# A Capacity Enhancement Method for Frequency-Hopping Anti-Jamming Communication Systems
## 3 Results
### Analysis of Anti-Interference Capability  
Resistance to Broadband Interference  
1. Information A Broadband-Jamming Capability  
The anti-interference gain is generally used to reflect the signal's ability to resist broadband interference. When the anti-jamming gain is enhanced by expanding the bandwidth, the anti-jamming gain is the expanded bandwidth compared with the bandwidth of the original information modulation signal, as shown in the following equation:  
\[\mathrm{G_{PA}=\frac{P_{i}}{P_{A}}=\frac{W_{s}N_{0}}{E_{b}r_{A}}=\frac{W_{s}}{ r_{A}Th_{A}}} \tag{22}\]  
\(\mathrm{G_{PA}}\) indicates Information A immunity gain, \(W_{s}\) denotes the total spreading bandwidth, \(r_{A}\) is the information rate of A, and \(\mathrm{Th_{A}}\) is the demodulation BER threshold of Information A.  
Anti-jamming gain is essentially the value of the power that the jamming source needs to prioritize relative to the jammed link in order to achieve the jamming effect when the jamming source is in the same location as the transmitter terminals of the jammed system with the same aperture antennae, and the jammed system has an infinite power link margin.  
Since there is no change in W and R before and after the capacity enhancement method is applied to Information A, the incremental Information B also barely affects the demodulation BER threshold, \(\mathrm{Th_{A}}\), of A. Thus, the signal A anti-interference gain is unchanged before and after the use of the capacity-boosting method, i.e., the addition of the transmitted Information B in the channel has little effect on signal A's ability to resist broadband interference.  
Information B Broadband Interference Resistance  
Similarly, the immunity gain of Information B can be expressed as follows:  
\[G_{\text{PB}}=\frac{P_{i}}{P_{B}}=\frac{W_{s}N_{0}}{E_{b}r_{B}}=\frac{W_{s}}{r_{B }Th_{B}} \tag{23}\]  
Since the expanded bandwidths of Information B and Information A are the same, the anti-interference gain of Information B depends on the product of the information rate of B and the demodulation threshold of B.  
In general, as long as the number of frequency-hopping points and the frequency-hopping speed reach a certain value, when the information rate of Information B is equal to that of Information A, and if the BER demodulation threshold is also the same, the anti-jamming ability of Information B and Information A is the same.  
3. Resistance to Narrowband Tracking Interference for Information A  
Information A's ability to resist narrowband tracking interference depends on factors such as the frequency-hopping speed and frequency-hopping pattern. The addition of incremental Information B does not reduce the frequency-hopping speed. The frequency-hopping pattern changes from being driven by sequence polynomials or functions to being driven by Information B, which drastically reduces its predictability. The ability of Information A to resist narrowband tracking interference is strengthened accordingly.  
4. Resistance to Narrowband Tracking Interference for Information B  
The demodulation of Information B uses power detection. When the narrowband interference signal exists on the same frequency as the signal, the power of Information B is strengthened, which is conducive to the judgment of Information B. Similarly, the frequency-hopping pattern of the signal is driven by Information B, which is unpredictable and decipherable. Therefore, Information B has a strong anti-narrowband interference capability.