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Probably not.....Voyager 1,the spacecraft to leave the solar system transmits scientific data to earth at rate of 115.2kbps..
Check under science data acquisiton strategy.... https://voyager.jpl.nasa.gov/science/
and maybe the same data transmission rate is needed for checking email on the internet or so.
Distance controls path loss vs frequency of carrier not the modulation, which results in carrier/noise ratio result. The Bit Error Rate(BER) is limited by SNR of demodulated carrier , so there are conversion factors for de- modulation type, noise bandwidth of receiver, signal bandwidth, modulation ratio.
Thus when BER is too high , modems will negotiate for a lower bit rate until a connect is completed. if the Receiver can reduce the noise level with signal bandwidth, then a longer range is achieved.
Voyager uses a 35 m antenna array for 160 bps real time data and a 70 m array for 115kbps bursts every week for 40 seconds.
Shannon's Law prevails with gains in SNR at the expense of antenna farm size to receive at a higher data rate. In WiFi a G modem will negotiate down to B rates when path loss or Rayleigh fading loss is too high. Rician fading is also affected by distance , as this is self cancellation effect ( from out of phase reflections) and by reducing to B rates only, can improve performance when in fringe areas over G rates (<= 11 vs. 54 Mbps ). this can be setup by either Router or mobile.
In any radio system, you need to get an usable power from a transmitter to a receiver, by using suitable antennas.
To transmit information, the signal must be modulated by e.g. data. The modulation generates a signal spectrum which requires a certain bandwidth to be transmitted from transmitter to receiver. The bandwidth in receiver is limited to such required width by filters, and it establishes the noise power above which signal power must be,The ratio of both powers, S/N, defines receiver and system quality to transmit information.
The data rate is a secondary modulation parameter. BY signal processing in a receiver, bit error rate varies with the S/N ratio , and both should be designed to certain minimum value to get a good transmission quality.
For various types of modulation and demodulation, methods were developed to improve BER over S/N, like forward error correction, adaptive filtering, etc. Such methods often take a part of data rate to function, so a careful analysis of a system is needed to understand and optimize it.
The distance between the transmit and receive antennas, plus propagation effects, affect the S/N ratio, and should be used in the primary system design steps.
I would suggest you to read a good textbook on radio and digital communication basics. Your question is generally difficult to answer in short, and many variations exist.
Once upon a time I used to do Telemetry Design and had all the formula for computing BER for any given variables. I used this for Rocket communication at Bristol Aerospace.
Ignoring group delay distortion effects in the channel, the carrier/noise ratio is not a function of modulation, but the conversion factors from C/N to S/N ratio are affected by many factors. The trade-off for data rate is signal bandwidth consumed and if noise level rises then S/N suffers at higher data rates.
In short, if nothing is changed in the system except the data rate, with random noise, the max distance is not affected by data rate. However, usually something is optimized to gain more data rate or more distance, such as get more signal bandwidth with multiple narrow channels or increase antenna gain etc.
e.g. to get the max distance, one would use a very narrow PLL tracking filter or DSP filters with wideband FM. THe log of the deviation ratio (modulation BW/rate) adds to SNR. This is how they send telemetry over galactic space so that C/N can be -50dB but S/N be +12dB with large deviation ratios and adaptive tracking filters.
Recall that in data transmission the important ratio is Eb/No, i.e., energy per bit over power spectral density of noise.
The relationship BER vs. Eb/no depends of the encoding/modulation system.
So, for a given power, decreasing data rate increases Eb (energy_per_bit = power_at_receiver * bit_time = power_at_receiver / bit_rate).
For a given transmitted power and a given receiving antenna, received power decreases with distance (as 1/R^2), and data rate must be reduced as R increases in order to have a sufficient Eb/No.
By the way, the data rate of 115 kbps in the Voyager spacecraft is an internal one. Data are stored an downlink from space to earth takes place at 160 bps.
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