# Low-Complexity GSM Detection Based on Maximum Ratio Combining
## 1 Introduction  
As a new multi-input multi-output (MIMO) antenna technology, spatial modulation (SM) has received considerable attention in the field of wireless communication [1, 2, 3]. However, since SM technology activates only one antenna per time slot to transmit data, its transmission rate is obviously lower than that of traditional MIMO technology. To solve the problem of the transmission rate of SM technology, generalized spatial modulation (GSM) technology was proposed in [4, 5]. In a GSM system, multiple antennas are activated to transmit the same or different modulation symbols in each time slot. Therefore, the spectrum efficiency of GSM technology is higher than SM technology. If the GSM system transmits the same modulation symbols on the selected transmit antenna combinations (TACs), it not only eliminates inter-channel interference (ICI), but also imports spatial diversity, which improves the accuracy of signal detection at the receiver. However, the structure inevitably increases the detection complexity at the receiver. To reduce the detection complexity and approximate the BER performance of the ML detector, various research results have been proposed in [6, 7, 8, 9, 10, 11, 12, 13]. Moreover, to make full use of the limited spectrum resources, more researchers have begun to focus on the adaptation of 5G architectures for future NetApps and verticals, and the white spaces in frequency bands [14, 15]. An improved sphere decoding (SD) detection algorithm was proposed in [6]. The enhanced SD algorithm can efficiently reduce the detection complexity by reducing the number of search tree branches of the traditional SD detector. In [7], tree-search SD and path-search SD algorithms were proposed to reduce the complexity of the SD algorithm in the GSM system. An ordered block minimum mean square error (OB-MMSE) detection algorithm was proposed in [8]. Firstly, the pseudo inverse operation is used to sort the possible TACs, and then for each ordered TAC the minimum mean square error (MMSE) detection algorithm is used to detect the modulation symbols. It can achieve near-ML performance with low-complexity. A low complexity grouping detection algorithm was presented in [9]. The transmitter divided the transmit antennas into several groups according to the number of active antennas and each group activated one antenna to transmit the modulation symbol, and the receiver carried out the packet successive detection. In [10], an efficient index-to-bit mapping for spatial bits based on Gray coding was proposed to improve the spatial bit-error rate (BER). A fully GSM (F-GSM) system was proposed in [11]. In an F-GSM system, the increment of data transmission rate is proportional to the base-2 logarithm of the number of the transmit antennas. The F-GSM system has a higher data transmission rate compared to the conventional GSM. The optimization framework of GSM and generalized orthogonal spatial modulation (GQSM) were proposed in [12], which extended the spatial constellation. A probability-ordering-based sphere decoding detector for jointly mapping generalized spatial modulation system was proposed in [13], which can reduce the computational complexity of the ML detector. To obtain the near-ML detection performance and lower complexity, two suboptimal detection algorithms are proposed in this paper. The two detectors can reduce the computational complexity by reducing the number of the TACs. For the estimation of the modulation symbol, the HLML algorithm [16] for M-QAM constellation and LCML algorithm [17] for M-PSK constellation are adopted. The computational complexity of estimating the modulation symbol is independent of the modulation order, so the complexity of symbol detection is greatly reduced. The rest of the paper is organized as follows. The system model of GSM is presented in Section 2. The proposed two suboptimal detection algorithms are illustrated in Sections 3 and 4, respectively. The simulation results and computational complexity analysis of the two proposed algorithms are presented in Section 5.