Shannon's equation relates the capacity of a channel, C (in bits/sec), to the bandwidth of that channel in Hz and the signal to noise ratio. (Note: that S/N is a power ratio, not in dB but the actual ratio. Also note, that logarithm is base 2 log, not base 10 or natural log.)

Now, this equation would quantify how much noise a jammer would need to introduce into the frequency channel, to disrupt communications. As long as the jammer knows how wide the RF channel is, and how much capacity the users are trying to get from that channel, a jammer can decide where to locate his device and how much noise power to introduce. The goal is, of course, to reduce the SNR at either end of the comms  channel enough to prevent communications from occurring.

The users can counter by reducing their capacity requirement (such as simplifying the QAM constellation), increasing power, changing their RF channel, or moving further away from the jamming device. Or a combination of these steps.

http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/iandm/part8/page1.html

http://www.vmsk.org/Shannon.pdf

One thing to keep in mind is that the noise assumed in the equation is Gaussian noise, white noise. There are potentially other ways of jamming a signal, such as to create reflections of the symbols or other such tricks, where clearly Shannon's equation by itself might not be enough to describe what's going on or how to protect oneself.

Dear Ameer,

Adding to the good answer by AbertIt is assumed that the jammer tries to corrupt the received signal at the site of the receiver since the  signal will be at its smallest level. Also, the  band width of the jamming signal is normally limited to the bandwidth of the original signal. so one assumes that the jamming signal is of narrow band width.

To combat such jamming one spreads the the transmitter signal by a spreading code is characterized by noise lie nature. There are different pseudo noise codes such as the maximum length codes. The rate of this code is called the chip rate and it is normally much greater than the bit rate which determines the bandwidth of the original signal.

This code is multiplied by the data sequence to spread it in bandwidth many times the original bandwidth. In this way this signal will appear as a noise for interception while at the intended receiver it will be despread again restoring the data by an autocorrelation process. The jamming signal will be spread at the receiver appearing as a white noise with a level much smaller than its narrow band jamming value.

So, using spreading with noise like code, the narrow band jammer will appear more or less as a white noise which justifies the use of the Shannon formula to calculate the the processing gain.

The other way one can model the communication system and calculates its bit error rate as a function of the signal to noise ratio by statistical methods.  

I appreciate that

Thank you very much

Dr. Abdelhalim Zekry

sr .Albert Manfredi

Best Regards

Interesting answer by Dr Zekry. If you can spread the channel, as you do with spread spectrum techniques like CDMA or UWB (or I suppose, even COFDM), then, looking at Shannon's equation as you posted it, you are making capacity C very low for a very wide bandwidth W. This leads you to a very low marginal SNR requirement. Which is why jamming becomes more difficult if spreading the signal is an option.

S/N = 2C/W - 1

You can see that low C and large W can give you very interesting marginal SNR requirement, where signal power can be considerably lower than noise power. But spreading the channel that way makes it more difficult to achieve the highest spectral efficiency, which is what everyone seems to be after these days. For example, you would need a much higher CDMA chip rate than OFDM symbol rate, to achieve the same channel capacity with CDMA. Ultimately, this places a hardware limit on spread spectrum techniques, which is why 4G and 5G cellular no longer use CDMA!

Another perhaps subtle point. The way spread spectrum techniques such as CDMA achieve "multiple access" is to treat all other users of the frequency channel as noise. Which in effect means that the more users are sharing the channel, the more noise every user experiences. So let's compare this with TDMA. In TDMA, each user gets a time slot. There is a hard upper bound, determined by the number of time slots, but the noise figure does not keep increasing with added users. In CDMA or UWB, there is no hard upper bound, however the noise power keeps increasing. So in reality, using spread spectrum does not truly solve the noise problem NECESSARILY, because when spread spectrum is used as a multiple access technique, it actually CREATES a lot of the noise.

I agree that a jammer is most effectively placed close to the receiver, where the signal is weakest. But in two-way communications, both sides of the link are transmitters and receivers. So I would say, if you're talking about cellular or WiFi, you want the jammer close to the base station or access point, to disrupt communications to every user, as opposed to close to the users, where you would disrupt only that one user. The idea being to disrupt the uplinks to the base station or access point.

Thank You dr .Albert Manfredi

according to your opinion What is the wisdom of diversity ٍspread-spectrum ( CSS, DSSS, FHSS, THSS ) and is there hybrid type in cellular or WiFi network and if there is found between any type will be ?

I appreciate your answer and help ..

Best Regards..

Hi Ameer, you might find this interesting, on DSSS compared with FHSS. But note that the FHSS they are discussing is actually a hybrid DSSS which also frequency hops!

http://www.rcmodelreviews.com/fhss_vs_dsss.shtml

The article in the above link argues that if you have many simultaneous users, FHSS will usually be better than DSSS. But obviously, that's only because DSSS alone is not spreading the band as much as the FHSS scheme is doing. There are certain practical limitations. Otherwise, I don't see why FHSS would ever beat DSSS, if the two spread the channel equally. In fact, I would prefer the DSSS, because it's probably more efficient than having to retune RF channels. Besides, it just seems a whole lot more clever.

Time hopping spread spectrum? Why not?

I like all of these spread spectrum schemes. In fact, when I first upgraded to 2G cellular, I looked specifically for a service that used CDMA. Just for the fun of it. To me, this was more important than any minor price differences.

Thank you Albert Manfredi