###### Abstract  
This paper investigates the error performance of cooperative decode-and-forward (DF) multiple-input multiple-output (MIMO) systems employing one-bit analog-to-digital converters (ADCs) over Rayleigh fading channels. In cooperative DF MIMO systems, detection errors at the relay may propagate to the destination, thereby degrading overall detection performance. Although joint maximum likelihood detection can efficiently mitigate error propagation by leveraging probabilistic information from a source-to-relay link, its computational complexity is impractical. To address this issue, an approximate maximum likelihood (AML) detection scheme is introduced, which significantly reduces complexity while maintaining reliable performance. However, its analysis under one-bit ADCs is challenging because of its nonlinearity. The main contributions of this paper are summarized as follows: (1  
Multi-input multi-output (MIMO) systems are a fundamental and effective approach for enhancing wireless communication performance by deploying multiple antennas at the transmitter and/or receiver [6; 7; 8; 9]. Multi-antenna configurations have been widely incorporated into modern wireless standards to exploit these advantages. Massive MIMO, which employs a large number of antennas, has gained significant attention because of its ability to improve both spectral and energy efficiency. However, implementing numerous antennas on the receiver side remains a practical challenge in mobile devices because of limitations in the physical form factor and increased hardware complexity. Cooperative communication has emerged as an effective solution to overcome this limitation without requiring additional antennas at the user end. Among cooperative strategies, the decode-and-forward (DF) protocol is attractive because of its favorable performance and relatively low implementation complexity [10; 11; 12]. However, DF systems are inherently susceptible to error propagation when a relay node incorrectly decodes the transmitted signal. Thus far, various detection strategies have been proposed [13; 14; 15], with joint maximum likelihood (JML) detection being known for achieving full diversity gain to mitigate this effect. However, the computational burden of JML detection at the destination limits its practical applicability in resource-constrained systems. Alternative approaches such as cooperative maximum ratio combining (MRC) [13] and pseudo-linear combiners [14] have been introduced; however, their applications are often restricted to single-antenna systems or orthogonal space-time block coded schemes. To address these limitations, a pairwise error probability (PEP)-based maximum likelihood (ML) detection method was proposed in [15], offering a good trade-off between performance and complexity. However, these studies assumed the availability of ideal or high-resolution analog-to-digital converters (ADCs), often being impractical for power- and cost-constrained devices. In this context, low-resolution analog-to-digital converters (ADCs) have emerged as a promising solution for reducing power consumption in future wireless systems characterized by wide bandwidths and large-scale antenna arrays [16; 17; 18]. Among these, one-bit ADCs provide the most significant power savings by quantizing received signals based only on their sign information. Although this extreme quantization leads to considerable energy efficiency, it introduces substantial nonlinear distortion [19; 20]. Research on one-bit ADCs has gained momentum, and their application in cooperative communication systems remains relatively underexplored. Recent studies have started addressing this gap [21; 22; 23; 24; 25]. For example, the studies in [21; 22] examined the capacity limits of multipair massive MIMO systems under one-bit quantization, while those in [23; 24] investigated multi-hop multi-user MIMO systems in which the adverse effects of one-bit ADCs were mitigated through supervised-learning-based techniques.