# Virtual Signal Processing-Based Integrated Multi-User Detection
## 1 Introduction  
The ever-increasing demand for wireless broadband services has driven the development of 5G technology. Compared to previous mobile communication systems, 5G is expected to offer larger system capacity, higher data rates, lower latency, and improved reliability [1]. As a key application in the 5G era, the Internet of Things (IoT) has been rapidly developing in recent years, leading to explosive growth in the number of IoT devices. It is estimated that by 2025, more than 41.6 billion IoT devices will be connected to networks worldwide [2, 3]. Therefore, efficiently supporting the data transmissions of more users under limited communication resources has become a critical issue warranting thorough investigation. By allocating different types of communication resources--such as frequency, time slots, code words, and spatial characteristics--to multiple users in an orthogonal manner, interference among concurrent data transmissions can be effectively avoided, thereby enabling resource sharing among users [4]. However, since the frequency resources available for wireless communication are limited, the emergence of various communication systemsand the increase in mobile users pose significant challenges to traditional orthogonal multiple access (OMA) methods. As a result, dynamic spectrum sharing methods have been proposed to facilitate multi-user communications. For example, cognitive radio (CR) [5,6] enables unlicensed or cognitive users to access the available authorized spectrum for data transmission. However, timely sensing of the licensed user's signal and withdrawal is critical for CR applications, as inappropriate spectrum access may interfere with authorized communications. Due to advancements in microelectronic technology, the processing capability of hardware has improved while costs have decreased. A receiver (Rx) can now decode data carried in multiple concurrent signals through complex signal processing. In recent years, non-orthogonal multiple access (NOMA) [7] has emerged as a promising medium access control (MAC) method for the 5G system. Uplink NOMA allows multiple transmitters (Txs) to transmit to a common Rx over the same frequency channel in a non-orthogonal manner, enabling the Rx to employ successive interference cancellation (SIC) [8] to mitigate co-channel interference (CCI). As mentioned above, in addition to resource sharing, receiver-side multi-user detection (MUD) is essential for achieving high system capacity and data rates. Existing MUD methods can be classified into linear detection and non-linear detection based on whether their structures involve feedback mechanisms. Linear MUD methods include linear de-correlation detection [7] and minimum mean squared error (MMSE) detection [8]. However, linear MUD [9] requires computing the inverse of the cross-correlation matrix of all users' channels, which incurs high computational complexity. Non-linear MUD, on the other hand, includes decision feedback detection methods such as SIC. SIC first recovers data information carried in certain signal components from the received mixed signal, then uses the decoded data and estimated channel state information (CSI) to reconstruct the previously detected signals. These reconstructed signals are subtracted from the received mixed signal, resulting in a reduced mixed signal. By performing this iterative processing on the reduced mixed signal, multiple users' signals can be detected. By combining MMSE and SIC, MMSE-SIC detection has been proposed and applied within the V-BLAST framework [10,11]. However, SIC has an error propagation problem [12], leading to a high bit-error rate (BER) for later-decoded users' data, which hampers its practical application. Although increasing the number of receiving antennas can enhance the Rx's signal processing capability and support more users' data transmissions, practical limitations such as device size and hardware costs make it unfeasible to increase the number of receiving antennas indefinitely.