This paper considers an uplink cell-free massive multi-input multi-output (mMIMO) system with multi-antenna access points (APs) and users, assuming low-resolution analog-to-digital converter (ADC) architecture is employed at the APs. Leveraging on the additive quantization noise model (AQNM), we derive a tight approximate expression for uplink spectral efficiency (SE). This trackable finding provides us with a tool for easily quantifying the impacts of the number of antenna arrays and the number of quantization bit of low-resolution ADCs. We find 5-bit is required in a cell-free mMIMO with low-resolution ADCs to achieve the same SE as a cell-free mMIMO with full-precision ADCs. Besides, when the number of antennas of the user is small, deploying more antennas at the users can boost the sum SE. Then, to further highlight the potential of low-resolution ADCs architecture, we also investigate the tradeoff between the SE and energy efficiency (EE) with design issues surrounding the quantization bit of low-resolution ADCs and the number of antenna arrays. The resulting observations reveal that by choosing a proper quantization bit, the cell-free mMIMO with low-resolution ADCs has the capability to enjoy a better SE-EE tradeoff compared to the perfect ADCs counterpart.INDEX TERMS Cell-free mMIMO, low-resolution ADC, AQNM, spectral efficiency, energy efficiency.

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In this paper, we present the detailed rate analysis for cell-free massive multiple-input multiple-output (MIMO) systems over spatially correlated Rayleigh fading channels. Taking the realistic impairment effects of spatial channel correlation, pilot contamination, and channel estimation errors into account, the lower-bounds of the achievable rates for both the uplink and downlink are derived with the lowcomplexity linear processing such as matched filter and conjugate beamforming, which enable us to take cognizance of the impacts of transmitted power, and the number of access points (APs). Based on the derived rate results, the asymptotic performance analysis is then carried out. Besides, we propose the sophisticated max-min power allocation strategies taking the actual requirements into consideration to provide uniformly good service to all users. However, the objective functions of the two optimization problems are both nonconcave. Fortunately, the former for uplink can be characterized as geometric programming (GP), whilst the latter for downlink merging the efficient tools of second-order-cone programming (SOCP). Lastly, the numerical results are shown to verify our analytical results and the effectiveness of the proposed max-min fairness algorithms.INDEX TERMS Cell-free massive MIMO, channel estimation, geometric programming, max-min fairness, second-order-cone programming, spatially correlated Rayleigh fading.

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