In the paper, operation algorithms of the N-OFDM modem for channels with the Additive White Gaussian Noise (AWGN) are considered. The algorithms are based on the Hartley transform under the optimal demodulation by the estimation of the received signals amplitudes using the Cauchy method. The experimental results for interference immunity estimation are provided for different values of spacing frequencies between subcarriers frequencies under the maximum possible multiplexing of N-OFDM signals spectrum with BPSK modulation. The numerical results were obtained by the mathematical modeling in Matlab. A method of modem time synchronization, suggested by the authors, is considered, and peak factor of N-OFDM signals and approaches for this factor reduction are analyzed.