# A Low Sampling Rate Receiver Design for Multi-Antenna Multi-User OFDM Systems
###### Abstract  
The future 6G mobile communication network will support an unprecedented amount of Internet of Things (IoT) devices, which will boost the demand for low cost terminals under the principle of green communication. One of the critical issues for low cost terminals is the sampling rate of analog-to-digital converters (ADCs) at the receivers. A high sampling rate of the ADC gives rise to a high energy consumption and high hardware cost for the terminal. In the conventional multi-user OFDM systems, all users have to sample the received signal with a sampling rate that is larger than or equal to the Nyquist rate, despite only a small fraction of the bandwidth (number of subcarriers) is allocated to each user. This paper proposes a low sampling rate receiver design for multi-antenna multi-user OFDM systems. With the aid of zero-forcing precoding, the sampling rate of the receiver can be reduced to \(1/K\) of the Nyquist rate, where \(K\) is the number of users. The simulation results show that with a significant reduction in sampling rate, performance loss is insignificant and acceptable in terms of bit error rate, mutual information and peak-to-average power ratio. low sampling rate; zero-forcing precoding; OFDM system +
Footnote †: journal:  
0000-0002-4480-3888-2222-3/11  
besides employing purely low bit quantization [12], some researchers have investigated a mixed ADC architecture, in which some of the antennas were equipped with low resolution ADCs [13; 14; 15]. It should be noted that low complexity receivers with low resolution ADCs have been developed very quickly in recent years through a variety of studies [16; 17; 18; 19; 20] utilizing message passing algorithms to design near-optimal low complexity receivers, which have made it possible to implement low resolution ADCs. This paper concentrates on a low sampling rate receiver design for OFDM systems. For traditional OFDM systems, the receiver is usually equipped with an ADC working at a sampling rate that is larger than or equal to the Nyquist rate \(f_{0}=N/T\), where \(N\) is the number of subcarriers and \(1/T\) is the subcarrier spacing. To reduce the sampling rate, [PERSON]. [21] investigated a delay-division multiplexing (DDM) scheme for orthogonal frequency-division multiple access (OFDMA) passive optical networks (OPNs), which deployed an ADC operating at a sampling rate below the Nyquist rate for each optical network unit. The sampling instant of the ADC was critical in the selection of the required data and thus, a method was proposed to carry out the adjustments required for the sampling delay to demodulate the expected data. Ref. [22] proposed a simple DDM scheme for OFDMA-OPNs and 2X2 wireless multi-input multi-output (MIMO), which enabled both wired and wireless users to receive the target data with a sub-Nyquist sampling rate ADC without the demodulation of all signals. Ref. [23] leveraged an optical shaping technique to realize low bandwidth, sub-Nyquist analog-to-digital conversion in DDM OFDM passive optical networks (PONs). Ref. [24] proposed a novel frequency diversity coded OFDM scheme, which allowed the receiver to sample the received signal at a low rate that was less than the Nyquist rate but also guaranteed a significant diversity-coding gain. Under this condition, an aliasing phenomenon occurred but was regarded as transmission diversity to the receiver. The design criteria of this coding scheme was to minimize the pairwise error probability and the construction frequency diversity code was based on linear block codes. Ref. [25] proposed a simple low sampling rate receiving scheme for a W-band (75-110 GHz) OFDM radio over fiber (RoF) system, which utilized multiple low-sampling-rate ADCs to replace a high-sampling-rate ADC in order to reduce the required sampling rate and the computation complexity of the OFDM demodulation. As for the aliases of the OFDM subcarriers, a digital preprocess that was related to time delays was employed to the low-sampling-rate ADCs to enable all of the subcarriers to be free from aliasing. Ref.