# Anti-Multipath Performance Improvement of an M-ary Position Phase Shift Keying Modulation System
## 1 Introduction  
The Internet-of-Things is a new concept that is increasingly attracting the attention of researchers and industries [1]. It is expected that by 2020, there will be 20 billion communicating objects in the world [2]. In order to meet the demand of so many connectce devices, LPWAN that can realize long-distance transmission and reduce communication power consumption is proposed [3]. Ultra-narrowband modulation with high spectral efficiency as the physical layer technology of LPWAN and can meet the large coverage and high reliability requirements of LPWAN [2; 4; 5; 6; 7; 8]. In order to achieve very high spectral efficiency without excessively reducing power efficiency, modulation of M-ary Position Phase Shift Keying (MPPSK) is proposed based on Extend Binary Phase Shift Keying (EBPSK) modulation [9; 10; 11]. As a multi-band form of EBPSK modulation, it is an efficient and flexible modulation method. The receiver can achieve demodulation by extracting tiny modulation information using a extremely narrow pass band filter called a digital impacting filter (DIF). In [12; 13], the special mechanism of DIF is explained in detail. MPPSK can flexibly select modulation schemes, change bit rate, power efficiency and spectrum efficiency by changing modulation parameters. Compared with traditional modulation methods, MPPSK also has the advantages of high bandwidth efficiency and line spectrum elimination. Therefore, it has important theoretical and practical significance. High-speed digital mobile communication is affected by frequency selective fading caused by multipath with various time delays [14]. Inter-symbol interference caused by frequency selective fadingaffects the correct demodulation of the demodulator, thereby limiting the maximum transmission data rate. In order to combat multipath fading, techniques such as diversity and equalization can be employed. The multipath separation technique is based on spread spectrum communication. Using the good autocorrelation property of the Pseudo-Noise Sequences, the receiver separates the multipath signal by correlating the multipath signal with multiple correlators [15; 16]. However, the spread of the signal spectrum reduces the spectrum utilization and the demodulator complexity is high. In [17], a multipath separation method based on the EBPSK modulation system is proposed. This scheme is only applicable to binary EBPSK modulation, and there are fewer scenarios available. When sub-path information is used to participate in the decision, the multipath separation scheme based on EBPSK modulation introduces all sub-path noise. In order to further improve the frequency band utilization, it is very important to study the anti-fading of multi-ary modulation technology in efficient modulation. In this paper, based on the waveform characteristics of MPPSK modulation, a multipath separation method based on MPPSK modulation is proposed and the multipath separation conditions are given. The modulation parameters are adjusted by the multipath delay value to achieve the separation of the multipath and the main path, thereby reducing the inter-symbol interference of the multipath signal to the main path signal and improving the anti-multipath interference ability of the signal. Compared with the scheme of separating multipath by signal spread spectrum, this scheme reduces the spectrum overhead. Compared with the multipath separation scheme proposed in [17] for binary ultra-narrowband signals, the multipath separation method proposed in this paper is applicable to the M-ary MPPSK signals with higher transmission rate. By using the normalized symbol joint decision proposed in this paper, the receiver reduces the introduced noise while utilizing multipath information, thereby reducing the bit error rate of the system. The rest of this paper is organized as follows. Section 2 introduces the channel model, MPPSK modulation and demodulation scheme. Section 3 introduces multipath delay estimation, modulation parameter design and normalized symbol joint decision.