# A Novel Expectation-Maximization-Based Blind Receiver for Low-Complexity Uplink STLC-NOMA Systems
###### Abstract  
In this paper, we revisit a two-user space-time line coded uplink non-orthogonal multiple access (STLC-NOMA) system for Internet-of-things (IoT) networks and propose a novel low-complexity STLC-NOMA system. The basic idea is that both IoT devices (stations: STAs) employ amplitude-shift keying (ASK) modulators and align their modulated symbols to in-phase and quadrature axes, respectively, before the STLC encoding. The phase distortion caused by wireless channels becomes compensated at the receiver side with the STLC, and thus each STA's signals are still aligned on their axes at the access point (AP) in the proposed uplink STLC-NOMA system. Then, the AP can decode the signals transmitted from STAs via a single-user maximum-likelihood (ML) detector with low-complexity, while the conventional uplink STLC-NOMA system exploits a multi-user joint ML detector with relatively high-complexity. We mathematically analyze the exact BER performance of the proposed uplink STLC-NOMA system. Furthermore, we propose a novel expectation-maximization (EM)-based blind energy estimation (BEE) algorithm to jointly estimate both transmit power and effective channel gain of each STA without the help of pilot signals at the AP. Somewhat interestingly, the proposed BEE algorithm works well even in short-packet transmission scenarios. It is worth noting that the proposed uplink STLC-NOMA architecture outperforms the conventional STLC-NOMA technique in terms of bit-error-rate (BER), especially with high-order modulation schemes, even though it requires lower computation complexity than the conventional technique at the receiver. amplitudes-shift keying (ASK); blind decoder; clustering; expectation-maximization (EM); Gaussian mixture model (GMM); Internet-of-things (IoT); low-complexity transceiver; space-time line code (STLC); uplink non-orthogonal multiple access (NOMA)  
14 September 202218 October 202218 October 202221 October 2022  
channel state information (CSI) is available only at the transmitter (CSIT). As summarized in Refs. [18; 19; 20], its applications to various MIMO communication systems have been actively investigated. In particular, we have proposed an STLC-applied NOMA (STLC-NOMA) system for uplink IoT networks while raising some issues about the conventional uplink NOMA systems [21; 22; 23]. Most existing literature on the uplink NOMA assumes that CSI for all users is available at the base station (BS). However, it is practically infeasible for an access point (AP) to acquire the full CSI of a massive number of IoT devices (stations: STAs) due to the high signaling overhead for exchanging pilot signals [23]. We exploited the channel reciprocity property in the time-division duplex (TDD) system and applied STLC to NOMA-based uplink IoT networks. In conclusion, we have observed that each STA in the two-user uplink STLC-NOMA network can achieve the same bit-error-rate (BER) performance as the STLC using orthogonal resources as the signal-to-noise ratio (SNR) increases. Moreover, we have concluded that the uplink STLC-NOMA system is remarkably adequate for IoT networks in which two STAs share common radio resource blocks, considering the complexity and spatial diversity gain. In this paper, we revisit the conventional two-user uplink STLC-NOMA system [23] and propose a novel low-complexity uplink STLC-NOMA system to strike the following shortcomings. * Although the joint maximum-likelihood (ML) detector achieves optimal BER performance for uplink NOMA systems, it results in significant computational complexity;
* The complex constellation diagram at the AP makes it intractable for the AP to estimate the effective channel gain of each STA blindly. To this end, instead of phase-shift keying (PSK) or quadrature amplitude modulation (QAM) with constellation rotation as in the conventional uplink STLC-NOMA system, we employ \(M\)-ary amplitude-shift keying (ASK) modulations for both STAs and align each STA's modulated symbols on each axis in the in-phase and quadrature (I-Q) plane.