On Gaussian Multiple Access Channel with Signal Dependent Noise

The motivation of this work is to examine how well methods, such as successive interference cancellation and interference alignment from information theoretic solution, work in real-world where the received signal is quantized for digital processing. As a first step, we consider Gaussian Multiple Access Channels with the quantization noise modeled as Gaussian noise, whose variance depends on the received signal power at the receiver. We call this model Gaussian Multiple Access Channel with Signal Dependent Noise. The achievable rate region of this model is given under finite transmitted signal power constraint, where the achievable scheme could be successive interference cancellation (SIC). This region is outer bounded by a finite region with unlimited received signal power, where the achievable scheme is time division multiple access (TDMA). Thus, one way to measure the usefulness of successive interference cancellation is to study the gap between the SIC region and the TDMA region under finite power constraints. For the symmetric maximum signal to channel noise ratio (SCNR) case, where the maximum SCNR of all users are the same, we show that the gap between the SIC region and the TDMA region is within 0.5 bits for any number of users. Furthermore, for this case, if the maximum quantization noise power due to one user is stronger than the channel noise power, then the sum rate difference between the SIC region and the TDMA region is within 0.5 bits. For the asymmetric maximum SCNR case, the gap can be small when all users have high SCNR (e.g., 30dB), where the receiver is equipped with a low precision ADC (e.g., 2-3 bits).