Linear Precoding With Low-Resolution DACs for Massive MU-MIMO-OFDM Downlink

Abstract

We consider the downlink of a massive multiuser (MU) multiple-input multiple-output (MIMO) system in which the base station (BS) is equipped with low-resolution digital-toanalog converters (DACs). In contrast to most existing results, we assume that the system operates over a frequency-selective wideband channel and uses orthogonal frequency division multiplexing (OFDM) to simplify equalization at the user equipments (UEs). Furthermore, we consider the practically relevant case of oversampling DACs. We theoretically analyze the uncoded bit error rate (BER) performance with linear precoders (e.g., zero forcing) and quadrature phase-shift keying using Bussgang's theorem. We also develop a lower bound on the informationtheoretic sum-rate throughput achievable with Gaussian inputs, which can be evaluated in closed form for the case of 1-bit DACs. For the case of multi-bit DACs, we derive approximate, yet accurate, expressions for the distortion caused by low-precision DACs, which can be used to establish lower bounds on the corresponding sum-rate throughput. Our results demonstrate that, for a massive MU-MIMO-OFDM system with a 128-antenna BS serving 16 UEs, only 3-4 DAC bits are required to achieve an uncoded BER of 10 −4 with a negligible performance loss compared to the infinite-resolution case at the cost of additional out-of-band emissions. Furthermore, our results highlight the importance of taking into account the inherent spatial and temporal correlations caused by low-precision DACs.

Performance Analysis of Quantized Uplink Massive MIMO-OFDM With Oversampling Under Adjacent Channel Interference

“…4a that the 5 dB SIR gain achieved with oversampling for the perfect CSI case can also be attained under imperfect channel knowledge when the error rates to achieve a BER value of 10 −3 is considered. 24 In fact, it is even more than 5 dB (about 6.5 dB) for imperfect CSI. This is because oversampling also enhances channel estimation quality which in turn results in a better error rate performance even further for the one-bit quantized system with imperfect CSI.…”

“…, as in the related studies [7], [13], [24]. Here, p[ ] is the power delay profile of the channel satisfying L−1 l=0 p[ ] = 1.…”

“…The covariance matrices of quantization noise for nonzero lags, namely C diag q [m], m = 0, are also assumed to be zero for multi-bit quantizers, which means that the correlation in time for the quantization noise is assumed to be zero. This assumption fails to be valid for very low ADC resolutions [24] or for high oversampling rates, as discussed in Appendix D, yet, it provides more accurate results as the number of quantization bits is increased [24], when clipping or overload distortion occurs with low probability. To ensure this, we will choose the step size ∆ small enough as will be discussed shortly.…”

“…Another study [13] analyzes massive MIMO structures with one-bit ADCs under frequency selective fading. In that work, quantization noise is regarded as an uncorrelated distortion in time and space, which fails to hold when oversampling is performed or when the number of users or noise variance is not high [12], [24]. However, it will be seen that our analysis takes into account the temporal and spatial correlation in the quantization distortion, which enables an accurate analysis.…”

“…• The analysis in the paper is general in that it can also be applied to the scenario where no ACI is present. For no ACI case, the analysis in the paper requires much less memory resources than the ones in [12], [24] for SINDR calculations while providing closed-form expressions for quantization noise covariance matrix for one-bit ADCs as in (19) and (20) (more details for this item are mentioned previously), takes into account the temporal and spatial correlation for the quantization noise, which are neglected in [7], [13], among which [13] does not cover the effect of oversampling, can clearly show the impact of system parameters (such as number of antennas, oversampling rate, etc.) and imperfect CSI on the system performance unlike [7], [24], where no channel estimation technique is proposed.…”