Uplink Achievable Rate in One-bit Quantized Massive MIMO with Superimposed Pilots

In this work, we consider a 1-bit quantized massive MIMO channel with superimposed pilot (SP) scheme, dubbed QSP. With linear minimum mean square error (LMMSE) channel estimator and maximum ratio combining (MRC) receiver at the BS, we derive an approximate lower bound on the achievable rate. When optimizing pilot and data powers, the optimal power allocation maximizing the data rate is obtained in a closed-form solution. Although there is a performance gap between the quantized and unquantized systems, it is shown that this gap diminishes as the number of BS antennas is asymptotically large. Moreover, we show that pilot removal from the received signal by using the channel estimate doesn't result in a significant increase in information, especially in the cases of low signal-to-noise ratio (SNR) and a large number of users. We present some numerical results to corroborate our analytical findings and insights are provided for further exploration of the quantized systems with SP.