Optimum memoryless bandpass nonlinearities

Abstract

Previous work on optimum memoryless bandpass nonlinearities (OMBPNLs) 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 narrow-band Gaussian noise. At low input signal-to-interference ratios (SIRs) the nonlinearity that maximises the output signal-to-noise-plus-interference-and-intermodulation ratio (SNIIMR) is identical with that which maximises 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 SIIMR of the 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 r/ (2 + r), where r is the input signal-to-noise ratio, regardless of the strength of the cochannel interference. Thus very large SIR improvements can be obtained without filtering, however large the bandwidth of the interference may be. Although the output SNIIMR will not exceed 0 dB when the input signal is weaker than the interference, it can be raised to useful levels by the processing gain associated with a spread-spectrum signal.