In the field of radar communication integration, it is a crucial link to design a common waveform signal that can simultaneously support radar detection function and communication information transmission function. In response to the problem of low autocorrelation performance after modulating communication information within radar signal pulses, an integrated radar and communication signal format based on nonlinear frequency modulation (NLFM) signal with high frequency band utilization and low autocorrelation sidelobe is proposed. The core of establishing NLFM-16QAM integrated radar and communication signal model is to take NLFM signal as the carrier of 16 order quadrature amplitude modulation (QAM) signal. The ambiguity function of NLFM-16QAM signal and the related radar and communication performance are analyzed. Noting that the randomness of the communication baseband signal in the proposed NLFM-16QAM waveform can degrade radar functionality and thus reduce moving-target detection performance, we introduce improvements at the receiver of the integrated system. Specifically, a wavelet packet noise reduction is proposed to process NLFM-16QAM signal in combination with natural gradient separation algorithm. Simulation results show that the proposed signal has larger frequency band utilization in comparison with the integrated radar and communication signals of low-order modulation. Compared with the autocorrelation performance of 16QAM-LFM signal, integral sidelobe ratio and peak sidelobe ratio of proposed signal are reduced by 23.07 dB and 26.08 dB respectively. After NLFM-16QAM signal is processed by the joint algorithm of the receiving end, the detection results of the moving target are significantly improved.