Optimum memoryless bandpass nonlinearities

Previous work on optimum memoryless bandpass nonlinearities is extended here and applied to cases involving various types of interference, which may, for example, include a cochannel or adjacent-channel angle-modulated waveform as well as narrowband Gaussian noise. At low input signal-to-interference ratios the nonlinearity that maximizes the output signal-to-noise-plus-interference-and-intermodulation ratio (SNIIMR) is identical with that which maximizes the signal´s probability of detection if the time-bandwidth product is large, i.e., the locally optimum Bayesian detector. Its performance is as much as 4.8 dB better than that of the optimum biased power-law rectifier. In the absence of noise, the output SNIIMR of the optimum memoryless bandpass nonlinearity (OMBPNL) is 0 dB whenever the desired signal is weaker than the interference. In the presence of weak input noise accompanying a weak input signal and a strong angle-modulated interfering waveform, the output SNIIMR of the OMBPNL becomes at least τ/(2+τ), where τ is the input signal-to-noise ratio (SNR), regardless of how strong the cochannel interference is. Thus, very large SNR improvements can be obtained without a notched filter, however large the bandwidth of the interference. Although the output SNIIMR will not exceed 0 dB when the input signal is weak, it can be raised to useful levels by the processing gain associated with a spread-spectrum signal