## 5 Results and Discussions  
Because the decision statistics of single-frequency interference after correlation despreading in a short-code DSSS system do not fully conform to a Gaussian distribution, the use of the SGA hypothesis method to analyze its performance may result in inconsistent findings when compared with actual performance of the short-code DSSS system against single-frequency interference. This paper calculates the BER of the system under single-frequency interference based on the SGA assumption analysis for two specific scenarios. This section validates the accuracy of the derived conclusions through simulation and experimentation. The simulation model is illustrated in Figure 1.  
Figure 2 demonstrates the interference component resulting from single-frequency interference with various frequency offsets after correlation processing. In this simulation, the bit rate is 10 bit/s, and the spread spectrum code used is an m-sequence with a period of 15. The transmitted data information consists of an all-1 sequence, and the SIR is \(-20\) dB. Different values are assigned to the interference frequency deviation (\(\Delta f\)): 0 Hz, 0.1 Hz, 0.5 Hz, and 10 Hz. These values respectively represent \(\Delta f=kR_{b}\) and \(\Delta f\
eq kR_{b}\), with \(k\) being an integer. It can be observed that at 0 Hz and 10 Hz interference frequency offsets, which correspond to an integer multiple of the bit rate, the interference component in the decision variable remains constant. However, for interference frequency offsets of 0.1 Hz and 0.5 Hz, which do not correspond to an integer multiple of the bit rate (\(\Delta f\
eq kR_{b}\)), the interference component in the decision variable exhibits sinusoidal waveform variations. The system's BER in the presence of single-frequency interference, which has the same frequency as the signal carrier, is illustrated in Figure 3. In the simulation, an m-sequence with a period of 15 is utilized, and two different phase deviations (\(\Delta\varphi\)) are considered: 0 and \(\pi/3\). It can be observed that the influence of single-frequency interference on the system presents a distinct threshold effect. When the input S  
Figure 2: Interference component sequences of single-frequency interference after correlation processing. value, the system operates without errors. However, when the input SIR is below the threshold value, the BER rapidly increases to 0.5. Specifically, for the case in which the interference and the signal carrier share the same frequency and phase, the maximum SIR that results in an error in the system is \(-23.6\) dB. On the other hand, when the phase deviation (\(\Delta\varphi\)) is set to \(\pi/3\), the maximum SIR of the system decreases to \(-29.6\) dB. These simulation results align well with the theoretical calculation formula of the SIR threshold in Section 3. The corresponding threshold SIR values for \(\Delta\varphi\) = 0 and \(\Delta\varphi\) = \(\pi/3\) are \(-23.52\) dB and \(-29.54\) dB, respectively. In order to further analyze the impact of the SIR threshold on the system's BER, Figure 4 illustrates the variation curve of the BER with the phase deviation (\(\Delta\varphi\)) in the presence of both single-frequency interference at the same frequency as the signal carrier and Gaussian white noise. In the simulation, \(E_{b}/N_{0}\) is set to 8.4 dB (resulting in a BER of \(10^{-4}\) only with Gaussian white noise interference), the SIR is \(-26.5\) dB (the SIR threshold at which the system produces an error when \(\Delta\varphi\) = \(\pi/4\)), and an m-sequence of period 15 is used. It can be observed that when the single-frequency interference frequency matches the carrier frequency, the theoretical BER curve of the DSSS-BPSK system aligns closely with the simulation curve. This indicates that the quantitative analysis of the system BER calculation is correct at this time. The BER of the system undergoes periodic changes as the phase deviation increases with \(\pi\) as the period.