## 2 MCSK Communication Technique
### Performance Analysis  
Compared with the traditional spread spectrum, MCSK improves the communication rate by increasing the amount of information modulated by each spread spectrum sequence. In MATLAB, we simulated and compared the BER performances of the DSSS system, CSK spread spectrum system, M-ary spread spectrum system and MCSK system in the additive white Gauss noise (AWGN) channel when the length of spread spectrum sequences in all these systems was 15, and all the spread spectrum sequences were composed of kasami sequences and their cyclic shift sequences. We set \(f_{c}\) to 10 kHz, the communication bandwidth to 4 kHz and the sampling rate to 48 kHz. Each system transmitted 1000 bits of data each time and repeated 200 experiments. As known in the DSSS system, one spread spectrum sequence carries only 1 bit of information. In the M-ary spread spectrum system, there were four spread spectrum sequences, so each of them could carry 2 bits of information. In the CSK system, a spread spectrum sequence was cyclically shifted to eight sequences, and each cyclic shift sequence could carry 3 bits of information. In the MCSK system, there were thirty-two spread spectrum sequences in total, and each of them could carry 5 bits of information. When the chip widths of four spread spectrum systems were all 0.5 ms, the communication rates of DSSS, CSK, M-ary system, and MCSK system were as shown in Table 1.  
Figure 2: Diagram of MCSK integral judgments.  
From the BER curves of these four systems in Figure 3, it can be seen that the anti-noise performances of them are arranged from high to low in order: DSSS system, M-ary spread spectrum system, CSK spread spectrum system, MCSK system. Compared with DSSS, the other three methods change from the single sequence decision to the multi-sequence decision, which results in the cross-correlation interference of other sequences. In the other three systems, the increase in communication rates is at the cost of reducing reliability. The total number of spread spectrum sequences in the MCSK system is the largest, that is, the cross-correlation interference at the receiver is the most serious, so the anti-noise performance of the MCSK system is the worst.  
When we take the communication rates as the reference standard, the performances of these four systems are simulated and compared in the AWGN channel again. The chip widths of four spread spectrum systems were all 0.5 ms. In the M-ary spread spectrum system, one sequence carried 2 bits of information. In the CSK system, one sequence carried 8 bits of information. Table 2 shows the communication rates and the length of the spread spectrum sequences of the four systems.  
As shown in Figure 4, in the communication BER of \(10^{-4}\) magnitude, the anti-noise performance of MCSK system is 1.5 dB higher than that of the CSK system, 2.8 dB higher than that of M-ary spread spectrum system and 4.2 dB higher than that of DSSS system, which is related to the larger spread-spectrum gain of the longer spread spectrum sequence.  
\begin{table}
\begin{tabular}{c c} \hline
**Communication System** & **Communication Rate** \\ \hline DSSS & 133.3 bps \\ M-ary & 266.7 bps \\ CSK & 399.0 bps \\ MCSK & 665.0 bps \\ \hline \end{tabular}
\end{table}
Table 1: Communication rates of systems.  
Figure 3: BER curves of four systems with the same length of spread spectrum sequences.  
\begin{table}
\begin{tabular}{c c c} \hline
**Communication System** & **Communication Rate** & **The Length of Spread Spectrum Sequences** \\ \hline DSSS & 285.7 bps & 7 \\ M-ary & 266.7 bps & 15 \\ CSK & 258.1 bps & 31 \\ MCSK & 253.9 bps & 63 \\ \hline \end{tabular}
\end{table}
Table 2: Parameters of four systems.