The success rate of a neural network (NN) classifier (rectified linear unit, 10 layers, softmax output layer activation)-based demodulator was proposed and evaluated for phase-shift keying (PSK) and quadrature amplitude modulation (QAM) modulated signals corrupted by additive white Gaussian, chisquared, uniform, and Rayleigh noise channels with signal-to-noise ratios (SNR) ranging from -20 dB to +20 dB. Low SNR are common in spectrum sensing, cognitive radio networks, underwater acoustics, target detection, remote sensing, seismic monitoring, and helicopter blade detection. This classifier-modulator performance was compared with that of the matched filter detector (MFD) for varying channel noise, constellation type (PSK or QAM), constellation size (M=2, 4, 8, 16), sample size (N), and training to test the data ratio. The classifier demodulator had a performance equal to or better than MFD in 98% of the scenarios.A training-to-test ratio of 70:30 or 80:20 is appropriate. The classifier performances of M-PSK and M-QAM are comparable. The superior performance of the NN classifier is more pronounced for M values greater than 2. N=5000 or higher is sufficient for most scenarios, and N=20000 is necessary for M=16. A higher success rate was obtained for additive chisquare and Rayleigh noise channels. The proposed demodulator performed significantly better than the matched filter for SNR values ≤ 0 dB. 16-QAM over an additive uniform noise channel had a better success rate for an SNR of 0 dB or less, whereas 16-QAM over an additive Rayleigh noise channel had a better success rate for an SNR of 5 dB or higher.