Using low-resolution analog-to-digital converters (ADCs) is a valuable solution to decrease power consumption and cost in massive MIMO systems. Previous studies show that the performance gap between low and high-resolution systems gets more prominent as the signal-to-noise ratio (SNR) increases since the detection performance starts to saturate at some point due to the stochastic resonance (SR) phenomenon. In our previous work, we proposed new quantization and detection schemes for one-bit massive MIMO systems operating under frequency-flat fading. This paper offers a new frequency domain equalization (FDE) scheme that can work with the previously proposed pseudo-random quantization (PRQ) scheme to mitigate the effects of SR to support high-order modulation schemes such as $64$-QAM and $256$-QAM. Our equalizer is based on a projected quasi-Newton method for one-bit uplink massive MIMO systems applicable for orthogonal frequency division multiplexing (OFDM) and single carrier (SC) transmission under frequency-selective fading. The proposed low-complexity detector can outperform the benchmark detector from the literature with very similar complexity. We analyze the effects of PRQ under frequency-selective fading for different scenarios and show that the PRQ scheme can close the performance gap between SC and OFDM systems by simulations.

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