Performance Analysis of 1-Bit Quantization with Oversampling for Higher-Order Constellations

In this work, we consider a real additive white Gaussian noise (AWGN) channel with 1-bit quantization and oversampling at the receiver side for transmission with higher-order amplitude-shift keying (ASK) constellations. We analytically compute the statistics of the detection variable for arbitrary real inputs and present an optimal as well as a suboptimal detection scheme. Furthermore, we evaluate the symbol error rate (SER) for a 4-ary ASK constellation and different detection schemes as well as oversampling factors. The SER curves show that a reliable communication can be established for higher-order ASK constellations when the oversampling factor is sufficiently high. Then, we optimize the 4-ASK constellation with respect to the SER. The results show that the minimum SER can be decreased significantly by increasing the distance between the inner and outer points of the input constellation. Finally, the results are extended to complex-valued constellations.