Introduction

Wireless communication systems are keystone in most modern technology. They allow us to collect GPS data on the fly, make calls, play video games, and more. Many factors affect the performance of a communication system, such as weather, geographic features, and system design details. A link budget is an analysis of a communication system that computes whether received signals can be successfully decoded. Link budgets are important in modelling the efficacy and performance of a communication system before it is actually built and put in use.

What is a communication system?

In its most simplified state, a wireless communication system consists of three components: a transmitter, a channel, and a receiver. Information bits are fed into the transmitter, which performs several operations on the data to prepare it for transmission. The resulting signal passes through the channel, or medium. Finally, the receiver receives the signal, and reverts the operations done by the transmitter to attempt to recover the original data.

1. Transmitter

The transmitter converts information bits into a signal ready for transmission. First, the information bits are encoded. The encoding scheme varies by implementation. For example, the 5G New Radio (5G NR) standard utilizes polar and low-density parity check (LDPC) codes. Encoding increases the reliability of the signal by introducing redundancy to the information. This improves the receiver's error correction capabilities. Next, the resulting encoded bits are modulated, creating a signal in which the information is embedded. Finally, the transmitting antenna amplifies the signal, increasing its power, and then the signal is transmitted.

2. Channel

After transmission, the signal travels through the channel on its way to the receiver. In wireless communications systems, the channel is open space, although it can be quite complex. For example, consider a telephone network. Imagine you are trying to make a call in a dense urban area. The many skyscrapers and cars around you interfere with the radio waves. Additionally, the radio waves might reflect off of the glass and other surfaces, causing them to reach the cellular base station at different times. Something as simple as a bird’s call or dog’s bark might also have an adverse effect on the signal. These forms of interference are known as noise, and must be accounted for when analyzing a wireless channel.

3. Receiver

The receiver antenna picks up the degraded signal, and attempts to recover the information embedded within by reverting the operations done by the transmitter. First, the signal is demodulated, and then decoding occurs, which extracts bits from the signal. In most real-world systems, decoding is a probabilistic process (soft decoding), rather than a hard-decision process (hard decoding). As such, the noise that the channel adds to the signal must be modelled accurately, and this model affects the performance of the decoding process.

A common metric for gauging system performance is by considering the bit error rate (BER), which is defined as the number of incorrectly decoded bits divided by the total number of information bits. A signal is considered successfully decoded if the BER is at most some predetermined number, oftentimes $10^{-7}$. In this case, we say that the communication link is closed.

Noise

In wireless communication systems, the channel usually accounts for the majority of the noise incurred by the signal. Noise is anything that clutters the signal, such as atmospheric conditions like temperature and rain and geographical features such as mountains. In the real world, it is impossible for a signal to have zero noise; there will always be some background noise.

The most common metric used to quantify noise is signal to noise ratio (SNR), which is defined as the ratio between the signal’s power and the noise’s power, usually expressed in decibels (dB). The SNR of a signal in dB is given by:

\text{SNR}_{\text{dB}} = 10 \cdot \log_{10} \left( \frac{P_{\text{signal}}}{P_{\text{noise}}} \right).

From now on, $\text{SNR}_{\text{dB}}$ and $\text{SNR}$ will be used interchangeably.

High SNR means that the signal is very clear, and the receiver should not have a hard time deciphering the original information. Low SNR means that the signal is garbled, and the receiver may err during the decoding process. In particular, there exists a specific SNR such that the link just barely closes, and such that any lower SNR will not close the link.

A Simple Example

An additive white Gaussian noise (AWGN) channel is perhaps the simplest channel model. "Additive" means that the effect of the noise is added to the existing signal. "White" refers to the uniform power spectral density across the system's frequency band. Finally, the noise has a zero-mean Gaussian (normal) distribution.

Assuming a real signal, the AWGN channel is therefore represented as a timeseries of values sampled from the distribution $\mathcal{N}(0, \sigma)$, where $\sigma$ is the noise variance. If $X_i$ is the $i$-th signal value and $N_i$ is the $i$-th channel value, then resultant noisy signal $Y$ at index $i$ is given by $Y_i = X_i + N_i$.

Link Budget Overview

The efficacy of a communications system is therefore determined by the SNR at the receiver. We use link budget computations to predict whether the required SNR is attained, and if so, under what conditions. In its most general form, link budgets compute the following:

P_{\text{received}} = P_{\text{transmitted}} + G - L,

where

• $P_{\text{received}}$: Power at receiver
• $P_{\text{transmitted}}$: Transmitted power
• $G$: Sum of all gains
• $L$: Sum of all losses

The figure below shows an example of a link budget computation.

In this example, the signal experiences some losses in the form of cables and transmissions. Then the transmit antenna adds some gain to the signal, after which the signal experiences most of its loss in the channel. When the signal reaches the receiver, the antenna amplifies it, and then the hardware attenuates it again. The received SNR is above the required SNR, so the link closes.

The difference between the received and required SNRs is called the link margin. A lower link margin means that the system's conditions are almost bad enough so that the link won't close.

Common Gains and Losses

Antenna Gain

Antenna gain describes how well the transmitter antenna directs power. It is measured in decibels relative to an isotropic radiator (dBi), where an isotropic radiator would have a gain of 0 dBi. An isotropic antenna transmits power equally in all directions. On the other hand, a directional antenna transmits power in a narrow beam. In this case, higher gain means the antenna can focus more energy in a specific direction, which increases the effective signal strength along that path. As an example, a directional antenna with a gain of 10 dBi will make the signal appear 10 dB stronger in its intended direction than a standard omnidirectional antenna.

Antenna gain is an important parameter in wireless communication that determines how effectively an antenna can focus and direct RF energy in a specific direction. It is important because it improves signal strength and extends coverage range, effectively increasing the system's performance. Antenna gain is measured in decibels relative to an isotropic radiator (dBi), where an isotropic radiator would have a gain of 0 dBi. An isotropic antenna is a theoreotical antenna that transmits power equally in all directions. On the other hand, a directional antenna transmits power in a narrow beam. In this case, higher gain means the antenna can focus more energy in a specific direction, which increases the effective signal strength along that path. As an example, a directional antenna with a gain of 10 dBi will make the signal appear 10 dB stronger in its intended direction than a standard isotropic antenna. Another type of antenna is the omnidirectional antenna, which can transmit energy in all directions in the horizontal plane of the antenna, but struggles with vertical coverage.

Different types of antenna have their pros and cons. Directional antennae, as mentioned above, can focus a lot more energy in a single direction than an omnidirectional antennae. On top of allowing for a higher-energy beam, directional antennae are also less prone to outside interference. However, this also requires precise alignment: if the beam is slightly off, the gain will not be as high as expected. Additionally, directional antennae also suffer from potential blind spots. As such, these antennae are more suited for applications such as ground-satellite links. Omnidirectional antennae, on the other hand, can transmit uniformly horizontally around the antenna, allowing for greater coverage. This makes them more suited for systems that require broad coverage, such as WiFi and cell networks. However, they do not have the range of directional antennae, and they are more prone to interference from unwanted signals.

In a wireless communication system, both the transmitter and receiver are fitted with an antenna. These antenna serve slightly different purposes. The transmitter antenna is responsible for converting electrical signals into electromagnetic waves, and then radiating them out. This requires a lot of power, so transmitter antennae are built with power efficiency in mind. In a ground-satellite link, for example, the distance between the transmitter and receiver can be thousands of miles. The transmit antenna needs a large amount of power to transmit a receivable signal. When a transmit antenna transmits at a power close to its maximum output, the strain on the transmitter introduces distortion to the signal, which can be classified as noise and therefore must be included in the link budget calculation. Given a set of link parameters, it turns out there is an analytical solution to the optimal power at which to transmit signals. The receive antenna, on the other hand, must be able to pick up very weak signals. Because of this, they are very susceptible to noise. As such, receivers are commonly equipped with a low noise amplifier (LNA), a component that amplifies a low-power signal without amplifiying the noise much. Therefore, the LNA a gain that must be accounted for in the link budget calculation.

Coding Gain

The practice of encoding information bits introduces redundancy, making it easier for the receiver to successfully decode the bits. This increase in performance can be represented by a so-called coding gain. To see why, consider the following figure, which plots BER against SNR of two signals, one uncoded and one with LDPC encoding, on a semi-log plot. These plots are called waterfall curves due to the steep drop-off in BER observed above a certain SNR.

To achieve a BER of $10^{-6}$, the LDPC-coded signal requires an SNR of 4 dB, while the uncoded signal requires an SNR of 10 dB. In this case, the addition of LDPC encoding introduces a gain of 6 dB.

Free Space Loss

Particularly in space to ground satellite communications systems, free space path loss (FSPL) is a key component of the link budget because it sets a baseline expectation for signal loss due purely to the distance and frequency used. Knowing the FSPL allows engineers to assess whether the remaining components in the link budget—transmit power, antenna gains, and other losses are adequate to deliver a signal that meets the minimum required SNR at the receiver. For long-range communications systems, the FSPL is usually the largest source of signal loss.

FSPL is computed using the Friis transmission formula, which states a relationship between the transmitted and received powers in a radio system. The formula for the FSPL is given as

\frac{P_{\text{received}}}{P_{\text{transmitted}}} = \left( \frac{4\pi d f}{c} \right)^2,

where d is the distance between the receiver and transmitter, f is the frequency of the signal, and c is the speed of light. Notice that as distance increases, the FSPL increases quadratically.

Atmospheric Loss

In space to ground communication systems, the signal incurs more losses than just the FSPL as it propagates through the atmosphere. One example of these losses is atmospheric loss. If the ground station is in a humid place that rains frequently, the atmosphere will heavily attenuate the signal. On the other hand, if the ground station is in a flat, dry location, the atmosphere will not have nearly as much of an impact on the signal’s SNR. When conducting link budget computations of these systems, it is important to have an accurate weather model so as to determine how much loss to expect from the atmosphere under certain conditions. For example, perhaps the most widely used weather model is the ITU-R (International Telecommunication Union - Radiocommunication Sector) model. This model computes attenuations related to cloud, rain, atmospheric gasses, and more. Some parameters that are used in the model’s computations include latitude/longitude and frequency of the signal.

References

https://www.waves.utoronto.ca/prof/svhum/ece422/notes/22-linkbudget.pdf

https://www.cdt21.com/design_guide/link-budget/

https://telcomaglobal.com/p/5g-nr-channel-codes

https://iopscience.iop.org/article/10.1088/1757-899X/242/1/012131/pdf