# Bandwidth vs Capacity

Two questions on wireless transmission, packed into one.

First: I am confused about the meaning of the term 'Bandwidth' in a wireless transmission environment. The two most common definitions I could find are:

• difference between the upper and lower frequencies in a continuous band of frequencies
• the maximum rate of information transfer (bps) across a given path

How do I reconcile these (assuming they are reconcilable)? In other words, why does the difference between the upper and lower frequencies in a frequency band equal the maximum rate of information transfer across the path transmitted? Can someone kindly explain the connection in a clear, visual way if possible?

Second: what is the relationship between 'Bandwidth', 'Capacity', and 'Throughput'? I have seen a bunch of analogies saying that the Bandwidth can be thought of as a pipe and that the throughput can be thought of as water flowing through this pipe, implying that the Bandwidth is some theoretical maximum transmission rate and that the throughput is the actual transmission rate (which can be lower due to various overheads). Is this the analogy right, and if so, what does 'Capacity' mean?

I would greatly appreciate answers to these questions if possible. Thanks.

• Your understanding is correct. Below are some additional details. Jun 8, 2020 at 11:54

Your understanding is correct. Here is an alternate definition from Wikipedia - Bandwidth

Bandwidth is the difference between the upper and lower frequencies in a continuous band of frequencies. It is typically measured in hertz, and depending on context, may specifically refer to passband bandwidth or baseband bandwidth.

Alternate definition:

The maximum amount of data transmitted over a wireless connection in a given amount of time.

For example wifi transmits at 2.4 GHz. Within the 2.4 GHz band their 14 possible channels that a wifi router could use, and each channel has upper lower and center frequency. Here is an example table.

A wifi router could use any of the above channels (Depending on local regulations) and transmit at any of the above defined frequencies all of which are in the 2.4 GHz frequency band. For example the router can transmit on channel 1 which has a lower frequency of 2401 MHz and upper frequency of 2423 MHz.

Bandwidth vs throughput

Throughput is how much information actually gets delivered in a certain amount of time. So if bandwidth is the max amount of data, throughput is how much of that data makes it to its destination – taking latency, network speed, packet loss and other factors into account.

Bandwidth vs speed

Bandwidth is how much information you receive every second, while speed is how fast that information is received or downloaded. Let's compare it to filling a bathtub. If the bathtub faucet has a wide opening, more water can flow at a faster rate than if the pipe was narrower. Think of the water as the bandwidth and the rate at which the water flows as the speed.

Assuming a wifi router chooses channel 1, their can be different upload and download speeds which is throughput. For example the current upload and download speeds are 6Mbps and 12Mbps. The maximum throughput can be 8Mbps and 16Mbps which I believe is capacity.

References:

Capacity is essentially throughput when observed through the lens of the effective number of user devices. WiFi devices use frequency based channels as explained above. Radio waves from different devices can cause interference, inducing errors and reduced throughput. The following discussion on modulation explains the why and how.

Besides the channel bandwidth (amount of frequency space to modulate) the method of modulation governs practical throughput. Modulation is the technique used to encode a binary stream into a radio wave. All radio frequency transmissions are a sine wave. The wave starts at 0 reaches a positive peak, descends through 0 to a negative peak and returns to 0. It does this at the rate of frequency, 2.4 or 5.8 billions of times per second in the case of current Wi-Fi. Modulation techniques form the wave and allow measurement at multiple points. Each point defines a bit (0 or 1) or, as a full wave, be taken as a whole to define a symbol.

The usable number of points is in a binary geometric progression: 2,4,8,...256... dependent on the clarity of the received signal. Advanced WiFi techniques allow the use of up to 256 bits per wave; however, usable throughput (error corrected) is dependent on the signal. Advanced techniques use multiple antennas (MIMO) to obtain the optimum corrected signal stream.

The IEEE identifies the maximums in its 802.11 Wi-Fi specification. The frequency bands used are 2.4 & 5.8Ghz. The different modulation schemes are designated by letters:

2.4Ghz: 802.11b - 11 Mbs, 802.11g - 54 Mbs, 802.11n - 600 Mbs

5.8GHz: 802.11a - 54 Mbs, 802.11ac - 6,922 Mbs

These Wi-Fi schemes use channels assigned to devices. Interference can occur, limiting throughput when many signals are in close proximity. In 2019, the IEEE adopted a new modulation standard 802.11ax which is essentially the LTE broadband scheme used for cellular data. This new standard is labeled as WiFi 6 and will be initially employed in the newly opened public (ISM) frequencies in the 1-6GHz bands.

This modulation technique does not assign particular channels to devices for transmissions from the base station. It uses a block of frequencies within a band in 1-100MHz increments. The incoming bitstream is converted to a time-domain spread (FFT), then transmitted over a single wave period across the majority of the block as symbols on individual frequency carriers. Because the modulation is limited only by the size of the block rather than a conventional channel bandwidth, an immense amount of data may be transmitted, almost 10Gbs with the ax standard.

However, uplink is limited to channelized speeds as the scheme uses shared channel modulation (FDMA). This is not a significant issue as the downlink speed is the critical metric for user devices.

Expect to see conventional WiFi (802.11a,b,g,n,ac) replaced in the future with ax type modulation. Standards have evolved over time for LTE, 4G going to 5G, with 8G in the works.

In wireless transmission, a radio frequency carrier is modulated by a signal of lower frequency and the composite result is transmitted as a complex radio wave. In the modulation process, what starts out as a pure RF carrier consisting of a single frequency is expanded to include all the sum and difference frequencies which result from mixing the carrier and the signal together. This means that a modulated carrier is no longer simply a single frequency occupying only a tiny slice of the radio frequency band in which it is operating, but instead occupies a finite bandwidth which encompasses the sum and difference frequencies- with the carrier in the center of that span and the sidebands (which represent the information content of the signal) extending out to higher and lower frequencies in the band.

Taking AM radio transmission as an example, if we want to transmit a broad range of audio signal information, we must set aside a broad slice of the radio spectrum for it because the highest audio frequencies contribute most to the width of sidebands from instant to instant.

So, in radio frequency engineering, the bandwidth of the transmission is set by the data rate of the signal that is modulating the carrier. This is the "classical" connection between bandwidth and data rate.