Hello researchers,
I've encountered a problem while utilizing Shannon's formula to calculate the transmission rate from various sources. It appears that the transmission rate is highly sensitive to distance given the values we're working with. Some results seem peculiar. For instance, why does it take 7 minutes to transmit data over 30 km, but 1000 days to transmit over 10,000 km?
Here are the parameters we are currently using:
- wireless_bandwidth_lb: 10 Mbit/s
- wireless_bandwidth_ub: 50 Mbit/s
- transmission_power: 0.6 Watts
- h (Channel fading coefficient): 0.8
- omega (white_gaussian_noise_power): 0.008 Watts
- theta (path_loss_exponent): 2.5
I suspect that "theta" is the main issue. A high theta value makes the result extremely sensitive to the distance. Therefore, we need a more reasonable value for theta. It's virtually impossible to run experiments and obtain sensible results with such skewed inputs.
Does anyone have suggestions or recommendations for these parameters?
Hi!
I believe your noise power is much larger than it should be. It is normally around 10^(-20) * bandwidth Watts.
However, the relative behavior that you describe is correct. If it takes 7 minutes to transfer something at a 30 km distance then it takes 7*(10000/30)^2.5/60/24 days to transmit it to 10000 km.
In practice, it is much likely not possible to transfer anything to a place 10000 km since the received signal power will be below the receiver's sensitivity level.
1
Shannon's formula for the channel capacity is given by:
C = B log2(1 + S/N)
where:
- C is the channel capacity in bits per second (bps)
- B is the bandwidth of the channel in hertz (Hz)
- S is the average signal power in watts (W)
- N is the average noise power in watts (W)
The channel capacity is the maximum theoretical rate at which information can be transmitted over a communication channel with a given bandwidth and noise level. In practice, it is not possible to achieve the channel capacity exactly due to various factors such as coding overhead and noise. However, Shannon's formula provides a useful upper bound on the achievable data rate.
Here is a brief description of each of the parameters in Shannon's formula:
- Bandwidth: The bandwidth of a communication channel is the range of frequencies that the channel can transmit. A higher bandwidth channel can transmit more information per second.
- Signal power: The signal power is the average power of the transmitted signal. A higher signal power can overcome more noise and achieve a higher data rate.
- Noise power: The noise power is the average power of the noise that is present on the communication channel. A lower noise power means that the channel is less noisy and can achieve a higher data rate.
Shannon's formula is used in a wide variety of communication systems, including wireless networks, optical networks, and cable networks. It is an essential tool for designing and optimizing communication systems to achieve the highest possible data rates.
Here are some examples of how Shannon's formula can be used:
- To calculate the maximum data rate that can be achieved over a wireless link with a given bandwidth and signal-to-noise ratio (SNR).
- To design a coding scheme that can achieve a data rate close to the channel capacity.
- To optimize the power allocation between the transmitter and receiver to achieve the highest possible data rate.
Shannon's formula is a powerful tool that can be used to improve the performance of communication systems.
Emil Björnson Thanks for the answer. Given that the path loss is included in the denominator in the Shannon formula*, is this the correct formula to determine the data transmission rate?
* Luo, Quyuan, et al. "Resource scheduling in edge computing: A survey." IEEE Communications Surveys & Tutorials 23.4 (2021): 2131-2165.
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