# Automatic Modulation Recognition Using Compressive Cyclic Features
## 4 Simulation and Performance Analysis  
In order to validate the proposed algorithm and evaluate its performance, we consider two modulation pools: \(\Omega_{1}=\{\)4 QAM,16 QAM,32 QAM\(\}\) for the scenario of intra-class recognition, and \(\Omega_{2}=\{\)8 ASK,16 PSK,16 QAM,4 QAM\(\}\) for the scenario of inter-class recognition. The transmit and receive filters are square-root raised cosine pulses with 0.35 roll-off factor. Accordingly, at the receiver, the signal is oversampled by a factor of 16 to eliminate aliasing. For each modulation type, 150 signals are generated for the training phase of the SVM system, and 1000 Monte Carlo trials are run as the testing phase. The number of processed symbols is equal to 4096. Each signal is generated with carrier frequency offset 500 Hz, symbol rate 1000 Hz. This classifier is tested in a variety of channel conditions, with a signal-to-noise ratio (SNR) range of 0 dB to 12 dB. The performance metric is the correct rate of recognition (COR)--the ratio between the number of correctly recognized signals and the total number of testing signals. A key parameter of interest is the compression ratio \(\gamma=M/N\) for sampling rate reduction. It is necessary that its impact on the performance of the proposed AMR algorithm be investigated in our simulations. Since the utilized estimators of cyclic statistics are biased due to the finite number of symbols (finite observation interval), a relatively large amount of symbols (e.g., 4096) are of great help to enhance the performance of the CC-based classifier [3]. Figure 1 plots the performance of the proposed algorithm (for the modulation pool \(\Omega_{1}\)) versus SNR, for \(\gamma=0.1,\ 0.2,\) and \(0.3\). The performance of the classical CC-based method with uniform samples which was proposed in [8] is also shown in the same figure. As one can easily notice fromFigure 1, all the curves degrade when SNR decreases. As is readily seen, when SNR \(\geq\) 9 dB, the proposed AMR provides a comparable performance (COR \(\geq\) 93%), with only 20% of samples utilized by the classical counterpart. Moreover, with \(\gamma=0.3\), the proposed method can achieve a perfect performance (COR \(=\) 95%) at 6 dB SNR. In Figure 2, for the modulation pool \(\Omega_{2}\), the performance maintains a similar trend as shown in Figure 1. It is noted that the performance for \(\gamma\geq 0.2\) is quite close to that of classical method when SNR \(\geq\) 6 dB. From Figures 1 and 2, we can conclude that regardless of the effect of noise, the more measurements are taken, the more excellent the performance can be. This is because the finite sample effect can be adequately alleviated as the length of measurements increases. Providing a proper tradeoff between SNR and \(\gamma\), the CS-based AMR can be totally treated as an alternative of the classical CC-based AMR, and affords dramatic savings of computational complexity and storage requirements. Figures 3 and 4 compare the performance of the proposed algorithm to the CS-based AMR proposed in [11] for \(\gamma=0.2\). It is apparent that these two curves almost converge, and the former slightly outperforms the latter in both cases. This mainly results from the fact that in the algorithm of [11], several lower-order CMs need to be estimated, which yields bias accumulation in the computation of CCs. With the SNR degrading, these two classifiers both exhibit unacceptably poor performance when SNR \(\leq\) 0 dB (not shown in Figures 3 and 4). Figure 1: Performance versus signal-to-noise ratio (SNR) for \(\Omega_{1}\). Figure 2: Performance versus SNR for \(\Omega_{2}\). The results above reveal the fact that for a fixed observation, the proposed AMR performance degrades as \(\gamma\) decreases. As a special case of \(\gamma=1\), the performance of the classical algorithm provides an upper bound. On the other hand, as shown in Tables 2 and 3, for an equivalent number of samples, nonuniform sampling has better classification performance than uniform sampling.