# Virtual Signal Processing-Based Integrated Multi-User Detection
## 1 Introduction
Therefore, utilizing a limited number of receiving antennas for multi-user detection (MUD) holds significant research importance. By exploiting interactions among multiple wireless signals, the authors of [12] proposed a MUD scheme named ICom/SIC-ZF, which incorporates interference combination (ICom) with zero-forcing (ZF) reception and SIC. This method treats all signals other than the desired signals (i.e., those to be detected) as a structured equivalent interference, and uses ZF to cancel this interference while recovering the desired signals. Subsequently, SIC is employed to subtract the detected signals from the received mixed signal. By iterating this process on the remaining mixed signal, all users' signal components can be detected sequentially. In [13], the authors utilized maximum likelihood (ML) to decode data from two overlapping wireless signals simultaneously under a single receiving antenna setting, based on the characteristics of various combinations of symbols carried in the mixed signal. However, with high-order modulation or a large number of users' signals, multiple symbol combinations can produce identical constellation points, leading to decoding errors. In such cases, the BER performance of this method diminishes significantly. The authors of [14] utilized intelligent reflecting surfaces (IRSs) to reflect a transmitted signal towards the intended Rx. By intelligently adjusting the reflecting parameters of the IRS, the reflected signal can interact with the directly arriving component to produce a desired signal at the Rx. Since neither the directly transmitted nor the reflected signal component carries legitimate data information, it becomes difficult or even impossible for an eavesdropper to intercept the legitimate user's information. In [15], an IRS was employed to reflect interference towards the affected Rx. The reflected interference serves as a recycling signal that interacts with the direct interference to generate a desired signal, thereby achieving interference recycling and enhancing data transmission. Based on the above discussions, this paper proposes a method called _Virtual Signal Processing-Based Integrated Multi-User Detection (VSP-IMUD)_. This approach achieves _integrated MUD (IMUD)_ by leveraging the spatial features of the equivalent desired signals that consist of multiple users' signals. First, we design a _channel ambiguity detection (CAD)_ module to avoid similarity or ambiguity among different equivalent (virtual) desired signal structures. In scenarios where similarity or ambiguity exists, directly applying IMUD may result in decoding errors and poor BER [13]. The CAD module identifies channels that yield ambiguity and then employs ICom/SIC-ZF to detect signals transmitted through these ambiguous channels. Once all signals transmitted through the ambiguous channels are decoded, the remaining signal components are treated as an equivalent desired signal through virtual signal combination. Based on the spatial characteristics of this equivalent desired signal, we can derive possible symbol combinations of the various desired signal components. Finally, we use ZF to recover the data sent from the Tx with the largest channel gain relative to the common Rx, and adopt it as the reference data to determine the exact symbol set of the equivalent signal. In this way, VSP-IMUD is realized. The contributions of this paper are two-fold:  
* Proposal of VSP-IMUD. This method allows for the integral decoding of data information carried in multiple signal components at once, based on the overall spatial characteristics of the received mixed signal. This enables the common Rx to perform multi-user detection (MUD) with fewer receiving antennas. * Proposal of CAD. This module first identifies channels that cause the structure of one equivalent desired signal to be ambiguous relative to another.