A method of transmitting information over a highly noisy communication channel

At the physical level, various technologies are used to transfer information. For example, technologies for transmitting electrical signals through wires, light pulses through optical fiber, sound signals through the air or under water, electromagnetic pulses. All technologies have a problem associated with limiting the range and quality of communication due to parasitic noise in the communication channel. The signal can be so noisy that it seems impossible to extract information from it. The problem is partly solved using the method of synchronous detection or the accumulation of a periodic signal. However, if there is a significant low-frequency noise component, or the frequency of the desired signal is clogged with periodic noise components, these methods are powerless. How can we help the cause?

To solve the problem, you can use information pulses with a pseudo-random profile. For example, such:

Pulse parameters: amplitude – 0.2 conv. units, number of spikes – 200, spike duration – 5, total duration – 2000.

Knowing the shape of such pulses (key), the transmitting and receiving sides can encode and decode the transmitted information, respectively. The transmitting side encodes the information message in the form of a time sequence of such pulses (each corresponds to a logical 1, for example) and gaps (0). The receiving side, on the other hand, extracts pulses from the incoming signal and decodes the message. Why are such impulses better, because they will also drown in noise with a weak reception, as impulses of other forms? The idea is that during decoding, individual spikes of each such pulse can be summed taking into account the sign. Positive spikes will be included in the sum with a + sign, negative ones with a – sign. After such an operation, all random and non-random noise components are compensated with a high probability, and the sum of the peak amplitudes will many times exceed the amplitude of one peak. When the sum of the spikes exceeds a certain (established) cutoff level of the total noise, the confidence probability of registering an information pulse will become sufficiently close to 1.

Below are two pieces of the signal that can enter the receiving path: Gaussian random noise and noise with an added pseudo-random pulse. Noise was generated in the interval (-3, 3) with RMS = 1. Large bursts are unlikely, so they can be omitted.

It is impossible to visually distinguish a piece of noise with an impulse from pure noise. Also, it will not be possible to do this through statistical analysis. Below are the histograms and ACFs of Gaussian and superimposed impulse noise.

When summing the sections of the noise with the impulse corresponding to the spikes, the sum of the amplitudes of the spikes of the information impulse grows relative to the sum of the noise components, reaching a value of 40 c.u. The probability of the sum of the noise components reaching such a value is rather small. In the calculations, a cutoff value of the total noise of 20 conventional units was chosen. The noise component is the arithmetic mean of the noise within the duration of one spike (5 cu).

Thus, the described method of organizing anti-jamming communication can not only significantly increase the communication range with the available transmitter power and receiver sensitivity, but also make the communication invisible.

What are the limitations of the method?

Firstly, it is the need for strict synchronization of clocks at the transmitting and receiving sides. The receiving side needs to know the moments in time at which to start mathematical processing of the incoming signal to extract information pulses. The better the clocks are synchronized, the higher the communication speed will be (more short pulses per unit of time). A compact atomic clock is perfect. However, watches with quartz oscillators will also work, especially if they are periodically fed by signals from satellites or synchronized by transmitting an information message with the current time of the transmitter to the receiver.

Secondly, it is necessary to know with sufficient accuracy the distance between the transmitter and the receiver. After all, while the signal will propagate, some time will pass, which must be added to the time of the transmitter when calculating. This is especially true for relatively slow acoustic communication.

Thirdly, the characteristics of the propagation medium can affect the signal speed, including dynamically. This must be taken into account when determining the time delay.

Fourth, these are the aforementioned limitations on transmitter power and receiver sensitivity. They are relevant for all communication technologies. If the amplitude of the spikes of information pulses at the receiving site is below the receiver sensitivity threshold (determined by the type of antenna, the quality of the receiving path), there will be simply nothing to add.

The described restrictions will affect the speed and relative complexity of organizing communication in this way. However, it can find its niche where long-range or discreet communication with low speed requirements is required. What do you think?

PS Calculations in Python are laid out here…