## 3 Spread-Spectrum Technology
### M-ary Spread-Spectrum  
The M-ary spread-spectrum communication system improves band utilization compared with a direct spread communication system. The theoretical communication rate is \(\lfloor\log_{2}M\rfloor\) times that of direct spreading using a random sequence of the same order, and each spreading symbol can carry \(\log_{2}(M)\) bits of information, where \(\lfloor\rfloor\) denotes rounding down. The M-ary spread-spectrum exploits both the good autocorrelation properties and the quasi-positive cross-correlation properties of pseudorandom codes, using different spread-spectrum sequences for different spread-spectrum symbols to characterize this information. M-ary spread-spectrum communication is illustrated in Figure 3.  
At the transmitter side, the data are divided into multiple groups of \(k\) bits through a serial-to-parallel conversion, which, for M-ary spreading, has \(2^{k}=M\). Each \(k\) bits of data constitute a spreading symbol, which is mapped to a spreading code according to certain rules. The \(k\) bits of data contain a total of \(2^{k}\) binary sequences, which also correspond to \(2^{k}\) spreading codes. The binary sequence is first converted to the corresponding decimal number \(p[m]\), \(0\leq p[m]\leq M-1\), and then \(c_{p[m]}(t)\) is selected as the spreading code from the mutually quasi-orthogonal M-ary spreading codes according to certain rules. We express \(c_{p[m]}(t)\) as  
\[C_{p[m]}(t)=\sum_{l=0}^{L-1}C_{p[m]}(l)g(t-lT_{c}) \tag{12}\]  
\(g(t)\) denotes a pulse-forming function. The orthogonal M-ary spread-spectrum receiver consists of M correlators, which makes the hardware complexity of the receiver relatively high. To overcome this problem, the CSK spread-spectrum method is used to exploit the cyclic correlation property of pseudo-random codes, which are used to achieve spread-spectrum communication by splitting the source information into a few bits of spread-spectrum symbols that are then mapped into spread-spectrum codes. M-ary spread-spectrum communication achieves the mapping of symbols to spreading codes using pseudo-random codes with different sequences of the same length, such as Gold codes, where each symbol corresponds to a spreading code of that length. In contrast, CSK maps symbols to spreading codes using different cyclic shifts of the same spreading code. CSK spreading reduces the hardware complexity while maintaining transmission efficiency, but introduces new problems.  
Figure 4a shows the results of cross-correlation between M-ary sequences of different principal polynomials of order seven, with a poor cross-correlation performance between spreading codes. Figure 4b plots the cross-correlation characteristics of a cyclic shift  
Figure 3: M-ary spread-spectrum communication system schematic.  
Figure 2: Direct spread-spectrum system communication schematic.  
sequence of an M-sequence of order seven, spaced by 15 code pieces and carrying three bits of eight any per symbol. In addition to the autocorrelation peak, there are several correlation peaks with similar energies. This indicates that if the signal is subject to severe multipath effects in the transmission process of the channel, such as the cross-correlation peak of spreading code 1 and cyclic code 2, which is close to the energy of the autocorrelation peak, the energy of the correlation peak is likely to exceed the energy of the autocorrelation peak under the influence of the superimposed multipath. This will result in a decoding error. The multipath component in this case cannot be regarded as noise and requires channel equalization, which leads to an increase in hardware complexity.