, J.L., Wang, B. and Wang, Y. (2017) New Blind Recognition Method of SCLD and OFDM in Alpha-Stable Noise. Int. J. Communications, Network and System Sciences, 10, 240-251. https://doi.org/10.4236/ijcns.2017.105B024