Carrier frequency of a channel, bandwidth and modulation

Question

I don't understand the meaning of carrier frequency with respect to a transmission channel and the modulation phase with respect to the carrier frequency. I'm at a beginning level, so I try to explain what I get: "the carrier frequency of a channel is that frequency at which a channel works in the sense that the signals with that frequency are well transmitted by the channel". For example, Wi-Fi works either 2.4 GHz or 5 GHz carrier frequency.

The bandwidth of a channel is the set of frequencies a channel can transmit. But what is the meaning of bandwidth of a channel with respect its carrier frequency? If Wi-Fi works with a bandwidth of 10 MHz and it has a carrier frequency of 2.4 GHz means that all signals with frequency x where 2.4 Ghz - 5 MHz <= x <= 2.4Ghz + 5 MHz are well transmitted?

Instead, the modulation process is that process in charge of shifting/moving the input signal into the carrier frequency of the channel. Why do I need to use modulation? Because usually channels work with higher frequencies than frequencies of input signals and this is a suitable way to transmit information through a channel.

Answer 1

The modulation process is required because you need an antenna of feasible dimensions:

• The useful signal frequency is too low to be sent as a wave by an antenna of feasible size.

• The carrier is what its name implies, a neutral wave used to carry a low frequency useful signal. The carrier frequency is not important per see, it just needs to be compatible with an antenna of feasible dimensions.

• The modulation process embeds the low frequency useful signal into a carrier. The carrier is radiated as a wave. The receiver analyses the modulated carrier received (demodulation) to recover the embedded low frequency useful signal. The carrier is then discarded.

I'm adding below the concepts used for Wi-Fi carrier and modulation.

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Allocated spectrum: A portion of the radio spectrum allocated by ITU to users. E.g. Wi-Fi 2.4 GHz is an application in the 2.4 GHz ISM band allocated by ITU, using frequencies between 2,400 MHz and 2,500 MHz (in most countries).

Wave: A wave is a sinusoidal electromagnetic field of some frequency. For Wi-Fi, we want the wave to be within the limits of the allocated band.

Wi-Fi channel: The Wi-Fi band is split into radio channels, that is portions of the Wi-Fi band, defined by their center frequency. The user can transmit using this frequency, and is allowed to also use the neighboring frequencies resulting from the modulation.

Antenna size: The size of the antenna determines its efficiency, that is which part of the power delivered to the antenna is actually radiated as a wave. This efficiency is also valid for a receiving antenna, it corresponds to the part of wave power converted into electrical power.

A wave of frequency f has a wavelength of c/f. An efficient antenna cannot be shorter than 1/4 of the wavelength. Ignoring many other factors like impedance and velocity factor, all lengths multiple of this minimum length can be made efficient (they can be made resonant).

Useful signal frequency, carrier, modulation: If you have to transmit a 1 Mbps digital signal as a radio wave of 1 MHz (I'm simplifying, using one bit per symbol), you're going to need an antenna of at least 300 m / 4 = 75 m, which is not feasible in the computer world.

The solution is to use another smaller wave for the transmission, and alter this wave, originally a pure sine wave, in some way and according to the 1 MHz signal you want to transmit. This is the role of the Wi-Fi band.

At 2.4 GHz, the wavelength is about 12.5 cm and the monopole antenna length is about 3.1 cm.

The wording is this one: The useful signal which cannot be transmitted by radio is the modulation (or modulating signal), the high-frequency wave which is going to be radiated (in the 2.4 GHz channel) is the carrier, and the alteration process is the modulation mode.

This alteration in the case of digital signals is often the phase of the wave, that's called phase shit keying (like in BPSK), or the amplitude of the wave like in quadrature amplitude modulation (QAM). Wi-Fi uses both.

Modulation result: The carrier frequency is the one of the channel used. After modulation, the carrier has still the same fundamental frequency but, because its phase is constantly changing, additional frequency components have been introduced, on each side of the pure carrier frequency. The higher the frequency of the modulating signal, the farther the components are moved away from the fundamental.

Now the modulated carrier occupies a band of some width of the radio spectrum, proportional to the modulating signal maximum frequency.

Bandwidth: As we are allocated one channel, in principle this width shouldn't exceed the channel width (bandwidth). On 2.4 GHz, a Wi-Fi channel is allocated a bandwidth of 5 MHz. However the Wi-Fi standard allows channels to overlap and actually occupy 20/22 MHz.

(Source)

That's because while the modulated carrier has many components which frequencies are on each side of the carrier fundamental frequency, the largest power is close to the fundamental, and decreases continuously while moving away from it. So the overlapping portions are actually lower power and the perturbation is manageable to some extend (however using channels 1, 6, 11 is advisable when multiple channels are to be used).

Sidebands: All components below the fundamental frequency form the lower sideband (LSB), all components above the fundamental form the upper sideband (USB). The sidebands are mirrored about the carrier, and are therefore redundant. The original carrier is still at the fundamental frequency and is still a pure sine, but its power has been reduced, the rest has been transferred to the sidebands. The sidebands are the efficient components.

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In the process the carrier frequency is not important, it's just a way to carry the useful lower frequency signal on an electromagnetic wave, using feasible antennas. However the bandwidth allocated around the carrier is important, it conditions the maximum frequency of the modulating signal, hence the maximum bitrate. You can see some bitrate (bps) requires some bandwidth (Hz). Exceeding the bitrate increases the bandwidth used (in excess of 20 MHz), adjacent channels are impacted by too powerful sidebands.

Answer 2

Wi-Fi works either 2.4 GHz or 5 GHz carrier frequency [...]

Both 2.4 GHz and 5 GHz are just the freq. band names, and not the carrier frequencies themselves. Each band basically defines a set of channels, so there are 14 channels in 2.4 GHz, and much more in 5 GHz. Please see https://en.wikipedia.org/wiki/List_of_WLAN_channels.

If Wi-Fi works with a bandwidth of 10 MHz and it has a carrier frequency of 2.4 GHz > means that all signals with frequency x where 2.4 Ghz - 5 MHz <= x <= 2.4Ghz + 5 MHz > are well transmitted?

Each channel has its own carrier frequency (i.e. central frequency), e.g. channel 6 in 2.4 GHz corresponds to 2437 MHz. If the bandwidth (which can be configured) is 22 MHz, then the modulated signal on channel 6 will be in range from (2437 MHz - 11 MHz) to (2437 MHz + 11 MHz), i.e. from 2426 MHz to 2448 MHz.

As you can see, the range from 2426 MHz to 2448 MHz overlaps with other channels, and this is absolutely legal in Wi-Fi (unlike GSM).